FluidX3D

The fastest and most memory efficient lattice Boltzmann CFD software, running on all GPUs via OpenCL. Free for non-commercial use.

(click on images to show videos on YouTube)

Update History

v1.0 (04.08.2022) changes (public release)
- public release
v1.1 (29.09.2022) changes (GPU voxelization)
- added solid voxelization on GPU (slow algorithm)
- added tool to print current camera position (key G)
- minor bug fix (workaround for Intel iGPU driver bug with triangle rendering)
v1.2 (24.10.2022) changes (force/torque compuatation)
- added functions to compute force/torque on objects
- added function to translate Mesh
- added Stokes drag validation setup
v1.3 (10.11.2022) changes (minor bug fixes)
- added unit conversion functions for torque
- FORCE_FIELD and VOLUME_FORCE can now be used independently
- minor bug fix (workaround for AMD legacy driver bug with binary number literals)
v1.4 (14.12.2022) changes (Linux graphics)
- complete rewrite of C++ graphics library to minimize API dependencies
- added interactive graphics mode on Linux with X11
- fixed streamline visualization bug in 2D
v2.0 (09.01.2023) changes (multi-GPU upgrade)
- added (cross-vendor) multi-GPU support on a single node (PC/laptop/server)
v2.1 (15.01.2023) changes (fast voxelization)
- made solid voxelization on GPU lightning fast (new algorithm, from minutes to milliseconds)
v2.2 (20.01.2023) changes (velocity voxelization)
- added option to voxelize moving/rotating geometry on GPU, with automatic velocity initialization for each grid point based on center of rotation, linear velocity and rotational velocity
- cells that are converted from solid->fluid during re-voxelization now have their DDFs properly initialized
- added option to not auto-scale mesh during read_stl(...), with negative size parameter
- added kernel for solid boundary rendering with marching-cubes
v2.3 (30.01.2023) changes (particles)
- added particles with immersed-boundary method (either passive or 2-way-coupled, only supported with single-GPU)
- minor optimization to GPU voxelization algorithm (workgroup threads outside mesh bounding-box return after ray-mesh intersections have been found)
- displayed GPU memory allocation size is now fully accurate
- fixed bug in write_line() function in src/utilities.hpp
- removed .exe file extension for Linux/macOS
v2.4 (11.03.2023) changes (UI improvements)
- added a help menu with key H that shows keyboard/mouse controls, visualization settings and simulation stats
- improvements to keyboard/mouse control (+/- for zoom, mouseclick frees/locks cursor)
- added suggestion of largest possible grid resolution if resolution is set larger than memory allows
- minor optimizations in multi-GPU communication (insignificant performance difference)
- fixed bug in temperature equilibrium function for temperature extension
- fixed erroneous double literal for Intel iGPUs in skybox color functions
- fixed bug in make.sh where multi-GPU device IDs would not get forwarded to the executable
- minor bug fixes in graphics engine (free cursor not centered during rotation, labels in VR mode)
- fixed bug in LBM::voxelize_stl() size parameter standard initialization
v2.5 (11.04.2023) changes (raytracing overhaul)
- implemented light absorption in fluid for raytracing graphics (no performance impact)
- improved raytracing framerate when camera is inside fluid
- fixed skybox pole flickering artifacts
- fixed bug where moving objects during re-voxelization would leave an erroneous trail of solid grid cells behind
v2.6 (16.04.2023) changes (Intel Arc patch)
- patched OpenCL issues of Intel Arc GPUs: now VRAM allocations >4GB are possible and correct VRAM capacity is reported
v2.7 (29.05.2023) changes (visualization upgrade)
- added slice visualization (key 2 / key 3 modes, then switch through slice modes with key T, move slice with keys Q/E)
- made flag wireframe / solid surface visualization kernels toggleable with key 1
- added surface pressure visualization (key 1 when FORCE_FIELD is enabled and lbm.calculate_force_on_boundaries(); is called)
- added binary .vtk export function for meshes with lbm.write_mesh_to_vtk(Mesh* mesh);
- added time_step_multiplicator for integrate_particles() function in PARTICLES extension
- made correction of wrong memory reporting on Intel Arc more robust
- fixed bug in write_file() template functions
- reverted back to separate cl::Context for each OpenCL device, as the shared Context otherwise would allocate extra VRAM on all other unused Nvidia GPUs
- removed Debug and x86 configurations from Visual Studio solution file (one less complication for compiling)
- fixed bug that particles could get too close to walls and get stuck, or leave the fluid phase (added boundary force)
v2.8 (24.06.2023) changes (documentation + polish)
- finally added more documentation
- cleaned up all sample setups in setup.cpp for more beginner-friendliness, and added required extensions in defines.hpp as comments to all setups
- improved loading of composite .stl geometries, by adding an option to omit automatic mesh repositioning, added more functionality to Mesh struct in utilities.hpp
- added uint3 resolution(float3 box_aspect_ratio, uint memory) function to compute simulation box resolution based on box aspect ratio and VRAM occupation in MB
- added bool lbm.graphics.next_frame(...) function to export images for a specified video length in the main_setup compute loop
- added VIS_... macros to ease setting visualization modes in headless graphics mode in lbm.graphics.visualization_modes
- simulation box dimensions are now automatically made equally divisible by domains for multi-GPU simulations
- fixed Info/Warning/Error message formatting for loading files and made Info/Warning/Error message labels colored
- added Ahmed body setup as an example on how body forces and drag coefficient are computed
- added Cessna 172 and Bell 222 setups to showcase loading composite .stl geometries and revoxelization of moving parts
- added optional semi-transparent rendering mode (#define GRAPHICS_TRANSPARENCY 0.7f in defines.hpp)
- fixed flickering of streamline visualization in interactive graphics
- improved smooth positioning of streamlines in slice mode
- fixed bug where mass and massex in SURFACE extension were also allocated in CPU RAM (not required)
- fixed bug in Q-criterion rendering of halo data in multi-GPU mode, reduced gap width between domains
- removed shared memory optimization from mesh voxelization kernel, as it crashes on Nvidia GPUs with new GPU drivers and is incompatible with old OpenCL 1.0 GPUs
- fixed raytracing attenuation color when no surface is at the simulation box walls with periodic boundaries
v2.9 (31.07.2023) changes (multithreading)
- added cross-platform parallel_for implementation in utilities.hpp using std::threads
- significantly (>4x) faster simulation startup with multithreaded geometry initialization and sanity checks
- faster calculate_force_on_object() and calculate_torque_on_object() functions with multithreading
- added total runtime and LBM runtime to lbm.write_status()
- fixed bug in voxelization ray direction for re-voxelizing rotating objects
- fixed bug in Mesh::get_bounding_box_size()
- fixed bug in print_message() function in utilities.hpp
v2.10 (05.11.2023) changes (frustrum culling)
- improved rasterization performance via frustrum culling when only part of the simulation box is visible
- improved switching between centered/free camera mode
- refactored OpenCL rendering library
- unit conversion factors are now automatically printed in console when units.set_m_kg_s(...) is used
- faster startup time for FluidX3D benchmark
- miner bug fix in voxelize_mesh(...) kernel
- fixed bug in shading(...)
- replaced slow (in multithreading) std::rand() function with standard C99 LCG
- more robust correction of wrong VRAM capacity reporting on Intel Arc GPUs
- fixed some minor compiler warnings
v2.11 (07.12.2023) changes (improved Linux graphics)
- interactive graphics on Linux are now in fullscreen mode too, fully matching Windows
- made CPU/GPU buffer initialization significantly faster with std::fill and enqueueFillBuffer (overall ~8% faster simulation startup)
- added operating system info to OpenCL device driver version printout
- fixed flickering with frustrum culling at very small field of view
- fixed bug where rendered/exported frame was not updated when visualization_modes changed
v2.12 (18.01.2024) changes (faster startup)
- ~3x faster source code compiling on Linux using multiple CPU cores if make is installed
- significantly faster simulation initialization (~40% single-GPU, ~15% multi-GPU)
- minor bug fix in Memory_Container::reset() function
v2.13 (11.02.2024) changes (improved .vtk export)
- data in exported .vtk files is now automatically converted to SI units
- ~2x faster .vtk export with multithreading
- added unit conversion functions for TEMPERATURE extension
- fixed graphical artifacts with axis-aligned camera in raytracing
- fixed get_exe_path() for macOS
- fixed X11 multi-monitor issues on Linux
- workaround for Nvidia driver bug: enqueueFillBuffer is broken for large buffers on Nvidia GPUs
- fixed slow numeric drift issues caused by -cl-fast-relaxed-math
- fixed wrong Maximum Allocation Size reporting in LBM::write_status()
- fixed missing scaling of coordinates to SI units in LBM::write_mesh_to_vtk()
v2.14 (03.03.2024) changes (visualization upgrade)
- coloring can now be switched between velocity/density/temperature with key Z
- uniform improved color palettes for velocity/density/temperature visualization
- color scale with automatic unit conversion can now be shown with key H
- slice mode for field visualization now draws fully filled-in slices instead of only lines for velocity vectors
- shading in VIS_FLAG_SURFACE and VIS_PHI_RASTERIZE modes is smoother now
- make.sh now automatically detects operating system and X11 support on Linux and only runs FluidX3D if last compilation was successful
- fixed compiler warnings on Android
- fixed make.sh failing on some systems due to nonstandard interpreter path
- fixed that make would not compile with multiple cores on some systems

