From 9ca9a921d13945fab523e73de0524cb473ec7e93 Mon Sep 17 00:00:00 2001
From: Humberto Medina <h.medina@aerofluids.org>
Date: Sun, 22 Sep 2024 18:55:25 +0100
Subject: [PATCH 01/40] reorganise documentation

---
 docs/makeLocal.jl                             |   8 +-
 docs/src/VV/test.jl                           |   2 -
 .../01_2d-isothermal-backward-facing-step.md  |   2 +-
 ...02_2d-incompressible-transient-cylinder.md |   2 +-
 .../03_2d-constant-temperature-flat-plate.md  |   2 +-
 .../04_2d-aerofoil-inflow-optimisation.md     | 188 ++++++++++++++++++
 docs/src/examples/05_2d-inflow-using-Flux.md  | 188 ++++++++++++++++++
 .../figures/01/2D_laminar_BFS_OF.csv          |   0
 .../figures/01/2D_laminar_BFS_XCALibre.csv    | Bin
 .../figures/01/BFS_1.5ms_Linear_VS_OF.png     | Bin
 .../figures/01/BFS_OpenFOAM.png               | Bin
 .../figures/01/BFS_XCALibre.png               | Bin
 .../figures/01/BFS_verification.svg           |   0
 .../figures/01/domain_mesh.png                | Bin
 docs/src/{VV => examples}/figures/01/plot.jl  |   0
 .../figures/02/cylinder_re100_comparison.gif  | Bin
 .../03/Nusselt_const_temp_lam_plate.png       | Bin
 docs/src/{VV => examples}/figures/03/mesh.png | Bin
 18 files changed, 384 insertions(+), 8 deletions(-)
 delete mode 100644 docs/src/VV/test.jl
 rename docs/src/{VV => examples}/01_2d-isothermal-backward-facing-step.md (98%)
 rename docs/src/{VV => examples}/02_2d-incompressible-transient-cylinder.md (90%)
 rename docs/src/{VV => examples}/03_2d-constant-temperature-flat-plate.md (98%)
 create mode 100644 docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
 create mode 100644 docs/src/examples/05_2d-inflow-using-Flux.md
 rename docs/src/{VV => examples}/figures/01/2D_laminar_BFS_OF.csv (100%)
 rename docs/src/{VV => examples}/figures/01/2D_laminar_BFS_XCALibre.csv (100%)
 rename docs/src/{VV => examples}/figures/01/BFS_1.5ms_Linear_VS_OF.png (100%)
 rename docs/src/{VV => examples}/figures/01/BFS_OpenFOAM.png (100%)
 rename docs/src/{VV => examples}/figures/01/BFS_XCALibre.png (100%)
 rename docs/src/{VV => examples}/figures/01/BFS_verification.svg (100%)
 rename docs/src/{VV => examples}/figures/01/domain_mesh.png (100%)
 rename docs/src/{VV => examples}/figures/01/plot.jl (100%)
 rename docs/src/{VV => examples}/figures/02/cylinder_re100_comparison.gif (100%)
 rename docs/src/{VV => examples}/figures/03/Nusselt_const_temp_lam_plate.png (100%)
 rename docs/src/{VV => examples}/figures/03/mesh.png (100%)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 79fbb013..547f5e74 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -14,10 +14,12 @@ USER_GUIDE_PAGES = Any[
     "5_postprocessing.md"
 ]
 
-VERIFICATION_VALIDATION_PAGES = Any[
+EXAMPLES_PAGES = Any[
     "01_2d-isothermal-backward-facing-step.md",
     "02_2d-incompressible-transient-cylinder.md",
-    "03_2d-constant-temperature-flat-plate.md"
+    "03_2d-constant-temperature-flat-plate.md",
+    "04_2d-aerofoil-inflow-optimisation.md",
+    "05_2d-inflow-using-Flux"
 ]
 
 makedocs(
@@ -28,7 +30,7 @@ makedocs(
     pages = [
         "Home" => "index.md",
         "quick_start.md",
-        "Verification & validation" => "VV/" .* VERIFICATION_VALIDATION_PAGES,
+        "Examples" => "examples/" .* EXAMPLES_PAGES,
         "User Guide" => "user_guide/" .* USER_GUIDE_PAGES,
         hide("Theory Guide" => "theory_guide/introduction.md"),
         "contributor_guide.md",
diff --git a/docs/src/VV/test.jl b/docs/src/VV/test.jl
deleted file mode 100644
index 2ac0de2d..00000000
--- a/docs/src/VV/test.jl
+++ /dev/null
@@ -1,2 +0,0 @@
-using XCALibre
-
diff --git a/docs/src/VV/01_2d-isothermal-backward-facing-step.md b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
similarity index 98%
rename from docs/src/VV/01_2d-isothermal-backward-facing-step.md
rename to docs/src/examples/01_2d-isothermal-backward-facing-step.md
index 197c5542..ee21729f 100644
--- a/docs/src/VV/01_2d-isothermal-backward-facing-step.md
+++ b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
@@ -1,4 +1,4 @@
-# 2D incompressible backward-facing step
+# Verification: 2D incompressible backward-facing step
 
 # Introduction
 ---
diff --git a/docs/src/VV/02_2d-incompressible-transient-cylinder.md b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
similarity index 90%
rename from docs/src/VV/02_2d-incompressible-transient-cylinder.md
rename to docs/src/examples/02_2d-incompressible-transient-cylinder.md
index 88cf8929..28169018 100644
--- a/docs/src/VV/02_2d-incompressible-transient-cylinder.md
+++ b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
@@ -1,4 +1,4 @@
-# 2D Unsteady incompressible cylinder
+# Verification: 2D Unsteady incompressible cylinder
 
 # Introduction
 ---
diff --git a/docs/src/VV/03_2d-constant-temperature-flat-plate.md b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
similarity index 98%
rename from docs/src/VV/03_2d-constant-temperature-flat-plate.md
rename to docs/src/examples/03_2d-constant-temperature-flat-plate.md
index 9be13aba..abe562c7 100644
--- a/docs/src/VV/03_2d-constant-temperature-flat-plate.md
+++ b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
@@ -1,4 +1,4 @@
-# 2D Constant temperature flat plate
+# Validation: 2D Constant temperature flat plate
 
 # Overview
 ---
diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
new file mode 100644
index 00000000..11e47461
--- /dev/null
+++ b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
@@ -0,0 +1,188 @@
+# Advanced: 2D Aerofoil inflow optimisation
+
+# Overview
+---
+A 2D constant temperature laminar flat plate case has been used to validate the weakly 
+compressible solver. The case provides a constant temperature boundary condition along the 
+wall of the domain. 
+
+The results of case are compared against the theoretical local Nusselt number correlation 
+for forced convection on constant temperature flat plate:
+
+``Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}``
+
+The correlation is valid for Prandtl numbers greater than 0.6.
+
+
+The boundaries are shown in the mesh figure and the tables below describe the boundary settings used.
+
+### Inlet
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Dirichlet ([0.2, 0.0, 0.0] m/s)   |
+| ``p``   |  Neumann (Zero-gradient)      |
+| ``T ``  |  FixedTemperature (300.0 K)    |
+
+### Wall
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  No-slip wall   |
+| ``p``   |  Neumann (Zero-gradient)      |
+| ``T ``  |  FixedTemperature (310.0 K)    |
+
+### Outlet
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Neumann (Zero-gradient)   |
+| ``p``   |  Dirichlet (0.0 Pa)     |
+| ``T ``  |  Neumann (Zero-gradient)    |
+
+### Top
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Neumann (Zero-gradient)   |
+| ``p``   |  Neumann (Zero-gradient)     |
+| ``T ``  |  Neumann (Zero-gradient)    |
+
+
+# Fluid Properties
+
+
+| Property | value      |
+| -------  | ---------- |
+| ``\nu``   |  0.0001    |
+| ``Pr``   |  0.71      |
+| ``c_p``  |  1005.0    |
+| ``\gamma`` | 1.4      |
+
+
+
+# Mesh
+---
+
+The mesh is shown in the figure below:
+
+
+![Figure of mesh.](figures/03/mesh.png)
+
+The streamwise cell length is 2mm with a total domain length of 1m. The near-wall cell height is 0.049mm with a domain height of 0.2m.
+
+
+# Case file
+---
+
+```jldoctest;  filter = r".*"s => s"", output = false
+using XCALibre
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "flatplate_2D_laminar.unv"
+mesh_file = joinpath(grids_dir, grid)
+
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+
+velocity = [0.2, 0.0, 0.0]
+nu = 1e-4
+Re = velocity[1]*1/nu
+cp = 1005.0
+gamma = 1.4
+Pr = 0.7
+
+model = Physics(
+    time = Steady(),
+    fluid =  Fluid{WeaklyCompressible}(
+        nu = nu,
+        cp = cp,
+        gamma = gamma,
+        Pr = Pr
+        ),
+    turbulence = RANS{Laminar}(),
+    energy = Energy{SensibleEnthalpy}(Tref = 288.15),
+    domain = mesh # mesh_dev  # use mesh_dev for GPU backend
+    )
+
+@assign! model momentum U (
+    Dirichlet(:inlet, velocity),
+    Neumann(:outlet, 0.0),
+    Wall(:wall, [0.0, 0.0, 0.0]),
+    Symmetry(:top, 0.0)
+)
+
+ @assign! model momentum p (
+    Neumann(:inlet, 0.0),
+    Dirichlet(:outlet, 100000.0),
+    Neumann(:wall, 0.0),
+    Neumann(:top, 0.0)
+)
+
+@assign! model energy h (
+    FixedTemperature(:inlet, T=300.0, model=model.energy),
+    Neumann(:outlet, 0.0),
+    FixedTemperature(:wall, T=310.0, model=model.energy),
+    Neumann(:top, 0.0)
+)
+
+schemes = (
+    U = set_schemes(divergence=Linear),
+    p = set_schemes(divergence=Linear),
+    h = set_schemes(divergence=Linear)
+)
+
+solvers = (
+    U = set_solver(
+        model.momentum.U;
+        solver      = BicgstabSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.7,
+    ),
+    p = set_solver(
+        model.momentum.p;
+        solver      = CgSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.3,
+    ),
+    h = set_solver(
+        model.energy.h;
+        solver      = BicgstabSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.7,
+        rtol = 1e-2,
+        atol = 1e-4
+    )
+)
+
+runtime = set_runtime(iterations=1000, write_interval=1000, time_step=1)
+
+hardware = set_hardware(backend=CPU(), workgroup=4)
+
+config = Configuration(
+    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+
+GC.gc()
+
+initialise!(model.momentum.U, velocity)
+initialise!(model.momentum.p, 100000.0)
+initialise!(model.energy.T, 300.0)
+
+residuals = run!(model, config)
+
+# output
+
+```
+
+# Results
+---
+
+The results of the model are compared to the theoretical correlation in the figure below:
+
+![Nusselt number distribution results.](figures/03/Nusselt_const_temp_lam_plate.png)
diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/05_2d-inflow-using-Flux.md
new file mode 100644
index 00000000..4584dffb
--- /dev/null
+++ b/docs/src/examples/05_2d-inflow-using-Flux.md
@@ -0,0 +1,188 @@
+# Advanced: 2D inflow using `Flux.jl`
+
+# Overview
+---
+A 2D constant temperature laminar flat plate case has been used to validate the weakly 
+compressible solver. The case provides a constant temperature boundary condition along the 
+wall of the domain. 
+
+The results of case are compared against the theoretical local Nusselt number correlation 
+for forced convection on constant temperature flat plate:
+
+``Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}``
+
+The correlation is valid for Prandtl numbers greater than 0.6.
+
+
+The boundaries are shown in the mesh figure and the tables below describe the boundary settings used.
+
+### Inlet
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Dirichlet ([0.2, 0.0, 0.0] m/s)   |
+| ``p``   |  Neumann (Zero-gradient)      |
+| ``T ``  |  FixedTemperature (300.0 K)    |
+
+### Wall
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  No-slip wall   |
+| ``p``   |  Neumann (Zero-gradient)      |
+| ``T ``  |  FixedTemperature (310.0 K)    |
+
+### Outlet
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Neumann (Zero-gradient)   |
+| ``p``   |  Dirichlet (0.0 Pa)     |
+| ``T ``  |  Neumann (Zero-gradient)    |
+
+### Top
+
+
+| Field | Boundary condition      |
+| -------  | ---------- |
+| ``U``   |  Neumann (Zero-gradient)   |
+| ``p``   |  Neumann (Zero-gradient)     |
+| ``T ``  |  Neumann (Zero-gradient)    |
+
+
+# Fluid Properties
+
+
+| Property | value      |
+| -------  | ---------- |
+| ``\nu``   |  0.0001    |
+| ``Pr``   |  0.71      |
+| ``c_p``  |  1005.0    |
+| ``\gamma`` | 1.4      |
+
+
+
+# Mesh
+---
+
+The mesh is shown in the figure below:
+
+
+![Figure of mesh.](figures/03/mesh.png)
+
+The streamwise cell length is 2mm with a total domain length of 1m. The near-wall cell height is 0.049mm with a domain height of 0.2m.
+
+
+# Case file
+---
+
+```jldoctest;  filter = r".*"s => s"", output = false
+using XCALibre
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "flatplate_2D_laminar.unv"
+mesh_file = joinpath(grids_dir, grid)
+
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+
+velocity = [0.2, 0.0, 0.0]
+nu = 1e-4
+Re = velocity[1]*1/nu
+cp = 1005.0
+gamma = 1.4
+Pr = 0.7
+
+model = Physics(
+    time = Steady(),
+    fluid =  Fluid{WeaklyCompressible}(
+        nu = nu,
+        cp = cp,
+        gamma = gamma,
+        Pr = Pr
+        ),
+    turbulence = RANS{Laminar}(),
+    energy = Energy{SensibleEnthalpy}(Tref = 288.15),
+    domain = mesh # mesh_dev  # use mesh_dev for GPU backend
+    )
+
+@assign! model momentum U (
+    Dirichlet(:inlet, velocity),
+    Neumann(:outlet, 0.0),
+    Wall(:wall, [0.0, 0.0, 0.0]),
+    Symmetry(:top, 0.0)
+)
+
+ @assign! model momentum p (
+    Neumann(:inlet, 0.0),
+    Dirichlet(:outlet, 100000.0),
+    Neumann(:wall, 0.0),
+    Neumann(:top, 0.0)
+)
+
+@assign! model energy h (
+    FixedTemperature(:inlet, T=300.0, model=model.energy),
+    Neumann(:outlet, 0.0),
+    FixedTemperature(:wall, T=310.0, model=model.energy),
+    Neumann(:top, 0.0)
+)
+
+schemes = (
+    U = set_schemes(divergence=Linear),
+    p = set_schemes(divergence=Linear),
+    h = set_schemes(divergence=Linear)
+)
+
+solvers = (
+    U = set_solver(
+        model.momentum.U;
+        solver      = BicgstabSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.7,
+    ),
+    p = set_solver(
+        model.momentum.p;
+        solver      = CgSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.3,
+    ),
+    h = set_solver(
+        model.energy.h;
+        solver      = BicgstabSolver,
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 0.7,
+        rtol = 1e-2,
+        atol = 1e-4
+    )
+)
+
+runtime = set_runtime(iterations=1000, write_interval=1000, time_step=1)
+
+hardware = set_hardware(backend=CPU(), workgroup=4)
+
+config = Configuration(
+    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+
+GC.gc()
+
+initialise!(model.momentum.U, velocity)
+initialise!(model.momentum.p, 100000.0)
+initialise!(model.energy.T, 300.0)
+
+residuals = run!(model, config)
+
+# output
+
+```
+
+# Results
+---
+
+The results of the model are compared to the theoretical correlation in the figure below:
+
+![Nusselt number distribution results.](figures/03/Nusselt_const_temp_lam_plate.png)
diff --git a/docs/src/VV/figures/01/2D_laminar_BFS_OF.csv b/docs/src/examples/figures/01/2D_laminar_BFS_OF.csv
similarity index 100%
rename from docs/src/VV/figures/01/2D_laminar_BFS_OF.csv
rename to docs/src/examples/figures/01/2D_laminar_BFS_OF.csv
diff --git a/docs/src/VV/figures/01/2D_laminar_BFS_XCALibre.csv b/docs/src/examples/figures/01/2D_laminar_BFS_XCALibre.csv
similarity index 100%
rename from docs/src/VV/figures/01/2D_laminar_BFS_XCALibre.csv
rename to docs/src/examples/figures/01/2D_laminar_BFS_XCALibre.csv
diff --git a/docs/src/VV/figures/01/BFS_1.5ms_Linear_VS_OF.png b/docs/src/examples/figures/01/BFS_1.5ms_Linear_VS_OF.png
similarity index 100%
rename from docs/src/VV/figures/01/BFS_1.5ms_Linear_VS_OF.png
rename to docs/src/examples/figures/01/BFS_1.5ms_Linear_VS_OF.png
diff --git a/docs/src/VV/figures/01/BFS_OpenFOAM.png b/docs/src/examples/figures/01/BFS_OpenFOAM.png
similarity index 100%
rename from docs/src/VV/figures/01/BFS_OpenFOAM.png
rename to docs/src/examples/figures/01/BFS_OpenFOAM.png
diff --git a/docs/src/VV/figures/01/BFS_XCALibre.png b/docs/src/examples/figures/01/BFS_XCALibre.png
similarity index 100%
rename from docs/src/VV/figures/01/BFS_XCALibre.png
rename to docs/src/examples/figures/01/BFS_XCALibre.png
diff --git a/docs/src/VV/figures/01/BFS_verification.svg b/docs/src/examples/figures/01/BFS_verification.svg
similarity index 100%
rename from docs/src/VV/figures/01/BFS_verification.svg
rename to docs/src/examples/figures/01/BFS_verification.svg
diff --git a/docs/src/VV/figures/01/domain_mesh.png b/docs/src/examples/figures/01/domain_mesh.png
similarity index 100%
rename from docs/src/VV/figures/01/domain_mesh.png
rename to docs/src/examples/figures/01/domain_mesh.png
diff --git a/docs/src/VV/figures/01/plot.jl b/docs/src/examples/figures/01/plot.jl
similarity index 100%
rename from docs/src/VV/figures/01/plot.jl
rename to docs/src/examples/figures/01/plot.jl
diff --git a/docs/src/VV/figures/02/cylinder_re100_comparison.gif b/docs/src/examples/figures/02/cylinder_re100_comparison.gif
similarity index 100%
rename from docs/src/VV/figures/02/cylinder_re100_comparison.gif
rename to docs/src/examples/figures/02/cylinder_re100_comparison.gif
diff --git a/docs/src/VV/figures/03/Nusselt_const_temp_lam_plate.png b/docs/src/examples/figures/03/Nusselt_const_temp_lam_plate.png
similarity index 100%
rename from docs/src/VV/figures/03/Nusselt_const_temp_lam_plate.png
rename to docs/src/examples/figures/03/Nusselt_const_temp_lam_plate.png
diff --git a/docs/src/VV/figures/03/mesh.png b/docs/src/examples/figures/03/mesh.png
similarity index 100%
rename from docs/src/VV/figures/03/mesh.png
rename to docs/src/examples/figures/03/mesh.png

From 7dd49e7fc6c4d0b896ff7811f08d6cf6ad8c1d81 Mon Sep 17 00:00:00 2001
From: Humberto Medina <h.medina@aerofluids.org>
Date: Sun, 22 Sep 2024 19:03:41 +0100
Subject: [PATCH 02/40] fix typo on example file name

---
 docs/makeLocal.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 547f5e74..7d388aa3 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -19,7 +19,7 @@ EXAMPLES_PAGES = Any[
     "02_2d-incompressible-transient-cylinder.md",
     "03_2d-constant-temperature-flat-plate.md",
     "04_2d-aerofoil-inflow-optimisation.md",
-    "05_2d-inflow-using-Flux"
+    "05_2d-inflow-using-Flux.md"
 ]
 
 makedocs(

From 107b804e47043396f38dc2161bf813bfaf5d2d0a Mon Sep 17 00:00:00 2001
From: Humberto Medina <h.medina@aerofluids.org>
Date: Thu, 26 Sep 2024 17:31:55 +0100
Subject: [PATCH 03/40] implement Tim's suggestions

---
 dev_notes.md                  |  7 ++++++-
 docs/src/contributor_guide.md | 10 +++++-----
 docs/src/index.md             |  8 ++++----
 docs/src/quick_start.md       |  2 +-
 4 files changed, 16 insertions(+), 11 deletions(-)

diff --git a/dev_notes.md b/dev_notes.md
index 0b1c5d76..d8c5c594 100644
--- a/dev_notes.md
+++ b/dev_notes.md
@@ -11,8 +11,13 @@
 - [x] Check Divergence BCs for Upwind scheme
 - [ ] Implement Upwind as deferred correction
 - [x] Do mesh conversion to new format within UNV read/writer (2D and 3D meshes)
-- [x ] Add tests
+- [x] Add tests
 - [x] Add documentation (becoming urgent)
+- [ ] Explore new ways to store output files from simulations
+  - [ ] Should this be a folder?
+  - [ ] Should we overwrite by default or warn?
+  - [ ] Should be create a new folder?
+  - [ ] Should the folder name be "results" or "iterations"/"time_steps"
 
 ### Mesh module
 
diff --git a/docs/src/contributor_guide.md b/docs/src/contributor_guide.md
index efb1a15a..37a235dc 100644
--- a/docs/src/contributor_guide.md
+++ b/docs/src/contributor_guide.md
@@ -11,7 +11,7 @@ From its humble beginning as a 1D diffusion example code to explore the features
 ## Some guidelines
 ---
 
-To help use keep the codebase consistent and allow us to merge future Pull Requests (PRs) more easily, we kindly request that contributors adhere to some basic guidelines. We are are trying to struck a balance between consistency and ease of contribution by aiming not to be overly demanding on contributors. A minimum set of guidelines is provided below (subject to review as the codebase evolves), in no particular order:
+To help use keep the codebase consistent and allow us to merge future Pull Requests (PRs) more easily, we kindly request that contributors adhere to some basic guidelines. We are trying to strike a balance between consistency and ease of contribution by aiming not to be overly demanding on contributors. A minimum set of guidelines is provided below (subject to review as the codebase evolves), in no particular order:
 
 ### Code style
 
@@ -35,12 +35,12 @@ To help use keep the codebase consistent and allow us to merge future Pull Reque
 | Module | Description |
 |:-------|:------------|
 XCALibre.Mesh | This module defines all types required to construct the mesh object used by the flow solvers. Two main mesh types are used `Mesh2` and `Mesh3` used for 2D and 3D simulations, respectively. Some access functions are also included in this module. |
-XCALibre.Fields | This module define the fields used to hold and represent the flow variable. Scalar, vector and tensor fields are defined e.g. `ScalarField`, etc. Information is stored at cell centres. These fields also have face variant where information is stored at face centres e.g. `FaceVectorField`. These fields are generally used to store fluxes. A limited set of field operations are also defined e.g. `getfield` to allow indexing field object directly. |
-XCALibre.ModelFramework | This module provides the framework used to define `scalar and vector model equations whilst storing information about the operators used. The data structure also defines sparse matrices used to storage discretisation information.  |
+XCALibre.Fields | This module defines the fields used to hold and represent the flow variable. Scalar, vector and tensor fields are defined e.g. `ScalarField`, etc. Information is stored at cell centres. These fields also have face variant where information is stored at face centres e.g. `FaceVectorField`. These fields are generally used to store fluxes. A limited set of field operations are also defined e.g. `getfield` to allow indexing field object directly. |
+XCALibre.ModelFramework | This module provides the framework used to define scalar and vector model equations whilst storing information about the operators used. The data structure also defines sparse matrices used to store discretisation information.  |
 XCALibre.Discretise | This module defines the various operators needed to represent each terms in a model equation and the main discretisation loop that linearises each term according to the schemes available. Boundary conditions are also implemented in this module. |
 XCALibre.Solve | This module includes all functions and logic needed to solve the linear system of equations that follows the equation discretisation. The internal API to solve these systems of equations is included in this module. |
 XCALibre.Calculate | Implementation of functions use to carry out calculations essential to the implementation of flow solvers is included in this module. This includes interpolation of variables from cell centroid to cell faces, gradient calculation, surface normals, etc. |
-XCALibre.ModelPhysics | This module includes the implemetations of all the physical models i.e. fluid, turbulence and energy models. |
+XCALibre.ModelPhysics | This module includes the implementations of all the physical models i.e. fluid, turbulence and energy models. |
 XCALibre.Simulate | This model contains information needed to set up a simulation, including the [`Configuration`](@ref) type used by all flow solvers. |
 XCALibre.Solvers | Implementations of the SIMPLE and PISO flow solvers from steady and unsteady solutions, including their compressible variant. |
 XCALibre.Postprocess | A limited set of functions for postprocessing are implemented in this module.  |
@@ -71,7 +71,7 @@ To fully characterise how mesh information is represented in XCALibre.jl, it is
 * Face normals for internal faces is always pointing in the direction from the ownerCell with the smallest ID to the largest. Since the discretisation loop is cell based, for the cell with the highest ID the direction must be reversed. This information is tracked in `Mesh3.nsign` which stores 1 if the face normal is correctly aligned or -1 if the normal needs to be reversed.
 * Boundary faces (e.g. patches) are stored consecutively in `Mesh3.Faces` starting at the beginning of the array followed by all the internal faces.
 * Boundary faces are those connected only to 1 `Cell`, thus, for these faces the entry `Face3D.ownerCells` is a 2-element vector with a repeated index e.g. [3, 3]
-* Boundary cells only store information for internal faces. This improves performance for the main discretisation loop (cell based) since it can always been assumed that non of the faces will be a boundary face, which are dealt with in a separate loop.
+* Boundary cells only store information for internal faces. This improves performance for the main discretisation loop (cell based) since it can always been assumed that none of the faces will be a boundary face, which are dealt with in a separate loop.
 
 
 ### Field types
diff --git a/docs/src/index.md b/docs/src/index.md
index 845f6d50..27f64989 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -10,7 +10,7 @@ XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose
 ## Why XCALibre.jl?
 ---
 
-For CFD researchers whose research involves developing new numerical methods, turbulence models, or novel CFD methodologies, the development process can be taxiing when using commercial packages and their imagination might be constrained by having to adhere to either limited access to internal code functionality or exhausted as they reformulate their ideas to fit within any interfaces provided by the code. There are excellent open source CFD packages where access to functionality or internals is available, however, they are either written in static languages such as C/C++ or dynamic languages such as Python. In static languages, the resulting code is likely highly performant but implementation can be slow and often has a high learning curve (specially if the developer/researcher has no prior knowledge of the language). On the other hand, dynamics languages such as Python can offer a nice development experience at the cost of low runtime or reduced performance. The development of XCALibre.jl was motivated when we discovered the Julia programming language, which promises an interactive and enjoyable implementation experience whilst being able to generate performant code. Thanks to the tools available in the Julia ecosystems (see [Main dependencies](@ref)) it is also possible to generate CPU and GPU code using Julia. As a side effect, XCALibre.jl can also link readily with the entire Julia ecosystem, including machine learning frameworks such as Flux.jl, Lux.jl, Knet.jl, etc. Thanks to a user-friendly API, ultimately, we hope that XCALibre.jl can be useful to anyone who has an interest in CFD. Enjoy and give us [feedback](@ref #10).
+For CFD researchers whose research involves developing new numerical methods, turbulence models, or novel CFD methodologies, the development process can be taxing when using commercial packages and their imagination might be constrained by having to adhere to either limited access to internal code functionality or exhausted as they reformulate their ideas to fit within any interfaces provided by the code. There are excellent open source CFD packages where access to functionality or internals is available, however, they are either written in static languages such as C/C++ or dynamic languages such as Python. In static languages, the resulting code is likely highly performant but implementation can be slow and often has a high learning curve (especially if the developer/researcher has no prior knowledge of the language). On the other hand, dynamic languages such as Python can offer a nice development experience at the cost of low runtime or reduced performance. The development of XCALibre.jl was motivated when we discovered the Julia programming language, which promises an interactive and enjoyable implementation experience whilst being able to generate performant code. Thanks to the tools available in the Julia ecosystems (see [Main dependencies](@ref)) it is also possible to generate CPU and GPU code using Julia. As an added bonus, XCALibre.jl can also link readily with the entire Julia ecosystem, including machine learning frameworks such as Flux.jl, Lux.jl, Knet.jl, etc. Thanks to a user-friendly API, ultimately, we hope that XCALibre.jl can be useful to anyone who has an interest in CFD. Enjoy and give us [feedback](@ref #10).
 
