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implicit.f90
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3044 lines (2783 loc) · 81.7 KB
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!#define my_mod_solide
module ludecomp
use decomp_2d, only : mytype
implicit none
private
public :: ludecomp7
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Interface for septadiag LU decomposition used in implicit mode
! ludecomp7_0 is called when ncly=0
! ludecomp7_12 is called when ncly=1 or 2
!
interface ludecomp7
module procedure ludecomp7_12
module procedure ludecomp7_0
end interface ludecomp7
contains
!*******************************************************************
!Decomposition LU matrice septadiag
subroutine ludecomp7_12(aam,bbm,ccm,ddm,eem,qqm,ggm,hhm,ssm,rrm,vvm,wwm,zzm,ny)
!
!*******************************************************************
use decomp_2d, only : mytype
implicit none
integer :: i,j,k,ny
real(mytype),dimension(ny), intent(in) :: aam,bbm,ccm,ddm,eem,rrm,qqm
real(mytype),dimension(ny), intent(out) :: ggm,hhm,ssm
real(mytype),dimension(ny), intent(out) :: vvm,wwm,zzm
ggm=0.;hhm=0.;ssm=0.
vvm=0.;wwm=0.;zzm=0.
ggm(1)=aam(1)
hhm(1)=bbm(1)
ssm(1)=ccm(1)
zzm(2)=ddm(2)/ggm(1)
ggm(2)=aam(2)-zzm(2)*hhm(1)
hhm(2)=bbm(2)-zzm(2)*ssm(1)
ssm(2)=ccm(2)-zzm(2)*rrm(1)
wwm(3)=eem(3)/ggm(1)
zzm(3)=(ddm(3)-wwm(3)*hhm(1))/ggm(2)
ggm(3)=aam(3)-wwm(3)*ssm(1)-zzm(3)*hhm(2)
hhm(3)=bbm(3)-wwm(3)*rrm(1)-zzm(3)*ssm(2)
ssm(3)=ccm(3)-zzm(3)*rrm(2)
do j=4,ny
vvm(j)=qqm(j)/ggm(j-3)
wwm(j)=(eem(j)-vvm(j)*hhm(j-3))/ggm(j-2)
zzm(j)=(ddm(j)-wwm(j)*hhm(j-2)-vvm(j)*ssm(j-3))/ggm(j-1)
ggm(j)=aam(j)-vvm(j)*rrm(j-3)-wwm(j)*ssm(j-2)-zzm(j)*hhm(j-1)
hhm(j)=bbm(j)-wwm(j)*rrm(j-2)-zzm(j)*ssm(j-1)
ssm(j)=ccm(j)-zzm(j)*rrm(j-1)
enddo
end subroutine ludecomp7_12
!
!*******************************************************************
!Decomposition LU matrice cyclique septadiag
subroutine ludecomp7_0(aam,bbm,ccm,ddm,eem,qqm,ggm,hhm,ssm,rrm,vvm,wwm,zzm,l1m,l2m,l3m,u1m,u2m,u3m,ny)
!
!*******************************************************************
use decomp_2d, only : mytype
implicit none
integer :: i,j,k,ny
real(mytype),dimension(ny), intent(in) :: aam,bbm,ccm,ddm,eem,rrm,qqm
real(mytype),dimension(ny), intent(out) :: ggm,hhm,ssm
real(mytype),dimension(ny), intent(out) :: vvm,wwm,zzm
real(mytype),dimension(ny), intent(out) :: l1m,l2m,l3m
real(mytype),dimension(ny), intent(out) :: u1m,u2m,u3m
! a=diag, b=diag+1, c=diag+2, r=diag+3
! d=diag-1, e=diag-2, q=diag-3
ggm=0.;hhm=0.;ssm=0. ! U part (diag, diag+1, diag+2, diag+3=rrm)
u1m=0.;u2m=0.;u3m=0. ! U cyclic part (last col, last-1, last-2)
vvm=0.;wwm=0.;zzm=0. ! L part (diag=1, diag-3, diag-2, diag-1)
l1m=0.;l2m=0.;l3m=0. ! L cyclic part (last row, last-1, last-2)
ggm(1)=aam(1)
hhm(1)=bbm(1)
ssm(1)=ccm(1)
u1m(1)=ddm(1)
u2m(1)=eem(1)
u3m(1)=qqm(1)
l1m(1)=bbm(ny)/ggm(1)
l2m(1)=ccm(ny-1)/ggm(1)
l3m(1)=rrm(ny-2)/ggm(1)
zzm(2)=ddm(2)/ggm(1)
ggm(2)=aam(2)-zzm(2)*hhm(1)
hhm(2)=bbm(2)-zzm(2)*ssm(1)
ssm(2)=ccm(2)-zzm(2)*rrm(1)
u1m(2)=eem(2)-zzm(2)*u1m(1)