How to get started?

Read the FluidX3D Documentation!

Compute Features - Getting the Memory Problem under Control

CFD model: lattice Boltzmann method (LBM)

streaming (part 2/2)
f₀^temp(x,t) = f₀(x, t)
f_i^temp(x,t) = f_{(t%2 ? i : (i%2 ? i+1 : i-1))}(i%2 ? x : x-e_i, t) for i ∈ [1, q-1]
collision
ρ(x,t) = (Σ_i f_i^temp(x,t)) + 1

u(x,t) = ¹∕_ρ(x,t) Σ_i c_i f_i^temp(x,t)

f_i^eq-shifted(x,t) = w_i ρ · (^(u_°c_i)²∕_(2c⁴) - ^(u_°u)∕_(2c²) + ^(u_°c_i)∕_c²) + w_i (ρ-1)

f_i^temp(x, t+Δt) = f_i^temp(x,t) + Ω_i(f_i^temp(x,t), f_i^eq-shifted(x,t), τ)
streaming (part 1/2)
f₀(x, t+Δt) = f₀^temp(x, t+Δt)
f_{(t%2 ? (i%2 ? i+1 : i-1) : i)}(i%2 ? x+e_i : x, t+Δt) = f_i^temp(x, t+Δt) for i ∈ [1, q-1]

variables and notation

variable	SI units	defining equation	description

x	m	x = (x,y,z)^T	3D position in Cartesian coordinates
t	s	-	time
ρ	^kg∕_m³	ρ = (Σ_i f_i)+1	mass density of fluid
p	^kg∕_m s²	p = c² ρ	pressure of fluid
u	^m∕_s	u = ¹∕_ρ Σ_i c_i f_i	velocity of fluid
ν	^m²∕_s	ν = ^μ∕_ρ	kinematic shear viscosity of fluid
μ	^kg∕_m s	μ = ρ ν	dynamic viscosity of fluid

f_i	^kg∕_m³	-	shifted density distribution functions (DDFs)
Δx	m	Δx = 1	lattice constant (in LBM units)
Δt	s	Δt = 1	simulation time step (in LBM units)
c	^m∕_s	c = ¹∕_√3 ^Δx∕_Δt	lattice speed of sound (in LBM units)
i	1	0 ≤ i < q	LBM streaming direction index
q	1	q ∈ { 9,15,19,27 }	number of LBM streaming directions
e_i	m	D2Q9 / D3Q15/19/27	LBM streaming directions
c_i	^m∕_s	c_i = ^e_i∕_Δt	LBM streaming velocities
w_i	1	Σ_i w_i = 1	LBM velocity set weights
Ω_i	^kg∕_m³	SRT or TRT	LBM collision operator
τ	s	τ = ^ν∕_c² + ^Δt∕₂	LBM relaxation time

velocity sets: D2Q9, D3Q15, D3Q19 (default), D3Q27
collision operators: single-relaxation-time (SRT/BGK) (default), two-relaxation-time (TRT)
DDF-shifting and other algebraic optimization to minimize round-off error

optimized to minimize VRAM footprint to 1/6 of other LBM codes

traditional LBM (D3Q19) with FP64 requires ~344 Bytes/cell
- 🟧🟧🟧🟧🟧🟧🟧🟧🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥
  (density 🟧, velocity 🟦, flags 🟨, 2 copies of DDFs 🟩/🟥; each square = 1 Byte)
- allows for 3 Million cells per 1 GB VRAM
FluidX3D (D3Q19) requires only 55 Bytes/cell with Esoteric-Pull+FP16
- 🟧🟧🟧🟧🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟨🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩
  (density 🟧, velocity 🟦, flags 🟨, DDFs 🟩; each square = 1 Byte)
- allows for 19 Million cells per 1 GB VRAM
- in-place streaming with Esoteric-Pull: eliminates redundant copy B of density distribution functions (DDFs) in memory; almost cuts memory demand in half and slightly increases performance due to implicit bounce-back boundaries; offers optimal memory access patterns for single-cell in-place streaming
- decoupled arithmetic precision (FP32) and memory precision (FP32 or FP16S or FP16C): all arithmetic is done in FP32 for compatibility on all hardware, but DDFs in memory can be compressed to FP16S or FP16C: almost cuts memory demand in half again and almost doubles performance, without impacting overall accuracy for most setups
- only 8 flag bits per lattice point (can be used independently / at the same time)
  - TYPE_S (stationary or moving) solid boundaries
  - TYPE_E equilibrium boundaries (inflow/outflow)
  - TYPE_T temperature boundaries
  - TYPE_F free surface (fluid)
  - TYPE_I free surface (interface)
  - TYPE_G free surface (gas)
  - TYPE_X remaining for custom use or further extensions
  - TYPE_Y remaining for custom use or further extensions

large cost saving: comparison of maximum single-GPU grid resolution for D3Q19 LBM

GPU VRAM capacity	1 GB	2 GB	3 GB	4 GB	6 GB	8 GB	10 GB	11 GB	12 GB	16 GB	20 GB	24 GB	32 GB	40 GB	48 GB	64 GB	80 GB	94 GB	128 GB	192 GB	256 GB
approximate GPU price	$25 GT 210	$25 GTX 950	$12 GTX 1060	$50 GT 730	$35 GTX 1060	$70 RX 470	$500 RTX 3080	$240 GTX 1080 Ti	$75 Tesla M40	$75 Instinct MI25	$900 RX 7900 XT	$205 Tesla P40	$600 Instinct MI60	$5500 A100	$2400 RTX 8000	$10k Instinct MI210	$11k A100	>$40k H100 NVL	? GPU Max 1550	~$10k MI300X	-
traditional LBM (FP64)	144³	182³	208³	230³	262³	288³	312³	322³	330³	364³	392³	418³	460³	494³	526³	578³	624³	658³	730³	836³	920³
FluidX3D (FP32/FP32)	224³	282³	322³	354³	406³	448³	482³	498³	512³	564³	608³	646³	710³	766³	814³	896³	966³	1018³	1130³	1292³	1422³
FluidX3D (FP32/FP16)	266³	336³	384³	424³	484³	534³	574³	594³	610³	672³	724³	770³	848³	912³	970³	1068³	1150³	1214³	1346³	1540³	1624³

cross-vendor multi-GPU support on a single PC/laptop/server

domain decomposition allows pooling VRAM from multiple GPUs for much larger grid resolution
each domain (GPU) can hold up to 4.29 billion (2³², 1624³) lattice points (225 GB memory)
GPUs don't have to be identical (not even from the same vendor), but similar VRAM capacity/bandwidth is recommended

domain communication architecture (simplified)