 
 ## Main features
@@ -47,10 +47,10 @@ XCALibre.jl ships with fluid solvers for steady and transient simulations, based
 
 !!! note
 
-    A solver for highly compressible flows (shock capturing) is currently in testing and will be available in the next major release. Currently the compressible solvers are based use a sensible energy approach for the energy equation.
+    A solver for highly compressible flows (shock capturing) is currently in testing and will be available in the next major release. Currently the compressible solvers are use a sensible energy approach for the energy equation.
 
 ### Turbulence and energy models
-The list of available turbulence models available is expected to expand. The following turbulence models are already available in XCALibre.jl
+The list of turbulence models available is expected to expand. The following turbulence models are already available in XCALibre.jl:
 
 * Reynolds-Averaged Navier-Stokes (RANS)
   * ``k-\omega`` - available in low-Reynolds (wall-resolving) and in high-Reynolds (wall functions) mode
@@ -101,7 +101,7 @@ U_eqn = (
 * Fine-tuning of the public API expected based on of user feedback
 
 ### Internals
-* Overhaul of field data. Currently, both vectors and tensors are built on the primitive scalar field object. Whilst this was convenience during the early development stage, the package has reach a level of maturity that makes this approach hard to maintain, adding unneeded complexity when working with tensors. We plan to define separate internals (how tensors are defined and stored in memory). It is anticipated that this will ease the implementation of models working with tensors, and give some performance gains since information will be stored closer in memory.
+* Overhaul of field data. Currently, both vectors and tensors are built on the primitive scalar field object. Whilst this was convenient during the early development stage, the package has reached a level of maturity that makes this approach hard to maintain, adding unneeded complexity when working with tensors. We plan to define separate internals (how tensors are defined and stored in memory). It is anticipated that this will ease the implementation of models working with tensors, give some performance gains and allow all fields to participate in Julia's broadcasting framework.
 
 
 ## Main dependencies
diff --git a/docs/src/quick_start.md b/docs/src/quick_start.md
index dfe1e667..83f3c630 100644
--- a/docs/src/quick_start.md
+++ b/docs/src/quick_start.md
@@ -155,6 +155,6 @@ pwd() # find active directory where the file "iteration_002000.vtk" was saved
 
 ### Output
 
-If you chose to run the example above, XCALibre.jl would have written a simulation result file to your computer. The name of the file is `iteration_002000.vtk`. The file will be located in your current active directory (you can check this by running `pwd()`). This file can be open directly in ParaView for further post-processing. You can find out more about [ParaView on their website](https://www.paraview.org/). The image below is the output solution generated by XCALibre.j to the example simulation above.
+If you chose to run the example above, XCALibre.jl would have written a simulation result file to your computer. The name of the file is `iteration_002000.vtk`. The file will be located in your current active directory (you can check this by running `pwd()`). This file can be open directly in ParaView for further post-processing. You can find out more about [ParaView on their website](https://www.paraview.org/). The image below is the output solution generated by XCALibre.jl to the example simulation above.
 
 ![Simulation result visualisation in ParaView](figures/quick_start_fig_bfs_2d_incompressible_laminar.svg)

From e54a09e0e5573517f26a4c134caa9a2e04458113 Mon Sep 17 00:00:00 2001
From: Humberto Medina <h.medina@aerofluids.org>
Date: Thu, 26 Sep 2024 17:32:17 +0100
Subject: [PATCH 04/40] update 2D cylinder example

---
 docs/makeLocal.jl                             |  2 +-
 ...02_2d-incompressible-transient-cylinder.md | 98 ++++++++++++++++++-
 examples/2D_BFS.jl                            |  2 +-
 examples/2D_cylinder.jl                       | 11 +--
 examples/2D_cylinder_U.jl                     | 33 +++----
 5 files changed, 115 insertions(+), 31 deletions(-)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 7d388aa3..50a1f501 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -25,7 +25,7 @@ EXAMPLES_PAGES = Any[
 makedocs(
     sitename = "XCALibre.jl",
     format = Documenter.HTML(),
-    # doctest = false, # only set to false when sorting out docs structure
+    doctest = false, # only set to false when sorting out docs structure
     modules = [XCALibre],
     pages = [
         "Home" => "index.md",
diff --git a/docs/src/examples/02_2d-incompressible-transient-cylinder.md b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
index 28169018..8f90494b 100644
--- a/docs/src/examples/02_2d-incompressible-transient-cylinder.md
+++ b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
@@ -7,4 +7,100 @@ To verify the correct implementation of the laminar flow solver, a simulation of
 
 ## Results
 
-![vorticity comparison with OpenFOAM](figures/02/cylinder_re100_comparison.gif)
\ No newline at end of file
+![vorticity comparison with OpenFOAM](figures/02/cylinder_re100_comparison.gif)
+
+## Simulation setup
+
+For those interested in running this case, this simulation can be replicated as follows.
+
+```jldoctest;  filter = r".*"s => s"", output = false
+
+using XCALibre
+# using CUDA # uncomment to run on GPU
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "cylinder_d10mm_5mm.unv"
+mesh_file = joinpath(grids_dir, grid)
+
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+
+mesh_dev = mesh
+# mesh_dev = adapt(CUDABackend(), mesh) # uncomment to run on GPU
+
+# Inlet conditions
+velocity = [0.5, 0.0, 0.0]
+noSlip = [0.0, 0.0, 0.0]
+nu = 1e-3
+Re = (0.2*velocity[1])/nu
+
+model = Physics(
+    time = Transient(),
+    fluid = Fluid{Incompressible}(nu = nu),
+    turbulence = RANS{Laminar}(),
+    energy = Energy{Isothermal}(),
+    domain = mesh_dev
+    )
+
+@assign! model momentum U ( 
+    Dirichlet(:inlet, velocity),
+    Neumann(:outlet, 0.0),
+    Wall(:cylinder, noSlip),
+    Neumann(:bottom, 0.0),
+    Neumann(:top, 0.0)
+)
+
+@assign! model momentum p (
+    Neumann(:inlet, 0.0),
+    Dirichlet(:outlet, 0.0),
+    Neumann(:cylinder, 0.0),
+    Neumann(:bottom, 0.0),
+    Neumann(:top, 0.0)
+)
+
+solvers = (
+    U = set_solver(
+        model.momentum.U;
+        solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax       = 1.0,
+        rtol = 1e-4,
+        atol = 1e-5
+    ),
+    p = set_solver(
+        model.momentum.p;
+        solver      = CgSolver, # BicgstabSolver, GmresSolver
+        preconditioner = Jacobi(), #NormDiagonal(),
+        convergence = 1e-7,
+        relax       = 0.8,
+        rtol = 1e-4,
+        atol = 1e-5
+    )
+)
+
+schemes = (
+    U = set_schemes(time=Euler, divergence=LUST, gradient=Midpoint),
+    p = set_schemes(time=Euler, gradient=Midpoint)
+)
+
+
+runtime = set_runtime(
+    # iterations=1000, write_interval=50, time_step=0.005) # uncomment to save files
+    iterations=1, write_interval=-1, time_step=0.005) # used for building documentation
+
+hardware = set_hardware(backend=CPU(), workgroup=1024)
+# hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
+
+config = Configuration(
+    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+
+GC.gc(true)
+
+initialise!(model.momentum.U, velocity)
+initialise!(model.momentum.p, 0.0)
+
+residuals = run!(model, config)
+
+# output
+
+```
\ No newline at end of file
diff --git a/examples/2D_BFS.jl b/examples/2D_BFS.jl
index e46f3329..6ba2737c 100644
--- a/examples/2D_BFS.jl
+++ b/examples/2D_BFS.jl
@@ -4,8 +4,8 @@ using XCALibre
 # backwardFacingStep_2mm, backwardFacingStep_10mm
 grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
 grid = "backwardFacingStep_5mm.unv"
-
 mesh_file = joinpath(grids_dir, grid)
+
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
 # mesh_dev = adapt(CUDABackend(), mesh)
diff --git a/examples/2D_cylinder.jl b/examples/2D_cylinder.jl
index 9cdf37a1..6a4fcdaa 100644
--- a/examples/2D_cylinder.jl
+++ b/examples/2D_cylinder.jl
@@ -1,12 +1,11 @@
-using Plots
 using XCALibre
 using CUDA # Run this if using NVIDIA GPU
 # using AMDGPU # Run this if using AMD GPU
 
-# quad, backwardFacingStep_2mm, backwardFacingStep_10mm, trig40
-mesh_file = "unv_sample_meshes/cylinder_d10mm_5mm.unv"
-# mesh_file = "unv_sample_meshes/cylinder_d10mm_2mm.unv"
-# mesh_file = "unv_sample_meshes/cylinder_d10mm_10-7.5-2mm.unv"
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "cylinder_d10mm_5mm.unv"
+mesh_file = joinpath(grids_dir, grid)
+
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
 # mesh_dev = adapt(CUDABackend(), mesh)
@@ -72,7 +71,7 @@ schemes = (
 # runtime = set_runtime(iterations=20, write_interval=10, time_step=1) # for proto
 runtime = set_runtime(iterations=500, write_interval=100, time_step=1)
 
-hardware = set_hardware(backend=CPU(), workgroup=4)
+hardware = set_hardware(backend=CPU(), workgroup=1024)
 # hardware = set_hardware(backend=CUDABackend(), workgroup=32)
 # hardware = set_hardware(backend=ROCBackend(), workgroup=32)
 
diff --git a/examples/2D_cylinder_U.jl b/examples/2D_cylinder_U.jl
index ed311dfe..c6de41ee 100644
--- a/examples/2D_cylinder_U.jl
+++ b/examples/2D_cylinder_U.jl
@@ -1,18 +1,16 @@
-using Plots
 using XCALibre
-using CUDA
+# using CUDA # uncomment to run on GPU
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "cylinder_d10mm_5mm.unv"
+mesh_file = joinpath(grids_dir, grid)
 
-# quad, backwardFacingStep_2mm, backwardFacingStep_10mm, trig40
-mesh_file = "unv_sample_meshes/cylinder_d10mm_5mm.unv"
-mesh_file = "unv_sample_meshes/cylinder_d10mm_2mm.unv"
-mesh_file = "unv_sample_meshes/cylinder_d10mm_10-7.5-2mm.unv"
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
-# mesh_dev = adapt(CUDABackend(), mesh)
 mesh_dev = mesh
+# mesh_dev = adapt(CUDABackend(), mesh) # uncomment to run on GPU
 
 # Inlet conditions
-
 velocity = [0.5, 0.0, 0.0]
 noSlip = [0.0, 0.0, 0.0]
 nu = 1e-3
@@ -70,15 +68,11 @@ schemes = (
 
 
 runtime = set_runtime(
-    iterations=250, write_interval=50, time_step=0.005)
-    # iterations=1, write_interval=50, time_step=0.005)
+    # iterations=1000, write_interval=50, time_step=0.005) # uncomment to save files
+    iterations=1000, write_interval=-1, time_step=0.005) # used to run only
 
-# 2mm mesh use settings below (to lower Courant number)
-# runtime = set_runtime(
-    # iterations=5000, write_interval=250, time_step=0.001) # Only runs on 32 bit
-
-# hardware = set_hardware(backend=CUDABackend(), workgroup=32)
-hardware = set_hardware(backend=CPU(), workgroup=4)
+hardware = set_hardware(backend=CPU(), workgroup=1024)
+# hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
 
 config = Configuration(
     solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
@@ -88,9 +82,4 @@ GC.gc(true)
 initialise!(model.momentum.U, velocity)
 initialise!(model.momentum.p, 0.0)
 
-residuals = run!(model, config, ncorrectors=1, inner_loops=2)
-
-plot(; xlims=(0,runtime.iterations), ylims=(1e-8,0))
-plot!(1:length(Rx), Rx, yscale=:log10, label="Ux")
-plot!(1:length(Ry), Ry, yscale=:log10, label="Uy")
-plot!(1:length(Rp), Rp, yscale=:log10, label="p")
\ No newline at end of file
+residuals = run!(model, config)
\ No newline at end of file

From 1670de5c8872312070fb3ac5add74b8d1bd9c392 Mon Sep 17 00:00:00 2001
From: Humberto Medina <h.medina@aerofluids.org>
Date: Thu, 26 Sep 2024 23:21:24 +0100
Subject: [PATCH 05/40] add docs for new example (neural network as inlet)

---
 docs/Project.toml                             |   6 +
 docs/makeLocal.jl                             |   5 +-
 .../03_2d-constant-temperature-flat-plate.md  |   2 +-
 .../04_2d-aerofoil-inflow-optimisation.md     | 184 +----------
 docs/src/examples/05_2d-inflow-using-Flux.md  | 294 ++++++++++++------
 examples/2D_BFS_neural_network.jl             |  68 ++--
 .../boundary_conditions/dirichlet.jl          |   2 +-
 .../boundary_conditions/dirichletFunction.jl  |  18 +-
 8 files changed, 246 insertions(+), 333 deletions(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index fe2a9521..8c86acf8 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,6 +1,12 @@
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 Documenter = "1.6"
diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 50a1f501..90c57b94 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -4,6 +4,7 @@ using AbstractTrees
 using XCALibre
 
 # push!(LOAD_PATH,"../src/") # for local build only
+ENV["GKSwstype"] = "100"
 
 USER_GUIDE_PAGES = Any[
     "0_introduction_and_workflow.md",
@@ -39,5 +40,5 @@ makedocs(
     ]
 )
 
-foreach(rm, filter(endswith(".vtk"), readdir("docs", join=true)))
-foreach(rm, filter(endswith(".vtu"), readdir("docs", join=true)))
\ No newline at end of file
+# foreach(rm, filter(endswith(".vtk"), readdir("docs", join=true)))
+# foreach(rm, filter(endswith(".vtu"), readdir("docs", join=true)))
\ No newline at end of file
diff --git a/docs/src/examples/03_2d-constant-temperature-flat-plate.md b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
index abe562c7..c2091030 100644
--- a/docs/src/examples/03_2d-constant-temperature-flat-plate.md
+++ b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
@@ -1,6 +1,6 @@
 # Validation: 2D Constant temperature flat plate
 
-# Overview
+# Introduction
 ---
 A 2D constant temperature laminar flat plate case has been used to validate the weakly 
 compressible solver. The case provides a constant temperature boundary condition along the 
diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
index 11e47461..3456cba7 100644
--- a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
@@ -1,188 +1,10 @@
 # Advanced: 2D Aerofoil inflow optimisation
 
-# Overview
+# Introduction
 ---
-A 2D constant temperature laminar flat plate case has been used to validate the weakly 
-compressible solver. The case provides a constant temperature boundary condition along the 
-wall of the domain. 
 
-The results of case are compared against the theoretical local Nusselt number correlation 
-for forced convection on constant temperature flat plate:
+To be completed.
 
-``Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}``
-
-The correlation is valid for Prandtl numbers greater than 0.6.
-
-
-The boundaries are shown in the mesh figure and the tables below describe the boundary settings used.
-
-### Inlet
-
-
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Dirichlet ([0.2, 0.0, 0.0] m/s)   |
-| ``p``   |  Neumann (Zero-gradient)      |
-| ``T ``  |  FixedTemperature (300.0 K)    |
-
-### Wall
-
-
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  No-slip wall   |
-| ``p``   |  Neumann (Zero-gradient)      |
-| ``T ``  |  FixedTemperature (310.0 K)    |
-
-### Outlet
-
-
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Neumann (Zero-gradient)   |
-| ``p``   |  Dirichlet (0.0 Pa)     |
-| ``T ``  |  Neumann (Zero-gradient)    |
-
-### Top
-
-
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Neumann (Zero-gradient)   |
-| ``p``   |  Neumann (Zero-gradient)     |
-| ``T ``  |  Neumann (Zero-gradient)    |
-
-
-# Fluid Properties
-
-
-| Property | value      |
-| -------  | ---------- |
-| ``\nu``   |  0.0001    |
-| ``Pr``   |  0.71      |
-| ``c_p``  |  1005.0    |
-| ``\gamma`` | 1.4      |
-
-
-
-# Mesh
----
-
-The mesh is shown in the figure below:
-
-
-![Figure of mesh.](figures/03/mesh.png)
-
-The streamwise cell length is 2mm with a total domain length of 1m. The near-wall cell height is 0.049mm with a domain height of 0.2m.
-
-
-# Case file
+# Set up
 ---
 
-```jldoctest;  filter = r".*"s => s"", output = false
-using XCALibre
-
-grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
-grid = "flatplate_2D_laminar.unv"
-mesh_file = joinpath(grids_dir, grid)
-
-mesh = UNV2D_mesh(mesh_file, scale=0.001)
-
-velocity = [0.2, 0.0, 0.0]
-nu = 1e-4
-Re = velocity[1]*1/nu
-cp = 1005.0
-gamma = 1.4
-Pr = 0.7
-
-model = Physics(
-    time = Steady(),
-    fluid =  Fluid{WeaklyCompressible}(
-        nu = nu,
-        cp = cp,
-        gamma = gamma,
-        Pr = Pr
-        ),
-    turbulence = RANS{Laminar}(),
-    energy = Energy{SensibleEnthalpy}(Tref = 288.15),
-    domain = mesh # mesh_dev  # use mesh_dev for GPU backend
-    )
-
-@assign! model momentum U (
-    Dirichlet(:inlet, velocity),
-    Neumann(:outlet, 0.0),
-    Wall(:wall, [0.0, 0.0, 0.0]),
-    Symmetry(:top, 0.0)
-)
-
- @assign! model momentum p (
-    Neumann(:inlet, 0.0),
-    Dirichlet(:outlet, 100000.0),
-    Neumann(:wall, 0.0),
-    Neumann(:top, 0.0)
-)
-
-@assign! model energy h (
-    FixedTemperature(:inlet, T=300.0, model=model.energy),
-    Neumann(:outlet, 0.0),
-    FixedTemperature(:wall, T=310.0, model=model.energy),
-    Neumann(:top, 0.0)
-)
-
-schemes = (
-    U = set_schemes(divergence=Linear),
-    p = set_schemes(divergence=Linear),
-    h = set_schemes(divergence=Linear)
-)
-
-solvers = (
-    U = set_solver(
-        model.momentum.U;
-        solver      = BicgstabSolver,
-        preconditioner = Jacobi(),
-        convergence = 1e-7,
-        relax       = 0.7,
-    ),
-    p = set_solver(
-        model.momentum.p;
-        solver      = CgSolver,
-        preconditioner = Jacobi(),
-        convergence = 1e-7,
-        relax       = 0.3,
-    ),
-    h = set_solver(
-        model.energy.h;
-        solver      = BicgstabSolver,
-        preconditioner = Jacobi(),
-        convergence = 1e-7,
-        relax       = 0.7,
-        rtol = 1e-2,
-        atol = 1e-4
-    )
-)
-
-runtime = set_runtime(iterations=1000, write_interval=1000, time_step=1)
-
-hardware = set_hardware(backend=CPU(), workgroup=4)
-
-config = Configuration(
-    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
-
-GC.gc()
-
-initialise!(model.momentum.U, velocity)
-initialise!(model.momentum.p, 100000.0)
-initialise!(model.energy.T, 300.0)
-
-residuals = run!(model, config)
-
-# output
-
-```
-
-# Results
----
-
-The results of the model are compared to the theoretical correlation in the figure below:
-
-![Nusselt number distribution results.](figures/03/Nusselt_const_temp_lam_plate.png)
diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/05_2d-inflow-using-Flux.md
index 4584dffb..dd9fce66 100644
--- a/docs/src/examples/05_2d-inflow-using-Flux.md
+++ b/docs/src/examples/05_2d-inflow-using-Flux.md
@@ -1,140 +1,246 @@
 # Advanced: 2D inflow using `Flux.jl`
 
-# Overview
+# Introduction
 ---
-A 2D constant temperature laminar flat plate case has been used to validate the weakly 
-compressible solver. The case provides a constant temperature boundary condition along the 
-wall of the domain. 
 
-The results of case are compared against the theoretical local Nusselt number correlation 
-for forced convection on constant temperature flat plate:
+In this example a simple neural network is constructed and used to define an inlet boundary condition for the x-component of the velocity vector. This example serves to illustrate how XCALibre.jl can easily integrate with the Julia ecosystem, and its functionality extended. 
 
-``Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}``
+The boundary condition is injected into the solution using the builtin `DirichletFunction` boundary condition, which is designed to pass arbitrary Julia functions to a given boundary.
 
-The correlation is valid for Prandtl numbers greater than 0.6.
+```@docs; canonical=false
+XCALibre.Discretise.DirichletFunction
+```
+
+In this example, instead of passing a Julia function, the boundary velocity profile will be given via a simple neural network. 
 
+    !!! Notice that this interface is experimental and subject to change. Currently it can only be used for vectors.
+# Set up steps
+---
 
-The boundaries are shown in the mesh figure and the tables below describe the boundary settings used.
 
-### Inlet
+### Install and load modules
 
+To be able to run this example the following modules need to be installed. This can be done by entering into package mode (using "]" in the REPL) and typing the following:
 
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Dirichlet ([0.2, 0.0, 0.0] m/s)   |
-| ``p``   |  Neumann (Zero-gradient)      |
-| ``T ``  |  FixedTemperature (300.0 K)    |
+```julia
+add Plots, XCALibre, Flux, StaticArrays, LinearAlgebra, KernelAbstractions, Adapt
+```
 
-### Wall
+This will download and install the required packages. Once installed, the packages can be loaded as follows:
+
+```@example flux
+
+using Plots
+using XCALibre
+using Flux
+using StaticArrays
+using Statistics
+using LinearAlgebra
+using KernelAbstractions
 
+```
 
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  No-slip wall   |
-| ``p``   |  Neumann (Zero-gradient)      |
-| ``T ``  |  FixedTemperature (310.0 K)    |
+### Build a neural network
 
-### Outlet
+Next, a neural network will be created to return a parabolic velocity profile. In this case, the training data will be generated using an analytical expression. 
 
+```@example flux
 
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Neumann (Zero-gradient)   |
-| ``p``   |  Dirichlet (0.0 Pa)     |
-| ``T ``  |  Neumann (Zero-gradient)    |
+actual(y) = begin
+    H = 1 # channel height
+    H2 = H/2
+    h = y - H2
+    vx = (1 - (h/H2)^2)
+    return vx
+end
 
-### Top
+```
 
+And define a simple 2-layer neural network to model the inlet function:
 
-| Field | Boundary condition      |
-| -------  | ---------- |
-| ``U``   |  Neumann (Zero-gradient)   |
-| ``p``   |  Neumann (Zero-gradient)     |
-| ``T ``  |  Neumann (Zero-gradient)    |
+```@example flux
+inflowNetwork = Chain(
+    Dense(1 => 6, sigmoid),
+    Dense(6 => 1)) |> f64
+```
 
+Now, we generate the training and testing datasets using the analytical function. The neural network is not yet trained but it can already be used (of course, the prediction is not yet very useful). The various datasets, and initial model predictions are shown in the figure below.
 
-# Fluid Properties
+```@example flux
 
+y_actual = [0:0.01:1;] # array of y-values for plotting
+vx_actual = actual.(y_actual)
 
-| Property | value      |
-| -------  | ---------- |
-| ``\nu``   |  0.0001    |
-| ``Pr``   |  0.71      |
-| ``c_p``  |  1005.0    |
-| ``\gamma`` | 1.4      |
+# Generate training dataset
+y_train = hcat(rand(0:(0.1/100):0.1, 100)...)./0.1
+vx_train = actual.(y_train)
 
+# Test locations selected randomly
+y_test = hcat(rand(0:(0.1/100):0.1, 100)...)./0.1
+vx_untrained = inflowNetwork(y_test)
 
+plot(y_actual, vx_actual, label="Actual", frame_style=:box, foreground_color_legend = nothing)
+scatter!(y_train', vx_train', label="Training data")
+scatter!(y_test', vx_untrained', label="Untrained output")
+savefig("flux_comparison_untrained.svg"); nothing # hide
+```
 
-# Mesh
----
+![](flux_comparison_untrained.svg)
 
-The mesh is shown in the figure below:
+The next step is to train the model as shown below. Finally, to make sure that the model has trained correctly, it is tested with at randomly generated points and the output compared with the analytical function as shown in the figure below.
 