u2m(2)=qqm(2)-zzm(2)*u2m(1)
u3m(2)= -zzm(2)*u3m(1)
l1m(2)=(ccm(ny) -hhm(1)*l1m(1))/ggm(2)
l2m(2)=(rrm(ny-1)-hhm(1)*l2m(1))/ggm(2)
l3m(2)=( -hhm(1)*l3m(1))/ggm(2)
wwm(3)=eem(3)/ggm(1)
zzm(3)=(ddm(3)-wwm(3)*hhm(1))/ggm(2)
ggm(3)=aam(3)-wwm(3)*ssm(1)-zzm(3)*hhm(2)
hhm(3)=bbm(3)-wwm(3)*rrm(1)-zzm(3)*ssm(2)
ssm(3)=ccm(3) -zzm(3)*rrm(2)
u1m(3)=qqm(3)-wwm(3)*u1m(1)-zzm(3)*u1m(2)
u2m(3)= -wwm(3)*u2m(1)-zzm(3)*u2m(2)
u3m(3)= -wwm(3)*u3m(1)-zzm(3)*u3m(2)
l1m(3)=(rrm(ny)-ssm(1)*l1m(1)-hhm(2)*l1m(2))/ggm(3)
l2m(3)=( -ssm(1)*l2m(1)-hhm(2)*l2m(2))/ggm(3)
l3m(3)=( -ssm(1)*l3m(1)-hhm(2)*l3m(2))/ggm(3)
do j=4,ny-3
vvm(j)=qqm(j)/ggm(j-3)
wwm(j)=(eem(j)-vvm(j)*hhm(j-3))/ggm(j-2)
zzm(j)=(ddm(j)-wwm(j)*hhm(j-2)-vvm(j)*ssm(j-3))/ggm(j-1)
ggm(j)=aam(j)-vvm(j)*rrm(j-3)-wwm(j)*ssm(j-2)-zzm(j)*hhm(j-1)
hhm(j)=bbm(j)-wwm(j)*rrm(j-2)-zzm(j)*ssm(j-1)
ssm(j)=ccm(j)-zzm(j)*rrm(j-1)
u1m(j)= - vvm(j)*u1m(j-3) - wwm(j)*u1m(j-2) - zzm(j)*u1m(j-1)
u2m(j)= - vvm(j)*u2m(j-3) - wwm(j)*u2m(j-2) - zzm(j)*u2m(j-1)
u3m(j)= - vvm(j)*u3m(j-3) - wwm(j)*u3m(j-2) - zzm(j)*u3m(j-1)
l1m(j)= - (rrm(j-3)*l1m(j-3)+ssm(j-2)*l1m(j-2)+hhm(j-1)*l1m(j-1))/ggm(j)
l2m(j)= - (rrm(j-3)*l2m(j-3)+ssm(j-2)*l2m(j-2)+hhm(j-1)*l2m(j-1))/ggm(j)
l3m(j)= - (rrm(j-3)*l3m(j-3)+ssm(j-2)*l3m(j-2)+hhm(j-1)*l3m(j-1))/ggm(j)
enddo
do j=ny-2,ny
vvm(j)=qqm(j)/ggm(j-3)
wwm(j)=(eem(j)-vvm(j)*hhm(j-3))/ggm(j-2)
zzm(j)=(ddm(j)-wwm(j)*hhm(j-2)-vvm(j)*ssm(j-3))/ggm(j-1)
ggm(j)=aam(j)-vvm(j)*rrm(j-3)-wwm(j)*ssm(j-2)-zzm(j)*hhm(j-1)
hhm(j)=bbm(j)-wwm(j)*rrm(j-2)-zzm(j)*ssm(j-1)
ssm(j)=ccm(j)-zzm(j)*rrm(j-1)
enddo
j=ny-2
u1m(j)= - vvm(j)*u1m(j-3)-wwm(j)*u1m(j-2)-zzm(j)*u1m(j-1) &
- l3m(j-1)*rrm(j-1)
u2m(j)= - vvm(j)*u2m(j-3)-wwm(j)*u2m(j-2)-zzm(j)*u2m(j-1) &
- l3m(j-2)*rrm(j-2) - l3m(j-1)*ssm(j-1)
u3m(j)= - vvm(j)*u3m(j-3)-wwm(j)*u3m(j-2)-zzm(j)*u3m(j-1) &
- l3m(j-3)*rrm(j-3) - l3m(j-2)*ssm(j-2) - l3m(j-1)*hhm(j-1)
do k=1,j-1
u1m(j)=u1m(j) - u1m(k)*l3m(k)
u2m(j)=u2m(j) - u2m(k)*l3m(k)
u3m(j)=u3m(j) - u3m(k)*l3m(k)
enddo
l1m(j)= - ( rrm(j-3)*l1m(j-3)+ssm(j-2)*l1m(j-2)+hhm(j-1)*l1m(j-1) &
+ vvm(ny)*u3m(j-1)+wwm(ny)*u3m(j) ) / ( ggm(j)+u3m(j) )
l2m(j)= - (rrm(j-3)*l2m(j-3)+ssm(j-2)*l2m(j-2)+hhm(j-1)*l2m(j-1) &
+ vvm(ny-1)*u3m(j-2)+wwm(ny-1)*u3m(j-1)+zzm(ny-1)*u3m(j) ) / (ggm(j)+u3m(j))
do k=1,j-1
l1m(j)=l1m(j) - l1m(k)*u3m(k) / (ggm(j)+u3m(j))
l2m(j)=l2m(j) - l2m(k)*u3m(k) / (ggm(j)+u3m(j))
enddo
j=ny-1
u1m(j)= - vvm(j)*u1m(j-3)-wwm(j)*u1m(j-2)-zzm(j)*u1m(j-1) &
- l2m(j-2)*rrm(j-2) - l2m(j-1)*ssm(j-1)
u2m(j)= - vvm(j)*u2m(j-3)-wwm(j)*u2m(j-2)-zzm(j)*u2m(j-1) &
- l2m(j-3)*rrm(j-3) - l2m(j-2)*ssm(j-2) - l2m(j-1)*hhm(j-1)
do k=1,j-1
u1m(j)=u1m(j) - u1m(k)*l2m(k)
u2m(j)=u2m(j) - u2m(k)*l2m(k)
enddo
l1m(j)= - (rrm(j-3)*l1m(j-3)+ssm(j-2)*l1m(j-2)+hhm(j-1)*l1m(j-1) &
+ vvm(ny)*u2m(j-2)+wwm(ny)*u2m(j-1)+zzm(ny)*u2m(j) ) / (ggm(j)+u2m(j));
do k=1,j-1
l1m(j)=l1m(j) - l1m(k)*u2m(k) / (ggm(j)+u2m(j));
enddo
j=ny
u1m(j)= - vvm(j)*u1m(j-3)-wwm(j)*u1m(j-2)-zzm(j)*u1m(j-1) &
- l1m(j-3)*rrm(j-3)-l1m(j-2)*ssm(j-2)-l1m(j-1)*hhm(j-1);
do k=1,j-1
u1m(j)=u1m(j) - u1m(k)*l1m(k)
enddo
end subroutine ludecomp7_0
!