++   .-----------------------------------------------------------------.   ++
++   |                              GPU 0                              |   ++
++   |                          LBM Domain 0                           |   ++
++   '-----------------------------------------------------------------'   ++
++              |                 selective                /|\             ++
++             \|/               in-VRAM copy               |              ++
++        .-------------------------------------------------------.        ++
++        |               GPU 0 - Transfer Buffer 0               |        ++
++        '-------------------------------------------------------'        ++
!!                            |     PCIe     /|\                           !!
!!                           \|/    copy      |                            !!
@@        .-------------------------.   .-------------------------.        @@
@@        | CPU - Transfer Buffer 0 |   | CPU - Transfer Buffer 1 |        @@
@@        '-------------------------'\ /'-------------------------'        @@
@@                           pointer  X   swap                             @@
@@        .-------------------------./ \.-------------------------.        @@
@@        | CPU - Transfer Buffer 1 |   | CPU - Transfer Buffer 0 |        @@
@@        '-------------------------'   '-------------------------'        @@
!!                           /|\    PCIe      |                            !!
!!                            |     copy     \|/                           !!
++        .-------------------------------------------------------.        ++
++        |               GPU 1 - Transfer Buffer 1               |        ++
++        '-------------------------------------------------------'        ++
++             /|\                selective                 |              ++
++              |                in-VRAM copy              \|/             ++
++   .-----------------------------------------------------------------.   ++
++   |                              GPU 1                              |   ++
++   |                          LBM Domain 1                           |   ++
++   '-----------------------------------------------------------------'   ++
##                                    |                                    ##
##                      domain synchronization barrier                     ##
##                                    |                                    ##
||   -------------------------------------------------------------> time   ||

domain communication architecture (detailed)

++   .-----------------------------------------------------------------.   ++
++   |                              GPU 0                              |   ++
++   |                          LBM Domain 0                           |   ++
++   '-----------------------------------------------------------------'   ++
++     |  selective in- /|\  |  selective in- /|\  |  selective in- /|\    ++
++    \|/ VRAM copy (X)  |  \|/ VRAM copy (Y)  |  \|/ VRAM copy (Z)  |     ++
++   .---------------------.---------------------.---------------------.   ++
++   |    GPU 0 - TB 0X+   |    GPU 0 - TB 0Y+   |    GPU 0 - TB 0Z+   |   ++
++   |    GPU 0 - TB 0X-   |    GPU 0 - TB 0Y-   |    GPU 0 - TB 0Z-   |   ++
++   '---------------------'---------------------'---------------------'   ++
!!          | PCIe /|\            | PCIe /|\            | PCIe /|\         !!
!!         \|/ copy |            \|/ copy |            \|/ copy |          !!
@@   .---------. .---------.---------. .---------.---------. .---------.   @@
@@   | CPU 0X+ | | CPU 1X- | CPU 0Y+ | | CPU 3Y- | CPU 0Z+ | | CPU 5Z- |   @@
@@   | CPU 0X- | | CPU 2X+ | CPU 0Y- | | CPU 4Y+ | CPU 0Z- | | CPU 6Z+ |   @@
@@   '---------\ /---------'---------\ /---------'---------\ /---------'   @@
@@      pointer X swap (X)    pointer X swap (Y)    pointer X swap (Z)     @@
@@   .---------/ \---------.---------/ \---------.---------/ \---------.   @@
@@   | CPU 1X- | | CPU 0X+ | CPU 3Y- | | CPU 0Y+ | CPU 5Z- | | CPU 0Z+ |   @@
@@   | CPU 2X+ | | CPU 0X- | CPU 4Y+ | | CPU 0Y- | CPU 6Z+ | | CPU 0Z- |   @@
@@   '---------' '---------'---------' '---------'---------' '---------'   @@
!!         /|\ PCIe |            /|\ PCIe |            /|\ PCIe |          !!
!!          | copy \|/            | copy \|/            | copy \|/         !!
++   .--------------------..---------------------..--------------------.   ++
++   |   GPU 1 - TB 1X-   ||    GPU 3 - TB 3Y-   ||   GPU 5 - TB 5Z-   |   ++
++   :====================::=====================::====================:   ++
++   |   GPU 2 - TB 2X+   ||    GPU 4 - TB 4Y+   ||   GPU 6 - TB 6Z+   |   ++
++   '--------------------''---------------------''--------------------'   ++
++    /|\ selective in-  |  /|\ selective in-  |  /|\ selective in-  |     ++
++     |  VRAM copy (X) \|/  |  VRAM copy (Y) \|/  |  VRAM copy (Z) \|/    ++
++   .--------------------..---------------------..--------------------.   ++
++   |        GPU 1       ||        GPU 3        ||        GPU 5       |   ++
++   |    LBM Domain 1    ||    LBM Domain 3     ||    LBM Domain 5    |   ++
++   :====================::=====================::====================:   ++
++   |        GPU 2       ||        GPU 4        ||        GPU 6       |   ++
++   |    LBM Domain 2    ||    LBM Domain 4     ||    LBM Domain 6    |   ++
++   '--------------------''---------------------''--------------------'   ++
##              |                     |                     |              ##
##              |      domain synchronization barriers      |              ##
##              |                     |                     |              ##
||   -------------------------------------------------------------> time   ||

peak performance on GPUs (datacenter/gaming/professional/laptop)
- single-GPU/CPU benchmarks
- multi-GPU benchmarks
powerful model extensions
- boundary types
  - stationary mid-grid bounce-back boundaries (stationary solid boundaries)
  - moving mid-grid bounce-back boundaries (moving solid boundaries)
  - equilibrium boundaries (non-reflective inflow/outflow)
  - temperature boundaries (fixed temperature)
- global force per volume (Guo forcing), can be modified on-the-fly
- local force per volume (force field)
  - optional computation of forces from the fluid on solid boundaries
- state-of-the-art free surface LBM (FSLBM) implementation:
  - volume-of-fluid model
  - fully analytic PLIC for efficient curvature calculation
  - improved mass conservation
  - ultra efficient implementation with only 4 kernels additionally to stream_collide() kernel
- thermal LBM to simulate thermal convection
  - D3Q7 subgrid for thermal DDFs
  - in-place streaming with Esoteric-Pull for thermal DDFs
  - optional FP16S or FP16C compression for thermal DDFs with DDF-shifting
- Smagorinsky-Lilly subgrid turbulence LES model to keep simulations with very large Reynolds number stable
  Π_αβ = Σ_i e_iα e_iβ (f_i - f_i^eq-shifted)
  
  Q = Σ_αβ Π_αβ²
  ______________________
  τ = ½ (τ₀ + √ τ₀² + ^(16√2)∕_(3π²) ^√Q∕_ρ )
- particles with immersed-boundary method (either passive or 2-way-coupled, single-GPU only)

Solving the Visualization Problem

FluidX3D can do simulations so large that storing the volumetric data for later rendering becomes unmanageable (like 120GB for a single frame, hundreds of TeraByte for a video)
instead, FluidX3D allows rendering raw simulation data directly in VRAM, so no large volumetric files have to be exported to the hard disk (see my technical talk)
the rendering is so fast that it works interactively in real time for both rasterization and raytracing
rasterization and raytracing are done in OpenCL and work on all GPUs, even the ones without RTX/DXR raytracing cores or without any rendering hardware at all (like A100, MI200, ...)
if no monitor is available (like on a remote Linux server), there is an ASCII rendering mode to interactively visualize the simulation in the terminal (even in WSL and/or through SSH)
rendering is fully multi-GPU-parallelized via seamless domain decomposition rasterization
with interactive graphics mode disabled, image resolution can be as large as VRAM allows for (4K/8K/16K and above)
(interacitive) visualization modes:
- flag wireframe / solid surface (and force vectors on solid cells or surface pressure if the extension is used)
- velocity field (with slice mode)
- streamlines (with slice mode)
- velocity-colored Q-criterion isosurface
- rasterized free surface with marching-cubes
- raytraced free surface with fast ray-grid traversal and marching-cubes, either 1-4 rays/pixel or 1-10 rays/pixel