+```@example flux
 
-![Figure of mesh.](figures/03/mesh.png)
+loss(inflowNetwork, y, vx) = mean(abs2.(inflowNetwork(y) .- vx))
 
-The streamwise cell length is 2mm with a total domain length of 1m. The near-wall cell height is 0.049mm with a domain height of 0.2m.
+opt =  Flux.setup(Adam(), inflowNetwork)
+data = [(y_train, vx_train)]
+for epoch in 1:20000
+    Flux.train!(loss, inflowNetwork, data, opt)
+end
+loss(inflowNetwork, data[1]...,)
 
+vx_trained = inflowNetwork(y_test)
 
-# Case file
----
 
-```jldoctest;  filter = r".*"s => s"", output = false
-using XCALibre
+plot(y_actual, vx_actual, label="Actual", frame_style=:box, foreground_color_legend = nothing)
+scatter!(y_test', vx_trained', label="Trained output")
+savefig("flux_comparison.svg"); nothing # hide
+```
+![](flux_comparison.svg)
+
+
+### Define inlet condition and interface
+
+The next step is to define some interfaces to allow passing the model as if it was a simple Julia function. This requires only 3 key ingredients. First, a struct is defined that will contain any user data needed as well as the model itself. In this case, the following structure has been used (but users are completely free to define their own structures).  The only requirements are that the structure should be a subtype of `XCALibreUserFunctor` and it must contain the `steady` property.
+
+```@example flux
+struct Inflow{F,I,O,N,V,T} <: XCALibreUserFunctor
+    U::F        # maximum velocity
+    H::F        # inlet height
+    input::I    # vector to hold input coordinates
+    output::O   # vector to hold model inferred values
+    network::N  # model itself
+    xdir::V     # struct used to define x-direction unit vector
+    steady::T   # required field! (Bool)
+end
+```
+
+Second, the struct above is used as a functor, defined following the requirements set by the `DirichletFunction` boundary condition. Essentially, this allows for external data to be stored in the `Inflow` object, which is then made "callable" to behave as a simple Julia function that returns the velocity vector at a given coordinate (`vec`) and time (`t`).
+
+```@example flux
+(bc::Inflow)(vec, t, i) = begin
+    velocity = @view bc.output[:,i]
+    return @inbounds SVector{3}(velocity[1], velocity[2], velocity[3])
+end
+```
+
+The third step is to define a new method for the `update_user_boundary!` function from the `Discretise` module. This function offers a mechanism to update the internals of the previously defined structure by calling the user-provided neural network model. In this particular example, this is not required since the boundary values are not changing in time (it would have been sufficient to doa single inference round and to simply story the values inside the `Inflow` struct). However, this function is implemented here to illustrate the interface and provide an example of a user-defined kernel. Notice that, in this particular example, the only purpose of this function is to scale the velocity field inferred by the neural network (since it was defined between 0 and 1).
+
+```@example flux
+
+XCALibre.Discretise.update_user_boundary!(
+    BC::DirichletFunction{I,V}, faces, cells, facesID_range, time, config
+    ) where{I,V<:Inflow} = 
+begin
+
+    (; hardware) = config
+    (; backend, workgroup) = hardware
+
+    kernel_range = length(facesID_range)
+    kernel! = _update_user_boundary!(backend, workgroup, kernel_range)
+    kernel!(BC, faces, cells, facesID_range, time, ndrange=kernel_range)
+    KernelAbstractions.synchronize(backend)
+
+    (; output, input, U, network, xdir) = BC.value
+    output .= U.*network(input).*xdir # convert to vector
+end
+
+@kernel function _update_user_boundary!(BC, faces, cells, facesID_range, time)
+    i = @index(Global)
+    startID = facesID_range[1]
+    fID = i + startID - 1
+    coords = faces[fID].centre
+    BC.value.input[i] = coords[2]/BC.value.H # scale coordinates
+end
+
+```
+
+### Create an instance of  `Inflow` 
+
+An instance of the `Inflow` object is now created. Notice that the `input` and `output` fields contain vectors to hold the boundary face information, thus, they must be of the same size as the number of boundary faces. The mesh is, therefore, loaded first.
+```@example flux
 
 grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
-grid = "flatplate_2D_laminar.unv"
+grid = "backwardFacingStep_5mm.unv"
 mesh_file = joinpath(grids_dir, grid)
 
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
-velocity = [0.2, 0.0, 0.0]
-nu = 1e-4
-Re = velocity[1]*1/nu
-cp = 1005.0
-gamma = 1.4
-Pr = 0.7
+nfaces = mesh.boundaries[1].IDs_range |> length
+```
+
+The `Inflow` functor is not constructed.
+
+```@example flux
+
+U = 0.5 # maximum velocity
+H = 0.1 # inlet height
+input = zeros(1,nfaces)
+input .= (H/2)/H
+output = U.*inflowNetwork(input).*[1 0 0]'
+@view output[:,2]
+
+inlet_profile= Inflow(
+    0.5,
+    0.1,
+    input,
+    output,
+    inflowNetwork,
+    [1,0,0],
+    true
+)
+
+```
+
+### Run simulation
+
+The final step is simply to set up and run a simulation in XCALibre.jl. Notice that this does not require any special considerations, only to remember to use the `DirichletFunction` boundary condition when setting the inlet velocity. The `inlet_profile` functor object is then passed to the boundary. 
+
+```@example flux
+
+velocity = [0.5, 0.0, 0.0]
+nu = 1e-3
+Re = velocity[1]*0.1/nu
 
 model = Physics(
     time = Steady(),
-    fluid =  Fluid{WeaklyCompressible}(
-        nu = nu,
-        cp = cp,
-        gamma = gamma,
-        Pr = Pr
-        ),
+    fluid = Fluid{Incompressible}(nu = nu),
     turbulence = RANS{Laminar}(),
-    energy = Energy{SensibleEnthalpy}(Tref = 288.15),
-    domain = mesh # mesh_dev  # use mesh_dev for GPU backend
+    energy = Energy{Isothermal}(),
+    domain = mesh
     )
 
 @assign! model momentum U (
-    Dirichlet(:inlet, velocity),
+    DirichletFunction(:inlet, inlet_profile), # Pass functor
     Neumann(:outlet, 0.0),
-    Wall(:wall, [0.0, 0.0, 0.0]),
-    Symmetry(:top, 0.0)
+    Dirichlet(:wall, [0.0, 0.0, 0.0]),
+    Dirichlet(:top, [0.0, 0.0, 0.0]),
 )
 
- @assign! model momentum p (
+@assign! model momentum p (
     Neumann(:inlet, 0.0),
-    Dirichlet(:outlet, 100000.0),
+    Dirichlet(:outlet, 0.0),
     Neumann(:wall, 0.0),
     Neumann(:top, 0.0)
 )
 
-@assign! model energy h (
-    FixedTemperature(:inlet, T=300.0, model=model.energy),
-    Neumann(:outlet, 0.0),
-    FixedTemperature(:wall, T=310.0, model=model.energy),
-    Neumann(:top, 0.0)
-)
-
 schemes = (
-    U = set_schemes(divergence=Linear),
-    p = set_schemes(divergence=Linear),
-    h = set_schemes(divergence=Linear)
+    U = set_schemes(divergence = Linear),
+    p = set_schemes()
 )
 
+
 solvers = (
     U = set_solver(
         model.momentum.U;
@@ -142,6 +248,8 @@ solvers = (
         preconditioner = Jacobi(),
         convergence = 1e-7,
         relax       = 0.7,
+        rtol = 1e-4,
+        atol = 1e-10
     ),
     p = set_solver(
         model.momentum.p;
@@ -149,21 +257,15 @@ solvers = (
         preconditioner = Jacobi(),
         convergence = 1e-7,
         relax       = 0.3,
-    ),
-    h = set_solver(
-        model.energy.h;
-        solver      = BicgstabSolver,
-        preconditioner = Jacobi(),
-        convergence = 1e-7,
-        relax       = 0.7,
-        rtol = 1e-2,
-        atol = 1e-4
+        rtol = 1e-4,
+        atol = 1e-10
     )
 )
 
-runtime = set_runtime(iterations=1000, write_interval=1000, time_step=1)
+runtime = set_runtime(
+    iterations=500, time_step=1, write_interval=500)
 
-hardware = set_hardware(backend=CPU(), workgroup=4)
+hardware = set_hardware(backend=CPU(), workgroup=1024)
 
 config = Configuration(
     solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
@@ -171,18 +273,14 @@ config = Configuration(
 GC.gc()
 
 initialise!(model.momentum.U, velocity)
-initialise!(model.momentum.p, 100000.0)
-initialise!(model.energy.T, 300.0)
+initialise!(model.momentum.p, 0.0)
 
 residuals = run!(model, config)
 
-# output
-
+"done!" # hide
 ```
 
-# Results
+# Simulation result
 ---
 
-The results of the model are compared to the theoretical correlation in the figure below:
-
-![Nusselt number distribution results.](figures/03/Nusselt_const_temp_lam_plate.png)
+Add figure here!
\ No newline at end of file
diff --git a/examples/2D_BFS_neural_network.jl b/examples/2D_BFS_neural_network.jl
index dc990710..5c55e755 100644
--- a/examples/2D_BFS_neural_network.jl
+++ b/examples/2D_BFS_neural_network.jl
@@ -1,13 +1,12 @@
 using Plots
 using XCALibre
 using Flux
+using StaticArrays
 using Statistics
 using LinearAlgebra
-using CUDA
-using StaticArrays
-using Adapt
-using Cthulhu
 using KernelAbstractions
+using Adapt
+# using CUDA
 
 actual(y) = begin
     H = 1 # channel height
@@ -40,9 +39,9 @@ loss(inflowNetwork, data[1]...,)
 scatter(y_train', inflowNetwork(y_train)', legend=:none)
 scatter!(vec(y_train), actual.(vec(y_train)), legend=:none)
 
-inflowNetwork([1])
-inflowNetwork_dev = inflowNetwork |> gpu
-inflowNetwork_dev(SVector{1}(1))
+# inflowNetwork([1])
+# inflowNetwork_dev = inflowNetwork |> gpu
+# inflowNetwork_dev(SVector{1}(1))
 
 
 struct Inflow{F,I,O,N,V,B} <: XCALibreUserFunctor
@@ -82,11 +81,17 @@ end
     BC.value.input[i] = coords[2]/BC.value.H
 end
 
-# inlet = Inflow(0.5f0, 0.1f0, Float32[1.0, 0.0, 0.0])
-nfaces = 10 # mesh.boundaries[1].IDs_range |> length
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "backwardFacingStep_5mm.unv"
+mesh_file = joinpath(grids_dir, grid)
+
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+
+nfaces = mesh.boundaries[1].IDs_range |> length
 U = 0.5
 H = 0.1
-input = zeros(1,10)
+input = zeros(1,nfaces)
 input .= (H/2)/H
 output = U.*inflowNetwork(input).*[1 0 0]'
 @view output[:,2]
@@ -102,7 +107,8 @@ inlet= Inflow(
 )
 
 # test = adapt(CUDABackend(), Storage([0.0], [0.0,0.0,0.0]))
-inlet_dev = adapt(CUDABackend(), inlet)
+inlet_dev = inlet
+# inlet_dev = adapt(CUDABackend(), inlet)
 
 (bc::Inflow)(vec, t, i) = begin
     velocity = @view bc.output[:,i]
@@ -110,19 +116,17 @@ inlet_dev = adapt(CUDABackend(), inlet)
     # return @inbounds SVector{3}(velocity)
 end
 
-inlet.update!(inlet, (0,0.0,0),0,2)
+# inlet.update!(inlet, (0,0.0,0),0,2)
 
 
 res = inlet(SVector{3}(0,0.05,0),0,2)
 res = inlet_dev(SVector{3}(0,0.05,0),0,2)
 CUDA.@allowscalar res = inlet_dev(SVector{3}(0,0.05,0),0,2)
 
-# backwardFacingStep_2mm, backwardFacingStep_10mm
-mesh_file = "unv_sample_meshes/backwardFacingStep_10mm.unv"
-mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
-mesh_dev = adapt(CUDABackend(), mesh)
-# mesh_dev = mesh
+
+# mesh_dev = adapt(CUDABackend(), mesh)
+mesh_dev = mesh
 
 velocity = [0.5, 0.0, 0.0]
 nu = 1e-3
@@ -187,8 +191,8 @@ solvers = (
 runtime = set_runtime(
     iterations=1000, time_step=1, write_interval=100)
 
-hardware = set_hardware(backend=CUDABackend(), workgroup=32)
-# hardware = set_hardware(backend=CPU(), workgroup=32)
+# hardware = set_hardware(backend=CUDABackend(), workgroup=32)
+hardware = set_hardware(backend=CPU(), workgroup=1024)
 
 config = Configuration(
     solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
@@ -199,29 +203,3 @@ initialise!(model.momentum.U, velocity)
 initialise!(model.momentum.p, 0.0)
 
 residuals = run!(model, config)# 9.39k allocs in 184 iterations
-
-plot(; xlims=(0,1000))
-plot!(1:length(Rx), Rx, yscale=:log10, label="Ux")
-plot!(1:length(Ry), Ry, yscale=:log10, label="Uy")
-plot!(1:length(Rp), Rp, yscale=:log10, label="p")
-
-# # PROFILING CODE
-
-using Profile, PProf
-
-GC.gc()
-initialise!(model.momentum.U, velocity)
-initialise!(model.momentum.p, 0.0)
-
-Profile.Allocs.clear()
-Profile.Allocs.@profile sample_rate=1.0 begin 
-    residuals = run!(model, config)
-end
-
-# Profile.print(format=:flat)
-
-PProf.Allocs.pprof()
-
-PProf.refresh()
-
-@profview_allocs residuals = run!(model, config) sample_rate=1
\ No newline at end of file
diff --git a/src/Discretise/boundary_conditions/dirichlet.jl b/src/Discretise/boundary_conditions/dirichlet.jl
index 104320ee..cef8cb1d 100644
--- a/src/Discretise/boundary_conditions/dirichlet.jl
+++ b/src/Discretise/boundary_conditions/dirichlet.jl
@@ -5,7 +5,7 @@ export Dirichlet
 
 Dirichlet boundary condition model.
 
-### Fields
+# Fields
 - 'ID' -- Boundary ID
 - `value` -- Scalar or Vector value for Dirichlet boundary condition.
 """
diff --git a/src/Discretise/boundary_conditions/dirichletFunction.jl b/src/Discretise/boundary_conditions/dirichletFunction.jl
index 602db0f3..da4fbe6c 100644
--- a/src/Discretise/boundary_conditions/dirichletFunction.jl
+++ b/src/Discretise/boundary_conditions/dirichletFunction.jl
@@ -4,13 +4,21 @@ export DirichletFunction
 abstract type XCALibreUserFunctor end
 
 """
-    DirichletFunction <: AbstractDirichlet
+    DirichletFunction(ID, value) <: AbstractDirichlet
 
-Dirichlet boundary condition model.
+Dirichlet boundary condition defined with user-provided function.
 
-### Fields
-- 'ID' -- Boundary ID
-- `value` -- Custom function for Dirichlet boundary condition.
+# Input
+- 'ID' Boundary name provided as symbol e.g. :inlet
+- `value` Custom function for Dirichlet boundary condition.
+
+# Function requirements
+
+The function pass to this boundary condition must have the following signature:
+
+    f(coords, time, index) = SVector{3}(ux, uy, uz)
+
+Where, `coords` is a vector containing the coordinates of a face, `time` is the current time in transient simulations (and the iteration number in steady simulations), and `index` is the local face index (from 1 to `N`, where `N` is the number of faces in a given boundary). The function must return an SVector (from StaticArrays.jl) representing the velocity vector. 
 """
 struct DirichletFunction{I,V} <: AbstractDirichlet
     ID::I

From 7395af38c2d1d434394eb597d2c5b2889777bbf0 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 26 Sep 2024 23:45:04 +0100
Subject: [PATCH 06/40] add cylinder animation to readme.md

---
 README.md                                     |   1 +
 .../figures/animated_cylinder_re1000-2x.gif   | Bin 0 -> 6908991 bytes
 2 files changed, 1 insertion(+)
 create mode 100644 docs/src/figures/animated_cylinder_re1000-2x.gif

diff --git a/README.md b/README.md
index 73d0ac1c..68a47080 100644
--- a/README.md
+++ b/README.md
@@ -16,6 +16,7 @@
 
 XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose Computational Fluid Dynamics (CFD) library for 2D and 3D simulations on structured/unstructured grids using the finite volume method. XCALibre.jl has been designed to act as a platform for developing, testing and using *XPU CFD Algorithms and Libraries* to give researchers in both academia and industry alike a tool that can be used to test out ideas easily within a framework that offers acceptable performance. To this end, XCALibre.jl has been implemented to offer both CPU multi-threaded capabilities or GPU acceleration using the same codebase (thanks to the unified programming framework provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)). Additionally, XCALibre.jl also offers a friendly API for those users who are interested in running CFD simulations with the existing solvers and models built into XCALibre.jl. 
 
+![](docs/src/figures/animated_cylinder_re1000-2x.gif)
 
 ## Installation
 
diff --git a/docs/src/figures/animated_cylinder_re1000-2x.gif b/docs/src/figures/animated_cylinder_re1000-2x.gif
new file mode 100644
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From 9aa493f6ffb4cb72d38e1ed23f4260ef1dcc0f8d Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 26 Sep 2024 23:53:18 +0100
Subject: [PATCH 07/40] add labels to figures

---
 docs/src/examples/05_2d-inflow-using-Flux.md | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/05_2d-inflow-using-Flux.md
index dd9fce66..71a72321 100644
--- a/docs/src/examples/05_2d-inflow-using-Flux.md
+++ b/docs/src/examples/05_2d-inflow-using-Flux.md
@@ -79,7 +79,10 @@ vx_train = actual.(y_train)
 y_test = hcat(rand(0:(0.1/100):0.1, 100)...)./0.1
 vx_untrained = inflowNetwork(y_test)
 
-plot(y_actual, vx_actual, label="Actual", frame_style=:box, foreground_color_legend = nothing)
+plot(
+    y_actual, vx_actual, label="Actual", 
+    frame_style=:box, foreground_color_legend = nothing,
+    xlabel="Dimensionless distance", ylabel="Normalised velocity")
 scatter!(y_train', vx_train', label="Training data")
 scatter!(y_test', vx_untrained', label="Untrained output")
 savefig("flux_comparison_untrained.svg"); nothing # hide
@@ -103,7 +106,10 @@ loss(inflowNetwork, data[1]...,)
 vx_trained = inflowNetwork(y_test)
 
 
-plot(y_actual, vx_actual, label="Actual", frame_style=:box, foreground_color_legend = nothing)
+plot(
+    y_actual, vx_actual, label="Actual", 
+    frame_style=:box, foreground_color_legend = nothing,
+    xlabel="Dimensionless distance", ylabel="Normalised velocity")
 scatter!(y_test', vx_trained', label="Trained output")
 savefig("flux_comparison.svg"); nothing # hide
 ```

From 9c53d0aeeb5a5dbd9495926108eac2af38719338 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 27 Sep 2024 00:15:42 +0100
Subject: [PATCH 08/40] add some commentary for restarting sims or changing to
 transient

---
 docs/src/user_guide/4_runtime_and_solvers.md | 12 +++++++++++-
 src/ModelPhysics/3_physics_API.jl            | 20 ++++++++++++++++++++
 2 files changed, 31 insertions(+), 1 deletion(-)

diff --git a/docs/src/user_guide/4_runtime_and_solvers.md b/docs/src/user_guide/4_runtime_and_solvers.md
index e46e5e95..579332f5 100644
--- a/docs/src/user_guide/4_runtime_and_solvers.md
+++ b/docs/src/user_guide/4_runtime_and_solvers.md
@@ -36,4 +36,14 @@ In XCALibre.jl the `run!` function is used to start a simulation, which will dis
 ```@docs; canonical=false
 run!()
 ```
----
\ No newline at end of file
+
+## Restarting simulations
+---
+
+It should be noted that when running a simulation with `run!`, the solution fields in the `Physics` model are mutated. Thus, running the simulation from the previous solution is simply a matter of reissuing the `run!` function. At present, this has the side effect of overwriting any existing solution files (`.vtk` or `.vtu`). Users must be aware of this behaviour.
+
+In some cases, it may be desirable to solve a problem with a steady solver and use the solution to run transient simulations. This is possible using the `change` function.
+
+```@docs; canonical=false
+XCALibre.ModelPhysics.change
+```
\ No newline at end of file
diff --git a/src/ModelPhysics/3_physics_API.jl b/src/ModelPhysics/3_physics_API.jl
index 03913754..91f6917d 100644
--- a/src/ModelPhysics/3_physics_API.jl
+++ b/src/ModelPhysics/3_physics_API.jl
@@ -1,5 +1,25 @@
 export change
 
+"""
+    change(model::Physics, property, value) => updatedModel::Physics
+
+A convenience function to change properties of an exisitng `Physics` model.
+
+# Input arguments
+- `model::Physics` a `Physics` model to modify
+- `property` is a symbol specifying the property to change 
+- `value` is the new setting for the specified `property`
+
+# Output
+
+This function return a new `Physics` object
+
+# Example
+
+To change a model to run a transient simulation e.g. after converging in steady state
+
+    modelTransient = change(model, :time, Transient())
+"""
 function change(model::Physics, property, value)
     @assert property ∈ fieldnames(Physics) throw(ArgumentError(
     """$value is not in Physics. 

From 4dbe871605a6cd42539f86647ede03f06a9f3cd5 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 27 Sep 2024 00:16:32 +0100
Subject: [PATCH 09/40] change makeLocal to force docstests

---
 docs/makeLocal.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 90c57b94..abf79139 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -26,7 +26,7 @@ EXAMPLES_PAGES = Any[
 makedocs(
     sitename = "XCALibre.jl",
     format = Documenter.HTML(),
-    doctest = false, # only set to false when sorting out docs structure
+    # doctest = false, # only set to false when sorting out docs structure
     modules = [XCALibre],
     pages = [
         "Home" => "index.md",

From ec52520fa919806d9f7877e99cbc597296a0d979 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 27 Sep 2024 01:51:14 +0100
Subject: [PATCH 10/40] delete image

---
 .../figures/01/BFS_1.5ms_Linear_VS_OF.png       | Bin 31115 -> 0 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)
 delete mode 100644 docs/src/examples/figures/01/BFS_1.5ms_Linear_VS_OF.png

diff --git a/docs/src/examples/figures/01/BFS_1.5ms_Linear_VS_OF.png b/docs/src/examples/figures/01/BFS_1.5ms_Linear_VS_OF.png
deleted file mode 100644
index 743f68458ac28ded9b88f5ae88aeb07e20f8c7d7..0000000000000000000000000000000000000000
GIT binary patch
literal 0
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z?MN=h%?l%_I5Jo_(AOsk|NjQjBu3vF<RT?f)^zIk`ypPDB1l6$Im?5J_w<szGUxqL
zX*ky@WvVsYI)#{(CDf^YO=!<Lv>_3Njqk$1P!IijK;LN#q-e4;GAuq+T+U>MW_{JN
zfQkYwtbJ%R0dgzJ%dP&ADiV9pJ+2CPTg|L+&Su!d#<Zd;#V3&=R{OKaOiYmRQEAA1
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From 07e369f42ad3bade9f7f61c76cdbc89a0d2827af Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 27 Sep 2024 02:25:07 +0100
Subject: [PATCH 11/40] modify workflow for docs to add main

---
 .github/workflows/documentation.yml | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml
index 26e22c29..64d90f53 100644
--- a/.github/workflows/documentation.yml
+++ b/.github/workflows/documentation.yml
@@ -3,7 +3,8 @@ name: Documentation
 on:
   push:
     branches:
-      - dev-0.3-main  # update to match your development branch (master, main, dev, trunk, ...)
+      - dev-0.3-main  # update to match your development branch (master, main, etc.)
+      - main
     tags: '*'
   pull_request:
 

From 577710e6ecaa768c72e4fe22f36d1b5b35fd4803 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sun, 29 Sep 2024 23:30:29 +0100
Subject: [PATCH 12/40] playing with limiters

---
 prototyping.jl                | 57 +++++++++++++++++++++++
 src/Solvers/Solvers_2_PISO.jl | 88 +++++++++++++++++++++++++++--------
 2 files changed, 126 insertions(+), 19 deletions(-)
 create mode 100644 prototyping.jl

diff --git a/prototyping.jl b/prototyping.jl
new file mode 100644
index 00000000..dfd40faa
--- /dev/null
+++ b/prototyping.jl
@@ -0,0 +1,57 @@
+using XCALibre
+using LinearAlgebra
+using Plots
+
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+# trig, trig40, trig100, quad, quad40, quad100
+grid = "trig40.unv"
+mesh_file = joinpath(grids_dir, grid)
+
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+
+phi = ScalarField(mesh)
+
+cell_xyz = getproperty.(mesh.cells, :centre)
+
+phi.values
+
+sin.(cell_xyz.⋅Ref([1,0,0])*π)
+
+phi.values .= sin.(cell_xyz.⋅Ref([1,0,0])*π)
+
+scatter(cell_xyz.⋅Ref([1,0,0]), phi.values)
+
+phi = assign(phi,
+    Dirichlet(:inlet, 0.0),
+    Dirichlet(:outlet, 0.0),
+    Neumann(:top, 0.0),
+    Neumann(:bottom, 0.0)
+) 
+
+gradPhi = Grad{Orthogonal}(phi)
+phif = FaceScalarField(mesh)
+
+solvers = (
+    phi = set_solver(
+        phi;
+        solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+        preconditioner = Jacobi(),
+        convergence = 1e-7,
+        relax = 1.0
+    ),
+)
+
+schemes = (phi = set_schemes(),)
+runtime = set_runtime(iterations=1, write_interval=-1, time_step=1)
+hardware = set_hardware(backend=CPU(), workgroup=1024)
+
+config = Configuration(
+    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+
+grad!(gradPhi, phif, phi, phi.BCs, 0, config)
+
+scatter(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values)
+
+XCALibre.Solvers.limit_gradient!(gradPhi, phi, config)
+
+scatter(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values)
diff --git a/src/Solvers/Solvers_2_PISO.jl b/src/Solvers/Solvers_2_PISO.jl
index a0304c11..23c12856 100644
--- a/src/Solvers/Solvers_2_PISO.jl
+++ b/src/Solvers/Solvers_2_PISO.jl
@@ -256,47 +256,97 @@ function limit_gradient!(∇F::Grad{S,FF,R,I,M}, F, config) where {S,FF,R<:Tenso
     KernelAbstractions.synchronize(backend)
 end
 
+# @kernel function _limit_gradient!(x, y, z, F, cells, cell_neighbours, cell_faces, cell_nsign, faces, minPhi, maxPhi)
+#     cID = @index(Global)
+
+#     cell = cells[cID]
+#     faces_range = cell.faces_range
+#     phiP = F[cID]
+#     maxPhi = minPhi = phiP
+
+#     for fi ∈ faces_range
+#         nID = cell_neighbours[fi]
+#         phiN = F[nID]
+#         maxPhi = max(phiN, maxPhi)
+#         minPhi = min(phiN, minPhi)
+#     end
+
+#     # g0 = ∇F[cID]
+#     g0 = SVector{3}(x[cID] , y[cID] , z[cID])
+
+#     cc = cell.centre
+
+#     for fi ∈ faces_range 
+#         fID = cell_faces[fi]
+#         face = faces[fID]
+#         nID = face.ownerCells[2]
+#         # phiN = F[nID]
+#         normal = face.normal
+#         nsign = cell_nsign[fi]
+#         na = nsign*normal
+
+#         fc = face.centre 
+#         cc_fc = fc - cc
+#         n0 = cc_fc/norm(cc_fc)
+#         gn = g0⋅n0
+#         δϕ = g0⋅cc_fc
+#         gτ = g0 - gn*n0
+#         if (maxPhi > phiP) && (δϕ > maxPhi - phiP)
+#             g0 = gτ + na*(maxPhi - phiP)
+#         elseif (minPhi < phiP) && (δϕ < minPhi - phiP)
+#             g0 = gτ + na*(minPhi - phiP)
+#         end            
+#     end
+#     x.values[cID] = g0[1]
+#     y.values[cID] = g0[2]
+#     z.values[cID] = g0[3]
+# end
+
 @kernel function _limit_gradient!(x, y, z, F, cells, cell_neighbours, cell_faces, cell_nsign, faces, minPhi, maxPhi)
     cID = @index(Global)
 
     cell = cells[cID]
     faces_range = cell.faces_range
     phiP = F[cID]
-
+    phiMax = phiMin = phiP
+ 
     for fi ∈ faces_range
         nID = cell_neighbours[fi]
         phiN = F[nID]
-        maxPhi = max(phiN, maxPhi)
-        minPhi = min(phiN, minPhi)
+        phiMax = max(phiN, phiMax)
+        phiMin = min(phiN, phiMin)
     end
 
