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HC_rot.f90
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module HC_rot
use globalvar,only:ix,jx,kx,kapper,dx,dy,dz,dxc,dyc,dzc,gm,margin,ndim,&
flag_mhd,dt,dt_cnd,nt,hc_split,hc_sch,hc_max,x,y,z,sor_omega,total_iter,&
neighbor,mpi_siz,total_prc,my_rank,x,y,z,tiny,hc_type,flag_mpi,flag_bnd,&
safety_cnd,nsub_max,time,pr_lim,ro_lim,flag_cyl
use scheme_rot,only:cq2pv_hd,pv2cq_hd,cq2pv_mhd,pv2cq_mhd
use MPI_rot,only:mpi_double_interface
use boundary_rot,only:PIPbnd,bnd_energy
implicit none
include "mpif.h"
integer,save::n_hc
integer,save::is,ie,js,je,ks,ke
! integer,parameter::hc_split=1,hc_sch=2,hc_max=500
integer,parameter::hc_unit=82
integer,allocatable,save::di(:),dj(:),dk(:)
integer ierr,status(6)
double precision,parameter::error=1.0d-5,epsi=1.0d-5
contains
subroutine initialize_HC(flag_hc)
integer,intent(inout)::flag_hc
if(flag_hc.eq.0) return
total_iter=0
is=margin(1)+1;ie=ix-margin(1)
js=margin(2)+1;je=jx-margin(2)
ks=margin(3)+1;ke=kx-margin(3)
select case(ndim)
case(1)
n_hc=3
allocate(di(n_hc),dj(n_hc),dk(n_hc))
di=(/0,-1,1/)
dj=(/0,0,0/)
dk=(/0,0,0/)
case(2)
select case(hc_split)
case(1)
n_hc=5
allocate(di(n_hc),dj(n_hc),dk(n_hc))
di=(/0,-1,1,0,0/)
dj=(/0,0,0,-1,1/)
dk=(/0,0,0,0,0/)
case(2)
n_hc=9
allocate(di(n_hc),dj(n_hc),dk(n_hc))
di=(/0,-1, 1, 0,0,-1, 1,-1,1/)
dj=(/0, 0, 0,-1,1,-1,-1, 1,1/)
dk=(/0, 0, 0, 0,0, 0, 0, 0,0/)
end select
case(3)
select case(hc_split)
case(1)
n_hc=7
allocate(di(n_hc),dj(n_hc),dk(n_hc))
di=(/0,-1,1,0,0,0,0/)
dj=(/0,0,0,-1,1,0,0/)
dk=(/0,0,0,0,0,-1,1/)
case(2)
n_hc=19
allocate(di(n_hc),dj(n_hc),dk(n_hc))
di=(/0,-1,1,0,0,0,0,-1, 1,-1,1,-1, 1,-1,1, 0, 0, 0,0/)
dj=(/0,0,0,-1,1,0,0,-1,-1, 1,1, 0, 0, 0,0,-1, 1,-1,1/)
dk=(/0,0,0,0,0,-1,1, 0, 0, 0,0,-1,-1, 1,1,-1,-1, 1,1/)
end select
end select
end subroutine initialize_HC
subroutine HC(U,nvar,mhd)
integer,intent(in)::nvar,mhd
double precision,intent(inout)::U(ix,jx,kx,nvar)
double precision ro(ix,jx,kx),pr(ix,jx,kx),te(ix,jx,kx)
double precision vx(ix,jx,kx),vy(ix,jx,kx),vz(ix,jx,kx)
double precision bx(ix,jx,kx),by(ix,jx,kx),bz(ix,jx,kx)
double precision matrix(ix,jx,kx,n_hc),source(ix,jx,kx)
integer count
if(mhd.eq.1) then
call cq2pv_mhd(ro,vx,vy,vz,pr,bx,by,bz,U)
else
call cq2pv_hd(ro,vx,vy,vz,pr,U)
endif
te=gm*(pr/ro)
!set matrix and source term
if(total_prc.ge.2) then
call mpiBND(ro,2)
call mpiBND(te,2)
call mpiBND(bx,2)
call mpiBND(by,2)
call mpiBND(bz,2)
endif
if(flag_mhd.eq.1.and.ndim.ge.2) then
select case(hc_split)
case(1)
if(ndim.eq.1) then
! call set_matrix_source_MHD2D5(matrix,source,ro,te,bx,by,bz)
call set_matrix_source_1D(matrix,source,ro,te)
else if(ndim.eq.2) then
call set_matrix_source_MHD2D5(matrix,source,ro,te,bx,by,bz)
else
! call set_matrix_source_MHD3D7(matrix,source,ro,te,bx,by,bz)
endif
case(2)
if(ndim.eq.2) then
call set_matrix_source_MHD2D9(matrix,source,ro,te,bx,by,bz)
! call set_matrix_source_MHD2D9_limiter(matrix,source,ro,te,bx,by,bz)
else
! call set_matrix_source_MHD3D19(matrix,source,ro,te,bx,by,bz)
endif
end select
else
if(ndim.eq.1) then
call set_matrix_source_1D(matrix,source,ro,te)
endif
endif
! call test_matrix(matrix,source,te)
!set boundary condition of matrix
call set_matrix_boundary(matrix)
!iteration schemes
select case(hc_sch)
case(1)
call SOR(matrix,te,source,count)
case(2)
if(total_prc.le.1) then
call BiCGstab(matrix,te,source,count)
else
call BiCGstabMPI(matrix,te,source,count)
endif
end select
total_iter=total_iter+count
!back to conservative
pr=(te*ro)/gm
call pv2cq_mhd(ro,vx,vy,vz,pr,bx,by,bz,U)