Solving the Compatibility Problem

FluidX3D is written in OpenCL 1.2, so it runs on any hardware from any vendor (Nvidia, AMD, Intel, ...):
- world's fastest datacenter GPUs, like H100, A100, MI250(X), MI210, MI100, V100(S), P100, ...
- gaming GPUs (desktop or laptop), like Nvidia GeForce, AMD Radeon, Intel Arc
- professional/workstation GPUs, like Nvidia Quadro, AMD Radeon Pro / FirePro
- integrated GPUs
- Intel Xeon Phi (requires installation of Intel OpenCL CPU Runtime (Repo))
- Intel/AMD CPUs (requires installation of Intel OpenCL CPU Runtime (Repo))
- even smartphone ARM GPUs
native cross-vendor multi-GPU implementation
- uses PCIe communication, so no SLI/Crossfire/NVLink/InfinityFabric required
- single-node parallelization, so no MPI installation required
- GPUs don't even have to be from the same vendor, but similar memory capacity and bandwidth are recommended
works on Windows and Linux with C++17, with limited support also for macOS and Android
supports importing and voxelizing triangle meshes from binary .stl files, with fast GPU voxelization
supports exporting volumetric data as binary .vtk files
supports exporting triangle meshes as binary .vtk files
supports exporting rendered images as .png/.qoi/.bmp files; encoding runs in parallel on the CPU while the simulation on GPU can continue without delay

Single-GPU/CPU Benchmarks

Here are performance benchmarks on various hardware in MLUPs/s, or how many million lattice cells are updated per second. The settings used for the benchmark are D3Q19 SRT with no extensions enabled (only LBM with implicit mid-grid bounce-back boundaries) and the setup consists of an empty cubic box with sufficient size (typically 256³). Without extensions, a single lattice cell requires:

a memory capacity of 93 (FP32/FP32) or 55 (FP32/FP16) Bytes
a memory bandwidth of 153 (FP32/FP32) or 77 (FP32/FP16) Bytes per time step
363 (FP32/FP32) or 406 (FP32/FP16S) or 1275 (FP32/FP16C) FLOPs per time step (FP32+INT32 operations counted combined)

In consequence, the arithmetic intensity of this implementation is 2.37 (FP32/FP32) or 5.27 (FP32/FP16S) or 16.56 (FP32/FP16C) FLOPs/Byte. So performance is only limited by memory bandwidth. The table in the left 3 columns shows the hardware specs as found in the data sheets (theoretical peak FP32 compute performance, memory capacity, theoretical peak memory bandwidth). The right 3 columns show the measured FluidX3D performance for FP32/FP32, FP32/FP16S, FP32/FP16C floating-point precision settings, with the (roofline model efficiency) in round brackets, indicating how much % of theoretical peak memory bandwidth are being used.

If your GPU/CPU is not on the list yet, you can report your benchmarks here.

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, ⚪ Apple, 🟡 ARM, 🟤 Glenfly

Device	FP32 [TFlops/s]	Mem [GB]	BW [GB/s]	FP32/FP32 [MLUPs/s]	FP32/FP16S [MLUPs/s]	FP32/FP16C [MLUPs/s]

🔴 Instinct MI250 (1 GCD)	45.26	64	1638	5638 (53%)	9030 (42%)	8506 (40%)
🔴 Instinct MI210	45.26	64	1638	6517 (61%)	9547 (45%)	8829 (41%)
🔴 Instinct MI100	46.14	32	1228	5093 (63%)	8133 (51%)	8542 (54%)
🔴 Instinct MI60	14.75	32	1024	3570 (53%)	5047 (38%)	5111 (38%)
🔴 Radeon VII	13.83	16	1024	4898 (73%)	7778 (58%)	5256 (40%)
🔵 Data Center GPU Max 1100	22.22	48	1229	3487 (43%)	6209 (39%)	3252 (20%)
🟢 H100 PCIe 80GB	51.01	80	2000	11128 (85%)	20624 (79%)	13862 (53%)
🟢 A100 SXM4 80GB	19.49	80	2039	10228 (77%)	18448 (70%)	11197 (42%)
🟢 A100 PCIe 80GB	19.49	80	1935	9657 (76%)	17896 (71%)	10817 (43%)
🟢 PG506-243 / PG506-242	22.14	64	1638	8195 (77%)	15654 (74%)	12271 (58%)
🟢 A100 SXM4 40GB	19.49	40	1555	8522 (84%)	16013 (79%)	11251 (56%)
🟢 A100 PCIe 40GB	19.49	40	1555	8526 (84%)	16035 (79%)	11088 (55%)
🟢 CMP 170HX	6.32	8	1493	7684 (79%)	12392 (64%)	6859 (35%)
🟢 A30	10.32	24	933	5004 (82%)	9721 (80%)	5726 (47%)
🟢 Tesla V100 SXM2 32GB	15.67	32	900	4471 (76%)	8947 (77%)	7217 (62%)
🟢 Tesla V100 PCIe 16GB	14.13	16	900	5128 (87%)	10325 (88%)	7683 (66%)
🟢 Quadro GV100	16.66	32	870	3442 (61%)	6641 (59%)	5863 (52%)
🟢 Titan V	14.90	12	653	3601 (84%)	7253 (86%)	6957 (82%)
🟢 Tesla P100 16GB	9.52	16	732	3295 (69%)	5950 (63%)	4176 (44%)
🟢 Tesla P100 12GB	9.52	12	549	2427 (68%)	4141 (58%)	3999 (56%)
🟢 GeForce GTX TITAN	4.71	6	288	1460 (77%)	2500 (67%)	1113 (30%)
🟢 Tesla K40m	4.29	12	288	1131 (60%)	1868 (50%)	912 (24%)
🟢 Tesla K80 (1 GPU)	4.11	12	240	916 (58%)	1642 (53%)	943 (30%)
🟢 Tesla K20c	3.52	5	208	861 (63%)	1507 (56%)	720 (27%)