     # g0 = ∇F[cID]
     g0 = SVector{3}(x[cID] , y[cID] , z[cID])
 
     cc = cell.centre
-
+    limiter = 1
+    limiterf = 1
     for fi ∈ faces_range 
         fID = cell_faces[fi]
         face = faces[fID]
         nID = face.ownerCells[2]
-        # phiN = F[nID]
+        phiN = F[nID]
         normal = face.normal
         nsign = cell_nsign[fi]
-        na = nsign*normal
+        # na = nsign*normal
 
         fc = face.centre 
-        cc_fc = fc - cc
-        n0 = cc_fc/norm(cc_fc)
-        gn = g0⋅n0
-        δϕ = g0⋅cc_fc
-        gτ = g0 - gn*n0
-        if (maxPhi > phiP) && (δϕ > maxPhi - phiP)
-            g0 = gτ + na*(maxPhi - phiP)
-        elseif (minPhi < phiP) && (δϕ < minPhi - phiP)
-            g0 = gτ + na*(minPhi - phiP)
-        end            
+        rf = fc - cc
+        δϕ = g0⋅rf
+        phif = phiP + δϕ
+        diff = phif - phiP
+        if diff > 0
+            limiterf = min(1, (phiN - phiP)/diff)
+        elseif diff < 0
+            # limiterf = min(1, (phiN - phiP)/diff)
+        elseif diff == 0
+            limiterf = 1
+        end
+        limiter = min(limiterf, limiter)
     end
-    x.values[cID] = g0[1]
-    y.values[cID] = g0[2]
-    z.values[cID] = g0[3]
+    x.values[cID] = limiter*g0[1]
+    y.values[cID] = limiter*g0[2]
+    z.values[cID] = limiter*g0[3]
 end
\ No newline at end of file

From f1d93fc09c56a9f18befc5f50305d19f84439448 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Tue, 1 Oct 2024 18:44:30 +0100
Subject: [PATCH 13/40] more robust implementation of gradient limiter

---
 prototyping.jl                | 15 +++++++++++-
 src/Solvers/Solvers_2_PISO.jl | 44 +++++++++++++++++++++--------------
 2 files changed, 40 insertions(+), 19 deletions(-)

diff --git a/prototyping.jl b/prototyping.jl
index dfd40faa..9e46288b 100644
--- a/prototyping.jl
+++ b/prototyping.jl
@@ -29,6 +29,7 @@ phi = assign(phi,
 ) 
 
 gradPhi = Grad{Orthogonal}(phi)
+gradPhi = Grad{Midpoint}(phi)
 phif = FaceScalarField(mesh)
 
 solvers = (
@@ -54,4 +55,16 @@ scatter(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values)
 
 XCALibre.Solvers.limit_gradient!(gradPhi, phi, config)
 
-scatter(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values)
+scatter!(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values, alpha=0.25)
+
+fRange = mesh.boundaries[3].IDs_range
+cIDs = mesh.boundary_cellsID[fRange]
+b1_xyz = getproperty.(mesh.cells[cIDs], :centre)
+scatter!(b1_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values[cIDs], alpha=0.50)
+
+vtkWriter = initialise_writer(mesh)
+
+write_vtk("uncorrected", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
+write_vtk("uncorrected_orthogonal", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
+write_vtk("corrected", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
+write_vtk("corrected_orthogonal", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
diff --git a/src/Solvers/Solvers_2_PISO.jl b/src/Solvers/Solvers_2_PISO.jl
index 23c12856..31441dd1 100644
--- a/src/Solvers/Solvers_2_PISO.jl
+++ b/src/Solvers/Solvers_2_PISO.jl
@@ -318,35 +318,43 @@ end
     end
 
     # g0 = ∇F[cID]
-    g0 = SVector{3}(x[cID] , y[cID] , z[cID])
+    grad0 = SVector{3}(x[cID] , y[cID] , z[cID])
 
     cc = cell.centre
     limiter = 1
     limiterf = 1
     for fi ∈ faces_range 
         fID = cell_faces[fi]
+        nID = cell_neighbours[fi]
         face = faces[fID]
-        nID = face.ownerCells[2]
-        phiN = F[nID]
+        cellN = cells[nID]
+        # nID = face.ownerCells[2]
+        # phiN = F[nID]
         normal = face.normal
         nsign = cell_nsign[fi]
-        # na = nsign*normal
-
-        fc = face.centre 
-        rf = fc - cc
-        δϕ = g0⋅rf
-        phif = phiP + δϕ
-        diff = phif - phiP
-        if diff > 0
-            limiterf = min(1, (phiN - phiP)/diff)
-        elseif diff < 0
-            # limiterf = min(1, (phiN - phiP)/diff)
-        elseif diff == 0
+        na = nsign*normal
+
+        # r = fc - cc
+        # fc = face.centre
+
+        nc = cellN.centre
+        r = nc - cc
+        δϕ = r⋅grad0
+
+        # rn = (nc - cc) ⋅ na
+        # gradn = grad0⋅na
+        # δϕ = rn* gradn
+        if δϕ > 0
+            limiterf = min(1, (phiMax - phiP)/δϕ)
+        elseif δϕ < 0
+            limiterf = min(1, (phiMin - phiP)/δϕ)
+        else
             limiterf = 1
         end
         limiter = min(limiterf, limiter)
     end
-    x.values[cID] = limiter*g0[1]
-    y.values[cID] = limiter*g0[2]
-    z.values[cID] = limiter*g0[3]
+    grad0 *= limiter
+    x.values[cID] = grad0[1]
+    y.values[cID] = grad0[2]
+    z.values[cID] = grad0[3]
 end
\ No newline at end of file

From 4855e7f5603498f5e3a28218ce7352659753931e Mon Sep 17 00:00:00 2001
From: Tim <140633759+TimW-24@users.noreply.github.com>
Date: Mon, 7 Oct 2024 12:20:51 +0100
Subject: [PATCH 14/40] Updated Optimisation Case Documentation

Added setup documentation, results to follow.
---
 .../04_2d-aerofoil-inflow-optimisation.md     | 251 +++++++++++++++++-
 1 file changed, 249 insertions(+), 2 deletions(-)

diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
index 3456cba7..ec8d0150 100644
--- a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
@@ -3,8 +3,255 @@
 # Introduction
 ---
 
-To be completed.
+Here, a simple optimisation is performed on a 2D NACA0012 aerofoil case. The optimal angle of attack for maximum lift-to-drag ratio is found using Bayesian optimisation, courtesy of the BayesianOptimization.jl package. This example serves to illustrate both how XCALibre.jl can easily integrate with the Julia ecosystem, and the ease with which post-processing functions can be written.
 
-# Set up
+# Optimisation Setup
 ---
 
+For those interested in running this example, the optimisation can be replicated by following these steps.
+
+### Install and load modules
+
+To be able to run this example the following modules need to be installed. This can be done by entering into package mode (using "]" in the REPL) and typing the following:
+
+```julia
+add Plots, Distributions, LinearAlgebra, GaussianProcesses, BayesianOptimization
+```
+
+This will download and install the required packages. Note that "CUDA" must also be added for GPU acceleration. Once installed, the packages can be loaded as follows:
+
+```@example optimisation
+
+using XCALibre, BayesianOptimization, Plots
+using LinearAlgebra, GaussianProcesses, Distributions
+#using CUDA # uncomment to run on GPU
+```
+
+### Define post processing functions
+
+In order to calculate the lift-to-drag ratio, the pressure and viscous forces over the aerofoil must be calculated and summed. The lift and drag components can then be calculated (noting the rotated inflow vector to allow for different aerofoil angles of attack with the same mesh). A function returning the coefficients of lift and drag (not specifically needed for this example) is also presented for convenience.
+
+```@example optimisation
+#Post-processing functions
+
+lift_to_drag(patch::Symbol, model, ρ, nu, α) = begin
+    Fp = pressure_force(patch, model.momentum.p, ρ)
+    Fv = viscous_force(patch, model.momentum.U, ρ, nu, model.turbulence.nut)
+    Ft = Fp + Fv
+    Ft = [cos(-α*π/180) -sin(-α*π/180) 0; sin(-α*π/180) cos(-α*π/180) 0; 0 0 1]*Ft # Rotation matrix to account for rotated inflow
+    aero_eff = Ft[2]/Ft[1]
+    print("Aerofoil L/D: ",round(aero_eff,sigdigits = 4))
+    return aero_eff
+end # Lift to drag ratio calculation
+
+aero_coeffs(patch::Symbol, chord, velocity, model, ρ, nu, α) = begin
+    Fp = pressure_force(patch, model.momentum.p, ρ)
+    Fv = viscous_force(patch, model.momentum.U, ρ, nu, model.turbulence.nut)
+    Ft = Fp + Fv
+    Ft = [cos(-α*π/180) -sin(-α*π/180) 0; sin(-α*π/180) cos(-α*π/180) 0; 0 0 1]*Ft # Rotation matrix to account for rotated inflow
+    C_l = 2Ft[2]/(ρ*(velocity[1]^2)*chord*0.001)
+    C_d = 2Ft[1]/(ρ*(velocity[1]^2)*chord*0.001)
+    print("Lift Coefficient: ",round(C_l,sigdigits = 4))
+    print("\nDrag Coefficient: ",round(C_d,sigdigits = 4))
+    return C_l,C_d
+end # Aerodynamic coefficient calculation
+```
+
+### Initialise 2D aerofoil mesh
+
+Next, the aerofoil mesh .unv file must be loaded and initialised. It must also be adapted to work with the GPU, if desired.
+
+```@example optimisation
+# Mesh
+mesh_file = "NACAMesh.unv"
+mesh = UNV2D_mesh(mesh_file, scale=0.001)
+#mesh = adapt(CUDABackend(), mesh) # uncomment to run on GPU
+```
+
+### Setup the CFD simulation as a function to be optimised
+
+The BayesianOptimization.jl package can optimise any Julia function that is passed to it. To interface with XCALibre.jl, the entire CFD simulation setup must simply be wrapped within a function, which can then be passed to the optimiser. The function must take the variable to be changed (angle of attack, in this case) as its input, and must return the desired output (lift-to-drag ratio). Therefore, the post-processing step to calculate lift-to-drag ratio is also wrapped in the same function.
+
+```@example optimisation
+function foil_optim(α::Vector{Float64})
+    println("\nSelected α value: $(α[1])")
+
+    # Parameters
+    chord = 250.0
+    Re = 500000
+    nu,ρ = 1.48e-5,1.225
+    Umag = (Re*nu)/(chord*0.001)
+    velocity = [Umag*cos(α[1]*π/180), Umag*sin(α[1]*π/180), 0.0] # Velocity calculation for given α
+    νR = 10
+    Tu = 0.025
+    k_inlet = 3/2*(Tu*norm(velocity))^2
+    ω_inlet = k_inlet/(νR*nu)
+
+    # Boundary Conditions
+    noSlip = [0.0, 0.0, 0.0]
+
+    model = Physics(
+        time = Steady(),
+        fluid = Fluid{Incompressible}(nu = nu),
+        turbulence = RANS{KOmega}(),
+        energy = Energy{Isothermal}(),
+        domain = mesh
+        )
+
+    @assign! model momentum U ( 
+        XCALibre.Dirichlet(:inlet, velocity),
+        XCALibre.Dirichlet(:bottom, velocity),
+        Neumann(:outlet, 0.0),
+        Neumann(:top, 0.0),
+        XCALibre.Dirichlet(:foil, noSlip)
+    )
+
+    @assign! model momentum p (
+        Neumann(:inlet, 0.0),
+        Neumann(:bottom, 0.0),
+        XCALibre.Dirichlet(:outlet, 0.0),
+        XCALibre.Dirichlet(:top, 0.0),
+        Neumann(:foil, 0.0)
+    )
+
+    @assign! model turbulence k (
+        XCALibre.Dirichlet(:inlet, k_inlet),
+        Neumann(:outlet, 0.0),
+        Neumann(:top, 0.0),
+        Neumann(:bottom, 0.0),
+        XCALibre.Dirichlet(:foil, 1e-15)
+    )
+
+    @assign! model turbulence omega (
+        XCALibre.Dirichlet(:inlet, ω_inlet),
+        Neumann(:outlet, 0.0),
+        Neumann(:top, 0.0),
+        Neumann(:bottom, 0.0),
+        OmegaWallFunction(:foil)
+    )
+
+    @assign! model turbulence nut (
+        Neumann(:inlet, 0.0),
+        Neumann(:outlet, 0.0),
+        Neumann(:top, 0.0),
+        Neumann(:bottom, 0.0), 
+        XCALibre.Dirichlet(:foil, 0.0)
+    )
+
+    schemes = (
+        U = set_schemes(divergence=Upwind,gradient=Midpoint),
+        p = set_schemes(divergence=Upwind),
+        k = set_schemes(divergence=Upwind,gradient=Midpoint),
+        omega = set_schemes(divergence=Upwind,gradient=Midpoint)
+    )
+
+    solvers = (
+        U = set_solver(
+            model.momentum.U;
+            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+            preconditioner = ILU0(), # Jacobi # ILU0
+            convergence = 1e-7,
+            relax       = 0.6,
+            rtol = 1e-1,
+        ),
+        p = set_solver(
+            model.momentum.p;
+            solver      = GmresSolver, # BicgstabSolver, GmresSolver # CgSolver
+            preconditioner = LDL(), # Jacobi
+            convergence = 1e-7,
+            relax       = 0.2,
+            rtol = 1e-2,
+        ),
+        k = set_solver(
+            model.turbulence.k;
+            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+            preconditioner = ILU0(),
+            convergence = 1e-7,
+            relax       = 0.6,
+            rtol = 1e-1,
+        ),
+        omega = set_solver(
+            model.turbulence.omega;
+            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+            preconditioner = ILU0(),
+            convergence = 1e-7,
+            relax       = 0.6,
+            rtol = 1e-1,
+        )
+    )
+
+    runtime = set_runtime(iterations=500, write_interval=500, time_step=1)
+
+    hardware = set_hardware(backend=CPU(), workgroup=1024)
+    #hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
+
+    config = Configuration(solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+    GC.gc()
+
+    initialise!(model.momentum.U, velocity)
+    initialise!(model.momentum.p, 0.0)
+    initialise!(model.turbulence.k, k_inlet)
+    initialise!(model.turbulence.omega, ω_inlet)
+    initialise!(model.turbulence.nut, k_inlet/ω_inlet)
+
+    residuals = run!(model, config)
+
+    # Residuals Graph
+    let
+        iterations = 1:length(residuals.Ux)
+        plot(; xlims=(0,runtime.iterations), ylims=(1e-10,0))
+        plot!(iterations, residuals.Ux, yscale=:log10, label="Ux")
+        plot!(iterations, residuals.Uy, yscale=:log10, label="Uy")
+        plot!(iterations, residuals.p, yscale=:log10, label="p")
+    end
+
+    aero_eff = lift_to_drag(:foil, model, ρ, nu, α[1]) # Calculates lift-to-drag ratio
+
+    
+    aero_eff_out = round(aero_eff,digits=3)
+    α_out = round(α[1],digits=3)
+    vtk_files = filter(x->endswith(x,".vtk"), readdir())
+    for file ∈ vtk_files
+        dest = "vtk_results/LD_Ratio = $(aero_eff_out), Alpha = $(α_out).vtk"
+        mv(file, dest, force=true)
+    end
+
+    return aero_eff
+end
+```
+Note that this code saves a single .vtk file of the last CFD iteration each time the optimiser samples the function. This .vtk file is then automatically renamed with that sample's results, and sorted into a /vtk_results subfolder (**which must be created before the optimisation is run**).
+
+### Configure and run the Bayesian optimisation
+
+Finally, the Bayesian optimiser must be configured before the optimisation can be performed. This example follows the BayesianOptimization.jl default configuration for the Gaussian process surrogate model, limiting input dimensions to 1 (the angle of attack). The surrogate model is then set to be optimised every 10 iterations. The inputs are limited to between 0 and 15 degrees. The problem is configured as a maximisation problem, with an initial sample period of 10 iterations and 75 maximum allowed iterations. The final line of the following code block is then run to perform the optimisation.
+
+```@example optimisation
+#Bayesian Optimisation (Using BayesianOptimization.jl)
+
+# Initialises the Gaussian process surrogate model
+model = ElasticGPE(1, #1 input dimension (α)
+                   mean = MeanConst(0.0),
+                   kernel = SEArd([0.0], 5.0),
+                   capacity = 3000)
+set_priors!(model.mean, [Normal(1, 2)])
+
+modeloptimizer = MAPGPOptimizer(every = 10, maxeval = 40) # Optimises the Gaussian process every 10 iterations
+
+# Optimisation Case Setup
+opt = BOpt(foil_optim, # Function to be optimised - encloses the CFD case
+            model, # Gaussian process surrogate model defined above
+            UpperConfidenceBound(),
+            modeloptimizer, # Model optimiser defined above
+            [0.0], [15.0], # Minimum and maximum α constraints       
+            repetitions = 1, # No repititions as CFD data is not noisy
+            maxiterations = 75, # Maximum iterations
+            sense = Max, # Maximisation problem
+            initializer_iterations = 10, # No. of initial random samples
+            verbosity = Progress)
+
+result = boptimize!(opt) # Runs the optimisation procedure
+```
+
+### Example Optimisation Results
+
+TBC

From 6176c4e5e97089b5297aa913795c548bffea26a3 Mon Sep 17 00:00:00 2001
From: Tim <140633759+TimW-24@users.noreply.github.com>
Date: Mon, 7 Oct 2024 14:05:44 +0100
Subject: [PATCH 15/40] Updated Optimisation Case Documentation

---
 docs/src/examples/04_2d-aerofoil-inflow-optimisation.md | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
index ec8d0150..030c7bf2 100644
--- a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
@@ -223,7 +223,7 @@ Note that this code saves a single .vtk file of the last CFD iteration each time
 
 ### Configure and run the Bayesian optimisation
 
-Finally, the Bayesian optimiser must be configured before the optimisation can be performed. This example follows the BayesianOptimization.jl default configuration for the Gaussian process surrogate model, limiting input dimensions to 1 (the angle of attack). The surrogate model is then set to be optimised every 10 iterations. The inputs are limited to between 0 and 15 degrees. The problem is configured as a maximisation problem, with an initial sample period of 10 iterations and 75 maximum allowed iterations. The final line of the following code block is then run to perform the optimisation.
+Finally, the Bayesian optimiser must be configured before the optimisation can be performed. This example follows the BayesianOptimization.jl default configuration for the Gaussian process surrogate model, limiting input dimensions to 1 (the angle of attack). The surrogate model is then set to be optimised every 10 iterations. The inputs are limited to between 0 and 15 degrees. The problem is configured as a maximisation problem, with an initial sample period of 10 iterations and 50 maximum allowed iterations. The final line of the following code block is then run to perform the optimisation.
 
 ```@example optimisation
 #Bayesian Optimisation (Using BayesianOptimization.jl)
@@ -244,7 +244,7 @@ opt = BOpt(foil_optim, # Function to be optimised - encloses the CFD case
             modeloptimizer, # Model optimiser defined above
             [0.0], [15.0], # Minimum and maximum α constraints       
             repetitions = 1, # No repititions as CFD data is not noisy
-            maxiterations = 75, # Maximum iterations
+            maxiterations = 50, # Maximum iterations
             sense = Max, # Maximisation problem
             initializer_iterations = 10, # No. of initial random samples
             verbosity = Progress)
@@ -252,6 +252,7 @@ opt = BOpt(foil_optim, # Function to be optimised - encloses the CFD case
 result = boptimize!(opt) # Runs the optimisation procedure
 ```
 
-### Example Optimisation Results
+# Example Optimisation Results
+---
 
 TBC

From de152267075a5fcf03377953824e91114f08ea69 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Mon, 7 Oct 2024 23:08:32 +0100
Subject: [PATCH 16/40] hack to resolve package conflict - this build will fail
 due to mesh file missing

---
 docs/Project.toml                                       | 2 ++
 docs/makeLocal.jl                                       | 2 +-
 docs/src/examples/04_2d-aerofoil-inflow-optimisation.md | 2 +-
 docs/src/examples/05_2d-inflow-using-Flux.md            | 2 +-
 4 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 8c86acf8..43651d51 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,7 +1,9 @@
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index abf79139..90c57b94 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -26,7 +26,7 @@ EXAMPLES_PAGES = Any[
 makedocs(
     sitename = "XCALibre.jl",
     format = Documenter.HTML(),
-    # doctest = false, # only set to false when sorting out docs structure
+    doctest = false, # only set to false when sorting out docs structure
     modules = [XCALibre],
     pages = [
         "Home" => "index.md",
diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
index 030c7bf2..183fba32 100644
--- a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
@@ -21,7 +21,7 @@ add Plots, Distributions, LinearAlgebra, GaussianProcesses, BayesianOptimization
 This will download and install the required packages. Note that "CUDA" must also be added for GPU acceleration. Once installed, the packages can be loaded as follows:
 
 ```@example optimisation
-
+using Pkg; Pkg.add("BayesianOptimization") # hide
 using XCALibre, BayesianOptimization, Plots
 using LinearAlgebra, GaussianProcesses, Distributions
 #using CUDA # uncomment to run on GPU
diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/05_2d-inflow-using-Flux.md
index 71a72321..bc41faf4 100644
--- a/docs/src/examples/05_2d-inflow-using-Flux.md
+++ b/docs/src/examples/05_2d-inflow-using-Flux.md
@@ -29,7 +29,7 @@ add Plots, XCALibre, Flux, StaticArrays, LinearAlgebra, KernelAbstractions, Adap
 This will download and install the required packages. Once installed, the packages can be loaded as follows:
 
 ```@example flux
-
+using Pkg; Pkg.rm("BayesianOptimization"); Pkg.add("Flux") # hide
 using Plots
 using XCALibre
 using Flux

From b42b520b018873c9604e1febf3bdc71bd7a801f4 Mon Sep 17 00:00:00 2001
From: mberto79 <h.medina@aerofluids.org>
Date: Tue, 8 Oct 2024 18:42:02 +0100
Subject: [PATCH 17/40] add comments/feedback from authors (almost all
 addressed)

---
 README.md                                     | 25 +++++------
 .../01_2d-isothermal-backward-facing-step.md  | 12 +++++-
 .../03_2d-constant-temperature-flat-plate.md  |  9 ++--
 docs/src/examples/05_2d-inflow-using-Flux.md  |  8 ++--
 docs/src/index.md                             |  4 +-
 docs/src/quick_start.md                       | 16 +++----
 docs/src/user_guide/1_preprocessing.md        | 25 +++++++----
 docs/src/user_guide/2_physics_and_models.md   | 42 +++++++++----------
 docs/src/user_guide/3_numerical_setup.md      |  8 ++--
 docs/src/user_guide/4_runtime_and_solvers.md  |  2 +-
 docs/src/user_guide/5_postprocessing.md       |  8 ++--
 .../Discretise_4_assign_boundaries.jl         |  2 +-
 .../boundary_conditions/dirichletFunction.jl  |  4 +-
 src/Simulate/Simulate_0_types.jl              | 17 +++++++-
 src/Solve/Solve_1_api.jl                      |  4 +-
 src/Solvers/Solvers_3_solver_dispatch.jl      |  4 +-
 16 files changed, 112 insertions(+), 78 deletions(-)

diff --git a/README.md b/README.md
index 68a47080..3b7b10c5 100644
--- a/README.md
+++ b/README.md
@@ -14,31 +14,31 @@
 ## What is XCALibre.jl?
 
 
-XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose Computational Fluid Dynamics (CFD) library for 2D and 3D simulations on structured/unstructured grids using the finite volume method. XCALibre.jl has been designed to act as a platform for developing, testing and using *XPU CFD Algorithms and Libraries* to give researchers in both academia and industry alike a tool that can be used to test out ideas easily within a framework that offers acceptable performance. To this end, XCALibre.jl has been implemented to offer both CPU multi-threaded capabilities or GPU acceleration using the same codebase (thanks to the unified programming framework provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)). Additionally, XCALibre.jl also offers a friendly API for those users who are interested in running CFD simulations with the existing solvers and models built into XCALibre.jl. 
+XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose Computational Fluid Dynamics (CFD) library for 2D and 3D simulations on structured/unstructured grids using the finite volume method. XCALibre.jl has been designed to act as a platform for developing, testing and using *XPU CFD Algorithms and Libraries* to give researchers in both academia and industry alike a tool that can be used to test out ideas easily within a framework that offers acceptable performance. To this end, XCALibre.jl has been implemented to offer both CPU multi-threaded capabilities or GPU acceleration using the same codebase (thanks to the unified programming framework provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)). XCALibre.jl also offers a friendly API for those users who are interested in running CFD simulations with the existing solvers and models built into XCALibre.jl. 
 
 ![](docs/src/figures/animated_cylinder_re1000-2x.gif)
 
 ## Installation
 
 
-First, you need to [download and install Julia in your system](https://julialang.org/downloads/). Once you have a working installation of Julia, XCALibre.jl can be installed using the built in package manager. 
+First, you need to [download and install Julia on your system](https://julialang.org/downloads/). Once you have a working installation of Julia, XCALibre.jl can be installed using the built-in package manager. 
 
-To install XCALibre.jl directly from Github, open a Julia REPL, press `]` to enter the package manager. The REPL prompt icon will change from **julia>** (green) to **pkg>** (and change colour to blue) or **(myenvironment) pkg>** where `myenvironment` is the name of the currently active Juila environment. Once in package manager mode enter
+XCALibre.jl is available directly from the the General Julia Registry. Thus, to install XCALibre.jl open a Julia REPL, press `]` to enter the package manager. The REPL prompt icon will change from **julia>** (green) to **pkg>** (and change colour to blue) or **(myenvironment) pkg>** where `myenvironment` is the name of the currently active Julia environment. Once you have activated the package manager mode enter
 
 ```julia
-pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git
+pkg> add XCALibre
 ```
 
-A specific branch can be installed by providing the branch name precided by a `#`, for example, to install the `dev-0.3-main` branch
+To install XCALibre.jl directly from Github enter the following command (for the latest release)
 
 ```julia
-pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git#dev-0.3-main
+pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git
 ```
 
-We plan to register XCALibre.jl so that is added to the General Julia Registry. Once this has been completed, to install XCALibre.jl use the following command (in package mode as detailed above)
+A specific branch can be installed by providing the branch name precided by a `#`, for example, to install the `dev-0.3-main` branch enter
 
 ```julia
-pkg> add XCALibre
+pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git#dev-0.3-main
 ```
 
 ## Main features
@@ -71,13 +71,14 @@ U_eqn = (
 ## Main dependencies
 
 
-XCALibre.jl is possible (and relies) on the functionality provided by other packages in the Julia ecosystem. For a full list of direct dependencies please refer to the Project.toml file included with this repository. We are thankful to the teams that have helped develop and maintain every single of our dependencies. Major functionally is provided by the following:
+XCALibre.jl relies on the functionality provided by other packages from the Julia ecosystem. For a full list of direct dependencies please refer to the Project.toml file included with this repository. We are thankful to the teams that have helped develop and maintain every single of our dependencies. Major functionally is provided by the following:
 
 * KernelAbstractions.jl - provides a unified parallel programming framework for CPUs and GPUs
-* Krylov.jl - provide solvers for linear systems at the heart of XCALibre.jl
+* Krylov.jl - provides solvers for linear systems at the heart of XCALibre.jl
 * LinearOperators.jl - wrappers for matrices and linear operators
-* Atomix.jl - enable atomix operations to ensure race conditions are avoided in parallel kernels
-* CUDA.jl, AMD.jl, Metal.jl and OneAPI.jl - not direct dependencies but packages enable GPU usage in Julia
+* Atomix.jl - enables atomix operations to ensure race conditions are avoided in parallel kernels
+* CUDA.jl, AMD.jl, Metal.jl and OneAPI.jl - not direct dependencies but packages enabling GPU usage in Julia
+* StaticArrays.jl - provides definitions and performant primitives for working with vectors and matrices
 
 ## Related projects
 
diff --git a/docs/src/examples/01_2d-isothermal-backward-facing-step.md b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
index ee21729f..f414748f 100644
--- a/docs/src/examples/01_2d-isothermal-backward-facing-step.md
+++ b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
@@ -3,7 +3,7 @@
 # Introduction
 ---
 
-The correct implementation of the laminar solver in XCALibre.jl has been verified by quantitatively comparing results with those obtained with OpenFOAM. The simulation set up and mesh file used to run the simulation with XCALibre.jl are available in this repository. The OpenFOAM case set up and mesh will be made available as well.
+The correct implementation of the laminar solver in XCALibre.jl has been verified by quantitatively comparing results with those obtained with OpenFOAM. The simulation set up and mesh file used to run the simulation with XCALibre.jl are available in this repository.
 