end module ludecomp
module matinv
use decomp_2d, only : mytype
implicit none
private
public :: septinv
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Interface for septadiag matrix inversion used in implicit mode
! septinv_0 is called when ncly=0
! septinv_12 is called when ncly=1 or 2
!
interface septinv
module procedure septinv_12
module procedure septinv_0
end interface septinv
contains
!********************************************************************
!INVERSE SEPTADIAG
subroutine septinv_12(xsol,bbb,ggm,hhm,ssm,rrm,vvm,wwm,zzm,nx,ny,nz)
!
!********************************************************************
use decomp_2d, only : mytype
implicit none
integer :: i,j,k,nx,ny,nz
real(mytype),dimension(nx,ny,nz),intent(out) :: xsol
real(mytype),dimension(nx,ny,nz),intent(in) :: bbb
real(mytype),dimension(ny),intent(in) :: ggm,hhm,ssm,rrm
real(mytype),dimension(ny),intent(in) :: vvm,wwm,zzm
do k=1,nz
do i=1,nx
!Descente
xsol(i,1,k)=bbb(i,1,k)
xsol(i,2,k)=bbb(i,2,k)-zzm(2)*xsol(i,1,k)
xsol(i,3,k)=bbb(i,3,k)-zzm(3)*xsol(i,2,k)-wwm(3)*xsol(i,1,k)
do j=4,ny
xsol(i,j,k)=bbb(i,j,k)-vvm(j)*xsol(i,j-3,k)-wwm(j)*xsol(i,j-2,k) &
-zzm(j)*xsol(i,j-1,k)
enddo
!
!Remontee
xsol(i,ny,k)=xsol(i,ny,k)/ggm(ny)
xsol(i,ny-1,k)=(xsol(i,ny-1,k)-hhm(ny-1)*xsol(i,ny,k))/ggm(ny-1)
xsol(i,ny-2,k)=(xsol(i,ny-2,k)-hhm(ny-2)*xsol(i,ny-1,k)- &
ssm(ny-2)*xsol(i,ny,k))/ggm(ny-2)
do j=ny-3,1,-1
xsol(i,j,k)=(xsol(i,j,k)-hhm(j)*xsol(i,j+1,k)-ssm(j)*xsol(i,j+2,k) &
-rrm(j)*xsol(i,j+3,k))/ggm(j)
enddo
enddo
enddo
end subroutine septinv_12
!
!********************************************************************
!INVERSE SEPTADIAG CYCLIQUE
subroutine septinv_0(xsol,bbb,ggm,hhm,ssm,rrm,vvm,wwm,zzm,l1m,l2m,l3m,u1m,u2m,u3m,nx,ny,nz)
!
!********************************************************************
use decomp_2d, only : mytype
implicit none
integer :: i,j,k,kk,nx,ny,nz
real(mytype),dimension(nx,ny,nz), intent(out) :: xsol
real(mytype),dimension(nx,ny,nz), intent(in) :: bbb
real(mytype),dimension(ny), intent(in) :: ggm,hhm,ssm,rrm
real(mytype),dimension(ny), intent(in) :: vvm,wwm,zzm
real(mytype),dimension(ny), intent(in) :: l1m,l2m,l3m
real(mytype),dimension(ny), intent(in) :: u1m,u2m,u3m
do k=1,nz
do i=1,nx
!Descente avec matrice triangulaire inf
xsol(i,1,k)=bbb(i,1,k)
xsol(i,2,k)=bbb(i,2,k)-zzm(2)*xsol(i,1,k)
xsol(i,3,k)=bbb(i,3,k)-zzm(3)*xsol(i,2,k)-wwm(3)*xsol(i,1,k)
do j=4,ny-3
xsol(i,j,k)=bbb(i,j,k)-vvm(j)*xsol(i,j-3,k)-wwm(j)*xsol(i,j-2,k) &
-zzm(j)*xsol(i,j-1,k)
enddo
j=ny-2
xsol(i,j,k)=bbb(i,j,k)-vvm(j)*xsol(i,j-3,k)-wwm(j)*xsol(i,j-2,k) &
-zzm(j)*xsol(i,j-1,k)
do kk=1,j-1
xsol(i,j,k)=xsol(i,j,k)-l3m(kk)*xsol(i,kk,k)
enddo
j=ny-1
xsol(i,j,k)=bbb(i,j,k)-vvm(j)*xsol(i,j-3,k)-wwm(j)*xsol(i,j-2,k) &
-zzm(j)*xsol(i,j-1,k)
do kk=1,j-1
xsol(i,j,k)=xsol(i,j,k)-l2m(kk)*xsol(i,kk,k)
enddo
j=ny
xsol(i,j,k)=bbb(i,j,k)-vvm(j)*xsol(i,j-3,k)-wwm(j)*xsol(i,j-2,k) &
-zzm(j)*xsol(i,j-1,k)
do kk=1,j-1
xsol(i,j,k)=xsol(i,j,k)-l1m(kk)*xsol(i,kk,k)
enddo
!
