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implicit.f90
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#ifdef IMPLICIT
!#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
real(mytype), dimension(ny,ny) :: mata, matl, matu, prod
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
#ifdef DEBUG
if (.false.) then
print *,'aam,bbm,ccm,ddm,eem,qqm,rrm'
do k=1,ny
print *,aam(k),bbm(k),ccm(k),ddm(k),eem(k),qqm(k),rrm(k)
enddo
print *,'ggm,hhm,ssm,rrm'
do k=1,ny
print *,ggm(k),hhm(k),ssm(k),rrm(k)
enddo
print *,'vvm,wwm,zzm'
do k=1,ny
print *,vvm(k),wwm(k),zzm(k)
enddo
mata=0.
matl=0.
matu=0.
j=1
mata(j,ny-2)=qqm(j)
mata(j,ny-1)=eem(j)
mata(j,ny )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
j=2
mata(j,ny-1)=qqm(j)
mata(j,ny )=eem(j)
mata(j,j-1 )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
j=3
mata(j,ny )=qqm(j)
mata(j,j-2 )=eem(j)
mata(j,j-1 )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
do j=4,ny-3
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,j+2)=ccm(j)
mata(j,j+3)=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
enddo
j=ny-2
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,j+2)=ccm(j)
mata(j,1 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
j=ny-1
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,1 )=ccm(j)
mata(j,2 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
j=ny
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,1 )=bbm(j)
mata(j,2 )=ccm(j)
mata(j,3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
print *,'A = '
do j=1,ny
print *,mata(j,:)
enddo
print *,'L = '
do j=1,ny
print *,matl(j,:)
enddo
print *,'U = '
do j=1,ny
print *,matu(j,:)
enddo
do i=1,ny
do j=1,ny
prod(i,j)=0.
do k=1,ny
prod(i,j)=prod(i,j)+matl(i,k)*matu(k,j)
enddo
enddo
enddo
print *,'A-L*U', maxval(abs(mata-prod)), maxloc(abs(mata-prod))
do j=1,ny
print *,mata(j,:)-prod(j,:)
enddo
endif
#endif
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
real(mytype), dimension(ny,ny) :: mata, matl, matu, prod
! 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
#ifdef DEBUG
if (.false.) then
print *,'aam,bbm,ccm,ddm,eem,qqm,rrm'
do k=1,ny
print *,aam(k),bbm(k),ccm(k),ddm(k),eem(k),qqm(k),rrm(k)
enddo
print *,'ggm,hhm,ssm,rrm,u1m,u2m,u3m'
do k=1,ny
print *,ggm(k),hhm(k),ssm(k),rrm(k),u1m(k),u2m(k),u3m(k)
enddo
print *,'vvm,wwm,zzm,l1m,l2m,l3m'
do k=1,ny
print *,vvm(k),wwm(k),zzm(k),l1m(k),l2m(k),l3m(k)
enddo
mata=0.
matl=0.
matu=0.
j=1
mata(j,ny-2)=qqm(j)
mata(j,ny-1)=eem(j)
mata(j,ny )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
j=2
mata(j,ny-1)=qqm(j)
mata(j,ny )=eem(j)
mata(j,j-1 )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
j=3
mata(j,ny )=qqm(j)
mata(j,j-2 )=eem(j)
mata(j,j-1 )=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1 )=bbm(j)
mata(j,j+2 )=ccm(j)
mata(j,j+3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
do j=4,ny-3
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,j+2)=ccm(j)
mata(j,j+3)=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
matu(j,j+3)=rrm(j)
enddo
j=ny-2
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,j+2)=ccm(j)
mata(j,1 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
matu(j,j+2)=ssm(j)
j=ny-1
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,j+1)=bbm(j)
mata(j,1 )=ccm(j)
mata(j,2 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
matu(j,j+1)=hhm(j)
j=ny
mata(j,j-3)=qqm(j)
mata(j,j-2)=eem(j)
mata(j,j-1)=ddm(j)
mata(j,j )=aam(j)
mata(j,1 )=bbm(j)
mata(j,2 )=ccm(j)
mata(j,3 )=rrm(j)
matl(j,j)=1.
matl(j,j-1)=zzm(j)
matl(j,j-2)=wwm(j)
matl(j,j-3)=vvm(j)
matu(j,j)=ggm(j)
do j=1,ny
matu(j,ny)=matu(j,ny)+u1m(j)
enddo
do j=1,ny-1
matu(j,ny-1)=matu(j,ny-1)+u2m(j)
enddo
do j=1,ny-2
matu(j,ny-2)=matu(j,ny-2)+u3m(j)
enddo
do j=1,ny-1
matl(ny,j)=matl(ny,j)+l1m(j)
enddo
do j=1,ny-2
matl(ny-1,j)=matl(ny-1,j)+l2m(j)
enddo
do j=1,ny-3
matl(ny-2,j)=matl(ny-2,j)+l3m(j)
enddo
print *,'A = '
do j=1,ny
print *,mata(j,:)
enddo
print *,'L = '
do j=1,ny
print *,matl(j,:)
enddo
print *,'U = '
do j=1,ny
print *,matu(j,:)
enddo
do i=1,ny
do j=1,ny
prod(i,j)=0.
do k=1,ny
prod(i,j)=prod(i,j)+matl(i,k)*matu(k,j)
enddo
enddo
enddo
print *,'A-L*U', maxval(abs(mata-prod)), maxloc(abs(mata-prod))
do j=1,ny
print *,mata(j,:)-prod(j,:)
enddo
endif
#endif
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),dimension(ysize(1),ysize(3)) :: bc1,bc2,bc3
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)
!!!!!!!!!!!!!