 # Simulation setup
 ---
@@ -102,8 +102,18 @@ residuals = run!(model, config);
 # Results
 ---
 
+## Domain and mesh
+
 ![Simulation domain](figures/01/domain_mesh.png)
+
+## OpenFoam solution
 ![Simulation domain](figures/01/BFS_OpenFOAM.png)
+
+## XCALibre solution
+
 ![Simulation domain](figures/01/BFS_XCALibre.png)
 
+## Quantitative comparision
+
+The figure below compares the results obtained with OpenFOAM and XCALibre.jl. The profiles are extracted along the y-direction at x = 0.5 m. 
 ![Comparison with OpenFOAM](figures/01/BFS_verification.svg)
\ No newline at end of file
diff --git a/docs/src/examples/03_2d-constant-temperature-flat-plate.md b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
index c2091030..0b852f11 100644
--- a/docs/src/examples/03_2d-constant-temperature-flat-plate.md
+++ b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
@@ -6,15 +6,14 @@ A 2D constant temperature laminar flat plate case has been used to validate the
 compressible solver. The case provides a constant temperature boundary condition along the 
 wall of the domain. 
 
-The results of case are compared against the theoretical local Nusselt number correlation 
+The Nusselt number values obtained from the simulation are compared against the theoretical local Nusselt number correlation 
 for forced convection on constant temperature flat plate:
 
 ``Nu_x = 0.332 Re_x^{1/2} Pr^{1/3}``
 
 The correlation is valid for Prandtl numbers greater than 0.6.
 
-
-The boundaries are shown in the mesh figure and the tables below describe the boundary settings used.
+## Boundary conditions
 
 ### Inlet
 
@@ -68,10 +67,10 @@ The boundaries are shown in the mesh figure and the tables below describe the bo
 # Mesh
 ---
 
-The mesh is shown in the figure below:
+The mesh is shown in the figure below. The plate is represented by the "wall" boundary. The flow moves from left to right ("inlet" to "outlet" boundaries). The x-axis is aligned with the wall boundary and the y-axis is position in the direction perpendicular to the wall.
 
 
-![Figure of mesh.](figures/03/mesh.png)
+![Figure 1](figures/03/mesh.png)
 
 The streamwise cell length is 2mm with a total domain length of 1m. The near-wall cell height is 0.049mm with a domain height of 0.2m.
 
diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/05_2d-inflow-using-Flux.md
index bc41faf4..9d499519 100644
--- a/docs/src/examples/05_2d-inflow-using-Flux.md
+++ b/docs/src/examples/05_2d-inflow-using-Flux.md
@@ -3,7 +3,7 @@
 # Introduction
 ---
 
-In this example a simple neural network is constructed and used to define an inlet boundary condition for the x-component of the velocity vector. This example serves to illustrate how XCALibre.jl can easily integrate with the Julia ecosystem, and its functionality extended. 
+In this example a simple neural network is constructed and used to define an inlet boundary condition for the x-component of the velocity vector. This example serves to illustrate how other packages from the Julia ecosystem can be integrated into `XCALibre.jl` to extend its functionality. In particular, this example will show how to build a basic neural network using `Flux.jl` to represent a parabolic velocity profile and how this neural network can be used to define an inlet condition in `XCALibre.jl`. 
 
 The boundary condition is injected into the solution using the builtin `DirichletFunction` boundary condition, which is designed to pass arbitrary Julia functions to a given boundary.
 
@@ -40,7 +40,7 @@ using KernelAbstractions
 
 ```
 
-### Build a neural network
+### Build a neural network model
 
 Next, a neural network will be created to return a parabolic velocity profile. In this case, the training data will be generated using an analytical expression. 
 
@@ -141,7 +141,7 @@ Second, the struct above is used as a functor, defined following the requirement
 end
 ```
 
-The third step is to define a new method for the `update_user_boundary!` function from the `Discretise` module. This function offers a mechanism to update the internals of the previously defined structure by calling the user-provided neural network model. In this particular example, this is not required since the boundary values are not changing in time (it would have been sufficient to doa single inference round and to simply story the values inside the `Inflow` struct). However, this function is implemented here to illustrate the interface and provide an example of a user-defined kernel. Notice that, in this particular example, the only purpose of this function is to scale the velocity field inferred by the neural network (since it was defined between 0 and 1).
+The third step is to define a new method for the `update_user_boundary!` function from the `Discretise` module. This function offers a mechanism to update the internals of the previously defined structure by calling the user-provided neural network model. In this particular example, this is not required since the boundary values are not changing in time (it would have been sufficient to do a single inference round and to simply store the values inside the `Inflow` struct). However, this function is implemented here to illustrate the interface, and provide an example of a user-defined kernel. Notice that, in this particular example, the only purpose of this function is to scale the velocity field inferred by the neural network (since it was defined with values between 0 and 1).
 
 ```@example flux
 
@@ -186,7 +186,7 @@ mesh = UNV2D_mesh(mesh_file, scale=0.001)
 nfaces = mesh.boundaries[1].IDs_range |> length
 ```
 
-The `Inflow` functor is not constructed.
+The `Inflow` functor is now constructed.
 
 ```@example flux
 
diff --git a/docs/src/index.md b/docs/src/index.md
index 27f64989..28478a40 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -5,7 +5,7 @@
 ## What is XCALibre.jl?
 ---
 
-XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose Computational Fluid Dynamics (CFD) library for 2D and 3D simulations on structured/unstructured grids using the finite volume method. XCALibre.jl has been designed to act as a platform for developing, testing and using *XPU CFD Algorithms and Libraries* to give researchers in both academia and industry alike a tool that can be used to test out ideas easily within a framework that offers acceptable performance. To this end, XCALibre.jl has been implemented to offer both CPU multi-threaded capabilities or GPU acceleration using the same codebase (thanks to the unified programming framework provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)). Additionally, XCALibre.jl also offers a friendly API for those users who are interested in running CFD simulations with the existing solvers and models built into XCALibre.jl. 
+XCALibre.jl (pronounced as the mythical sword *Excalibur*) is a general purpose Computational Fluid Dynamics (CFD) library for 2D and 3D simulations on structured/unstructured grids using the finite volume method. XCALibre.jl has been designed to act as a platform for developing, testing and using *XPU CFD Algorithms and Libraries* to give researchers in both academia and industry alike a tool that can be used to test out ideas easily within a framework that offers acceptable performance. To this end, XCALibre.jl has been implemented to offer both CPU multi-threaded capabilities or GPU acceleration using the same codebase (thanks to the unified programming framework provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/)). XCALibre.jl also offers a friendly API for those users who are interested in running CFD simulations with the existing solvers and models built into XCALibre.jl. 
 
 ## Why XCALibre.jl?
 ---
@@ -47,7 +47,7 @@ XCALibre.jl ships with fluid solvers for steady and transient simulations, based
 
 !!! note
 
-    A solver for highly compressible flows (shock capturing) is currently in testing and will be available in the next major release. Currently the compressible solvers are use a sensible energy approach for the energy equation.
+    A solver for highly compressible flows (shock capturing) is currently in testing and will be available in the next major release. Currently the compressible solvers use a sensible energy approach for the energy equation.
 
 ### Turbulence and energy models
 The list of turbulence models available is expected to expand. The following turbulence models are already available in XCALibre.jl:
diff --git a/docs/src/quick_start.md b/docs/src/quick_start.md
index 83f3c630..dcb15cae 100644
--- a/docs/src/quick_start.md
+++ b/docs/src/quick_start.md
@@ -5,24 +5,24 @@
 ## Installation
 ---
 
-First, you need to [download and install Julia in your system](https://julialang.org/downloads/). Once you have a working installation of Julia, XCALibre.jl can be installed using the built in package manager. 
+First, you need to [download and install Julia on your system](https://julialang.org/downloads/). Once you have a working installation of Julia, XCALibre.jl can be installed using the built-in package manager. 
 
-To install XCALibre.jl directly from Github, open a Julia REPL, press `]` to enter the package manager. The REPL prompt icon will change from **julia>** (green) to **pkg>** (and change colour to blue) or **(myenvironment) pkg>** where `myenvironment` is the name of the currently active Juila environment. Once in package manager mode enter
+XCALibre.jl is available directly from the the General Julia Registry. Thus, to install XCALibre.jl open a Julia REPL, press `]` to enter the package manager. The REPL prompt icon will change from **julia>** (green) to **pkg>** (and change colour to blue) or **(myenvironment) pkg>** where `myenvironment` is the name of the currently active Julia environment. Once you have activated the package manager mode enter
 
 ```julia
-pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git
+pkg> add XCALibre
 ```
 
-A specific branch can be installed by providing the branch name precided by a `#`, for example, to install the `dev-0.3-main` branch
+To install XCALibre.jl directly from Github enter the following command (for the latest release)
 
 ```julia
-pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git#dev-0.3-main
+pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git
 ```
 
-We plan to register XCALibre.jl so that is added to the General Julia Registry. Once this has been completed, to install XCALibre.jl use the following command (in package mode as detailed above)
+A specific branch can be installed by providing the branch name precided by a `#`, for example, to install the `dev-0.3-main` branch enter
 
 ```julia
-pkg> add XCALibre
+pkg> add XCALibre https://github.com/mberto79/XCALibre.jl.git#dev-0.3-main
 ```
 
 !!! note
@@ -40,7 +40,7 @@ The example below illustrates the top-level API used in XCALibre.jl. It shows th
 * [Runtime and solvers](@ref) setup (steps 8 to 11)
 * [Post-processing](@ref) (step 12)
 
-Once you have installed Julia and XCALibre.jl, the example below can be run by copying the contents shown below and pasting them on a file. The file can be executed within vscode, the Julia REPL or from a system terminal. 
+Once you have installed Julia and XCALibre.jl, the example below can be run by copying the contents shown below and pasting them in a file. The file can be executed within vscode, the Julia REPL or from a system terminal. 
 
 * To run in vscode check the information for using [Julia in vscode](https://code.visualstudio.com/docs/languages/julia)
 * To run in the [Julia REPL](https://docs.julialang.org/en/v1/stdlib/REPL/), simply launch Julia and type `include("name_of_your_file.jl")`
diff --git a/docs/src/user_guide/1_preprocessing.md b/docs/src/user_guide/1_preprocessing.md
index ccf7dbd7..dc8b73a4 100644
--- a/docs/src/user_guide/1_preprocessing.md
+++ b/docs/src/user_guide/1_preprocessing.md
@@ -1,5 +1,5 @@
 # Pre-processing
-*super brief summary*
+*First steps required to set up a simulation*
 
 ## Mesh generation and requirements
 ---
@@ -10,11 +10,11 @@ XCALibre.jl is an unstructured Finite Volume Method (FVM) library, therefore, we
 
 ### Mesh conversion
 
-XCALibre.jl at present supports `.unv` mesh formats (which can be generated using [SALOME](https://www.salome-platform.org/)) for simulations in 2D and 3D domains. Additionally, XCALibre.jl also supports the [OpenFOAM](https://openfoam.org/) mesh format for simulations in 3D only (for now). 
+XCALibre.jl at present supports `.unv` mesh formats (which can be generated using [SALOME](https://www.salome-platform.org/)) for simulations in 2D and 3D domains. XCALibre.jl also supports the [OpenFOAM](https://openfoam.org/) mesh format for simulations in 3D only (for now). 
 
 !!! note
 
-    Currently, XCALibre.jl only supports loading mesh files stored in ASCII format. Please ensure that when saving grid files they are not saved in binary. Most mesh generation programmes offer the option to export in ASCII (test-based) formats.
+    Currently, XCALibre.jl only supports loading mesh files stored in ASCII format. Please ensure that when saving grid files they are not saved in binary format. Most mesh generation programmes offer the option to export in ASCII (text-based) formats.
 
 The following functions are provided for importing mesh files:
 
@@ -52,17 +52,17 @@ In this section we summarise the key limitations of the mesh loaders presented a
 
 In XCALibre.jl the mesh object is very important, as it will not only provide geometry information about the simulation/s, but it is also used to automatically dispatch methods to run on the appropriate backend. Therefore, users must first select the backend they wish to use for the simulations, and then "adapt" the mesh to use the correct backend. 
 
-`XCALIbre.jl` aims to work with all the backends supported by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/). However, since internally `XCALibre.jl` uses sparse arrays to reduce its memory footprint some GPU backends are not currently supported since this functionality is not yet available. Thus, currently only a subset of backends are supported:
+`XCALIbre.jl` aims to work with all the backends supported by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/). However, since internally `XCALibre.jl` uses sparse arrays to reduce its memory footprint, some GPU backends are not currently supported since this functionality is not yet available. Thus, currently only a subset of backends are supported:
 
 * CPU (multithreaded and tested)
 * NVidia GPUs (tested)
 * AMD GPUs (not tested - feedback welcome)
 
-Selecting a given backend is straight forward. Below examples are provided by assigning a backend to the symbol `backend` and assigning the mesh object to the appropriate backend device using the symbol `mesh_dev`
+Selecting a given backend is straight-forward. The examples below show how to assign a backend (CPU or GPU) to the symbol `backend` and converting the mesh object to run a simulation on the corresponding backend. The converted mesh is assigned to the symbol `mesh_dev` for clarity.
 
 ### CPU backend
 
-Selecting the CPU backend is straight forward. See the example below. Notice that `CPU()` is a backend type provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/) which we re-export for convenience.
+Selecting the CPU backend is straight-forward. See the example below. Notice that `CPU()` is a backend type provided by [KernelAbstractions.jl](https://juliagpu.github.io/KernelAbstractions.jl/stable/) which we re-export for convenience.
 
 CPU Example 
 ```julia
@@ -73,9 +73,9 @@ mesh_dev = mesh # dummy reference to emphasise the mesh in on our chosen dev (or
 
 ### GPU backends 
 
-To run on GPUS, the process is also quite simple, but does require a few additional steps.
+To execute the code on GPUS, the process is also quite simple, but does require a few additional steps.
 * Install the corresponding Julia library that supports your hardware. For NVidia GPUs, the [CUDA.jl](https://github.com/JuliaGPU/CUDA.jl) package is required. For AMD GPUs, the [AMDGPU.jl](https://github.com/JuliaGPU/AMDGPU.jl) package is needed.
-* Move the mesh object to the backend device using the `adapt` method which for convenience we re-export from [Adapt.jl](https://github.com/JuliaGPU/Adapt.jl)
+* Move the mesh object to the backend device using the `adapt` method, which for convenience we re-export from [Adapt.jl](https://github.com/JuliaGPU/Adapt.jl)
 
 Example for Nvidia GPU
 ```julia
@@ -89,4 +89,13 @@ Example for AMD GPU
 mesh = # call function to load mesh e.g. UNV2_mesh, UNV3_mesh or FOAM3D_mesh
 backend = ROCBackend()
 mesh_dev = adapt(backend, mesh) # make mesh object backend compatible and move to GPU
+```
+
+## Hardware configuration
+---
+
+In order to configure the backend the `set_hardware` function can be used. 
+
+```@docs; canonical=false
+set_hardware
 ```
\ No newline at end of file
diff --git a/docs/src/user_guide/2_physics_and_models.md b/docs/src/user_guide/2_physics_and_models.md
index c25e9647..a7e5d573 100644
--- a/docs/src/user_guide/2_physics_and_models.md
+++ b/docs/src/user_guide/2_physics_and_models.md
@@ -1,10 +1,10 @@
 # Physics and models
-*super brief summary*
+*Information about setting up a `Physics` object and boundary conditions to represent the flow physics*
 
 ## Physics model definition
 ---
 
-The `Physics` object is part of the highest level API in `XCALibre.jl`. `Physics` objects are a means for users to set up the physics and models that are relevant to their particular CFD simulation. Internally, the `Physics` model created is pass to solvers and it is used for dispatch (solvers, algorithms and models). Thus, it is important to ensure that the information provided to this object is correct and representative of the user's intentions. `Physics` models consist of a struct with the  fields shown below. All fields must be provided to the solvers otherwise the construction of the object will fail.
+The `Physics` object is part of the highest level API in `XCALibre.jl`. `Physics` objects are a means for users to set up the physics and models that are relevant to their particular CFD simulation. Internally, the `Physics` model created is passed to solvers and is used for dispatch (solvers, algorithms and models). Thus, it is important to ensure that the information provided to this object is correct and representative of the user's intentions. `Physics` models consist of a struct with the  fields shown below. All fields must be provided to the solvers otherwise the construction of the object will fail.
 
 ```julia
 struct Physics{T,F,M,Tu,E,D,BI}
@@ -47,7 +47,7 @@ This will provide users with all the fields that make up the `Physics` object. T
 ## Time models
 ---
 
-Earlier in this section, the dynamic nature of Julia was mentioned in the context of extracting fields for the `Physics` model used in XCALibre.jl. In the following sections this benefit of using Julia will be exploited further. XCALibre.jl takes advantage of Julia's rich type system and we define `Abstract` types to organise major functionality. For example, time models are subtypes of the abstract type `AbstractTimeModel`. Therefore, out-of-the-box we get for free a means to explore implemented features in XCALibre.jl. For example, to identify the time models implemented, we need simply need to type the following in the REPL:
+Earlier in this section, the dynamic nature of Julia was mentioned in the context of extracting fields for the `Physics` model used in XCALibre.jl. In the following sections this benefit of using Julia will be exploited further. XCALibre.jl takes advantage of Julia's rich type system and we define `Abstract` types to organise major functionality. For example, time models are subtypes of the abstract type `AbstractTimeModel`. Therefore, out-of-the-box we get for free a means to explore implemented features in XCALibre.jl. For example, to identify the time models implemented, we simply need to type the following in the REPL:
 
 ```@repl 
 using XCALibre
@@ -56,9 +56,9 @@ using InteractiveUtils # Load from standard library
 Main.subtypes(AbstractTimeModel)
 ```
 
-From the output it can be seen that there are two time models in XCALibre.jl for `Steady` or `Transient` simulations. These are singleton types and contain (at present) not internal fields or data. They are largely used by XCALibre.jl to dispatch either steady or transient solvers. We starting to get a picture of how the `Physics` object is constructed. For example, to specify a Steady simulation
+From the output it can be seen that there are two time models in XCALibre.jl for `Steady` or `Transient` simulations. These are singleton types and contain (at present) no internal fields or data. They are largely used by XCALibre.jl to dispatch either steady or transient solvers. We are starting to get a picture of how the `Physics` object is constructed. For example, to specify a Steady simulation
 
-For example, the time model can be specified as `Steady` as follows
+The time model can be specified as `Steady` as follows:
 ```julia
 Physics(
     time = Steady()
@@ -85,7 +85,7 @@ begin
 end
 ```
 
-From the subtype tree above, we can see that XCALibre.jl offers 2 major abstract fluid types, `AbstractIncompressible` and `AbstractCompressible`. The concrete fluid types are 3:
+From the subtype tree above, we can see that XCALibre.jl offers 2 major abstract fluid types, `AbstractIncompressible` and `AbstractCompressible`. There are 3 concrete fluid types:
 
 * `Incompressible` - for simulations were the fluid density does not change with pressure
 * `WeaklyCompressible` - for simulation were the fluid density is allowed to change (no shockwaves)
@@ -102,9 +102,9 @@ For compressible fluids (weak formulation)
 ```julia
 Fluid{WeaklyCompressible}(; nu, cp, gamma, Pr)
 ```
-where the input variable represent the following:
+where the input variables represent the following:
 
-* `nu` - viscosity
+* `nu` - kinematic viscosity
 * `rho` - fluid density
 * `gamma` - specific heat ratio
 * `Pr` - Prandlt number
@@ -122,7 +122,7 @@ Physics(
 ## Turbulence models
 ---
 
-Below is a representation the `AbstractTurbulenceModel` inheritance tree. It shows turbulence models available. Turbulence models are defined using the `RANS` and `LES` constructors and passing a specific turbulence model type. As it will be illustrated in the flowing sections.
+Below is a representation of the `AbstractTurbulenceModel` inheritance tree. It shows turbulence models available. Turbulence models are defined using the `RANS` and `LES` constructors and passing a specific turbulence model type. As it will be illustrated in the flowing sections.
 
 ```@repl
 using XCALibre # hide
@@ -139,13 +139,13 @@ Laminar model: no user input is required. This is a dummy model that does not co
 RANS{Laminar}() # only constructor needed
 ```
 
-KOmega model: the standard 2 equation Wilcox model coefficients are passed by default. This model solve an additional 3 equation for `k`, `omega` and `nut` which must be provided with boundary conditions.
+KOmega model: the standard 2 equation Wilcox model coefficients are passed by default. This model solves 2 transport equations for the turbulent kinetic energy and the specific dissipation rate,  `k` and `omega`, respectively. Subsequently, `k` and `omega` are used to update the turbulent eddy viscosity, `nut`. These 3 fields must be provided with boundary conditions. 
 ```julia
 RANS{KOmega}() # will set the default coefficient values shown below
 RANS{KOmega}(; β⁺=0.09, α1=0.52, β1=0.072, σk=0.5, σω=0.5) # set defaults
 RANS{KOmega}(β1=0.075) # user can choose to change a single coefficient
 ```
-KOmegaLKE model: the user must provide a reference turbulence intensity (`Tu`) and a tuple of symbols specifying wall boundaries. This model uses 3 equations (`k`, `kl`, `omega`) and updates the eddy viscosity (`nut`) these must be provided with boundary conditions.
+KOmegaLKE model: the user must provide a reference turbulence intensity (`Tu`) and a tuple of symbols specifying wall boundaries. This model uses 3 equations (`k`, `kl`, `omega`) to update the eddy viscosity (`nut`). These fields must be provided with boundary conditions.
 ```julia
 RANS{KOmegaLKE}(; Tu::Number, walls::Tuple) # no defaults defined
 RANS{KOmegaLKE}(Tu = 0.01, walls=(:cylinder,)) # user should provide information for Tu and walls
@@ -163,7 +163,7 @@ Physics(
 
 ### LES models
 
-Smagorinsky model: the standard model constant is pass by default. Boundary conditions for `nut` must be provided generally zero gradient conditions work well. No special wall functions for `nut` in LES mode are available.
+Smagorinsky model: the standard model constant is passed by default. Boundary conditions for `nut` must be provided, generally zero gradient conditions work well. No special wall functions for `nut` in LES mode are available.
 ```julia
 LES{Smagorinsky}() # default constructor will use value below
 LES{Smagorinsky}(; C=0.15) # default value provided by default
@@ -181,7 +181,7 @@ Physics(
 
 !!! note
 
-    In the specification above the time model was set as `Transient` since `LES` models are strictly time-resolving. A simulation might run when the `Steady` model is chosen, but the results would likely not be reliable. `XCALibre.jl` by design offers flexibility for users to customise their setup, the consequence is that is also falls on users to define a combination of models that is appropriate. Likewise, in the example above an `Isothermal` energy model would have to be selected. See [Energy models](@ref)
+    In the specification above the time model was set as `Transient` since `LES` models are strictly time-resolving. A simulation might run when the `Steady` model is chosen, but the results would likely not be reliable. `XCALibre.jl` by design offers flexibility for users to customise their setup, the consequence is that it falls on users to define a combination of models that is appropriate. Likewise, in the example above an `Isothermal` energy model would have to be selected. See [Energy models](@ref)
 
 ## Energy models
 ---
@@ -251,7 +251,7 @@ Physics(
 ## Boundary conditions
 ---
 
-The final step to completely capture the physics for the simulation is to define boundary conditions in order to find a concrete solution of the model equations being solved. XCALibre.jl offers a range of boundary condition. As before, boundary conditions are specified by type and the are classified under the `AbstractBoundary` type and subdivided into 4 additional abstract types `AbstractDirichlet`, `AbstractNeumann`, `AbstractPhysicalConstraint` and `AbstractWallFunction`. The complete abstract tree is illustrated below.
+The final step to completely capture the physics for the simulation is to define boundary conditions in order to find a concrete solution of the model equations being solved. XCALibre.jl offers a range of boundary conditions. As before, boundary conditions are specified by type and the are classified under the `AbstractBoundary` type and subdivided into 4 additional abstract types `AbstractDirichlet`, `AbstractNeumann`, `AbstractPhysicalConstraint` and `AbstractWallFunction`. The complete abstract tree is illustrated below.
 
 ```@repl
 using XCALibre # hide
@@ -264,8 +264,8 @@ print_tree(AbstractBoundary) # hide
 
 Philosophically, the four subtypes represent different physical types of boundary conditions:
 
-* `AbstractDirichlet` boundary conditions are used to assign a concrete value to a boundary.
-* `AbstractNeumann` boundaries are used to fix the gradient at the boundary.
+* `AbstractDirichlet` boundary conditions are used to assign a concrete value to field at the boundary.
+* `AbstractNeumann` boundaries are used to fix the field gradient at the boundary.
 * `AbstractPhysicalConstraint` boundaries represent physical constraints imposed on the domain.
 * `AbstractWallFunction` represent models for treating flow or turbulence quantities in wall regions.
 
@@ -282,7 +282,7 @@ FixedTemperature(name; T, model::EnergyModel<:AbstractEnergyModel)
 ```
 * `name` is a symbol providing the boundary name
 * `T` is a keyword argument to define the temperate value to be assigned at the boundary
-* `model` is a keyworkd argument that expects an instance of the energy model to be used e.g. `SensibleEnergy`
+* `model` is a keyword argument that expects an instance of the energy model to be used e.g. `SensibleEnergy`
 
 ```julia
 DirichletFunction(name, func)
@@ -290,7 +290,7 @@ DirichletFunction(name, func)
 
 * `name` is a symbol providing the boundary name
 * `func` is a function identifier. `func` is a user-defined function (but can also be a neural network) that returns a scalar or vector as a function of time and space.
-* `func` must adhere to an internal contract. See XXX for more details
+* `func` must adhere to an internal contract. See [`XCALibre.Discretise.DirichletFunction`](@ref) for more details.
 
 ### `AbstractNeumann` conditions
 
@@ -316,9 +316,9 @@ Wall(name, value)
 
 !!! note
     
-    Currently, the value provided at the wall is not used internally. This mean that this boundary condition current acts a a no slip boundary. This will be extended to allow non-slip boundaries or moving walls.
+    Currently, the value provided at the wall is not used internally. This mean that this boundary condition currently acts as a no slip boundary. This will be extended to allow slip boundaries or moving walls.
 