!Remontee avec matrice triangulaire sup.
xsol(i,ny,k)=xsol(i,ny,k)/(ggm(ny)+u1m(ny))
xsol(i,ny-1,k)=(xsol(i,ny-1,k)-(hhm(ny-1)+u1m(ny-1))*xsol(i,ny,k))/(ggm(ny-1)+u2m(ny-1))
xsol(i,ny-2,k)=(xsol(i,ny-2,k)-(hhm(ny-2)+u2m(ny-2))*xsol(i,ny-1,k)- &
(ssm(ny-2)+u1m(ny-2))*xsol(i,ny,k))/(ggm(ny-2)+u3m(ny-2))
do j=ny-3,1,-1
xsol(i,j,k)=(xsol(i,j,k)-hhm(j)*xsol(i,j+1,k)-ssm(j)*xsol(i,j+2,k) &
-rrm(j)*xsol(i,j+3,k) &
-u3m(j)*xsol(i,ny-2,k) &
-u2m(j)*xsol(i,ny-1,k) &
-u1m(j)*xsol(i,ny,k) )/ggm(j)
enddo
enddo
enddo
end subroutine septinv_0
!
end module matinv
!********************************************************************
!
subroutine inttimp (ux1,uy1,uz1,gx,gy,gz,hx,hy,hz,ta1,tb1,tc1,px1,py1,pz1,&
td1,te1,tf1,ux2,uy2,uz2,ta2,tb2,tc2,td2,te2,tf2)
!
!********************************************************************
USE param
USE variables
USE decomp_2d
use derivY
use matinv
implicit none
integer :: ijk,nxyz,i,j,k,code
!real(mytype) :: xcst,x,z,r,liss ! pour VERIF inversion matrice, modification module param
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: ux1,uy1,uz1
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: px1,py1,pz1
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: gx,gy,gz
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: hx,hy,hz
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: ta1,tb1,tc1
real(mytype),dimension(xsize(1),xsize(2),xsize(3)) :: td1,te1,tf1
real(mytype),dimension(ysize(1),ysize(2),ysize(3)) :: ux2,uy2,uz2
real(mytype),dimension(ysize(1),ysize(2),ysize(3)) :: ta2,tb2,tc2
real(mytype),dimension(ysize(1),ysize(2),ysize(3)) :: td2,te2,tf2,di2
real(mytype) :: x, y, z
td1=0.;te1=0.;tf1=0.
ta2=0.;tb2=0.;tc2=0.;td2=0.;te2=0.;tf2=0.
ux2=0.;uy2=0.;uz2=0.
nxyz=xsize(1)*xsize(2)*xsize(3)
if ((nscheme.eq.2).or.(nscheme.eq.3)) then
if (nrank.eq.0) print *,'RK scheme not ready, abort computation'
call decomp_2d_finalize
CALL MPI_FINALIZE(code)
call exit(0)
endif
!!!!!!!!!!!!!
!! CN2+AB2 !!
!!!!!!!!!!!!!
if (nscheme.eq.1) then
if ((itime.eq.1).and.(ilit.eq.0)) then
!START WITH EXPLICIT EULER + IMPLICIT CN SCHEMES
do k=1,xsize(3)
do j=1,xsize(2)
do i=1,xsize(1)
!uhat
td1(i,j,k)= gdt(itr)*ta1(i,j,k)
te1(i,j,k)= gdt(itr)*tb1(i,j,k)
tf1(i,j,k)= gdt(itr)*tc1(i,j,k)
!save (N+Lxz)(n-1)
gx(i,j,k)=ta1(i,j,k)
gy(i,j,k)=tb1(i,j,k)
gz(i,j,k)=tc1(i,j,k)
enddo
enddo
enddo
else !CONTINUE WITH EXPLICIT AB2 + IMPLICIT CN SCHEMES
do k=1,xsize(3)
do j=1,xsize(2)
do i=1,xsize(1)
!uhat
td1(i,j,k)= adt(itr)*ta1(i,j,k)+bdt(itr)*gx(i,j,k)-px1(i,j,k)
te1(i,j,k)= adt(itr)*tb1(i,j,k)+bdt(itr)*gy(i,j,k)-py1(i,j,k)
tf1(i,j,k)= adt(itr)*tc1(i,j,k)+bdt(itr)*gz(i,j,k)-pz1(i,j,k)
!save (N+Lxz)(n-1)
gx(i,j,k)=ta1(i,j,k)
gy(i,j,k)=tb1(i,j,k)
gz(i,j,k)=tc1(i,j,k)
enddo
enddo
enddo
endif
endif
!!!!!!!!!!!!!!!
!!! CN2+AB3 !!!
!!!!!!!!!!!!!!!