🔴 Radeon RX 7900 XTX	61.44	24	960	3665 (58%)	7644 (61%)	7716 (62%)
🔴 Radeon PRO W7900	61.30	48	864	3107 (55%)	5939 (53%)	5780 (52%)
🔴 Radeon RX 7900 XT	51.61	20	800	3013 (58%)	5856 (56%)	5986 (58%)
🔴 Radeon PRO W7800	45.20	32	576	1872 (50%)	4426 (59%)	4145 (55%)
🔴 Radeon RX 7600	21.75	8	288	1250 (66%)	2561 (68%)	2512 (67%)
🔴 Radeon RX 6900 XT	23.04	16	512	1968 (59%)	4227 (64%)	4207 (63%)
🔴 Radeon RX 6800 XT	20.74	16	512	2008 (60%)	4241 (64%)	4224 (64%)
🔴 Radeon PRO W6800	17.83	32	512	1620 (48%)	3361 (51%)	3180 (48%)
🔴 Radeon RX 6700 XT	13.21	12	384	1408 (56%)	2883 (58%)	2908 (58%)
🔴 Radeon RX 6800M	11.78	12	384	1439 (57%)	3190 (64%)	3213 (64%)
🔴 Radeon RX 6700M	10.60	10	320	1194 (57%)	2388 (57%)	2429 (58%)
🔴 Radeon RX 5700 XT	9.75	8	448	1368 (47%)	3253 (56%)	3049 (52%)
🔴 Radeon RX 5600 XT	6.73	6	288	1136 (60%)	2214 (59%)	2148 (57%)
🔴 Radeon RX Vega 64	13.35	8	484	1875 (59%)	2878 (46%)	3227 (51%)
🔴 Radeon RX 580 4GB	6.50	4	256	946 (57%)	1848 (56%)	1577 (47%)
🔴 Radeon R9 390X	5.91	8	384	1733 (69%)	2217 (44%)	1722 (35%)
🔴 Radeon HD 7850	1.84	2	154	112 (11%)	120 ( 6%)	635 (32%)
🔵 Arc A770 LE	19.66	16	560	2663 (73%)	4568 (63%)	4519 (62%)
🔵 Arc A750 LE	17.20	8	512	2555 (76%)	4314 (65%)	4047 (61%)
🔵 Arc A580	12.29	8	512	2534 (76%)	3889 (58%)	3488 (52%)
🔵 Arc A380	4.20	6	186	622 (51%)	1097 (45%)	1115 (46%)
🟢 GeForce RTX 4090	82.58	24	1008	5624 (85%)	11091 (85%)	11496 (88%)
🟢 RTX 6000 Ada	91.10	48	960	4997 (80%)	10249 (82%)	10293 (83%)
🟢 L40S	91.61	48	864	3788 (67%)	7637 (68%)	7617 (68%)
🟢 GeForce RTX 4080	55.45	16	717	3914 (84%)	7626 (82%)	7933 (85%)
🟢 GeForce RTX 4070 Ti Super	44.10	16	672	3694 (84%)	6435 (74%)	7295 (84%)
🟢 GeForce RTX 4070	29.15	12	504	2646 (80%)	4548 (69%)	5016 (77%)
🟢 GeForce RTX 4080M	33.85	12	432	2577 (91%)	5086 (91%)	5114 (91%)
🟢 GeForce RTX 3090 Ti	40.00	24	1008	5717 (87%)	10956 (84%)	10400 (79%)
🟢 GeForce RTX 3090	39.05	24	936	5418 (89%)	10732 (88%)	10215 (84%)
🟢 GeForce RTX 3080 Ti	37.17	12	912	5202 (87%)	9832 (87%)	9347 (79%)
🟢 GeForce RTX 3080 12GB	32.26	12	912	5071 (85%)	9657 (81%)	8615 (73%)
🟢 RTX A6000	40.00	48	768	4421 (88%)	8814 (88%)	8533 (86%)
🟢 GeForce RTX 3080 10GB	29.77	10	760	4230 (85%)	8118 (82%)	7714 (78%)
🟢 GeForce RTX 3070	20.31	8	448	2578 (88%)	5096 (88%)	5060 (87%)
🟢 GeForce RTX 3060 Ti	16.49	8	448	2644 (90%)	5129 (88%)	4718 (81%)
🟢 RTX A4000	19.17	16	448	2500 (85%)	4945 (85%)	4664 (80%)
🟢 RTX A5000M	16.59	16	448	2228 (76%)	4461 (77%)	3662 (63%)
🟢 GeForce RTX 3060	13.17	12	360	2108 (90%)	4070 (87%)	3566 (76%)
🟢 GeForce RTX 3060M	10.94	6	336	2019 (92%)	4012 (92%)	3572 (82%)
🟢 GeForce RTX 3050M Ti	7.60	4	192	1181 (94%)	2341 (94%)	2253 (90%)
🟢 GeForce RTX 3050M	7.13	4	192	1180 (94%)	2339 (94%)	2016 (81%)
🟢 Titan RTX	16.31	24	672	3471 (79%)	7456 (85%)	7554 (87%)
🟢 Quadro RTX 6000	16.31	24	672	3307 (75%)	6836 (78%)	6879 (79%)
🟢 Quadro RTX 8000 Passive	14.93	48	624	2591 (64%)	5408 (67%)	5607 (69%)
🟢 GeForce RTX 2080 Ti	13.45	11	616	3194 (79%)	6700 (84%)	6853 (86%)
🟢 GeForce RTX 2080 Super	11.34	8	496	2434 (75%)	5284 (82%)	5087 (79%)
🟢 Quadro RTX 5000	11.15	16	448	2341 (80%)	4766 (82%)	4773 (82%)
🟢 GeForce RTX 2060 Super	7.18	8	448	2503 (85%)	5035 (87%)	4463 (77%)
🟢 Quadro RTX 4000	7.12	8	416	2284 (84%)	4584 (85%)	4062 (75%)
🟢 GeForce RTX 2060 KO	6.74	6	336	1643 (75%)	3376 (77%)	3266 (75%)
🟢 GeForce RTX 2060	6.74	6	336	1681 (77%)	3604 (83%)	3571 (82%)
🟢 GeForce GTX 1660 Super	5.03	6	336	1696 (77%)	3551 (81%)	3040 (70%)
🟢 Tesla T4	8.14	15	300	1356 (69%)	2869 (74%)	2887 (74%)
🟢 GeForce GTX 1660 Ti	5.48	6	288	1467 (78%)	3041 (81%)	3019 (81%)
🟢 GeForce GTX 1660	5.07	6	192	1016 (81%)	1924 (77%)	1992 (80%)
🟢 GeForce GTX 1650M 896C	2.72	4	192	963 (77%)	1836 (74%)	1858 (75%)
🟢 GeForce GTX 1650M 1024C	3.20	4	128	706 (84%)	1214 (73%)	1400 (84%)
🟢 T500	3.04	4	80	339 (65%)	578 (56%)	665 (64%)
🟢 Titan Xp	12.15	12	548	2919 (82%)	5495 (77%)	5375 (76%)
🟢 GeForce GTX 1080 Ti	12.06	11	484	2631 (83%)	4837 (77%)	4877 (78%)
🟢 GeForce GTX 1080	9.78	8	320	1623 (78%)	3100 (75%)	3182 (77%)
🟢 GeForce GTX 1060 6GB	4.57	6	192	997 (79%)	1925 (77%)	1785 (72%)
🟢 GeForce GTX 1060M	4.44	6	192	983 (78%)	1882 (75%)	1803 (72%)
🟢 GeForce GTX 1050M Ti	2.49	4	112	631 (86%)	1224 (84%)	1115 (77%)
🟢 Quadro P1000	1.89	4	82	426 (79%)	839 (79%)	778 (73%)
🟢 GeForce GTX 970	4.17	4	224	980 (67%)	1721 (59%)	1623 (56%)
🟢 Quadro M4000	2.57	8	192	899 (72%)	1519 (61%)	1050 (42%)
🟢 Tesla M60 (1 GPU)	4.82	8	160	853 (82%)	1571 (76%)	1557 (75%)
🟢 GeForce GTX 960M	1.51	4	80	442 (84%)	872 (84%)	627 (60%)
🟢 GeForce GTX 770	3.33	2	224	800 (55%)	1215 (42%)	876 (30%)
🟢 GeForce GTX 680 4GB	3.33	4	192	783 (62%)	1274 (51%)	814 (33%)
🟢 Quadro K2000	0.73	2	64	312 (75%)	444 (53%)	171 (21%)
🟢 GeForce GT 630 (OEM)	0.46	2	29	151 (81%)	185 (50%)	78 (21%)
🟢 Quadro NVS 290	0.03	0.256	6	1 ( 2%)	1 ( 1%)	1 ( 1%)
🟤 Arise 1020	1.50	2	19	6 ( 5%)	6 ( 2%)	6 ( 2%)