-`Symmetry` boundary condition can be use to assign a symmetry constraint to a given boundary patch in the domain. It can be used for both vector and scalar quantities.
+`Symmetry` boundary condition can be used to assign a symmetry constraint to a given boundary patch in the domain. It can be used for both vector and scalar quantities.
 ```julia
 Symmetry(name)
 ```
@@ -358,7 +358,7 @@ NutWallFunction(name)
 
 ### Assigning conditions (macro)
 
-XCALibre.jl requires that a boundary condition is assigned to every single patch in the domain (as defined within the mesh object) for every the fields that is part of the solution. To facilitate this process, XCALibre.jl provides the `@assign` macro for convenience. The `@assign` macro has the following signature:
+XCALibre.jl requires that a boundary condition is assigned to every single patch in the domain (as defined within the mesh object) for every field that is part of the solution. To facilitate this process, XCALibre.jl provides the `@assign` macro for convenience. The `@assign` macro has the following signature:
 
 ```julia
 @assign! model::Physics <physical model> <field> (
diff --git a/docs/src/user_guide/3_numerical_setup.md b/docs/src/user_guide/3_numerical_setup.md
index 869bf618..0b885ee2 100644
--- a/docs/src/user_guide/3_numerical_setup.md
+++ b/docs/src/user_guide/3_numerical_setup.md
@@ -1,5 +1,5 @@
 # Numerical setup
-*super brief summary*
+*Available discretisation schemes, linear solvers and preconditioners*
 
 ## Discretisation schemes
 ---
@@ -25,7 +25,7 @@ print_tree(AbstractScheme) # hide
 |:-------|:------------|
 | SteadyState | sets the time derivative to zero |
 | Euler | First order implicit Euler scheme |
-| CrankNicolson | Second order central scheme (not implemented) |
+| CrankNicolson | Second order central scheme (not implemented yet) |
 ---
 #### Laplacian schemes
 
@@ -52,7 +52,7 @@ print_tree(AbstractScheme) # hide
 ---
 ### Specifying schemes
 
-XCALibre.jl flow solvers offer considerable flexibility to users for defining discretisation schemes. However, this means that for schemes must be specified for every term of every equation solved. The schemes must be provided as a `NamedTuple` where each keyword corresponds to the fields being solved, e.g. (U = ..., p = ..., k = ..., <field> = ...). To facilitate this process, the [`set_schemes`](@ref) function is provided. Used without any inputs `set_schemes` uses the default values provided (see details below).
+XCALibre.jl flow solvers offer considerable flexibility to users for defining discretisation schemes. However, this means that discretisation schemes must be specified for every term of every equation solved. The schemes must be provided as a `NamedTuple` where each keyword corresponds to the fields being solved, e.g. (U = ..., p = ..., k = ..., <field> = ...). To facilitate this process, the [`set_schemes`](@ref) function is provided. Used without any inputs `set_schemes` uses the default values provided (see details below).
 
 ```@docs; canonical=false
 set_schemes
@@ -105,7 +105,7 @@ print_tree(PreconditionerType) # hide
 
     Only the `Jacobi` and `NormDiagonal` preconditioners have GPU ready implementations. At present these have the most robust implementation and they can be used with both CPU and GPU backends. The other preconditioners can only be used on the CPU. Notice that on our tests the `LDL` preconditioner only works when paired with the `GmresSolver` on the CPU. Also notice that the implementation of the `DILU` preconditioner, although functions, is only experimental. Work on improving the offering of preconditioners is ongoing.
 
-Below an example is provided in context. Here, we are setting solvers for both the velocity field `U` and the pressure field `p` and packing them into a `NamedTuple` "solvers". The `Jacobi` preconditioner is use in both solvers. Notice that preconditioners are specified with an instance of their type i.e. `Jacobi()`. Internally, the preconditioner instance is used for dispatch. This tupple will then be pass on to create the final `Configuration` object.
+Below an example is provided in context. Here, we are setting solvers for both the velocity field `U` and the pressure field `p` and packing them into a `NamedTuple` "solvers". The `Jacobi` preconditioner is used in both solvers. Notice that preconditioners are specified with an instance of their type i.e. `Jacobi()`. Internally, the preconditioner instance is used for dispatch. This tupple will then be passed on to create the final `Configuration` object.
 
 ```@meta
 DocTestSetup = quote
diff --git a/docs/src/user_guide/4_runtime_and_solvers.md b/docs/src/user_guide/4_runtime_and_solvers.md
index 579332f5..57973044 100644
--- a/docs/src/user_guide/4_runtime_and_solvers.md
+++ b/docs/src/user_guide/4_runtime_and_solvers.md
@@ -22,7 +22,7 @@ Configuration
 ## Initialising fields
 ---
 
-The last (optional) step before running the simulation is to provide a guess for all the fields being solved. Although this step is optional, in most cases the flow solvers will perform better when initialised. To set an initial value for a field, the `initialise!` function is provided, which assigns a starting value to a given field.
+The last (optional) step before running the simulation is to provide an initial guess for all the fields being solved. Although this step is optional, in most cases the flow solvers will perform better when initialised. To set an initial value for a field, the `initialise!` function is provided, which assigns a starting value to a given field.
 
 ```@docs; canonical=false
 initialise!
diff --git a/docs/src/user_guide/5_postprocessing.md b/docs/src/user_guide/5_postprocessing.md
index 86a07d75..ebf10a41 100644
--- a/docs/src/user_guide/5_postprocessing.md
+++ b/docs/src/user_guide/5_postprocessing.md
@@ -4,9 +4,9 @@
 ## ParaView
 ---
 
-All solvers in XCALibre.jl will write simulation results in formats that can be loaded directed in [ParaView](https://www.paraview.org/), which is the leading open-source project for scientific visualisation and postprocessing. More information about how to use [ParaView](https://www.paraview.org/) can be found in the [resources](https://www.paraview.org/resources/) page on their website.
+All solvers in XCALibre.jl will write simulation results in formats that can be loaded directly in [ParaView](https://www.paraview.org/), which is the leading open-source project for scientific visualisation and postprocessing. More information about how to use [ParaView](https://www.paraview.org/) can be found in the [resources](https://www.paraview.org/resources/) page on their website.
 
-XCALibre.jl uses two different `VTK` format depending on the type of flow solver used. For 2D simulations, the results are written to file using the `.vtk` file format. 3D simulations are written using the unstructured `VTK` file format, `.vtu`. 
+XCALibre.jl uses two different `VTK` formats depending on the type of flow solver used. For 2D simulations, the results are written to file using the `.vtk` file format. 3D simulations are written using the unstructured `VTK` file format, `.vtu`. 
 
 !!! note
 
@@ -15,7 +15,7 @@ XCALibre.jl uses two different `VTK` format depending on the type of flow solver
 ## Available functions
 ---
 
-Although [ParaView](https://www.paraview.org/) offers considerable flexibility for postprocessing results. Users may also wish to carry out more advanced or different analyses on their CFD results. At present XCALibre.jl offer a limited set of pre-defined postprocessing functions, however, defining new custom postprocessing functions is reasonably straight forward since these can be written in pure Julia. In this section, examples of postprocessing functions will be provided as an illustration. 
+Although [ParaView](https://www.paraview.org/) offers considerable flexibility for postprocessing results, users may also wish to carry out more advanced or different analyses on their CFD results. At present XCALibre.jl offers a limited set of pre-defined postprocessing functions, however, defining new custom postprocessing functions is reasonably straight-forward since these can be written in pure Julia. In this section, examples of postprocessing functions will be provided as an illustration. 
 
 !!! note
 
@@ -29,7 +29,7 @@ In this example, a function is shown that can be used to calculate the average o
 boundary_average
 ```
 
-To calculate pressure and viscous forces. The following functions are available:
+To calculate pressure and viscous forces, the following functions are available:
 
 ```@docs; canonical=false
 pressure_force
diff --git a/src/Discretise/Discretise_4_assign_boundaries.jl b/src/Discretise/Discretise_4_assign_boundaries.jl
index 991af96c..ebfe2e79 100644
--- a/src/Discretise/Discretise_4_assign_boundaries.jl
+++ b/src/Discretise/Discretise_4_assign_boundaries.jl
@@ -182,7 +182,7 @@ The `set_schemes` function is used at the top-level API to help users define dis
 
 # inputs
 
-- `time` is used to set the time schemes(default is `SteadyState`)
+- `time` is used to set the time schemes (default is `SteadyState`)
 - `divergence` is used to set the divergence scheme (default is `Linear`) 
 - `laplacian` is used to set the laplacian scheme (default is `Linear`)
 - `gradient`  is used to set the gradient scheme (default is `Orthogonal`)
diff --git a/src/Discretise/boundary_conditions/dirichletFunction.jl b/src/Discretise/boundary_conditions/dirichletFunction.jl
index da4fbe6c..fa32df29 100644
--- a/src/Discretise/boundary_conditions/dirichletFunction.jl
+++ b/src/Discretise/boundary_conditions/dirichletFunction.jl
@@ -9,12 +9,12 @@ abstract type XCALibreUserFunctor end
 Dirichlet boundary condition defined with user-provided function.
 
 # Input
-- 'ID' Boundary name provided as symbol e.g. :inlet
+- `ID` Boundary name provided as symbol e.g. :inlet
 - `value` Custom function for Dirichlet boundary condition.
 
 # Function requirements
 
-The function pass to this boundary condition must have the following signature:
+The function passed to this boundary condition must have the following signature:
 
     f(coords, time, index) = SVector{3}(ux, uy, uz)
 
diff --git a/src/Simulate/Simulate_0_types.jl b/src/Simulate/Simulate_0_types.jl
index 7b7b25f9..bc5492e3 100644
--- a/src/Simulate/Simulate_0_types.jl
+++ b/src/Simulate/Simulate_0_types.jl
@@ -9,7 +9,7 @@ export set_hardware
         hardware::HW
     end
 
-The `Configuration` type is pass to all flow solvers and provides all the relevant configuration to run a simulation. 
+The `Configuration` type is passed to all flow solvers and provides all the relevant information to run a simulation. 
 
 # Inputs 
 
@@ -33,6 +33,21 @@ config = Configuration(
 end
 Adapt.@adapt_structure Configuration
 
+
+"""
+    hardware = set_hardware(backend, workgroup)
+
+Function used to configure the backend.
+
+# Inputs
+
+- `backend` named tuple used to specify the backend e.g. `CPU()`, `CUDABackend()` or other backends supported by `KernelAbstraction.jl`
+- `workgroup::Int` this is an integer specifying the number of workers that cooperate in a parallel run. For GPUs this could be set to the size of the device's warp e.g. `workgroup = 32`. On CPUs, the default value in `KernelAbstractions.jl` is currently `workgroup = 1024`.
+
+# Output
+
+This function returns a `NamedTuple` with the fields `backend` and `workgroup` which are accessed by internally in `XCALibre.jl` to execute a given kernel.
+"""
 set_hardware(;backend, workgroup) = begin
     (backend=backend, workgroup=workgroup)
 end
diff --git a/src/Solve/Solve_1_api.jl b/src/Solve/Solve_1_api.jl
index 4facfe09..899b9a37 100644
--- a/src/Solve/Solve_1_api.jl
+++ b/src/Solve/Solve_1_api.jl
@@ -37,7 +37,7 @@ This function is used to provide solver settings that will be used internally in
 # Input arguments
 
 - `field` reference to the field to which the solver settings will apply (used to provide integer and float types required)
-- `solver` solver object from Krylov.jl and it could be one of `BicgstabSolver`, `CgSolver`, `GmresSolver` which are reexported in XCALibre.jl
+- `solver` solver object from Krylov.jl and it could be one of `BicgstabSolver`, `CgSolver`, `GmresSolver` which are re-exported in XCALibre.jl
 - `preconditioner` instance of preconditioner to be used e.g. Jacobi()
 - `convergence` sets the stopping criteria of this field
 - `relax` specifies the relaxation factor to be used e.g. set to 1 for no relaxation
@@ -94,7 +94,7 @@ This is a convenience function to set the top-level runtime information. The inp
 # Input arguments
 
 * `iterations::Integer` specifies the number of iterations in a simulation run.
-* `write_interval::Integer` define how often simulation results are written to file. The interval is currently based on number of iterations. Set to `-1` to run without writing results to file.
+* `write_interval::Integer` defines how often simulation results are written to file (on the current working directory). The interval is currently based on number of iterations. Set to `-1` to run without writing results to file.
 * `time_step::Number` the time step to use in the simulation. Notice that for steady solvers this is simply a counter and it is recommended to simply use `1`.
 
 # Example
diff --git a/src/Solvers/Solvers_3_solver_dispatch.jl b/src/Solvers/Solvers_3_solver_dispatch.jl
index 3ce70f7f..ef2476ce 100644
--- a/src/Solvers/Solvers_3_solver_dispatch.jl
+++ b/src/Solvers/Solvers_3_solver_dispatch.jl
@@ -20,9 +20,9 @@ This is the top level API function to initiate a simulation. It uses the user-pr
 - Transient weakly compressible (PISO algorithm for coupling)
 
 # Input arguments
-- `model` reference to a `Physics`` model defined by the user.
+- `model` reference to a `Physics` model defined by the user.
 - `config` Configuration structure defined by the user with solvers, schemes, runtime and hardware structures configuration details.
-- `limit_gradient` flag use to activate gradient limiters in the solver (default = `false`)
+- `limit_gradient` flag used to activate gradient limiters in the solver (default = `false`)
 - `pref` Reference pressure value for cases that do not have a pressure defining BC. Incompressible solvers only (default = `nothing`)
 - `ncorrectors` number of non-orthogonality correction loops (default = `0`)
 - `inner_loops` number to inner loops used in transient solver based on PISO algorithm (default = `0`)

From 2d324c4833109a17a40ba209656802e01178ed05 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Wed, 9 Oct 2024 18:42:42 +0100
Subject: [PATCH 18/40] temporarily remove optim example and playing with
 logging

---
 ...w-optimisation.md => 04_2d-aerofoil-inflow-optimisation.md | 0
 docs/Project.toml                                             | 2 --
 docs/makeLocal.jl                                             | 3 +--
 ...{05_2d-inflow-using-Flux.md => 04_2d-inflow-using-Flux.md} | 4 +++-
 4 files changed, 4 insertions(+), 5 deletions(-)
 rename docs/src/examples/04_2d-aerofoil-inflow-optimisation.md => 04_2d-aerofoil-inflow-optimisation.md (100%)
 rename docs/src/examples/{05_2d-inflow-using-Flux.md => 04_2d-inflow-using-Flux.md} (98%)

diff --git a/docs/src/examples/04_2d-aerofoil-inflow-optimisation.md b/04_2d-aerofoil-inflow-optimisation.md
similarity index 100%
rename from docs/src/examples/04_2d-aerofoil-inflow-optimisation.md
rename to 04_2d-aerofoil-inflow-optimisation.md
diff --git a/docs/Project.toml b/docs/Project.toml
index 43651d51..3b92ea96 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -2,8 +2,6 @@
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
-Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
-GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 90c57b94..fc28bb76 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -19,8 +19,7 @@ EXAMPLES_PAGES = Any[
     "01_2d-isothermal-backward-facing-step.md",
     "02_2d-incompressible-transient-cylinder.md",
     "03_2d-constant-temperature-flat-plate.md",
-    "04_2d-aerofoil-inflow-optimisation.md",
-    "05_2d-inflow-using-Flux.md"
+    "04_2d-inflow-using-Flux.md"
 ]
 
 makedocs(
diff --git a/docs/src/examples/05_2d-inflow-using-Flux.md b/docs/src/examples/04_2d-inflow-using-Flux.md
similarity index 98%
rename from docs/src/examples/05_2d-inflow-using-Flux.md
rename to docs/src/examples/04_2d-inflow-using-Flux.md
index 9d499519..22375848 100644
--- a/docs/src/examples/05_2d-inflow-using-Flux.md
+++ b/docs/src/examples/04_2d-inflow-using-Flux.md
@@ -29,7 +29,8 @@ add Plots, XCALibre, Flux, StaticArrays, LinearAlgebra, KernelAbstractions, Adap
 This will download and install the required packages. Once installed, the packages can be loaded as follows:
 
 ```@example flux
-using Pkg; Pkg.rm("BayesianOptimization"); Pkg.add("Flux") # hide
+using Logging; Logging.disable_logging(Logging.Info) # hide
+using Pkg; Pkg.add("Flux") # hide
 using Plots
 using XCALibre
 using Flux
@@ -283,6 +284,7 @@ initialise!(model.momentum.p, 0.0)
 
 residuals = run!(model, config)
 
+Pkg.rm("Flux") # hide
 "done!" # hide
 ```
 

From a91d8ce87285c9049b699adbd3fa7e60b5b25133 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Wed, 9 Oct 2024 23:21:19 +0100
Subject: [PATCH 19/40] update 2d cylinder laminar case

---
 examples/2D_cylinder_U.jl | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/examples/2D_cylinder_U.jl b/examples/2D_cylinder_U.jl
index c6de41ee..4c136616 100644
--- a/examples/2D_cylinder_U.jl
+++ b/examples/2D_cylinder_U.jl
@@ -1,5 +1,5 @@
 using XCALibre
-# using CUDA # uncomment to run on GPU
+using CUDA # uncomment to run on GPU
 
 grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
 grid = "cylinder_d10mm_5mm.unv"
@@ -8,7 +8,7 @@ mesh_file = joinpath(grids_dir, grid)
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
 
 mesh_dev = mesh
-# mesh_dev = adapt(CUDABackend(), mesh) # uncomment to run on GPU
+mesh_dev = adapt(CUDABackend(), mesh) # uncomment to run on GPU
 
 # Inlet conditions
 velocity = [0.5, 0.0, 0.0]
@@ -47,8 +47,8 @@ solvers = (
         preconditioner = Jacobi(),
         convergence = 1e-7,
         relax       = 1.0,
-        rtol = 1e-4,
-        atol = 1e-5
+        rtol = 1e-6,
+        atol = 1e-15
     ),
     p = set_solver(
         model.momentum.p;
@@ -56,8 +56,8 @@ solvers = (
         preconditioner = Jacobi(), #NormDiagonal(),
         convergence = 1e-7,
         relax       = 0.8,
-        rtol = 1e-4,
-        atol = 1e-5
+        rtol = 1e-6,
+        atol = 1e-15
     )
 )
 
@@ -69,10 +69,10 @@ schemes = (
 
 runtime = set_runtime(
     # iterations=1000, write_interval=50, time_step=0.005) # uncomment to save files
-    iterations=1000, write_interval=-1, time_step=0.005) # used to run only
+    iterations=4000, write_interval=-1, time_step=0.005) # used to run only
 
-hardware = set_hardware(backend=CPU(), workgroup=1024)
-# hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
+hardware = set_hardware(backend=CPU(), workgroup=16384)
+hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
 
 config = Configuration(
     solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)

From d952d497758f5fcc536421f1845065b67e41d331 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Wed, 9 Oct 2024 23:56:25 +0100
Subject: [PATCH 20/40] Make coef matrix linearOperator

---
 src/Solve/Solve_1_api.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/Solve/Solve_1_api.jl b/src/Solve/Solve_1_api.jl
index 899b9a37..2284cdda 100644
--- a/src/Solve/Solve_1_api.jl
+++ b/src/Solve/Solve_1_api.jl
@@ -183,7 +183,7 @@ function solve_system!(phiEqn::ModelEquation, setup, result, component, config)
     b = _b(phiEqn, component)
 
     solve!(
-        solver, A, b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
+        solver, LinearOperator(A), b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
         )
     KernelAbstractions.synchronize(backend)
     kernel! = solve_copy_kernel!(backend, workgroup)

From bd66200b9efee985c3392b9c0dde1b7c038c11f2 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Wed, 9 Oct 2024 23:57:20 +0100
Subject: [PATCH 21/40] reduce number of copies to GPU (can still be improved
 by doing to solver setup and do only once)

---
 src/Discretise/Discretise_5_apply_bcs.jl | 22 ++++++++++++++--------
 1 file changed, 14 insertions(+), 8 deletions(-)

diff --git a/src/Discretise/Discretise_5_apply_bcs.jl b/src/Discretise/Discretise_5_apply_bcs.jl
index f67e355d..0d7b7472 100644
--- a/src/Discretise/Discretise_5_apply_bcs.jl
+++ b/src/Discretise/Discretise_5_apply_bcs.jl
@@ -33,9 +33,12 @@ function _apply_boundary_conditions!(
     ione = one(integer)
 
     # Loop over boundary conditions to apply boundary conditions 
+    boundaries_cpu = get_boundaries(mesh.boundaries)
+
     for BC ∈ BCs
         # Copy to CPU
-        facesID_range = get_boundaries(BC, mesh.boundaries)
+        # facesID_range = get_boundaries(BC, mesh.boundaries)
+        facesID_range = boundaries_cpu[BC.ID].IDs_range
         start_ID = facesID_range[1]
 
         # update user defined boundary storage (if needed)
@@ -57,19 +60,22 @@ update_user_boundary!(
     BC::AbstractBoundary, faces, cells, facesID_range, time, config) = nothing
 
 # Function to prevent redundant CPU copy
-function get_boundaries(BC, boundaries::Array)
-    facesID_range = boundaries[BC.ID].IDs_range
-    return facesID_range
+# function get_boundaries(BC, boundaries::Array)
+function get_boundaries(boundaries::Array)
+    # facesID_range = boundaries[BC.ID].IDs_range
+    # return facesID_range
+    return boundaries
 end
 
 # Function to copy from GPU to CPU
-# function get_boundaries(BC, boundaries::CuArray)
-function get_boundaries(BC, boundaries::AbstractGPUArray)
+# function get_boundaries(BC, boundaries::AbstractGPUArray)
+function get_boundaries(boundaries::AbstractGPUArray)
     # Copy boundaries to CPU
     boundaries_cpu = Array{eltype(boundaries)}(undef, length(boundaries))
     copyto!(boundaries_cpu, boundaries)
-    facesID_range = boundaries_cpu[BC.ID].IDs_range
-    return facesID_range
+    # facesID_range = boundaries_cpu[BC.ID].IDs_range
+    # return facesID_range
+    return boundaries_cpu
 end
 
 # Apply boundary conditions kernel definition

From 0066d9f52a7d61efbd4e10e14ba1c24232e0c1e4 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 10 Oct 2024 00:18:28 +0100
Subject: [PATCH 22/40] update call to `get_boundaries` in RANS models

---
 src/ModelPhysics/Turbulence/RANS_functions.jl | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/src/ModelPhysics/Turbulence/RANS_functions.jl b/src/ModelPhysics/Turbulence/RANS_functions.jl
index 4b75708c..5f936ac3 100644
--- a/src/ModelPhysics/Turbulence/RANS_functions.jl
+++ b/src/ModelPhysics/Turbulence/RANS_functions.jl
@@ -102,7 +102,8 @@ function constrain!(eqn, BC, model, config)
     # turbFields = model.turbulence.fields
     turbulence = model.turbulence
 
-    facesID_range = get_boundaries(BC, boundaries)
+    # facesID_range = get_boundaries(BC, boundaries)
+    facesID_range = get_boundaries(boundaries)
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -180,7 +181,8 @@ function set_cell_value!(field, BC, model, config)
     (; fluid, turbulence) = model
     # turbFields = turbulence.fields
 
-    facesID_range = get_boundaries(BC, boundaries)
+    # facesID_range = get_boundaries(BC, boundaries)
+    facesID_range = get_boundaries(boundaries)
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -252,7 +254,8 @@ function set_production!(P, BC, model, gradU, config)
     # Extract physics models
     (; fluid, momentum, turbulence) = model
 
-    facesID_range = get_boundaries(BC, boundaries)
+    # facesID_range = get_boundaries(BC, boundaries)
+    facesID_range = get_boundaries(boundaries)
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -322,7 +325,8 @@ function correct_nut_wall!(νtf, BC, model, config)
     # Extract physics models
     (; fluid, turbulence) = model
 
-    facesID_range = get_boundaries(BC, boundaries)
+    # facesID_range = get_boundaries(BC, boundaries)
+    facesID_range = get_boundaries(boundaries)
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel

From 86e577471f2112e9352fe6a414731866d7ed9d1f Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 10 Oct 2024 00:26:21 +0100
Subject: [PATCH 23/40] fix RANS model wall function calls to new
 get_boundaries function

---
 src/ModelPhysics/Turbulence/RANS_functions.jl | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/src/ModelPhysics/Turbulence/RANS_functions.jl b/src/ModelPhysics/Turbulence/RANS_functions.jl
index 5f936ac3..07220a11 100644
--- a/src/ModelPhysics/Turbulence/RANS_functions.jl
+++ b/src/ModelPhysics/Turbulence/RANS_functions.jl
@@ -103,7 +103,8 @@ function constrain!(eqn, BC, model, config)
     turbulence = model.turbulence
 
     # facesID_range = get_boundaries(BC, boundaries)
-    facesID_range = get_boundaries(boundaries)
+    boundaries_cpu = get_boundaries(boundaries)
+    facesID_range = boundaries_cpu[BC.ID].IDs_range
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -182,7 +183,8 @@ function set_cell_value!(field, BC, model, config)
     # turbFields = turbulence.fields
 
     # facesID_range = get_boundaries(BC, boundaries)
-    facesID_range = get_boundaries(boundaries)
+    boundaries_cpu = get_boundaries(boundaries)
+    facesID_range = boundaries_cpu[BC.ID].IDs_range
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -255,7 +257,8 @@ function set_production!(P, BC, model, gradU, config)
     (; fluid, momentum, turbulence) = model
 
     # facesID_range = get_boundaries(BC, boundaries)
-    facesID_range = get_boundaries(boundaries)
+    boundaries_cpu = get_boundaries(boundaries)
+    facesID_range = boundaries_cpu[BC.ID].IDs_range
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel
@@ -326,7 +329,8 @@ function correct_nut_wall!(νtf, BC, model, config)
     (; fluid, turbulence) = model
 
     # facesID_range = get_boundaries(BC, boundaries)
-    facesID_range = get_boundaries(boundaries)
+    boundaries_cpu = get_boundaries(boundaries)
+    facesID_range = boundaries_cpu[BC.ID].IDs_range
     start_ID = facesID_range[1]
 
     # Execute apply boundary conditions kernel

From e8ae3c8ca22c83c15bf2bb541f42e4e387fbe47a Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 10 Oct 2024 01:16:58 +0100
Subject: [PATCH 24/40] remove construction of linearoperator for A (should be
 done once to save on per it construction time)

---
 src/Solve/Solve_1_api.jl | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/Solve/Solve_1_api.jl b/src/Solve/Solve_1_api.jl
index 2284cdda..944c0815 100644
--- a/src/Solve/Solve_1_api.jl
+++ b/src/Solve/Solve_1_api.jl
@@ -183,7 +183,8 @@ function solve_system!(phiEqn::ModelEquation, setup, result, component, config)
     b = _b(phiEqn, component)
 
     solve!(
-        solver, LinearOperator(A), b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
+        # solver, LinearOperator(A), b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
+        solver, A, b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
         )
     KernelAbstractions.synchronize(backend)
     kernel! = solve_copy_kernel!(backend, workgroup)

From 2a01ef4129af62a42d5f06ffa2db0166b9331605 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 10 Oct 2024 01:45:02 +0100
Subject: [PATCH 25/40] add  linearoperator field to scalar and vector equation
 to be used by `solve!`