if (nscheme==4) then
if ((itime.eq.1).and.(ilit.eq.0)) then
if (nrank==0) print *,'start AB3 with Euler',itime
!START WITH EXPLICIT EULER + IMPLICIT CN SCHEMES
do k=1,xsize(3)
do j=1,xsize(2)
do i=1,xsize(1)
!uhat
td1(i,j,k)= dt*ta1(i,j,k)
te1(i,j,k)= dt*tb1(i,j,k)
tf1(i,j,k)= dt*tc1(i,j,k)
!save (N+Lxz)(n-1)
gx(i,j,k)=ta1(i,j,k)
gy(i,j,k)=tb1(i,j,k)
gz(i,j,k)=tc1(i,j,k)
enddo
enddo
enddo
else if ((itime.eq.2).and.(ilit.eq.0)) then
if (nrank==0) print *,'then with AB2',itime
!THEN AB2 + IMPLICIT CN SCHEMES
do k=1,xsize(3)
do j=1,xsize(2)
do i=1,xsize(1)
!uhat
td1(i,j,k)= 1.5*dt*ta1(i,j,k)-0.5*dt*gx(i,j,k)-px1(i,j,k)
te1(i,j,k)= 1.5*dt*tb1(i,j,k)-0.5*dt*gy(i,j,k)-py1(i,j,k)
tf1(i,j,k)= 1.5*dt*tc1(i,j,k)-0.5*dt*gz(i,j,k)-pz1(i,j,k)
!save (N+Lxz)(n-1)&(n-2)
hx(i,j,k)=gx(i,j,k)
hy(i,j,k)=gy(i,j,k)
hz(i,j,k)=gz(i,j,k)
gx(i,j,k)=ta1(i,j,k)
gy(i,j,k)=tb1(i,j,k)
gz(i,j,k)=tc1(i,j,k)
enddo
enddo
enddo
else !FINALLY EXPLICIT AB3 + IMPLICIT CN SCHEMES
do k=1,xsize(3)
do j=1,xsize(2)
do i=1,xsize(1)
!uhat
td1(i,j,k)= adt(itr)*ta1(i,j,k)+bdt(itr)*gx(i,j,k) &
+cdt(itr)*hx(i,j,k)-px1(i,j,k)
te1(i,j,k)= adt(itr)*tb1(i,j,k)+bdt(itr)*gy(i,j,k) &
+cdt(itr)*hy(i,j,k)-py1(i,j,k)
tf1(i,j,k)= adt(itr)*tc1(i,j,k)+bdt(itr)*gz(i,j,k) &
+cdt(itr)*hz(i,j,k)-pz1(i,j,k)
!save (N+Lxz)(n-1)
hx(i,j,k)=gx(i,j,k)
hy(i,j,k)=gy(i,j,k)
hz(i,j,k)=gz(i,j,k)
gx(i,j,k)=ta1(i,j,k)
gy(i,j,k)=tb1(i,j,k)
gz(i,j,k)=tc1(i,j,k)
enddo
enddo
enddo
endif
endif
!Y-PENCIL FOR MATRIX INVERSION
call transpose_x_to_y(ux1,ux2)
call transpose_x_to_y(uy1,uy2)
call transpose_x_to_y(uz1,uz2)
call transpose_x_to_y(td1,ta2)
call transpose_x_to_y(te1,tb2)
call transpose_x_to_y(tf1,tc2)
!ta2: A.uhat
!td2:(A+xcstB).un
if (ncly.eq.0) then
call multmatrix7(td2,ta2,ux2,0)
call multmatrix7(te2,tb2,uy2,0)
call multmatrix7(tf2,tc2,uz2,0)
elseif (ncly.eq.1) then
call multmatrix7(td2,ta2,ux2,1)
call multmatrix7(te2,tb2,uy2,0)
call multmatrix7(tf2,tc2,uz2,1)
elseif (ncly.eq.2) then
call multmatrix7(td2,ta2,ux2,0)
call multmatrix7(te2,tb2,uy2,0)
call multmatrix7(tf2,tc2,uz2,0)
endif
!SECOND MEMBRE COMPLET BBB=A uhat+(A+xcst.B)u^n
!in ta2,tb2,tc2
ta2(:,:,:)=td2(:,:,:)+ta2(:,:,:)
tb2(:,:,:)=te2(:,:,:)+tb2(:,:,:)
tc2(:,:,:)=tf2(:,:,:)+tc2(:,:,:)
! CL Burgraff
if (itype.eq.7) then
do k=1,ysize(3)
z=(k-1+ystart(3)-1)*dz
j=ysize(2)
y=(j-1+ystart(2)-1)*dy
do i=1,ysize(1)
x=(i-1+ystart(1)-1)*dx
ta2(i,ysize(2),k)= 8.*(x**4-2.*x**3+x**2)*(4.*y**3-2.*y)
enddo
enddo
endif
!
!Inversion systeme lineaire Mx=b: (A-xcst.B)u^n+1=uhat+(A+xcst.B)u^n
ux2=0.; uy2=0.; uz2=0.;
if (ncly.eq.0) then
call septinv(ux2,ta2,ggm0,hhm0,ssm0,rrm0,vvm0,wwm0,zzm0,l1m,l2m,l3m,u1m,u2m,u3m,ysize(1),ysize(2),ysize(3))
call septinv(uy2,tb2,ggm0,hhm0,ssm0,rrm0,vvm0,wwm0,zzm0,l1m,l2m,l3m,u1m,u2m,u3m,ysize(1),ysize(2),ysize(3))
call septinv(uz2,tc2,ggm0,hhm0,ssm0,rrm0,vvm0,wwm0,zzm0,l1m,l2m,l3m,u1m,u2m,u3m,ysize(1),ysize(2),ysize(3))
elseif (ncly.eq.1) then
call septinv(ux2,ta2,ggm11,hhm11,ssm11,rrm11,vvm11,wwm11,zzm11,ysize(1),ysize(2),ysize(3))
call septinv(uy2,tb2,ggm10,hhm10,ssm10,rrm10,vvm10,wwm10,zzm10,ysize(1),ysize(2),ysize(3))
call septinv(uz2,tc2,ggm11,hhm11,ssm11,rrm11,vvm11,wwm11,zzm11,ysize(1),ysize(2),ysize(3))
elseif (ncly.eq.2) then
call septinv(ux2,ta2,ggm,hhm,ssm,rrm,vvm,wwm,zzm,ysize(1),ysize(2),ysize(3))
call septinv(uy2,tb2,ggm,hhm,ssm,rrm,vvm,wwm,zzm,ysize(1),ysize(2),ysize(3))
call septinv(uz2,tc2,ggm,hhm,ssm,rrm,vvm,wwm,zzm,ysize(1),ysize(2),ysize(3))
endif
call transpose_y_to_x(ux2,ux1)
call transpose_y_to_x(uy2,uy1)
call transpose_y_to_x(uz2,uz1)
! IF ab2 OR ab3
if ((nscheme.eq.1).or.(nscheme.eq.4)) then
! IF NOT (first time step with no restart)
if ( (ilit.eq.1).or.(itime.gt.1) ) then
ux1(:,:,:)=ux1(:,:,:)+px1(:,:,:)
uy1(:,:,:)=uy1(:,:,:)+py1(:,:,:)
uz1(:,:,:)=uz1(:,:,:)+pz1(:,:,:)
endif
endif
return
end subroutine inttimp
!********************************************************************
!PREMULT FOR INTTIMP WITH SEPTADIAG
subroutine multmatrix7(td2,ta2,ux2,npaire)
!
