forked from OpenCFD-IMECH/OpenCFD-EC
-
Notifications
You must be signed in to change notification settings - Fork 0
/
sub_Finite_Difference1.f90
298 lines (260 loc) · 8.46 KB
/
sub_Finite_Difference1.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
!----差分-有限体积混合算法----------------
! Copyright by Li Xinliang (c) lixl@imech.ac.cn
subroutine init_FDM
use Global_var
use FDM_data
implicit none
call read_para_FDM
call comput_Jacobian_FDM
end
!---------------------------------------------------
subroutine read_para_FDM
use Global_var
use FDM_data
implicit none
logical ext
integer:: ntmp(10), nbk,k, m,ierr
integer, allocatable :: BFDM(:)
Type (Mesh_TYPE),pointer:: MP
Type (Block_TYPE),pointer:: B
nbk=0
if(my_id .eq. 0) then
inquire(file="FDM.in",exist=ext)
if(ext) then
print*, "Find FDM.in, read it ..."
open(99,file="FDM.in")
read(99,*)
read(99,*)
read(99,*) FD_Flux, FD_scheme ! 内嵌差分法采用的通量方式、数值格式
read(99,*)
read(99,*) nbk ! 内嵌差分法的块数
allocate(BFDM(nbk))
read(99,*)
read(99,*) (BFDM(k),k=1,nbk)
close(99)
else
print*, "No FDM.in, Donot use hybrid FVM/FDM"
endif
endif
ntmp(1)=FD_Flux
ntmp(2)=FD_Scheme
ntmp(3)=nbk
call MPI_bcast(ntmp(1),3,MPI_Integer,0, MPI_COMM_WORLD,ierr)
FD_Flux=ntmp(1)
FD_Scheme=ntmp(2)
nbk=ntmp(3)
if(nbk .ne. 0) then
if(my_id .ne. 0) allocate(BFDM(nbk))
call MPI_bcast(BFDM,nbk,MPI_Integer,0, MPI_COMM_WORLD,ierr)
endif
MP=>Mesh(1) ! 仅最密的网格使用FDM
do m=1,MP%Num_Block
B=> MP%Block(m) ! 本块
B%IFLAG_FVM_FDM=Method_FVM
Loop1: do k=1,nbk
if( BFDM(k) == B%block_no ) then
B%IFLAG_FVM_FDM=Method_FDM
exit Loop1
endif
enddo Loop1
print*, "my_id, block_no, FDM, FD_Flux, FD_Scheme=", my_id, B%block_no, B%IFLAG_FVM_FDM
enddo
end
!-----计算差分法相关的Jacobian系数-------------------
subroutine comput_Jacobian_FDM
use Global_var
use FDM_data
implicit none
Type (Block_TYPE),pointer:: B
Type (FDM_Block_Type),pointer:: Bm
real(PRE_EC),allocatable,dimension(:,:,:):: x,y,z
integer:: i,j,k,m,nMesh,nB,nx,ny,nz
character(len=50):: filename
!---------------------------------------------------------
! 依赖的全局数据：
! Num_Mesh （整型变量） 网格的套数 （例如，采用3重网格，则该数为3）
! Mesh(k)%Num_Block 网格的块数；
! Flag_FDM(:) （整型数组）, 如果Flag_FDM(k)=0, 则第k块网格采用有限体积法， 如果为1，则采用有限差分法；
!----------------------------------------------------------
! 创建数据结构
allocate(FDM_Mesh(Num_Mesh))
do m=1,Num_Mesh
Num_block=Mesh(m)%Num_Block
allocate(FDM_Mesh(m)%Block(Num_block))
do nB=1,Num_block
Bm=>FDM_Mesh(m)%Block(nB)
B=>Mesh(m)%Block(nB)