---
 src/ModelFramework/ModelFramework.jl         |  1 +
 src/ModelFramework/ModelFramework_0_types.jl | 16 +++++++++++-----
 src/Solve/Solve_1_api.jl                     |  4 +++-
 3 files changed, 15 insertions(+), 6 deletions(-)

diff --git a/src/ModelFramework/ModelFramework.jl b/src/ModelFramework/ModelFramework.jl
index f7bf02a2..3d088dce 100644
--- a/src/ModelFramework/ModelFramework.jl
+++ b/src/ModelFramework/ModelFramework.jl
@@ -4,6 +4,7 @@ using Accessors
 using SparseArrays
 using StaticArrays
 using Adapt
+using LinearOperators
 
 using Krylov
 using KernelAbstractions
diff --git a/src/ModelFramework/ModelFramework_0_types.jl b/src/ModelFramework/ModelFramework_0_types.jl
index 1c551844..0a2f0fc4 100644
--- a/src/ModelFramework/ModelFramework_0_types.jl
+++ b/src/ModelFramework/ModelFramework_0_types.jl
@@ -101,8 +101,9 @@ end
 # Linear system matrix equation
 
 ## ORIGINAL STRUCTURE PARAMETERISED FOR GPU
-struct ScalarEquation{VTf<:AbstractVector, ASA<:AbstractSparseArray} <: AbstractEquation
+struct ScalarEquation{VTf<:AbstractVector, ASA<:AbstractSparseArray, OP} <: AbstractEquation
     A::ASA
+    opA::OP
     b::VTf
     R::VTf
     Fx::VTf
@@ -114,17 +115,20 @@ ScalarEquation(mesh::AbstractMesh) = begin
     mesh_temp = adapt(CPU(), mesh) # WARNING: Temp solution 
     i, j, v = sparse_matrix_connectivity(mesh_temp) # This needs to be a kernel
     backend = _get_backend(mesh)
+    A = _convert_array!(sparse(i, j, v), backend)
     ScalarEquation(
-        _convert_array!(sparse(i, j, v), backend),
+        A,
+        LinearOperator(A),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend)
         )
 end
 
-struct VectorEquation{VTf<:AbstractVector, ASA<:AbstractSparseArray} <: AbstractEquation
+struct VectorEquation{VTf<:AbstractVector, ASA<:AbstractSparseArray, OP} <: AbstractEquation
     A0::ASA
     A::ASA
+    opA::OP
     bx::VTf
     by::VTf
     bz::VTf
@@ -138,9 +142,11 @@ VectorEquation(mesh::AbstractMesh) = begin
     mesh_temp = adapt(CPU(), mesh) # WARNING: Temp solution 
     i, j, v = sparse_matrix_connectivity(mesh_temp) # This needs to be a kernel
     backend = _get_backend(mesh)
+    A = _convert_array!(sparse(i, j, v), backend) 
     VectorEquation(
-        _convert_array!(sparse(i, j, v), backend) ,
-        _convert_array!(sparse(i, j, v), backend) ,
+        _convert_array!(sparse(i, j, v), backend),
+        A,
+        LinearOperator(A),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),
diff --git a/src/Solve/Solve_1_api.jl b/src/Solve/Solve_1_api.jl
index 944c0815..563c5c6b 100644
--- a/src/Solve/Solve_1_api.jl
+++ b/src/Solve/Solve_1_api.jl
@@ -180,11 +180,13 @@ function solve_system!(phiEqn::ModelEquation, setup, result, component, config)
     (; values) = result
     
     A = _A(phiEqn)
+    opA = phiEqn.equation.opA
     b = _b(phiEqn, component)
 
     solve!(
         # solver, LinearOperator(A), b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
-        solver, A, b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
+        # solver, A, b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
+        solver, opA, b, values; M=P, itmax=itmax, atol=atol, rtol=rtol
         )
     KernelAbstractions.synchronize(backend)
     kernel! = solve_copy_kernel!(backend, workgroup)

From 266077841aa7c4acf2aab939636cebdc24fcd6cb Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Thu, 10 Oct 2024 02:04:34 +0100
Subject: [PATCH 26/40] update mesh path for 3D BFS case

---
 examples/3D_BFS.jl | 12 +++++++-----
 1 file changed, 7 insertions(+), 5 deletions(-)

diff --git a/examples/3D_BFS.jl b/examples/3D_BFS.jl
index bb489459..e15d85a6 100644
--- a/examples/3D_BFS.jl
+++ b/examples/3D_BFS.jl
@@ -2,13 +2,15 @@ using Plots
 using XCALibre
 using CUDA
 
-# bfs_unv_tet_15mm, 10mm, 5mm, 4mm, 3mm
-mesh_file = "unv_sample_meshes/bfs_unv_tet_4mm.unv"
-mesh_file = "unv_sample_meshes/bfs_unv_tet_5mm.unv"
-mesh_file = "unv_sample_meshes/bfs_unv_tet_10mm.unv"
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "bfs_unv_tet_4mm.unv"
+grid = "bfs_unv_tet_5mm.unv"
+grid = "bfs_unv_tet_10mm.unv"
+
+mesh_file = joinpath(grids_dir, grid)
+
 @time mesh = UNV3D_mesh(mesh_file, scale=0.001)
 
-mesh_file = "unv_sample_meshes/bfs_OF_tet_meshes/5mm/polyMesh/"
 @time mesh = FOAM3D_mesh(mesh_file, scale=0.001, integer_type=Int64, float_type=Float64)
 
 mesh_dev = adapt(CUDABackend(), mesh)

From 813ec77c4d66534cfe7ca1efeef42a256394cc1c Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 00:29:07 +0100
Subject: [PATCH 27/40] update project file

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index 076061c8..062887a8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -43,9 +43,9 @@ KernelAbstractions = "0.9.25"
 Krylov = "0.9"
 LDLFactorizations = "0.10"
 LinearOperators = "2.8"
+PrecompileTools = "1.2"
 ProgressMeter = "1.10"
 Reexport = "1.2"
 Setfield = "1.1"
 StaticArrays = "1.9"
 julia = "1.8"
-PrecompileTools = "1.2"

From cee30e500ef4852f9f247e6435e43afc34bd1273 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 00:29:50 +0100
Subject: [PATCH 28/40] add commented code as reminder to explore alternative
 matrix format/s for solvers

---
 src/ModelFramework/ModelFramework_0_types.jl | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/src/ModelFramework/ModelFramework_0_types.jl b/src/ModelFramework/ModelFramework_0_types.jl
index 0a2f0fc4..98ba3618 100644
--- a/src/ModelFramework/ModelFramework_0_types.jl
+++ b/src/ModelFramework/ModelFramework_0_types.jl
@@ -119,6 +119,8 @@ ScalarEquation(mesh::AbstractMesh) = begin
     ScalarEquation(
         A,
         LinearOperator(A),
+        # KrylovOperator(A), # small gain in performance
+        # A,
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend)
@@ -147,6 +149,8 @@ VectorEquation(mesh::AbstractMesh) = begin
         _convert_array!(sparse(i, j, v), backend),
         A,
         LinearOperator(A),
+        # KrylovOperator(A),
+        # A,
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),
         _convert_array!(zeros(Tf, nCells), backend),

From 6c7839cac6b55c9e44d8ad4bd130fdded43f8cb9 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 00:33:28 +0100
Subject: [PATCH 29/40] add naca mesh for optimisation example

---
 examples/0_GRIDS/NACAMesh.unv | 263175 +++++++++++++++++++++++++++++++
 1 file changed, 263175 insertions(+)
 create mode 100644 examples/0_GRIDS/NACAMesh.unv

diff --git a/examples/0_GRIDS/NACAMesh.unv b/examples/0_GRIDS/NACAMesh.unv
new file mode 100644
index 00000000..356e7818
--- /dev/null
+++ b/examples/0_GRIDS/NACAMesh.unv
@@ -0,0 +1,263175 @@
+    -1
+   164
+         1  SI: Meter (newton)         2
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+    2.7314999999999998E+2
+    -1
+    -1
+  2420
+         1
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+         1         0         0
+Global Cartesian Coordinate System
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+         8      1100         0         0         8      1101         0         0
+         8      1102         0         0         8      1103         0         0
+         8      1104         0         0         8      1105         0         0
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+         8      1110         0         0         8      1111         0         0
+         8      1112         0         0         8      1113         0         0
+         8      1114         0         0         8      1115         0         0
+         8      1116         0         0         8      1117         0         0
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+         8      1120         0         0         8      1121         0         0
+         8      1122         0         0         8      1123         0         0
+         8      1124         0         0         8      1125         0         0
+         8      1126         0         0         8      1127         0         0
+         8      1128         0         0         8      1129         0         0
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+         8      1148         0         0         8      1149         0         0
+         8      1150         0         0         8      1151         0         0
+         8      1152         0         0         8      1153         0         0
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+         8      1156         0         0         8      1157         0         0
+         8      1158         0         0         8      1159         0         0
+         8      1160         0         0         8      1161         0         0
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+         8      1164         0         0         8      1165         0         0
+         8      1166         0         0         8      1167         0         0
+         8      1168         0         0         8      1169         0         0
+         8      1170         0         0         8      1171         0         0
+         8      1172         0         0         8      1173         0         0
+         8      1174         0         0         8      1175         0         0
+         8      1176         0         0         8      1177         0         0
+         8      1178         0         0         8      1179         0         0
+         8      1180         0         0         8      1181         0         0
+         8      1182         0         0         8      1183         0         0
+         8      1184         0         0         8      1185         0         0
+         8      1186         0         0         8      1187         0         0
+         8      1188         0         0         8      1189         0         0
+         8      1190         0         0         8      1191         0         0
+         8      1192         0         0         8      1193         0         0
+         8      1194         0         0         8      1195         0         0
+         8      1196         0         0         8      1197         0         0
+         8      1198         0         0         8      1199         0         0
+         8      1200         0         0         8      1201         0         0
+         8      1202         0         0         8      1203         0         0
+         8      1204         0         0         8      1205         0         0
+         8      1206         0         0         8      1207         0         0
+         8      1208         0         0         8      1209         0         0
+         8      1210         0         0         8      1211         0         0
+         8      1212         0         0         8      1213         0         0
+         8      1214         0         0         8      1215         0         0
+         8      1216         0         0         8      1217         0         0
+         8      1218         0         0         8      1219         0         0
+         8      1220         0         0         8      1221         0         0
+         8      1222         0         0         8      1223         0         0
+         8      1224         0         0         8      1225         0         0
+         8      1226         0         0         8      1227         0         0
+         8      1228         0         0         8      1229         0         0
+         8      1230         0         0         8      1231         0         0
+         8      1232         0         0         8      1233         0         0
+         8      1234         0         0         8      1235         0         0
+         8      1236         0         0         8      1237         0         0
+         8      1238         0         0         8      1239         0         0
+         8      1240         0         0         8      1241         0         0
+         8      1242         0         0         8      1243         0         0
+         8      1244         0         0         8      1245         0         0
+         8      1246         0         0         8      1247         0         0
+         8      1248         0         0         8      1249         0         0
+         8      1250         0         0         8      1251         0         0
+         8      1252         0         0         8      1253         0         0
+         8      1254         0         0         8      1255         0         0
+         8      1256         0         0         8      1257         0         0
+         8       403         0         0         8       404         0         0
+         8       405         0         0         8       406         0         0
+         8       407         0         0         8       408         0         0
+         8       409         0         0         8       410         0         0
+         8       411         0         0         8       412         0         0
+         8       413         0         0         8       414         0         0
+         8       415         0         0         8       416         0         0
+         8       417         0         0
+    -1

From d671efe3ee3af6095f0e6541ec2be67414b2d20c Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 00:35:37 +0100
Subject: [PATCH 30/40] remove prototyping file

---
 prototyping.jl | 70 --------------------------------------------------
 1 file changed, 70 deletions(-)
 delete mode 100644 prototyping.jl

diff --git a/prototyping.jl b/prototyping.jl
deleted file mode 100644
index 9e46288b..00000000
--- a/prototyping.jl
+++ /dev/null
@@ -1,70 +0,0 @@
-using XCALibre
-using LinearAlgebra
-using Plots
-
-grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
-# trig, trig40, trig100, quad, quad40, quad100
-grid = "trig40.unv"
-mesh_file = joinpath(grids_dir, grid)
-
-mesh = UNV2D_mesh(mesh_file, scale=0.001)
-
-phi = ScalarField(mesh)
-
-cell_xyz = getproperty.(mesh.cells, :centre)
-
-phi.values
-
-sin.(cell_xyz.⋅Ref([1,0,0])*π)
-
-phi.values .= sin.(cell_xyz.⋅Ref([1,0,0])*π)
-
-scatter(cell_xyz.⋅Ref([1,0,0]), phi.values)
-
-phi = assign(phi,
-    Dirichlet(:inlet, 0.0),
-    Dirichlet(:outlet, 0.0),
-    Neumann(:top, 0.0),
-    Neumann(:bottom, 0.0)
-) 
-
-gradPhi = Grad{Orthogonal}(phi)
-gradPhi = Grad{Midpoint}(phi)
-phif = FaceScalarField(mesh)
-
-solvers = (
-    phi = set_solver(
-        phi;
-        solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
-        preconditioner = Jacobi(),
-        convergence = 1e-7,
-        relax = 1.0
-    ),
-)
-
-schemes = (phi = set_schemes(),)
-runtime = set_runtime(iterations=1, write_interval=-1, time_step=1)
-hardware = set_hardware(backend=CPU(), workgroup=1024)
-
-config = Configuration(
-    solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
-
-grad!(gradPhi, phif, phi, phi.BCs, 0, config)
-
-scatter(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values)
-
-XCALibre.Solvers.limit_gradient!(gradPhi, phi, config)
-
-scatter!(cell_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values, alpha=0.25)
-
-fRange = mesh.boundaries[3].IDs_range
-cIDs = mesh.boundary_cellsID[fRange]
-b1_xyz = getproperty.(mesh.cells[cIDs], :centre)
-scatter!(b1_xyz.⋅Ref([1,0,0]), gradPhi.result.x.values[cIDs], alpha=0.50)
-
-vtkWriter = initialise_writer(mesh)
-
-write_vtk("uncorrected", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
-write_vtk("uncorrected_orthogonal", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
-write_vtk("corrected", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)
-write_vtk("corrected_orthogonal", mesh, vtkWriter, ("gradPhi", gradPhi.result.x)) #, Ux, Uy, Uz, p)

From c1ddfca1588ecf8ba645d18fcfb719656f569352 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 00:43:41 +0100
Subject: [PATCH 31/40] add optim example

---
 docs/makeLocal.jl                                            | 3 ++-
 .../src/examples/05_2d-aerofoil-inflow-optimisation.md       | 5 ++++-
 2 files changed, 6 insertions(+), 2 deletions(-)
 rename 04_2d-aerofoil-inflow-optimisation.md => docs/src/examples/05_2d-aerofoil-inflow-optimisation.md (99%)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index fc28bb76..57d52d44 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -19,7 +19,8 @@ EXAMPLES_PAGES = Any[
     "01_2d-isothermal-backward-facing-step.md",
     "02_2d-incompressible-transient-cylinder.md",
     "03_2d-constant-temperature-flat-plate.md",
-    "04_2d-inflow-using-Flux.md"
+    "04_2d-inflow-using-Flux.md",
+    "05_2d-aerofoil-inflow-optimisation.md"
 ]
 
 makedocs(
diff --git a/04_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
similarity index 99%
rename from 04_2d-aerofoil-inflow-optimisation.md
rename to docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
index 183fba32..3843d0c3 100644
--- a/04_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
@@ -207,7 +207,6 @@ function foil_optim(α::Vector{Float64})
 
     aero_eff = lift_to_drag(:foil, model, ρ, nu, α[1]) # Calculates lift-to-drag ratio
 
-    
     aero_eff_out = round(aero_eff,digits=3)
     α_out = round(α[1],digits=3)
     vtk_files = filter(x->endswith(x,".vtk"), readdir())
@@ -250,6 +249,10 @@ opt = BOpt(foil_optim, # Function to be optimised - encloses the CFD case
             verbosity = Progress)
 
 result = boptimize!(opt) # Runs the optimisation procedure
+
+using Pkg; Pkg.rm("BayesianOptimization") # hide
+
+"done"
 ```
 
 # Example Optimisation Results

From c5aa3b774c9002da16596a2e1919dda85b0fccd3 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Fri, 11 Oct 2024 15:54:30 +0100
Subject: [PATCH 32/40] Tim's optimisation example updated and building
 correctly

---
 docs/Project.toml                             |   1 +
 .../01_2d-isothermal-backward-facing-step.md  |   4 +-
 ...02_2d-incompressible-transient-cylinder.md |   6 +-
 .../03_2d-constant-temperature-flat-plate.md  |   1 +
 docs/src/examples/04_2d-inflow-using-Flux.md  |  21 ++-
 .../05_2d-aerofoil-inflow-optimisation.md     | 154 +++++++++++++----
 .../figures/04/BFS_neural_network_profile.png | Bin 0 -> 15774 bytes
 optimisation_iterations_vs_experiment.svg     | 155 ++++++++++++++++++
 8 files changed, 294 insertions(+), 48 deletions(-)
 create mode 100644 docs/src/examples/figures/04/BFS_neural_network_profile.png
 create mode 100644 optimisation_iterations_vs_experiment.svg

diff --git a/docs/Project.toml b/docs/Project.toml
index 3b92ea96..0533632c 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -2,6 +2,7 @@
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
diff --git a/docs/src/examples/01_2d-isothermal-backward-facing-step.md b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
index f414748f..22b1942b 100644
--- a/docs/src/examples/01_2d-isothermal-backward-facing-step.md
+++ b/docs/src/examples/01_2d-isothermal-backward-facing-step.md
@@ -83,8 +83,8 @@ solvers = (
     )
 )
 
-runtime = set_runtime(
-    iterations=2000, time_step=1, write_interval=2000)
+runtime = set_runtime(iterations=2000, time_step=1, write_interval=2000)
+runtime = set_runtime(iterations=1, time_step=1, write_interval=-1) # hide
 
 config = Configuration(
     solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
diff --git a/docs/src/examples/02_2d-incompressible-transient-cylinder.md b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
index 8f90494b..20e7a75c 100644
--- a/docs/src/examples/02_2d-incompressible-transient-cylinder.md
+++ b/docs/src/examples/02_2d-incompressible-transient-cylinder.md
@@ -84,9 +84,9 @@ schemes = (
 )
 
 
-runtime = set_runtime(
-    # iterations=1000, write_interval=50, time_step=0.005) # uncomment to save files
-    iterations=1, write_interval=-1, time_step=0.005) # used for building documentation
+runtime = set_runtime(iterations=1000, write_interval=50, time_step=0.005) 
+runtime = set_runtime(iterations=1, write_interval=-1, time_step=0.005) # hide
+
 
 hardware = set_hardware(backend=CPU(), workgroup=1024)
 # hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
diff --git a/docs/src/examples/03_2d-constant-temperature-flat-plate.md b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
index 0b852f11..b559b9d7 100644
--- a/docs/src/examples/03_2d-constant-temperature-flat-plate.md
+++ b/docs/src/examples/03_2d-constant-temperature-flat-plate.md
@@ -161,6 +161,7 @@ solvers = (
 )
 
 runtime = set_runtime(iterations=1000, write_interval=1000, time_step=1)
+runtime = set_runtime(iterations=1, write_interval=-1, time_step=1) # hide
 
 hardware = set_hardware(backend=CPU(), workgroup=4)
 
diff --git a/docs/src/examples/04_2d-inflow-using-Flux.md b/docs/src/examples/04_2d-inflow-using-Flux.md
index 22375848..475e77c2 100644
--- a/docs/src/examples/04_2d-inflow-using-Flux.md
+++ b/docs/src/examples/04_2d-inflow-using-Flux.md
@@ -29,8 +29,12 @@ add Plots, XCALibre, Flux, StaticArrays, LinearAlgebra, KernelAbstractions, Adap
 This will download and install the required packages. Once installed, the packages can be loaded as follows:
 
 ```@example flux
-using Logging; Logging.disable_logging(Logging.Info) # hide
-using Pkg; Pkg.add("Flux") # hide
+# using Logging; Logging.disable_logging(Logging.Info) # hide
+using Pkg; # hide
+installed = "BayesianOptimization" ∈ keys(Pkg.project().dependencies) # hide
+installed && Pkg.rm("BayesianOptimization", io=devnull) #hide
+Pkg.add("Flux", io=devnull) # hide
+
 using Plots
 using XCALibre
 using Flux
@@ -38,7 +42,7 @@ using StaticArrays
 using Statistics
 using LinearAlgebra
 using KernelAbstractions
-
+nothing # hide
 ```
 
 ### Build a neural network model
@@ -269,8 +273,8 @@ solvers = (
     )
 )
 
-runtime = set_runtime(
-    iterations=500, time_step=1, write_interval=500)
+runtime = set_runtime(iterations=500, time_step=1, write_interval=500)
+runtime = set_runtime(iterations=1, time_step=1, write_interval=-1) # hide
 
 hardware = set_hardware(backend=CPU(), workgroup=1024)
 
@@ -284,11 +288,12 @@ initialise!(model.momentum.p, 0.0)
 
 residuals = run!(model, config)
 
-Pkg.rm("Flux") # hide
-"done!" # hide
+Pkg.rm("Flux", io=devnull) # hide
+nothing # hide
+"done"
 ```
 
 # Simulation result
 ---
 
-Add figure here!
\ No newline at end of file
+![Comparison with OpenFOAM](figures/04/BFS_neural_network_profile.png)
\ No newline at end of file
diff --git a/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
index 3843d0c3..738a5449 100644
--- a/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
@@ -3,7 +3,7 @@
 # Introduction
 ---
 
-Here, a simple optimisation is performed on a 2D NACA0012 aerofoil case. The optimal angle of attack for maximum lift-to-drag ratio is found using Bayesian optimisation, courtesy of the BayesianOptimization.jl package. This example serves to illustrate both how XCALibre.jl can easily integrate with the Julia ecosystem, and the ease with which post-processing functions can be written.
+Here, a simple optimisation is performed on a 2D NACA0012 aerofoil case. The optimal angle of attack for maximum lift-to-drag ratio is found using `BayesianOptimization.jl`. This example serves to illustrate both how `XCALibre.jl` can easily integrate with the Julia ecosystem, and the ease with which post-processing functions can be written.
 
 # Optimisation Setup
 ---
@@ -21,10 +21,15 @@ add Plots, Distributions, LinearAlgebra, GaussianProcesses, BayesianOptimization
 This will download and install the required packages. Note that "CUDA" must also be added for GPU acceleration. Once installed, the packages can be loaded as follows:
 
 ```@example optimisation
-using Pkg; Pkg.add("BayesianOptimization") # hide
+using Pkg; # hide
+installed = "Flux" ∈ keys(Pkg.project().dependencies) # hide
+installed && Pkg.rm("Flux", io=devnull) #hide
+Pkg.add("BayesianOptimization", io=devnull) # hide
+
 using XCALibre, BayesianOptimization, Plots
 using LinearAlgebra, GaussianProcesses, Distributions
-#using CUDA # uncomment to run on GPU
+# using CUDA # uncomment to run on GPU
+nothing # hide
 ```
 
 ### Define post processing functions
@@ -32,8 +37,7 @@ using LinearAlgebra, GaussianProcesses, Distributions
 In order to calculate the lift-to-drag ratio, the pressure and viscous forces over the aerofoil must be calculated and summed. The lift and drag components can then be calculated (noting the rotated inflow vector to allow for different aerofoil angles of attack with the same mesh). A function returning the coefficients of lift and drag (not specifically needed for this example) is also presented for convenience.
 
 ```@example optimisation
-#Post-processing functions
-
+# Lift to drag ratio calculation
 lift_to_drag(patch::Symbol, model, ρ, nu, α) = begin
     Fp = pressure_force(patch, model.momentum.p, ρ)
     Fv = viscous_force(patch, model.momentum.U, ρ, nu, model.turbulence.nut)
@@ -42,8 +46,9 @@ lift_to_drag(patch::Symbol, model, ρ, nu, α) = begin
     aero_eff = Ft[2]/Ft[1]
     print("Aerofoil L/D: ",round(aero_eff,sigdigits = 4))
     return aero_eff
-end # Lift to drag ratio calculation
+end 
 
+# Aerodynamic coefficient calculation
 aero_coeffs(patch::Symbol, chord, velocity, model, ρ, nu, α) = begin
     Fp = pressure_force(patch, model.momentum.p, ρ)
     Fv = viscous_force(patch, model.momentum.U, ρ, nu, model.turbulence.nut)
@@ -54,23 +59,26 @@ aero_coeffs(patch::Symbol, chord, velocity, model, ρ, nu, α) = begin
     print("Lift Coefficient: ",round(C_l,sigdigits = 4))
     print("\nDrag Coefficient: ",round(C_d,sigdigits = 4))
     return C_l,C_d
-end # Aerodynamic coefficient calculation
+end 
 ```
 
-### Initialise 2D aerofoil mesh
+### Import 2D aerofoil mesh
 
-Next, the aerofoil mesh .unv file must be loaded and initialised. It must also be adapted to work with the GPU, if desired.
+Next, the aerofoil mesh .unv file must be imported. It must also be adapted to work with the GPU, if desired.
 
 ```@example optimisation
-# Mesh
-mesh_file = "NACAMesh.unv"
+grids_dir = pkgdir(XCALibre, "examples/0_GRIDS")
+grid = "NACAMesh.unv"
+mesh_file = joinpath(grids_dir, grid)
+
 mesh = UNV2D_mesh(mesh_file, scale=0.001)
-#mesh = adapt(CUDABackend(), mesh) # uncomment to run on GPU
+mesh_dev = mesh # running on CPU 
+# mesh_dev = adapt(CUDABackend(), mesh) # uncomment to run on GPU
 ```
 