⚪ M2 Max GPU 38CU 32GB	9.73	22	400	2405 (92%)	4641 (89%)	2444 (47%)
⚪ M1 Ultra GPU 64CU 128GB	16.38	98	800	4519 (86%)	8418 (81%)	6915 (67%)
⚪ M1 Max GPU 24CU 32GB	6.14	22	400	2369 (91%)	4496 (87%)	2777 (53%)
⚪ M1 Pro GPU 16CU 16GB	4.10	11	200	1204 (92%)	2329 (90%)	1855 (71%)
⚪ M1 GPU 8CU 16GB	2.05	11	68	384 (86%)	758 (85%)	759 (86%)
🔴 Radeon 780M (Z1 Extreme)	8.29	8	102	443 (66%)	860 (65%)	820 (62%)
🔴 Radeon Vega 8 (4750G)	2.15	27	57	263 (71%)	511 (70%)	501 (68%)
🔴 Radeon Vega 8 (3500U)	1.23	7	38	157 (63%)	282 (57%)	288 (58%)
🔵 Iris Xe Graphics (i7-1265U)	1.92	13	77	342 (68%)	621 (62%)	574 (58%)
🔵 UHD Graphics Xe 32EUs	0.74	25	51	128 (38%)	245 (37%)	216 (32%)
🔵 UHD Graphics 770	0.82	30	90	342 (58%)	475 (41%)	278 (24%)
🔵 UHD Graphics 630	0.46	7	51	151 (45%)	301 (45%)	187 (28%)
🔵 UHD Graphics P630	0.46	51	42	177 (65%)	288 (53%)	137 (25%)
🔵 HD Graphics 5500	0.35	3	26	75 (45%)	192 (58%)	108 (32%)
🔵 HD Graphics 4600	0.38	2	26	105 (63%)	115 (35%)	34 (10%)
🟡 Mali-G610 MP4 (Orange Pi 5 Plus)	0.06	16	34	43 (19%)	59 (13%)	19 ( 4%)
🟡 Mali-G72 MP18 (Samsung S9+)	0.24	4	29	14 ( 7%)	17 ( 5%)	12 ( 3%)
🟡 Qualcomm Adreno 530 (LG G6)	0.33	2	30	1 ( 1%)	1 ( 0%)	1 ( 0%)

🔴 2x EPYC 9654	29.49	1536	922	1381 (23%)	1814 (15%)	1801 (15%)
🔵 2x Xeon CPU Max 9480	13.62	256	614	2037 (51%)	1520 (19%)	1464 (18%)
🔵 2x Xeon Platinum 8480+	14.34	512	614	2162 (54%)	1845 (23%)	1884 (24%)
🔵 2x Xeon Platinum 8380	11.78	2048	410	1410 (53%)	1159 (22%)	1298 (24%)
🔵 2x Xeon Platinum 8358	10.65	256	410	1285 (48%)	1007 (19%)	1120 (21%)
🔵 1x Xeon Platinum 8358	5.33	128	205	444 (33%)	463 (17%)	534 (20%)
🔵 2x Xeon Platinum 8256	1.95	1536	282	396 (22%)	158 ( 4%)	175 ( 5%)
🔵 2x Xeon Platinum 8153	4.10	384	256	691 (41%)	290 ( 9%)	328 (10%)
🔵 2x Xeon Gold 6128	2.61	192	256	254 (15%)	185 ( 6%)	193 ( 6%)
🔵 Xeon Phi 7210	5.32	192	102	415 (62%)	193 (15%)	223 (17%)
🔵 4x Xeon E5-4620 v4	2.69	512	273	460 (26%)	275 ( 8%)	239 ( 7%)
🔵 2x Xeon E5-2630 v4	1.41	64	137	264 (30%)	146 ( 8%)	129 ( 7%)
🔵 2x Xeon E5-2623 v4	0.67	64	137	125 (14%)	66 ( 4%)	59 ( 3%)
🔵 2x Xeon E5-2680 v3	1.92	64	137	209 (23%)	305 (17%)	281 (16%)
🔵 Core i7-13700K	2.51	64	90	481 (82%)	374 (32%)	373 (32%)
🔵 Core i7-1265U	1.23	32	77	128 (26%)	62 ( 6%)	58 ( 6%)
🔵 Core i9-11900KB	0.84	32	51	109 (33%)	195 (29%)	208 (31%)
🔵 Core i9-10980XE	3.23	128	94	286 (47%)	251 (21%)	223 (18%)
🔵 Core i5-9600	0.60	16	43	146 (52%)	127 (23%)	147 (27%)
🔵 Core i7-8700K	0.71	16	51	152 (45%)	134 (20%)	116 (17%)
🔵 Xeon E-2176G	0.71	64	42	201 (74%)	136 (25%)	148 (27%)
🔵 Core i7-7700HQ	0.36	12	38	81 (32%)	82 (16%)	108 (22%)
🔵 Core i7-4770	0.44	16	26	104 (62%)	69 (21%)	59 (18%)
🔵 Core i7-4720HQ	0.33	16	26	58 (35%)	13 ( 4%)	47 (14%)

Multi-GPU Benchmarks

Multi-GPU benchmarks are done at the largest possible grid resolution with cubic domains, and either 2x1x1, 2x2x1 or 2x2x2 of these domains together. The (percentages in round brackets) are single-GPU roofline model efficiency, and the (multiplicators in round brackets) are scaling factors relative to benchmarked single-GPU performance.

Colors: 🔴 AMD, 🔵 Intel, 🟢 Nvidia, ⚪ Apple, 🟡 ARM, 🟤 Glenfly

Device	FP32 [TFlops/s]	Mem [GB]	BW [GB/s]	FP32/FP32 [MLUPs/s]	FP32/FP16S [MLUPs/s]	FP32/FP16C [MLUPs/s]

🔴 1x Instinct MI250 (1 GCD)	45.26	64	1638	5638 (53%)	9030 (42%)	8506 (40%)
🔴 1x Instinct MI250 (2 GCD)	90.52	128	3277	9460 (1.7x)	14313 (1.6x)	17338 (2.0x)
🔴 2x Instinct MI250 (4 GCD)	181.04	256	6554	16925 (3.0x)	29163 (3.2x)	29627 (3.5x)
🔴 4x Instinct MI250 (8 GCD)	362.08	512	13107	27350 (4.9x)	52258 (5.8x)	53521 (6.3x)

🔴 1x Instinct MI210	45.26	64	1638	6347 (59%)	8486 (40%)	9105 (43%)
🔴 2x Instinct MI210	90.52	128	3277	7245 (1.1x)	12050 (1.4x)	13539 (1.5x)
🔴 4x Instinct MI210	181.04	256	6554	8816 (1.4x)	17232 (2.0x)	16892 (1.9x)
🔴 8x Instinct MI210	362.08	512	13107	13546 (2.1x)	27996 (3.3x)	27820 (3.1x)
🔴 16x Instinct MI210	724.16	1024	26214	18094 (2.9x)	37360 (4.4x)	37922 (4.2x)
🔴 24x Instinct MI210	1086.24	1536	39322	22056 (3.5x)	45033 (5.3x)	44631 (4.9x)
🔴 32x Instinct MI210	1448.32	2048	52429	23881 (3.8x)	50952 (6.0x)	48848 (5.4x)

🔴 1x Radeon VII	13.83	16	1024	4898 (73%)	7778 (58%)	5256 (40%)
🔴 2x Radeon VII	27.66	32	2048	8113 (1.7x)	15591 (2.0x)	10352 (2.0x)
🔴 4x Radeon VII	55.32	64	4096	12911 (2.6x)	24273 (3.1x)	17080 (3.2x)
🔴 8x Radeon VII	110.64	128	8192	21946 (4.5x)	30826 (4.0x)	24572 (4.7x)

🔵 1x DC GPU Max 1100	22.22	48	1229	3487 (43%)	6209 (39%)	3252 (20%)
🔵 2x DC GPU Max 1100	44.44	96	2458	6301 (1.8x)	11815 (1.9x)	5970 (1.8x)
🔵 4x DC GPU Max 1100	88.88	192	4915	12162 (3.5x)	22777 (3.7x)	11759 (3.6x)