if(B%IFLAG_FVM_FDM .eq. Method_FDM) then ! 该块采用差分法计算
nx=B%nx-1; ny=B%ny-1; nz=B%nz-1
allocate(Bm%ix(nx,ny,nz), Bm%iy(nx,ny,nz), Bm%iz(nx,ny,nz), &
Bm%jx(nx,ny,nz), Bm%jy(nx,ny,nz), Bm%jz(nx,ny,nz), &
Bm%kx(nx,ny,nz), Bm%ky(nx,ny,nz), Bm%kz(nx,ny,nz), Bm%jac(nx,ny,nz))
endif
enddo
enddo
!---------------------------------------------------------------
! Comput Jocabian coefficients
do nMesh=1,Num_Mesh
! write(filename,"('test-Jacobian-'I1.1'.dat')") nMesh
! open(99,file=filename)
! write(99,*) "variables=x,y,z,ix,iy,iz,jx,jy,jz,kx,ky,kz,Jac"
do m=1,Mesh(nMesh)%Num_Block
B => Mesh(nMesh)%Block(m)
Bm => FDM_Mesh(nMesh)%Block(m)
if(B%IFLAG_FVM_FDM .ne. Method_FDM ) cycle ! only for FDM (Finite difference method)
! print*, " Comput Jocabian Coefficient, Block No.", m
nx=B%nx-1 ! 网格点数（若物理量储存于网格中心，指的是网格中心的数目）
ny=B%ny-1
nz=B%nz-1
! 申请内存 储存坐标
allocate(x(nx,ny,nz),y(nx,ny,nz),z(nx,ny,nz))
! 物理量所在点的坐标 （若物理量储存在网格中心，则为网格中心点的坐标）
do k=1,nz
do j=1,ny
do i=1,nx
x(i,j,k)=B%xc(i,j,k)
y(i,j,k)=B%yc(i,j,k)
z(i,j,k)=B%zc(i,j,k)
enddo
enddo
enddo
! 计算Jacobian系数
call grid_Jacobian(nx,ny,nz, x(1,1,1),y(1,1,1),z(1,1,1), &
Bm%ix(1,1,1),Bm%iy(1,1,1),Bm%iz(1,1,1), &
Bm%jx(1,1,1),Bm%jy(1,1,1),Bm%jz(1,1,1), &
Bm%kx(1,1,1),Bm%ky(1,1,1),Bm%kz(1,1,1), &
Bm%Jac(1,1,1) )
! write(99,*) "zone i= ", nx, " j= ", ny , " k= ", nz
! do k=1,nz
! do j=1,ny
! do i=1,nx
! write(99,"(13f20.8)") x(i,j,k),y(i,j,k), z(i,j,k), &
! Bm%ix(i,j,k),Bm%iy(i,j,k),Bm%iz(i,j,k),Bm%jx(i,j,k),Bm%jy(i,j,k),Bm%jz(i,j,k), &
! Bm%kx(i,j,k),Bm%ky(i,j,k),Bm%kz(i,j,k),Bm%Jac(i,j,k)
! enddo
! enddo
! enddo
deallocate(x,y,z)
enddo
! close(99)
enddo
if(my_id ==0) print*, "comput Jocabian OK ..."
end subroutine comput_Jacobian_FDM
!c================================================================
subroutine grid_Jacobian(nx,ny,nz,x,y,z,ix,iy,iz,jx,jy,jz,kx,ky,kz,Jac)
use precision_EC
implicit none
integer:: nx,ny,nz,i,j,k
real(PRE_EC),dimension(nx,ny,nz):: x,y,z,ix,iy,iz,jx,jy,jz,kx,ky,kz,Jac
real(PRE_EC),allocatable,dimension(:,:,:):: xi,xj,xk,yi,yj,yk,zi,zj,zk
real(PRE_EC):: Jac1,xi1,xj1,xk1,yi1,yj1,yk1,zi1,zj1,zk1
allocate(xi(nx,ny,nz),xj(nx,ny,nz),xk(nx,ny,nz), &
yi(nx,ny,nz),yj(nx,ny,nz),yk(nx,ny,nz), &
zi(nx,ny,nz),zj(nx,ny,nz),zk(nx,ny,nz))
call dx3d(nx,ny,nz,x,xi)
call dx3d(nx,ny,nz,y,yi)
call dx3d(nx,ny,nz,z,zi)
call dy3d(nx,ny,nz,x,xj)
call dy3d(nx,ny,nz,y,yj)
call dy3d(nx,ny,nz,z,zj)
call dz3d(nx,ny,nz,x,xk)
call dz3d(nx,ny,nz,y,yk)