!********************************************************************
USE param
USE variables
USE derivY
USE decomp_2d
implicit none
integer :: npaire
integer :: i,j,k,code
!real(mytype) :: xcst ! modification module param
real(mytype),dimension(ysize(1),ysize(2),ysize(3)), intent(inout) :: ux2
real(mytype),dimension(ysize(1),ysize(2),ysize(3)), intent(inout) :: td2,ta2
real(mytype),dimension(ysize(1),ysize(2),ysize(3)) :: di2
!xcst= xnu*gdt(itr)*0.5
!A.uhat
if (istret.ne.0) then
do j=1,ysize(2)
ta2(:,j,:)=ta2(:,j,:)/pp2y(j)
enddo
endif
if (ncly.eq.0) then
td2(:,1,:) = alsajy*ta2(:,2,:) + ta2(:,1,:) + alsajy*ta2(:,ysize(2),:)
do j=2,ysize(2)-1
td2(:,j,:) = alsajy*ta2(:,j-1,:) + ta2(:,j,:) + alsajy*ta2(:,j+1,:)
enddo
td2(:,ysize(2),:) = alsajy*ta2(:,ysize(2)-1,:) + ta2(:,ysize(2),:) + alsajy*ta2(:,1,:)
ta2=td2
elseif (ncly.eq.1) then
if (npaire.eq.0) then
td2(:,1,:) = ta2(:,1,:)
else
td2(:,1,:) = 2.*alsajy*ta2(:,2,:) + ta2(:,1,:)
endif
do j=2,ysize(2)-1
td2(:,j,:) = alsajy*ta2(:,j-1,:) + ta2(:,j,:) + alsajy*ta2(:,j+1,:)
enddo
if (npaire.eq.0) then
td2(:,ysize(2),:) = ta2(:,ysize(2),:)
else
td2(:,ysize(2),:) = 2.*alsajy*ta2(:,ysize(2)-1,:) + ta2(:,ysize(2),:)
endif
ta2=td2
elseif (ncly.eq.2) then
td2(:,1,:) = 0.
td2(:,2,:) = alsa2y*ta2(:,1,:) + ta2(:,2,:) + alsa2y*ta2(:,3,:)
td2(:,3,:) = alsa3y*ta2(:,2,:) + ta2(:,3,:) + alsa3y*ta2(:,4,:)
do j=4,ysize(2)-3
td2(:,j,:) = alsajy*ta2(:,j-1,:) + ta2(:,j,:) + alsajy*ta2(:,j+1,:)
enddo
td2(:,ysize(2)-2,:) = alsaty*ta2(:,ysize(2)-3,:) + ta2(:,ysize(2)-2,:) + alsaty*ta2(:,ysize(2)-1,:)
td2(:,ysize(2)-1,:) = alsamy*ta2(:,ysize(2)-2,:) + ta2(:,ysize(2)-1,:) + alsamy*ta2(:,ysize(2),:)
td2(:,ysize(2),:) = 0.
ta2=td2
endif
!(A+nu*dt.B).un
if (ncly.eq.0) then
call deryy(td2,ux2,di2,sy,sfyp,ssyp,swyp,ysize(1),ysize(2),ysize(3),1)
elseif (ncly.eq.1) then
if (npaire==0) then
call deryy(td2,ux2,di2,sy,sfy,ssy,swy,ysize(1),ysize(2),ysize(3),0)
else
call deryy(td2,ux2,di2,sy,sfyp,ssyp,swyp,ysize(1),ysize(2),ysize(3),1)
endif
elseif (ncly.eq.2) then
call deryy(td2,ux2,di2,sy,sfyp,ssyp,swyp,ysize(1),ysize(2),ysize(3),1)
endif
if (istret.ne.0) then
do j=1,ysize(2)
ux2(:,j,:)=ux2(:,j,:)/pp2y(j)
enddo
endif
if (ncly.eq.0) then
td2(:,1,:) = alsajy*ux2(:,2,:) + ux2(:,1,:) + alsajy*ux2(:,ysize(2),:) &
+ xcst*td2(:,1,:)
do j=2,ysize(2)-1
td2(:,j,:) = alsajy*ux2(:,j-1,:) + ux2(:,j,:) + alsajy*ux2(:,j+1,:) &
+ xcst*td2(:,j,:)
enddo
td2(:,ysize(2),:) = alsajy*ux2(:,ysize(2)-1,:) + ux2(:,ysize(2),:) + alsajy*ux2(:,1,:) &
+ xcst*td2(:,ysize(2),:)
elseif (ncly.eq.1) then
if (npaire.eq.0) then
td2(:,1,:) = ux2(:,1,:) + xcst*td2(:,1,:)
else
td2(:,1,:) = 2.*alsajy*ux2(:,2,:) + ux2(:,1,:) &
+ xcst*td2(:,1,:)
endif
do j=2,ysize(2)-1
td2(:,j,:) = alsajy*ux2(:,j-1,:) + ux2(:,j,:) + alsajy*ux2(:,j+1,:) &
+ xcst*td2(:,j,:)
enddo
if (npaire.eq.0) then
td2(:,ysize(2),:) = ux2(:,ysize(2),:) + xcst*td2(:,ysize(2),:)
else
td2(:,ysize(2),:) = 2.*alsajy*ux2(:,ysize(2)-1,:) + ux2(:,ysize(2),:) &
+ xcst*td2(:,ysize(2),:)
endif
elseif (ncly.eq.2) then
td2(:,1,:) = 0.