 ### Setup the CFD simulation as a function to be optimised
 
-The BayesianOptimization.jl package can optimise any Julia function that is passed to it. To interface with XCALibre.jl, the entire CFD simulation setup must simply be wrapped within a function, which can then be passed to the optimiser. The function must take the variable to be changed (angle of attack, in this case) as its input, and must return the desired output (lift-to-drag ratio). Therefore, the post-processing step to calculate lift-to-drag ratio is also wrapped in the same function.
+The `BayesianOptimization.jl` package can optimise a Julia function that is passed to it. To interface with XCALibre.jl, the entire CFD simulation setup must simply be wrapped within a function, which can then be passed to the optimiser. The function must take the variable to be changed (angle of attack, in this case) as its input, and must return the desired output (lift-to-drag ratio). Therefore, the post-processing step to calculate lift-to-drag ratio is also wrapped in the same function.
 
 ```@example optimisation
 function foil_optim(α::Vector{Float64})
@@ -79,9 +87,9 @@ function foil_optim(α::Vector{Float64})
     # Parameters
     chord = 250.0
     Re = 500000
-    nu,ρ = 1.48e-5,1.225
-    Umag = (Re*nu)/(chord*0.001)
-    velocity = [Umag*cos(α[1]*π/180), Umag*sin(α[1]*π/180), 0.0] # Velocity calculation for given α
+    nu, ρ = 1.48e-5, 1.225
+    Umag = (Re*nu)/(chord*0.001) # Calculate velocity magnitude for given Reynolds number
+    velocity = [Umag*cos(α[1]*π/180), Umag*sin(α[1]*π/180), 0.0] # Velocity calculation
     νR = 10
     Tu = 0.025
     k_inlet = 3/2*(Tu*norm(velocity))^2
@@ -95,7 +103,7 @@ function foil_optim(α::Vector{Float64})
         fluid = Fluid{Incompressible}(nu = nu),
         turbulence = RANS{KOmega}(),
         energy = Energy{Isothermal}(),
-        domain = mesh
+        domain = mesh_dev
         )
 
     @assign! model momentum U ( 
@@ -103,7 +111,7 @@ function foil_optim(α::Vector{Float64})
         XCALibre.Dirichlet(:bottom, velocity),
         Neumann(:outlet, 0.0),
         Neumann(:top, 0.0),
-        XCALibre.Dirichlet(:foil, noSlip)
+        Wall(:foil, noSlip)
     )
 
     @assign! model momentum p (
@@ -139,41 +147,41 @@ function foil_optim(α::Vector{Float64})
     )
 
     schemes = (
-        U = set_schemes(divergence=Upwind,gradient=Midpoint),
+        U = set_schemes(divergence=Upwind, gradient=Midpoint),
         p = set_schemes(divergence=Upwind),
-        k = set_schemes(divergence=Upwind,gradient=Midpoint),
-        omega = set_schemes(divergence=Upwind,gradient=Midpoint)
+        k = set_schemes(divergence=Upwind, gradient=Midpoint),
+        omega = set_schemes(divergence=Upwind, gradient=Midpoint)
     )
 
     solvers = (
         U = set_solver(
             model.momentum.U;
-            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
+            solver = BicgstabSolver, # BicgstabSolver, GmresSolver
             preconditioner = ILU0(), # Jacobi # ILU0
             convergence = 1e-7,
-            relax       = 0.6,
+            relax = 0.6,
             rtol = 1e-1,
         ),
         p = set_solver(
             model.momentum.p;
-            solver      = GmresSolver, # BicgstabSolver, GmresSolver # CgSolver
-            preconditioner = LDL(), # Jacobi
+            solver = GmresSolver, # change to BicgstabSolver for GPU runs
+            preconditioner = LDL(), # change to Jacobi() for GPU runs
             convergence = 1e-7,
-            relax       = 0.2,
+            relax = 0.2,
             rtol = 1e-2,
         ),
         k = set_solver(
             model.turbulence.k;
-            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
-            preconditioner = ILU0(),
+            solver = BicgstabSolver,
+            preconditioner = ILU0(), # change to Jacobi() for GPU runs
             convergence = 1e-7,
-            relax       = 0.6,
+            relax = 0.6,
             rtol = 1e-1,
         ),
         omega = set_solver(
             model.turbulence.omega;
-            solver      = BicgstabSolver, # BicgstabSolver, GmresSolver
-            preconditioner = ILU0(),
+            solver      = BicgstabSolver,
+            preconditioner = ILU0(), # change to Jacobi() for GPU runs
             convergence = 1e-7,
             relax       = 0.6,
             rtol = 1e-1,
@@ -181,11 +189,13 @@ function foil_optim(α::Vector{Float64})
     )
 
     runtime = set_runtime(iterations=500, write_interval=500, time_step=1)
+    runtime = set_runtime(iterations=20, write_interval=-1, time_step=1) # hide
 
     hardware = set_hardware(backend=CPU(), workgroup=1024)
-    #hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
+    # hardware = set_hardware(backend=CUDABackend(), workgroup=32) # uncomment to run on GPU
 
     config = Configuration(solvers=solvers, schemes=schemes, runtime=runtime, hardware=hardware)
+
     GC.gc()
 
     initialise!(model.momentum.U, velocity)
@@ -207,6 +217,7 @@ function foil_optim(α::Vector{Float64})
 
     aero_eff = lift_to_drag(:foil, model, ρ, nu, α[1]) # Calculates lift-to-drag ratio
 
+    # relocate XCALibre.jl vtk output files
     aero_eff_out = round(aero_eff,digits=3)
     α_out = round(α[1],digits=3)
     vtk_files = filter(x->endswith(x,".vtk"), readdir())
@@ -218,6 +229,7 @@ function foil_optim(α::Vector{Float64})
     return aero_eff
 end
 ```
+
 Note that this code saves a single .vtk file of the last CFD iteration each time the optimiser samples the function. This .vtk file is then automatically renamed with that sample's results, and sorted into a /vtk_results subfolder (**which must be created before the optimisation is run**).
 
 ### Configure and run the Bayesian optimisation
@@ -225,7 +237,8 @@ Note that this code saves a single .vtk file of the last CFD iteration each time
 Finally, the Bayesian optimiser must be configured before the optimisation can be performed. This example follows the BayesianOptimization.jl default configuration for the Gaussian process surrogate model, limiting input dimensions to 1 (the angle of attack). The surrogate model is then set to be optimised every 10 iterations. The inputs are limited to between 0 and 15 degrees. The problem is configured as a maximisation problem, with an initial sample period of 10 iterations and 50 maximum allowed iterations. The final line of the following code block is then run to perform the optimisation.
 
 ```@example optimisation
-#Bayesian Optimisation (Using BayesianOptimization.jl)
+# Bayesian Optimisation (using BayesianOptimization.jl)
+isdir("vtk_results") || mkdir("vtk_results")
 
 # Initialises the Gaussian process surrogate model
 model = ElasticGPE(1, #1 input dimension (α)
@@ -248,14 +261,85 @@ opt = BOpt(foil_optim, # Function to be optimised - encloses the CFD case
             initializer_iterations = 10, # No. of initial random samples
             verbosity = Progress)
 
+opt = BOpt(foil_optim, # hide
+            model, # hide
+            UpperConfidenceBound(),
+            modeloptimizer, # hide
+            [0.0], [15.0], # hide      
+            repetitions = 1, # hide
+            maxiterations = 5, # hide
+            sense = Max, # hide
+            initializer_iterations = 2, # hide
+            verbosity = Progress) # hide
+
 result = boptimize!(opt) # Runs the optimisation procedure
 
-using Pkg; Pkg.rm("BayesianOptimization") # hide
+using Pkg; Pkg.rm("BayesianOptimization", io=devnull) # hide
 
+nothing # hide
 "done"
 ```
 
 # Example Optimisation Results
 ---
 
-TBC
+```@eval
+using Plots
+
+alpha_in = [2.8125, 10.3125, 14.0625, 6.5625, 4.6875, 12.1875, 8.4375, 0.9375, 1.40625, 8.90625, 6.779625965220729, 6.77968472431049, 6.7797314426495054, 6.77976068608606, 6.779786764662929, 6.7798083933298825, 6.779824452011973, 6.779839305833187, 6.779851985125758, 6.779864532650939, 6.7799660687298875, 6.7799701746255465, 6.779970295228141, 6.77997431759257, 6.779983415563036, 6.7799837395243685, 6.779983935151504, 6.779987648165338, 6.779990776177305, 6.779984858208577, 6.779969245384916, 6.779974853301299, 6.77996639334403, 6.779975137863877, 6.77996588653741, 6.7799787767924995, 6.779980463194295, 6.779982645115559, 6.779984123782711, 6.779985756585738, 6.780065815803057, 6.780066942543943, 6.780081725020423, 6.780063344501922, 6.780112623430458, 6.780065445290062, 6.780112028947505, 6.780088979322628, 6.78008982572309, 6.780090816324224, 6.852129317102274, 15.0, 6.755034985210623, 6.761466922699926, 6.766457867346942, 6.7701094609872365, 6.772562674953314, 6.774340290374087, 6.775562986686579, 6.776273742423618, 13.474012044415156, 12.361866906130413, 8.195985025525076, 5.334843671454779, 4.308592858166856, 2.6894603132241217, 2.858340694577276, 3.9867902638528654, 9.814658247047763, 1.932233467710785, 14.719640732627886, 9.682863385862596, 10.90134524899545, 12.877578634990728, 4.343344626917736]
+
+aeroeff_out = [12.28662476568946, 15.996066573412422, 12.086660285887401, 18.095030718054726, 16.684759975625713, 14.101557983835567, 17.514651235093766, 4.6215245234556415, 6.787202918357864, 17.203294519181156, 18.1170435016882, 18.116757960309155, 18.117178450363166, 18.116980351431625, 18.116775418289507, 18.117332562156935, 18.116999501527403, 18.116946514089875, 18.11690912331511, 18.117181857003985, 18.117047847973517, 18.117081881041535, 18.117198176532845, 18.1172141350244, 18.117151423600156, 18.11701162747253, 18.117196229004325, 18.117302063623146, 18.117642349199684, 18.117122449593182, 18.11704990315254, 18.11745842192904, 18.1171359979369, 18.117344466780477, 18.117133217540022, 18.117057989337816, 18.116782216736464, 18.11721596351545, 18.117119958415003, 18.117170377304056, 18.117352502260307, 18.117163143088185, 18.117300338277143, 18.117066185177936, 18.11722389239519, 18.11713622798166, 18.116993107467152, 18.116991271960444, 18.117083277331048, 18.11714354615574, 18.097362115270933, 11.114298598972901, 18.108943497471795, 18.108780485320025, 18.108790519425263, 18.109037299059956, 18.108833040375593, 18.108767451351685, 18.1084445814309, 18.10857933786505, 12.690741887963036, 9.845212599830074, 17.636745115382112, 17.47574058124154, 16.058798546800677, 11.877430534208012, 12.4272778301407, 15.41709457750829, 16.462303743958294, 9.053215612096695, 11.382140258128832, 16.578166324395593, 15.519321514686421, 13.356080135399708, 16.116845772757824]
+
+iteration = [1:25;]
+
+scatter(
+    alpha_in[1:25],aeroeff_out[1:25],xlabel="Angle of Attack, α [°]", ylabel="Aerodynamic Efficiency, Cl/Cd [-]",label="",
+    legend=true,
+    # marker=(:cross,4),
+    zcolor=iteration,
+    c=:linear_ternary_red_0_50_c52_n256,
+    colorbar_title="Optimiser Iteration",
+    xlims=[0,15.15], ylims=[0,20], clim=(0,25),
+    frame_style=:box
+    )
+
+max_exp_alpha = ([6.479310344827586,6.479310344827586],[0,19])
+
+plot!(max_exp_alpha,line=(:dash,:black),label="")
+
+plot!(
+    sort(alpha_in[1:50]), aeroeff_out[sortperm(alpha_in[1:50])],
+    label="", line=(:solid,:black,0.5)
+    )
+annotate!(8.25, 2.5, Plots.text("Experimental\noptimum α", 10))
+savefig("optimisation_iterations_vs_experiment.svg"); nothing # hide
+nothing
+
+fig1 = scatter(
+    iteration[1:15],aeroeff_out[1:15],xlabel="Optimiser Iteration [-]", ylabel="Aerodynamic Efficiency, Cl/Cd [-]",label="",
+    ylim = (0,20),
+    legend=true,# marker=(:cross,4,:black)
+    ) #L/D against iteration number graph
+
+fig2 = scatter(iteration[1:15],alpha_in[1:15],xlabel="Optimiser Iteration [-]", ylabel="Angle of Attack, α [°]",label="",
+ylim = (0,15),
+legend=true, #marker=(:cross,4,:black)
+) #α against iteration number graph
+
+
+# exp_alpha = [0.1724137931034484, 2.068965517241379, 4.482758620689655, 6.479310344827586, 8.441064638783269, 10.344827586206897, 11.206896551724139, 12.551020408163264, 14.13793103448276]
+# exp_aeroeff = [8.872377622377625, 36.656207598371786, 52.94361173623201, 53.41160498793243, 53.10395622895623, 50.95347249317206, 48.78298051001016, 4.906565656565657, 3.354085331846068]
+# fig2 = scatter(exp_alpha,exp_aeroeff,xlabel="Angle of Attack, α [°]", ylabel="Aerodynamic Efficiency, Cl/Cd [-]",title="Experimental Data (NACA0012, Re=500,000)",
+# legend=false,marker=(:circle,4,:black)) #Experimental data
+
+plot(fig1, fig2, frame_style=:box)
+
+savefig("optimisation_vs_iteration.svg"); nothing # hide
+nothing
+
+# output
+
+```
+![](optimisation_iterations_vs_experiment.svg)
+
+![](optimisation_vs_iteration.svg)
diff --git a/docs/src/examples/figures/04/BFS_neural_network_profile.png b/docs/src/examples/figures/04/BFS_neural_network_profile.png
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From aeb5e66456c2acc615e223a6ba4526824c9d2961 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sat, 12 Oct 2024 15:03:13 +0100
Subject: [PATCH 33/40] add missing hyperlinks forcompressible solvers

---
 docs/make.jl      | 2 ++
 docs/src/index.md | 4 ++--
 2 files changed, 4 insertions(+), 2 deletions(-)

diff --git a/docs/make.jl b/docs/make.jl
index 71a33de5..6e6a1c80 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -7,5 +7,7 @@ include("makeLocal.jl")
 # for more information.
 deploydocs(
     repo = "github.com/mberto79/XCALibre.jl.git",
+    devurl = "dev",
+    versions = ["stable" => "v^", devurl => devurl],
     devbranch = "dev-0.3-main"
 )
diff --git a/docs/src/index.md b/docs/src/index.md
index 28478a40..93c3ad2b 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -42,8 +42,8 @@ XCALibre.jl ships with fluid solvers for steady and transient simulations, based
 
 * [Steady incompressible flows](@ref XCALibre.Solvers.simple!)
 * [Steady weakly compressible flows](@ref XCALibre.Solvers.csimple!)
-* Transient incompressible flows
-* Transient weakly compressible flows
+* [Transient incompressible flows](@ref XCALibre.Solvers.piso!)
+* [Transient weakly compressible flows](@ref XCALibre.Solvers.cpiso!)
 
 !!! note
 

From d0725216f8ee3c3f852f935fb90d20b178f483b4 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sat, 12 Oct 2024 16:37:35 +0100
Subject: [PATCH 34/40] add note to explain how units work in XCALibre.jl

---
 docs/src/examples/04_2d-inflow-using-Flux.md            | 5 ++++-
 docs/src/examples/05_2d-aerofoil-inflow-optimisation.md | 1 +
 docs/src/user_guide/1_preprocessing.md                  | 4 ++++
 3 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/docs/src/examples/04_2d-inflow-using-Flux.md b/docs/src/examples/04_2d-inflow-using-Flux.md
index 475e77c2..c022079d 100644
--- a/docs/src/examples/04_2d-inflow-using-Flux.md
+++ b/docs/src/examples/04_2d-inflow-using-Flux.md
@@ -13,7 +13,10 @@ XCALibre.Discretise.DirichletFunction
 
 In this example, instead of passing a Julia function, the boundary velocity profile will be given via a simple neural network. 
 
-    !!! Notice that this interface is experimental and subject to change. Currently it can only be used for vectors.
+!!! note
+    
+    This interface is experimental and subject to change. Currently it can only be used for vectors.
+
 # Set up steps
 ---
 
diff --git a/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
index 738a5449..dfa842a0 100644
--- a/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
+++ b/docs/src/examples/05_2d-aerofoil-inflow-optimisation.md
@@ -29,6 +29,7 @@ Pkg.add("BayesianOptimization", io=devnull) # hide
 using XCALibre, BayesianOptimization, Plots
 using LinearAlgebra, GaussianProcesses, Distributions
 # using CUDA # uncomment to run on GPU
+"done"
 nothing # hide
 ```
 
diff --git a/docs/src/user_guide/1_preprocessing.md b/docs/src/user_guide/1_preprocessing.md
index dc8b73a4..7baffb0f 100644
--- a/docs/src/user_guide/1_preprocessing.md
+++ b/docs/src/user_guide/1_preprocessing.md
@@ -8,6 +8,10 @@ As with all CFD solvers, defining a suitable mesh is one of the most important s
 
 XCALibre.jl is an unstructured Finite Volume Method (FVM) library, therefore, we are able to support grids of arbitrary polyhedral cells. In XCALibre.jl a cell-centred FVM approach has been implemented, which is popular since it allows the representation of complex geometries and it is used by most commercial and many open source CFD solvers.
 
+!!! units
+
+    XCALIbre.jl does not enforce units strictly. Units are implicitly provided by the mesh. You can use the `scale` keyword when importing a mesh to control the units used e.g. if the mesh file was created in millimetres, set `scale=0.001` to work in metres. Thus, it is important to ensure that consistent units are used through all configuration entries. It is highly recommended that SI units are used. 
+
 ### Mesh conversion
 
 XCALibre.jl at present supports `.unv` mesh formats (which can be generated using [SALOME](https://www.salome-platform.org/)) for simulations in 2D and 3D domains. XCALibre.jl also supports the [OpenFOAM](https://openfoam.org/) mesh format for simulations in 3D only (for now). 

From 927b1c27a8c2955dfc37dccb9c607863e6e1520d Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sat, 12 Oct 2024 16:39:43 +0100
Subject: [PATCH 35/40] update documeter.jl action to use SSH key

---
 .github/workflows/documentation.yml | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml
index 64d90f53..c0c785cd 100644
--- a/.github/workflows/documentation.yml
+++ b/.github/workflows/documentation.yml
@@ -4,7 +4,6 @@ on:
   push:
     branches:
       - dev-0.3-main  # update to match your development branch (master, main, etc.)
-      - main
     tags: '*'
   pull_request:
 
@@ -26,5 +25,5 @@ jobs:
         run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
       - name: Build and deploy
         env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # If authenticating with GitHub Actions token
+          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
         run: julia --project=docs/ docs/make.jl
\ No newline at end of file

From fba96d67bdc0387d90eb357ff762949d0af8d115 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sat, 12 Oct 2024 16:58:26 +0100
Subject: [PATCH 36/40] Fixed doc build error

---
 docs/make.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/make.jl b/docs/make.jl
index 6e6a1c80..763553ba 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -8,6 +8,6 @@ include("makeLocal.jl")
 deploydocs(
     repo = "github.com/mberto79/XCALibre.jl.git",
     devurl = "dev",
-    versions = ["stable" => "v^", devurl => devurl],
+    versions = ["stable" => "v^", "dev" => "dev"],
     devbranch = "dev-0.3-main"
 )

From c5270c6167ed471d557d32dc4faf101f641135aa Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Sat, 12 Oct 2024 17:17:53 +0100
Subject: [PATCH 37/40] add support for TagBot actions

---
 .github/workflows/TagBot.yml | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 .github/workflows/TagBot.yml

diff --git a/.github/workflows/TagBot.yml b/.github/workflows/TagBot.yml
new file mode 100644
index 00000000..ef908969
--- /dev/null
+++ b/.github/workflows/TagBot.yml
@@ -0,0 +1,31 @@
+name: TagBot
+on:
+  issue_comment:
+    types:
+      - created
+  workflow_dispatch:
+    inputs:
+      lookback:
+        default: "3"
+permissions:
+  actions: read
+  checks: read
+  contents: write
+  deployments: read
+  issues: read
+  discussions: read
+  packages: read
+  pages: read
+  pull-requests: read
+  repository-projects: read
+  security-events: read
+  statuses: read
+jobs:
+  TagBot:
+    if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
+    runs-on: ubuntu-latest
+    steps:
+      - uses: JuliaRegistries/TagBot@v1
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ssh: ${{ secrets.DOCUMENTER_KEY }}
\ No newline at end of file

From d9a28b76fb2ef82525f1c6605143e2711b7ca770 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Mon, 14 Oct 2024 10:12:46 +0100
Subject: [PATCH 38/40] add changelog as dependency for documentation builds

---
 docs/Project.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/docs/Project.toml b/docs/Project.toml
index 0533632c..98bca401 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,7 +1,9 @@
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
+Changelog = "5217a498-cd5d-4ec6-b8c2-9b85a09b6e3e"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+DocumenterTools = "35a29f4d-8980-5a13-9543-d66fff28ecb8"
 GaussianProcesses = "891a1506-143c-57d2-908e-e1f8e92e6de9"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

From 395c0a64c3a4831ec62cc9bf30de9561d52c77fb Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Mon, 14 Oct 2024 11:20:26 +0100
Subject: [PATCH 39/40] add framework to create release notes via Changelog.jl

---
 CHANGELOG.md              | 59 ++++++++++++++++++++++++++++++++++++
 docs/makeLocal.jl         | 10 +++++-
 docs/src/release_notes.md | 64 ++++++++++++++++++++++++++++++++++++++-
 3 files changed, 131 insertions(+), 2 deletions(-)
 create mode 100644 CHANGELOG.md

diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
index 00000000..54dda00c
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,59 @@
+# Release notes
+
+The format used for this `changelog` is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
+and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html). Notice that until the package reaches version `v1.0.0` minor releases are likely to be `breaking`. Starting from version `v3.0.1` breaking changes will be recorded here. 
+
+## Version [v0.3.1] - 2024-10-18
+
+### Added
+* Vastly improved documentation with new examples provided
+* Changelog added to record changes more clearly. Record kept in [Release notes](@ref)
+
+### Fixed
+* The calculation of gradients can be limited for stability. This functionality can be activated by passing the key work argument `limit_gradient` to the `run!` function. The implementation has been improved for robustness.
+
+### Changed
+* Master branch protected and requires PRs to push changes
+
+### Breaking
+* No breaking changes
+
+### Deprecated
+* No functions deprecated
+
+### Removed
+* No functionality has been removed
+
+## Version [v0.3.0] - 2024-09-21
+
+* New name - XCALibre.jl - which is now registered in the General Julia registry
+* Can do 3D and GPU accelerated simulations
+* Can read .unv and OpenFOAM mesh files (3D)
+* Can do incompressible and compressible simulations
+* RANS and LES models available
+* User-provided functions or neural networks for boundary conditions
+* Reasonably complete "user" documentation now provided
+* Made repository public (in v0.2 the work was kept in a private repository and could only do 2D simulations)
+* Tidy up mesh type definitions by @mberto79 in #5
+* Adapt code base to work with new mesh format by @mberto79 in [#6]
+* Mesh boundary struct changes PR by @TomMazin in [#7]
+* Mesh boundary struct changes PR fix by @TomMazin in [#8]
+
+
+## Version [v0.2.0] - 2023-01-23
+
+* New mesh format and type implemented that are GPU friendly.
+* No functionality changes
+
+## Version [v0.1.0] - 2023-01-23
+
+### Initial release
+
+2D implementation of classic incompressible solvers for laminar and turbulent flows:
+
+* Framework for equation definition
+* SIMPLE nad PISO algorithms
+* Read UNV meshes in 2D
+* Capability for RANS models
+* Various discretisation schemes available
+* Planned extension to 3D and GPU acceleration!
\ No newline at end of file
diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index 57d52d44..e6829dad 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -1,11 +1,19 @@
 using Documenter
 using InteractiveUtils
 using AbstractTrees
+using Changelog
 using XCALibre
 
-# push!(LOAD_PATH,"../src/") # for local build only
 ENV["GKSwstype"] = "100"
 
+# Generate a Documenter-friendly changelog from CHANGELOG.md
+Changelog.generate(
+    Changelog.Documenter(),
+    joinpath(@__DIR__, "..", "CHANGELOG.md"),
+    joinpath(@__DIR__, "src", "release_notes.md");
+    repo = "github.com/mberto79/XCALibre.jl",
+)
+
 USER_GUIDE_PAGES = Any[
     "0_introduction_and_workflow.md",
     "1_preprocessing.md",
diff --git a/docs/src/release_notes.md b/docs/src/release_notes.md
index abf7bdee..799f9193 100644
--- a/docs/src/release_notes.md
+++ b/docs/src/release_notes.md
@@ -1 +1,63 @@
-# Release Notes
\ No newline at end of file
+```@meta
+EditURL = "https://github.com/github.com/mberto79/XCALibre.jl/blob/master/CHANGELOG.md"
+```
+
+# Release notes
+
+The format used for this `changelog` is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
+and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html). Notice that until the package reaches version `v1.0.0` minor releases are likely to be `breaking`. Starting from version `v3.0.1` breaking changes will be recorded here. 
+
+## Version [v0.3.1](https://github.com/github.com/mberto79/XCALibre.jl/releases/tag/v0.3.1) - 2024-10-18
+
+### Added
+* Vastly improved documentation with new examples provided
+* Changelog added to record changes more clearly. Record kept in [Release notes](@ref)
+
+### Fixed
+* The calculation of gradients can be limited for stability. This functionality can be activated by passing the key work argument `limit_gradient` to the `run!` function. The implementation has been improved for robustness.
+
+### Changed
+* Master branch protected and requires PRs to push changes
+
+### Breaking
+* No breaking changes
+
+### Deprecated
+* No functions deprecated
+
+### Removed
+* No functionality has been removed
+
+## Version [v0.3.0](https://github.com/github.com/mberto79/XCALibre.jl/releases/tag/v0.3.0) - 2024-09-21
+
+* New name - XCALibre.jl - which is now registered in the General Julia registry
+* Can do 3D and GPU accelerated simulations
+* Can read .unv and OpenFOAM mesh files (3D)
+* Can do incompressible and compressible simulations
+* RANS and LES models available
+* User-provided functions or neural networks for boundary conditions
+* Reasonably complete "user" documentation now provided
+* Made repository public (in v0.2 the work was kept in a private repository and could only do 2D simulations)
+* Tidy up mesh type definitions by @mberto79 in #5
+* Adapt code base to work with new mesh format by @mberto79 in [#6](https://github.com/github.com/mberto79/XCALibre.jl/issues/6)
+* Mesh boundary struct changes PR by @TomMazin in [#7](https://github.com/github.com/mberto79/XCALibre.jl/issues/7)
+* Mesh boundary struct changes PR fix by @TomMazin in [#8](https://github.com/github.com/mberto79/XCALibre.jl/issues/8)
+
+
+## Version [v0.2.0](https://github.com/github.com/mberto79/XCALibre.jl/releases/tag/v0.2.0) - 2023-01-23
+
+* New mesh format and type implemented that are GPU friendly.
+* No functionality changes
+
+## Version [v0.1.0](https://github.com/github.com/mberto79/XCALibre.jl/releases/tag/v0.1.0) - 2023-01-23
+
+### Initial release
+
+2D implementation of classic incompressible solvers for laminar and turbulent flows:
+
+* Framework for equation definition
+* SIMPLE nad PISO algorithms
+* Read UNV meshes in 2D
+* Capability for RANS models
+* Various discretisation schemes available
+* Planned extension to 3D and GPU acceleration!
\ No newline at end of file

From badfdf438aff7e7c6a8ac904cf7e058fb3f5da16 Mon Sep 17 00:00:00 2001
From: Humberto <h.medina@aerofluids.org>
Date: Mon, 14 Oct 2024 11:22:12 +0100
Subject: [PATCH 40/40] enable doctests

---
 docs/makeLocal.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/makeLocal.jl b/docs/makeLocal.jl
index e6829dad..edad4755 100644
--- a/docs/makeLocal.jl
+++ b/docs/makeLocal.jl
@@ -34,7 +34,7 @@ EXAMPLES_PAGES = Any[
 makedocs(
     sitename = "XCALibre.jl",
     format = Documenter.HTML(),
-    doctest = false, # only set to false when sorting out docs structure
+    # doctest = false, # only set to false when sorting out docs structure
     modules = [XCALibre],
     pages = [
         "Home" => "index.md",