call dz3d(nx,ny,nz,z,zk)
do k=1,nz
do j=1,ny
do i=1,nx
xi1=xi(i,j,k); xj1=xj(i,j,k); xk1=xk(i,j,k)
yi1=yi(i,j,k); yj1=yj(i,j,k); yk1=yk(i,j,k)
zi1=zi(i,j,k); zj1=zj(i,j,k); zk1=zk(i,j,k)
Jac1=1.d0/(xi1*yj1*zk1+yi1*zj1*xk1+zi1*xj1*yk1-zi1*yj1*xk1-yi1*xj1*zk1-xi1*zj1*yk1) ! 1./Jocabian = d(x,y,z)/d(i,j,k)
Jac(i,j,k)=Jac1
ix(i,j,k)=Jac1*(yj1*zk1-zj1*yk1)
iy(i,j,k)=Jac1*(zj1*xk1-xj1*zk1)
iz(i,j,k)=Jac1*(xj1*yk1-yj1*xk1)
jx(i,j,k)=Jac1*(yk1*zi1-zk1*yi1)
jy(i,j,k)=Jac1*(zk1*xi1-xk1*zi1)
jz(i,j,k)=Jac1*(xk1*yi1-yk1*xi1)
kx(i,j,k)=Jac1*(yi1*zj1-zi1*yj1)
ky(i,j,k)=Jac1*(zi1*xj1-xi1*zj1)
kz(i,j,k)=Jac1*(xi1*yj1-yi1*xj1)
if(Jac1 .lt. 0) print*, " Jocabian < 0 !!!, i,j,k, Jac1"
enddo
enddo
enddo
deallocate(xi,yi,zi,xj,yj,zj,xk,yk,zk)
end subroutine grid_Jacobian
!c==========================================================================================
! 采用差分方法计算三个方向的导数 （内部6阶中心差分，边界处降阶）, 用于计算Jacobian系数
subroutine dx0(nx,f,fx)
use precision_EC
implicit none
integer:: nx,i
real(PRE_EC):: b1,b2,a1,a2,a3
real(PRE_EC):: f(nx),fx(nx)
b1=8.d0/(12.d0)
b2=1.d0/(12.d0)
a1=1.d0/(60.d0)
a2=-3.d0/(20.d0)
a3=3.d0/(4.d0)
do i=4,nx-3
fx(i) =a1*(f(i+3)-f(i-3)) +a2*(f(i+2)-f(i-2)) +a3*(f(i+1)-f(i-1)) ! 6th centred
enddo
fx(1)=(-3.d0*f(1)+4.d0*f(2)-f(3))/2.d0
fx(2)=(-2.d0*f(1)-3.d0*f(2)+6.d0*f(3)-f(4)) /6.d0
fx(3)=b1*(f(4)-f(2)) -b2*(f(5)-f(1))
fx(nx-2)=b1*(f(nx-1)-f(nx-3)) -b2*(f(nx)-f(nx-4))
fx(nx-1)=(f(nx-3)-6.d0*f(nx-2)+3.d0*f(nx-1) +2.d0*f(nx))/6.d0
fx(nx)=(f(nx-2)-4.d0*f(nx-1)+3.d0*f(nx))/2.d0
end
!-----------------------------------------------------------------------
subroutine dx3d(nx,ny,nz,f,fx)
use precision_EC
implicit none
integer:: nx,ny,nz,i,j,k
real(PRE_EC):: f(nx,ny,nz),fx(nx,ny,nz),f1d(nx),fx1d(nx)
do k=1,nz
do j=1,ny
do i=1,nx
f1d(i)=f(i,j,k)
enddo
call dx0(nx,f1d,fx1d)
do i=1,nx
fx(i,j,k)=fx1d(i)
enddo
enddo
enddo
end subroutine dx3d
subroutine dy3d(nx,ny,nz,f,fy)
use precision_EC
implicit none
integer:: nx,ny,nz,i,j,k
real(PRE_EC):: f(nx,ny,nz),fy(nx,ny,nz),f1d(ny),fx1d(ny)
do k=1,nz
do i=1,nx
do j=1,ny
f1d(j)=f(i,j,k)
enddo
call dx0(ny,f1d,fx1d)
do j=1,ny
fy(i,j,k)=fx1d(j)
enddo
enddo
enddo
end subroutine dy3d
subroutine dz3d(nx,ny,nz,f,fz)
use precision_EC
implicit none
integer:: nx,ny,nz,i,j,k
real(PRE_EC):: f(nx,ny,nz),fz(nx,ny,nz),f1d(nz),fx1d(nz)
do j=1,ny
do i=1,nx
do k=1,nz
f1d(k)=f(i,j,k)
enddo
call dx0(nz,f1d,fx1d)
do k=1,nz
fz(i,j,k)=fx1d(k)
enddo
enddo
enddo
end subroutine dz3d