td2(:,2,:) = alsa2y*ux2(:,1,:) + ux2(:,2,:) + alsa2y*ux2(:,3,:) &
+ xcst*td2(:,2,:)
td2(:,3,:) = alsa3y*ux2(:,2,:) + ux2(:,3,:) + alsa3y*ux2(:,4,:) &
+ xcst*td2(:,3,:)
do j=4,ysize(2)-3
td2(:,j,:) = alsajy*ux2(:,j-1,:) + ux2(:,j,:) + alsajy*ux2(:,j+1,:) &
+ xcst*td2(:,j,:)
enddo
td2(:,ysize(2)-2,:) = alsaty*ux2(:,ysize(2)-3,:) + ux2(:,ysize(2)-2,:) + alsaty*ux2(:,ysize(2)-1,:) &
+ xcst*td2(:,ysize(2)-2,:)
td2(:,ysize(2)-1,:) = alsamy*ux2(:,ysize(2)-2,:) + ux2(:,ysize(2)-1,:) + alsamy*ux2(:,ysize(2),:) &
+ xcst*td2(:,ysize(2)-1,:)
td2(:,ysize(2),:) = 0.
endif
end subroutine multmatrix7
!********************************************************************
!
subroutine implicit_schemes()
!
!********************************************************************
USE param
USE derivY
USE variables
USE var
use ludecomp
implicit none
integer :: i,j,k
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!! MATRICE M2 TIME IMPLICIT !!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!
!FOR VELOCITY !!!!!!!
!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!
xcst = xnu*dt*0.5
!!!!!!!!!!!!!!!!!!!!!!
!CAS SEPTADIAGONALE !!
!!!!!!!!!!!!!!!!!!!!!!
!!! NCL = 2, dirichlet imposé, fonction nulle à la paroi
!
!DIAG
aam(1 )=as1y
aam(ny )=asny
aam(2 )=-2.*as2y
aam(ny-1 )=-2.*asmy
aam(3 )=-2.*(as3y+bs3y)
aam(ny-2 )=-2.*(asty+bsty)
aam(4:ny-3)=-2.*(asjy+bsjy+csjy)
if (istret==0) then
aam = 1.-xcst*aam
else
aam = 1./pp2y -xcst*aam
endif
!CL sur aam
aam(1 )=1.
aam(ny)=1.
!
!DIAG SUP 1
bbm(1 )=bs1y
bbm(ny )=bsny
bbm(2 )=as2y
bbm(ny-1 )=asmy
bbm(3 )=as3y
bbm(ny-2 )=asty
bbm(4:ny-3)=asjy
bbm = -xcst*bbm
if (istret==0) then
bbm(2 )=bbm(2 )+alsa2y
bbm(ny-1 )=bbm(ny-1 )+alsamy
bbm(3 )=bbm(3 )+alsa3y
bbm(ny-2 )=bbm(ny-2 )+alsaty
bbm(4:ny-3)=bbm(4:ny-3)+alsajy
else
bbm(2 )=bbm(2 )+alsa2y/pp2y(3)
bbm(ny-1 )=bbm(ny-1 )+alsamy/pp2y(ny)
bbm(3 )=bbm(3 )+alsa3y/pp2y(4)
bbm(ny-2 )=bbm(ny-2 )+alsaty/pp2y(ny-1)
bbm(4:ny-3)=bbm(4:ny-3)+alsajy/pp2y(5:ny-2)
endif
!CL sur bbm
bbm(1 )=0.
bbm(ny)=0.
!
!DIAG SUP 2
ccm(1 )=cs1y
ccm(ny )=csny
ccm(2 )=0.
ccm(ny-1 )=0.
ccm(3 )=bs3y
ccm(ny-2 )=bsty
ccm(4:ny-3)=bsjy
ccm = -xcst*ccm
!CL sur ccm
ccm(1 )=0.
ccm(ny)=0.
!
!DIAG SUP 3
rrm(1 )=ds1y
rrm(ny )=dsny
rrm(2 )=0.
rrm(ny-1 )=0.
rrm(3 )=0.
rrm(ny-2 )=0.
rrm(4:ny-3)=csjy
rrm = -xcst*rrm
!CL sur rrm
rrm(1 )=0.
rrm(ny)=0.
!
!DIAG INF 1
if (istret==0) then
ddm=bbm
else
ddm(1 )=bs1y
ddm(ny )=bsny
ddm(2 )=as2y
ddm(ny-1 )=asmy
ddm(3 )=as3y
ddm(ny-2 )=asty
ddm(4:ny-3)=asjy
ddm = -xcst*ddm
ddm(2 )=ddm(2 )+alsa2y/pp2y(1)
ddm(ny-1 )=ddm(ny-1 )+alsamy/pp2y(ny-2)
ddm(3 )=ddm(3 )+alsa3y/pp2y(2)
ddm(ny-2 )=ddm(ny-2 )+alsaty/pp2y(ny-3)
ddm(4:ny-3)=ddm(4:ny-3)+alsajy/pp2y(3:ny-4)
!CL sur ddm
ddm(1 )=0.
ddm(ny)=0.
endif
!