🟢 1x A100 PCIe 80GB	19.49	80	1935	9657 (76%)	17896 (71%)	10817 (43%)
🟢 2x A100 PCIe 80GB	38.98	160	3870	15742 (1.6x)	27165 (1.5x)	17510 (1.6x)
🟢 4x A100 PCIe 80GB	77.96	320	7740	25957 (2.7x)	52056 (2.9x)	33283 (3.1x)

🟢 1x PG506-243 / PG506-242	22.14	64	1638	8195 (77%)	15654 (74%)	12271 (58%)
🟢 2x PG506-243 / PG506-242	44.28	128	3277	13885 (1.7x)	24168 (1.5x)	20906 (1.7x)
🟢 4x PG506-243 / PG506-242	88.57	256	6554	23097 (2.8x)	41088 (2.6x)	36130 (2.9x)

🟢 1x A100 SXM4 40GB	19.49	40	1555	8543 (84%)	15917 (79%)	8748 (43%)
🟢 2x A100 SXM4 40GB	38.98	80	3110	14311 (1.7x)	23707 (1.5x)	15512 (1.8x)
🟢 4x A100 SXM4 40GB	77.96	160	6220	23411 (2.7x)	42400 (2.7x)	29017 (3.3x)
🟢 8x A100 SXM4 40GB	155.92	320	12440	37619 (4.4x)	72965 (4.6x)	63009 (7.2x)

🟢 1x A100 SXM4 40GB	19.49	40	1555	8522 (84%)	16013 (79%)	11251 (56%)
🟢 2x A100 SXM4 40GB	38.98	80	3110	13629 (1.6x)	24620 (1.5x)	18850 (1.7x)
🟢 4x A100 SXM4 40GB	77.96	160	6220	17978 (2.1x)	30604 (1.9x)	30627 (2.7x)

🟢 1x Tesla V100 SXM2 32GB	15.67	32	900	4471 (76%)	8947 (77%)	7217 (62%)
🟢 2x Tesla V100 SXM2 32GB	31.34	64	1800	7953 (1.8x)	15469 (1.7x)	12932 (1.8x)
🟢 4x Tesla V100 SXM2 32GB	62.68	128	3600	13135 (2.9x)	26527 (3.0x)	22686 (3.1x)

🟢 1x Tesla K40m	4.29	12	288	1131 (60%)	1868 (50%)	912 (24%)
🟢 2x Tesla K40m	8.58	24	577	1971 (1.7x)	3300 (1.8x)	1801 (2.0x)
🟢 3x K40m + 1x Titan Xp	17.16	48	1154	3117 (2.8x)	5174 (2.8x)	3127 (3.4x)

🟢 1x Tesla K80 (1 GPU)	4.11	12	240	916 (58%)	1642 (53%)	943 (30%)
🟢 1x Tesla K80 (2 GPU)	8.22	24	480	2086 (2.3x)	3448 (2.1x)	2174 (2.3x)

🟢 1x RTX A6000	40.00	48	768	4421 (88%)	8814 (88%)	8533 (86%)
🟢 2x RTX A6000	80.00	96	1536	8041 (1.8x)	15026 (1.7x)	14795 (1.7x)
🟢 4x RTX A6000	160.00	192	3072	14314 (3.2x)	27915 (3.2x)	27227 (3.2x)
🟢 8x RTX A6000	320.00	384	6144	19311 (4.4x)	40063 (4.5x)	39004 (4.6x)

🟢 1x Quadro RTX 8000 Pa.	14.93	48	624	2591 (64%)	5408 (67%)	5607 (69%)
🟢 2x Quadro RTX 8000 Pa.	29.86	96	1248	4767 (1.8x)	9607 (1.8x)	10214 (1.8x)

🟢 1x GeForce RTX 2080 Ti	13.45	11	616	3194 (79%)	6700 (84%)	6853 (86%)
🟢 2x GeForce RTX 2080 Ti	26.90	22	1232	5085 (1.6x)	10770 (1.6x)	10922 (1.6x)
🟢 4x GeForce RTX 2080 Ti	53.80	44	2464	9117 (2.9x)	18415 (2.7x)	18598 (2.7x)
🟢 7x 2080 Ti + 1x A100 40GB	107.60	88	4928	16146 (5.1x)	33732 (5.0x)	33857 (4.9x)

🔵 1x A770 + 🟢 1x Titan Xp	24.30	24	1095	4717 (1.7x)	8380 (1.7x)	8026 (1.6x)

FAQs

General

How to learn using FluidX3D?

Follow the FluidX3D Documentation!
What physical model does FluidX3D use?

FluidX3D implements the lattice Boltzmann method, a type of direct numerical simulation (DNS), the most accurate type of fluid simulation, but also the most computationally challenging. Optional extension models include volume force (Guo forcing), free surface (volume-of-fluid and PLIC), a temperature model and Smagorinsky-Lilly subgrid turbulence model.
FluidX3D only uses FP32 or even FP32/FP16, in contrast to FP64. Are simulation results physically accurate?

Yes, in all but extreme edge cases. The code has been specially optimized to minimize arithmetic round-off errors and make the most out of lower precision. With these optimizations, accuracy in most cases is indistinguishable from FP64 double-precision, even with FP32/FP16 mixed-precision. Details can be found in this paper.
Why is the domain size limited to 2³² grid points?

The 32-bit unsigned integer grid index will overflow above this number. Using 64-bit index calculation would slow the simulation down by ~20%, as 64-bit uint is calculated on special function units and not the regular GPU cores. 2³² grid points with FP32/FP16 mixed-precision is equivalent to 225GB memory and single GPUs currently are only at 128GB, so it should be fine for a while to come. For higher resolutions above the single-domain limit, use multiple domains (typically 1 per GPU, but multiple domains on the same GPU also work).
Compared to the benchmark numbers stated here, efficiency seems much lower but performance is slightly better for most devices. How can this be?

In that paper, the One-Step-Pull swap algorithm is implemented, using only misaligned reads and coalesced writes. On almost all GPUs, the performance penalty for misaligned writes is much larger than for misaligned reads, and sometimes there is almost no penalty for misaligned reads at all. Because of this, One-Step-Pull runs at peak bandwidth and thus peak efficiency.
Here, a different swap algorithm termed Esoteric-Pull is used, a type of in-place streaming. This makes the LBM require much less memory (93 vs. 169 (FP32/FP32) or 55 vs. 93 (FP32/FP16) Bytes/cell for D3Q19), and also less memory bandwidth (153 vs. 171 (FP32/FP32) or 77 vs. 95 (FP32/FP16) Bytes/cell per time step for D3Q19) due to so-called implicit bounce-back boundaries. However memory access now is half coalesced and half misaligned for both reads and writes, so memory access efficiency is lower. For overall performance, these two effects approximately cancel out. The benefit of Esoteric-Pull - being able to simulate domains twice as large with the same amount of memory - clearly outweights the cost of slightly lower memory access efficiency, especially since performance is not reduced overall.
Why don't you use CUDA? Wouldn't that be more efficient?

No, that is a wrong myth. OpenCL is exactly as efficient as CUDA on Nvidia GPUs if optimized properly. Here I did roofline model and analyzed OpenCL performance on various hardware. OpenCL efficiency on modern Nvidia GPUs can be 100% with the right memory access pattern, so CUDA can't possibly be any more efficient. Without any performance advantage, there is no reason to use proprietary CUDA over OpenCL, since OpenCL is compatible with a lot more hardware.
Why no multi-relaxation-time (MRT) collision operator?