!! 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==2) 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)
bc1(:,:)=ux2(:,ny-1,:)
bc2(:,:)=uy2(:,ny-1,:)
bc3(:,:)=uz2(:,ny-1,:)
!ta2: A.uhat
!td2:(A+xcstB).un
if (ncly.eq.0) then
call multmatrix7(td2,ta2,ux2)
call multmatrix7(te2,tb2,uy2)
call multmatrix7(tf2,tc2,uz2)
elseif (ncly.eq.1) then
elseif (ncly.eq.2) then
call multmatrix7(td2,ta2,ux2)
call multmatrix7(te2,tb2,uy2)
call multmatrix7(tf2,tc2,uz2)
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
!
! CONDITIONS AUX LIMITES
ta2(:,ny,:)=bc1(:,:)
tb2(:,ny,:)=bc2(:,:)
tc2(:,ny,:)=bc3(:,:)
!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)
#ifdef DEBUG
if (.false.) then
!VERIFICATION INVERSION CORRECTE, CAS NCLY=1
!Mx-b=0 ?
! ux
if (nrank.eq.0) print *,'Check matrix inversion for ux - NCLY=1'
call deryy(td2,ux2,di2,sy,sfyp,ssyp,swyp,ysize(1),ysize(2),ysize(3),1)
td2(:,1,:)=ux2(:,1,:)+alsajy*(2.*ux2(:,2,:)) - xcst*td2(:,1,:)*pp2y(1)
do j=2,ysize(2)-1
td2(:,j,:)=alsajy*ux2(:,j-1,:) + ux2(:,j,:) + alsajy*ux2(:,j+1,:) - xcst*td2(:,j,:)*pp2y(j)
enddo
td2(:,ysize(2),:)=ux2(:,ysize(2),:)+alsajy*(2.*ux2(:,ysize(2)-1,:)) - xcst*td2(:,ysize(2),:)*pp2y(ysize(2))
td2=td2-ta2
call transpose_y_to_x(td2,td1)
call test_scalar_min_max(td1)
! uy
if (nrank.eq.0) print *,'Check matrix inversion for uy - NCLY=1'
call deryy(td2,uy2,di2,sy,sfy,ssy,swy,ysize(1),ysize(2),ysize(3),0)
td2(:,1,:)=uy2(:,1,:)+0.*alsajy*(uy2(:,2,:)+uy2(:,ysize(2),:)) - xcst*td2(:,j,:)*pp2y(1)
do j=2,ysize(2)-1
td2(:,j,:)=alsajy*uy2(:,j-1,:) + uy2(:,j,:) + alsajy*uy2(:,j+1,:) - xcst*td2(:,j,:)*pp2y(j)
enddo
td2(:,ysize(2),:)=uy2(:,ysize(2),:)+0.*alsajy*(uy2(:,ysize(2)-1,:)+uy2(:,1,:)) - xcst*td2(:,ysize(2),:)*pp2y(ysize(2))
td2=td2-tb2
call transpose_y_to_x(td2,td1)
call test_scalar_min_max(td1)
! uz
if (nrank.eq.0) print *,'Check matrix inversion for uz - NCLY=1'
call deryy(td2,uz2,di2,sy,sfyp,ssyp,swyp,ysize(1),ysize(2),ysize(3),1)
td2(:,1,:)=uz2(:,1,:)+alsajy*(2.*uz2(:,2,:)) - xcst*td2(:,1,:)*pp2y(1)
do j=2,ysize(2)-1
td2(:,j,:)=alsajy*uz2(:,j-1,:) + uz2(:,j,:) + alsajy*uz2(:,j+1,:) - xcst*td2(:,j,:)*pp2y(j)
enddo
td2(:,ysize(2),:)=uz2(:,ysize(2),:)+alsajy*(2.*uz2(:,ysize(2)-1,:)) - xcst*td2(:,ysize(2),:)*pp2y(ysize(2))
td2=td2-tc2
call transpose_y_to_x(td2,td1)
call test_scalar_min_max(td1)
endif
#endif
! IF ab2 OR ab3
if ((nscheme.eq.1).or.(nscheme.eq.2)) 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)
!
!********************************************************************
USE param
USE variables
USE derivY
USE decomp_2d
implicit none
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 (.true.) then
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
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
else
do k=1,ysize(3)
do i=1,ysize(1)
td2(i,1,k)=0.!
td2(i,2,k)=alsa2y*ta2(i,1,k)+ta2(i,2,k)+alsa2y*ta2(i,3,k)
td2(i,3,k)=alsa3y*ta2(i,2,k)+ta2(i,3,k)+alsa3y*ta2(i,4,k)
do j=4,ysize(2)-3
td2(i,j,k)=alsajy*ta2(i,j-1,k)+ta2(i,j,k)+alsajy*ta2(i,j+1,k)
enddo
td2(i,ysize(2)-2,k)=alsaty*ta2(i,ysize(2)-3,k)+ta2(i,ysize(2)-2,k)+alsaty*ta2(i,ysize(2)-1,k)
td2(i,ysize(2)-1,k)=alsamy*ta2(i,ysize(2)-2,k)+ta2(i,ysize(2)-1,k)+alsamy*ta2(i,ysize(2),k)
td2(i,ysize(2),k)=0.!
enddo
enddo
do k=1,ysize(3)
do j=1,ysize(2)
do i=1,ysize(1)
ta2(i,j,k)=td2(i,j,k)
enddo
enddo
enddo
endif
!(A+nu*dt.B).un
if (.true.) then
if (ncly.eq.0) then