!DIAG INF 2
eem=ccm
!
!DIAG INF 3
qqm=rrm
!!! NCL = 1, npaire=0, dirichlet imposé, fonction impaire
!
! DIAG
aam10(1 )=0.
aam10(ny )=0.
aam10(2 )=-2.*asjy-3.*bsjy-2.*csjy
aam10(ny-1 )=aam10(2)
aam10(3:ny-2)=-2.*(asjy+bsjy+csjy)
if (istret==0) then
aam10 = 1. - xcst*aam10
else
aam10 = 1./pp2y - xcst*aam10
endif
!
!DIAG SUP 1
bbm10(1 )=0.
bbm10(ny )=0.
bbm10(2 )=asjy-csjy
bbm10(ny-1 )=asjy
bbm10(3 )=asjy
bbm10(ny-2 )=asjy-csjy
bbm10(4:ny-3)=asjy
if (istret==0) then
bbm10 = alsajy - xcst*bbm10
else
bbm10(2:ny-1) = alsajy/pp2y(3:ny) - xcst*bbm10(2:ny-1)
endif
!CL sur bbm10
bbm10(1 )=0.
bbm10(ny)=0.
!
!DIAG SUP 2
ccm10(1 )=0.
ccm10(ny )=0.
ccm10(2 )=bsjy
ccm10(ny-1 )=0.
ccm10(3 )=bsjy
ccm10(ny-2 )=bsjy
ccm10(4:ny-3)=bsjy
ccm10 = -xcst*ccm10
!
!DIAG SUP 3
rrm10(1 )=0.
rrm10(ny )=0.
rrm10(2 )=csjy
rrm10(ny-1 )=0.
rrm10(3 )=csjy
rrm10(ny-2 )=0.
rrm10(4:ny-3)=csjy
rrm10 = -xcst*rrm10
!
!DIAG INF 1
ddm10(1 )=0.
ddm10(ny )=0.
ddm10(2 )=asjy
ddm10(ny-1 )=asjy-csjy
ddm10(3 )=asjy-csjy
ddm10(ny-2 )=asjy
ddm10(4:ny-3)=asjy
if (istret==0) then
ddm10 = alsajy - xcst*ddm10
else
ddm10(2:ny-1) = alsajy/pp2y(1:ny-2) - xcst*ddm10(2:ny-1)
endif
!CL sur ddm10
ddm10(1 )=0.
ddm10(ny)=0.
!
!DIAG INF 2
eem10(1 )=0.
eem10(ny )=0.
eem10(2 )=0.
eem10(ny-1 )=bsjy
eem10(3 )=bsjy
eem10(ny-2 )=bsjy
eem10(4:ny-3)=bsjy
eem10 = -xcst*eem10
!
!DIAG INF 3
qqm10(1 )=0.
qqm10(ny )=0.
qqm10(2 )=0.
qqm10(ny-1 )=csjy
qqm10(3 )=0.
qqm10(ny-2 )=csjy
qqm10(4:ny-3)=csjy
qqm10 = -xcst*qqm10
!!! NCL = 1, npaire=1, neumann imposé, fonction paire
!
! DIAG
aam11(1 )=-2.*(asjy+bsjy+csjy)
aam11(ny )=aam11(1)
aam11(2 )=-2.*asjy-bsjy-2.*csjy
aam11(ny-1 )=aam11(2)
aam11(3:ny-2)=-2.*(asjy+bsjy+csjy)
if (istret==0) then
aam11 = 1. - xcst*aam11
else
aam11 = 1./pp2y - xcst*aam11
endif
!
!DIAG SUP 1
bbm11(1 )=2.*asjy
bbm11(ny )=0.
bbm11(2 )=asjy+csjy
bbm11(ny-1 )=asjy
bbm11(3 )=asjy
bbm11(ny-2 )=asjy+csjy
bbm11(4:ny-3)=asjy
if (istret==0) then
bbm11 = alsajy - xcst*bbm11
else
bbm11(1:ny-1) = alsajy/pp2y(2:ny) - xcst*bbm11(1:ny-1)
endif
!CL sur bbm11
if (istret.eq.0) then
bbm11(1 )=bbm11(1)+alsajy
else
bbm11(1 )=bbm11(1)+alsajy/pp2y(2)
endif
bbm11(ny)=0.
!
!DIAG SUP 2
ccm11(1 )=2.*bsjy
ccm11(ny )=0.
ccm11(2 )=bsjy
ccm11(ny-1 )=0.
ccm11(3 )=bsjy
ccm11(ny-2 )=bsjy
ccm11(4:ny-3)=bsjy
ccm11 = -xcst*ccm11
!
!DIAG SUP 3
rrm11(1 )=2.*csjy
rrm11(ny )=0.
rrm11(2 )=csjy
rrm11(ny-1 )=0.
rrm11(3 )=csjy
rrm11(ny-2 )=0.
rrm11(4:ny-3)=csjy
rrm11 = -xcst*rrm11
!
!DIAG INF 1
ddm11(1 )=0.
ddm11(ny )=2.*asjy
ddm11(2 )=asjy
ddm11(ny-1 )=asjy+csjy
ddm11(3 )=asjy+csjy
ddm11(ny-2 )=asjy
ddm11(4:ny-3)=asjy
if (istret==0) then