The idea of MRT is to linearly transform the DDFs into "moment space" by matrix multiplication and relax these moments individually, promising better stability and accuracy. In practice, in the vast majority of cases, it has zero or even negative effects on stability and accuracy, and simple SRT is much superior. Apart from the kinematic shear viscosity and conserved terms, the remaining moments are non-physical quantities and their tuning is a blackbox. Although MRT can be implemented in an efficient manner with only a single matrix-vector multiplication in registers, leading to identical performance compared to SRT by remaining bandwidth-bound, storing the matrices vastly elongates and over-complicates the code for no real benefit.

Hardware

Can FluidX3D run on multiple GPUs at the same time?

Yes. The simulation grid is then split in domains, one for each GPU (domain decomposition method). The GPUs essentially pool their memory, enabling much larger grid resolution and higher performance. Rendering is parallelized across multiple GPUs as well; each GPU renders its own domain with a 3D offset, then rendered frames from all GPUs are overlayed with their z-buffers. Communication between domains is done over PCIe, so no SLI/Crossfire/NVLink/InfinityFabric is required. All GPUs must however be installed in the same node (PC/laptop/server). Even unholy combinations of Nvidia/AMD/Intel GPUs will work, although it is recommended to only use GPUs with similar memory capacity and bandwidth together. Using a fast gaming GPU and slow integrated GPU together would only decrease performance due to communication overhead.
I'm on a budget and have only a cheap computer. Can I run FluidX3D on my toaster PC/laptop?

Absolutely. Today even the most inexpensive hardware, like integrated GPUs or entry-level gaming GPUs, support OpenCL. You might be a bit more limited on memory capacity and grid resolution, but you should be good to go. I've tested FluidX3D on very old and inexpensive hardware and even on my Samsung S9+ smartphone, and it runs just fine, although admittedly a bit slower.
I don't have an expensive workstation GPU, but only a gaming GPU. Will performance suffer?

No. Efficiency on gaming GPUs is exactly as good as on their "professional"/workstation counterparts. Performance often is even better as gaming GPUs have higher boost clocks.
Do I need a GPU with ECC memory?

No. Gaming GPUs work just fine. Some Nvidia GPUs automatically reduce memory clocks for compute applications to almost entirely eliminate memory errors.
My GPU does not support CUDA. Can I still use FluidX3D?

Yes. FluidX3D uses OpenCL 1.2 and not CUDA, so it runs on any GPU from any vendor since around 2012.
I don't have a dedicated graphics card at all. Can I still run FluidX3D on my PC/laptop?

Yes. FluidX3D also runs on all integrated GPUs since around 2012, and also on CPUs.
I need more memory than my GPU can offer. Can I run FluidX3D on my CPU as well?

Yes. You only need to install the Intel OpenCL CPU Runtime.
In the benchmarks you list some very expensive hardware. How do you get access to that?

As a PhD candidate in computational physics, I used FluidX3D for my research, so I had access to BZHPC, SuperMUC-NG and JSC JURECA-DC supercomputers.

Graphics

I don't have an RTX/DXR GPU that supports raytracing. Can I still use raytracing graphics in FluidX3D?

Yes, and at full performance. FluidX3D does not use a bounding volume hierarchy (BVH) to accelerate raytracing, but fast ray-grid traversal instead, implemented directly in OpenCL C. This is much faster than BVH for moving isosurfaces in the LBM grid (~N vs. ~N²+log(N) runtime; LBM itself is ~N³), and it does not require any dedicated raytracing hardware. Raytracing in FluidX3D runs on any GPU that supports OpenCL 1.2.
I have a datacenter/mining GPU without any video output or graphics hardware. Can FluidX3D still render simulation results?

Yes. FluidX3D does all rendering (rasterization and raytracing) in OpenCL C, so no display output and no graphics features like OpenGL/Vulkan/DirectX are required. Rendering is just another form of compute after all. Rendered frames are passed to the CPU over PCIe and then the CPU can either draw them on screen through dedicated/integrated graphics or write them to the hard drive.
I'm running FluidX3D on a remote (super-)computer and only have an SSH terminal. Can I still use graphics somehow?

Yes, either directly as interactive ASCII graphics in the terminal or by storing rendered frames on the hard drive and then copying them over via `scp -r user@server.url:"~/path/to/images/folder" .`.

Licensing

I want to learn about programming/software/physics/engineering. Can I use FluidX3D for free?

Yes. Anyone can use FluidX3D for free for public research, education or personal use. Use by scientists, students and hobbyists is free of charge and well encouraged.
I am a scientist/teacher with a paid position at a public institution. Can I use FluidX3D for my research/teaching?

Yes, you can use FluidX3D free of charge. This is considered research/education, not commercial use. To give credit, the references listed below should be cited. If you publish data/results generated by altered source versions, the altered source code must be published as well.
I work at a company in CFD/consulting/R&D or related fields. Can I use FluidX3D commercially?

No. Commercial use is not allowed with the current license.
Is FluidX3D open-source?

No. "Open-source" as a technical term is defined as freely available without any restriction on use, but I am not comfortable with that. I have written FluidX3D in my spare time and no one should milk it for profits while I remain uncompensated, especially considering what other CFD software sells for. The technical term for the type of license I choose is "source-available no-cost non-commercial". The source code is freely available, and you are free to use, to alter and to redistribute it, as long as you do not sell it or make a profit from derived products/services, and as long as you do not use it for any military purposes (see the license for details).
Will FluidX3D at some point be available with a commercial license?

Maybe I will add the option for a second, commercial license later on. If you are interested in commercial use, let me know. For non-commercial use in science and education, FluidX3D is and will always be free.

External Code/Libraries/Images used in FluidX3D

OpenCL-Headers for GPU parallelization (Khronos Group)
Win32 API for interactive graphics in Windows (Microsoft)
X11/Xlib for interactive graphics in Linux (The Open Group)
marching-cubes tables for isosurface generation on GPU (Paul Bourke)
src/lodepng.cpp and src/lodepng.hpp for .png encoding and decoding (Lode Vandevenne)
SimplexNoise class in src/utilities.hpp for generating continuous noise in 2D/3D/4D space (Stefan Gustavson)
skybox/skybox8k.png for free surface raytracing (HDRI Hub)

References

Lehmann, M.: Computational study of microplastic transport at the water-air interface with a memory-optimized lattice Boltzmann method. PhD thesis, (2023)
Lehmann, M.: Esoteric Pull and Esoteric Push: Two Simple In-Place Streaming Schemes for the Lattice Boltzmann Method on GPUs. Computation, 10, 92, (2022)
Lehmann, M., Krause, M., Amati, G., Sega, M., Harting, J. and Gekle, S.: Accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit, and customized 16-bit number formats. Phys. Rev. E 106, 015308, (2022)
Lehmann, M.: Combined scientific CFD simulation and interactive raytracing with OpenCL. IWOCL'22: International Workshop on OpenCL, 3, 1-2, (2022)
Lehmann, M., Oehlschlägel, L.M., Häusl, F., Held, A. and Gekle, S.: Ejection of marine microplastics by raindrops: a computational and experimental study. Micropl.&Nanopl. 1, 18, (2021)
Lehmann, M.: High Performance Free Surface LBM on GPUs. Master's thesis, (2019)
Lehmann, M. and Gekle, S.: Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes. Computation, 10, 21, (2022)

Contact

FluidX3D is solo-developed and maintained by Dr. Moritz Lehmann.
For any questions, feedback or other inquiries, contact me at dr.moritz.lehmann@gmail.com.
Updates are posted on Mastodon via @ProjectPhysX/#FluidX3D and on YouTube.

Name		Name	Last commit message	Last commit date
Latest commit History 193 Commits
skybox		skybox
src		src
.gitattributes		.gitattributes
.gitignore		.gitignore
CITATION.cff		CITATION.cff
DOCUMENTATION.md		DOCUMENTATION.md
FluidX3D.sln		FluidX3D.sln
FluidX3D.vcxproj		FluidX3D.vcxproj
LICENSE.md		LICENSE.md
README.md		README.md
make.sh		make.sh
makefile		makefile

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