end subroutine HC
subroutine SOR(matrix,te,source,count)
integer,intent(inout)::count
double precision,intent(in)::matrix(ix,jx,kx,n_hc)
double precision,intent(inout)::te(ix,jx,kx),source(ix,jx,kx)
double precision residual(ix,jx,kx)
integer i,j,k,n
double precision total_resi,total_source,tmp
residual(is:ie,js:je,ks:ke)=source(is:ie,js:je,ks:ke)
do n=1,n_hc
residual(is:ie,js:je,ks:ke)=residual(is:ie,js:je,ks:ke) &
-matrix(is:ie,js:je,ks:ke,n)* &
te(is+di(n):ie+di(n),js+dj(n):je+dj(n),ks+dk(n):ke:dk(n))
enddo
total_resi=sum(residual(is:ie,js:je,ks:ke)**2)
total_source=sum(source(is:ie,js:je,ks:ke)**2)
count=0
select case(hc_split)
case(1)
do while(sqrt(total_resi/total_source).gt.error.and.count.le.hc_max)
do k=ks,ke; do j=js,je;do i=is,ie
residual(i,j,k)=source(i,j,k)-(matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k))
te(i,j,k)=te(i,j,k)+sor_omega*residual(i,j,k)/matrix(i,j,k,1)
enddo;enddo;enddo
total_resi=sum(residual(is:ie,js:je,ks:ke)**2)
count=count+1
enddo
case(2)
do while(sqrt(total_resi/total_source).gt.error.and.count.le.hc_max)
do k=ks,ke; do j=js,je;do i=is,ie
residual(i,j,k)=source(i,j,k)-(matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k) &
+matrix(i,j,k,6)*te(i-1,j-1,k)+matrix(i,j,k,7)*te(i+1,j-1,k) &
+matrix(i,j,k,8)*te(i-1,j+1,k)+matrix(i,j,k,9)*te(i+1,j+1,k))
te(i,j,k)=te(i,j,k)+sor_omega*residual(i,j,k)/matrix(i,j,k,1)
enddo;enddo;enddo
total_resi=sum(residual(is:ie,js:je,ks:ke)**2)
count=count+1
enddo
end select
end subroutine SOR
subroutine BiCGstab(matrix,te,source,count)
integer,intent(inout)::count
double precision,intent(in)::matrix(ix,jx,kx,n_hc)
double precision,intent(inout)::te(ix,jx,kx),source(ix,jx,kx)
double precision residual(ix,jx,kx)
integer i,j,k,n
double precision total_resi,total_source,tmp
double precision alpha,alphau,alphad
double precision beta,betau,betad
double precision omega,omegau,omegad
double precision pk(ix,jx,kx),r0(ix,jx,kx),Apk(ix,jx,kx),tkp(ix,jx,kx)
double precision atk
! residual(is:ie,js:je,ks:ke)=source(is:ie,js:je,ks:ke)
residual=source
do n=1,n_hc
residual(is:ie,js:je,ks:ke)=residual(is:ie,js:je,ks:ke) &
-matrix(is:ie,js:je,ks:ke,n)* &
te(is+di(n):ie+di(n),js+dj(n):je+dj(n),ks+dk(n):ke:dk(n))
enddo
total_resi=sum(residual(is:ie,js:je,ks:ke)**2)
total_source=sum(source(is:ie,js:je,ks:ke)**2)
count=0
r0=residual
pk=r0
apk=0
! print *,"TOTAL_RESI",total_resi,total_source
! stop
select case(hc_split)
case(1)
do while(sqrt(total_resi/total_source).gt.error.and.count.le.hc_max)
alphau=0.0d0;alphad=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
apk(i,j,k)=matrix(i,j,k,1)*pk(i,j,k) &
+matrix(i,j,k,2)*pk(i-1,j,k)+matrix(i,j,k,3)*pk(i+1,j,k) &
+matrix(i,j,k,4)*pk(i,j-1,k)+matrix(i,j,k,5)*pk(i,j+1,k)
alphau=alphau+(residual(i,j,k)*r0(i,j,k))
alphad=alphad+(r0(i,j,k)*apk(i,j,k))
enddo;enddo;enddo
alpha=alphau/alphad
tkp=residual-alpha*apk
omegau=0.0d0;omegad=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
atk=matrix(i,j,k,1)*tkp(i,j,k) &
+matrix(i,j,k,2)*tkp(i-1,j,k)+matrix(i,j,k,3)*tkp(i+1,j,k) &
+matrix(i,j,k,4)*tkp(i,j-1,k)+matrix(i,j,k,5)*tkp(i,j+1,k)
omegau=omegau+tkp(i,j,k)*atk
omegad=omegad+atk*atk
enddo;enddo;enddo
omega=omegau/omegad
te=te+alpha*pk+omega*tkp
betau=0.0d0;betad=0.0d0;total_resi=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
residual(i,j,k)=source(i,j,k)-( &
matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k))
betau=betau+r0(i,j,k)*residual(i,j,k)
total_resi=total_resi+residual(i,j,k)*residual(i,j,k)
enddo;enddo;enddo
beta=betau/alphau*alpha/omega
pk=residual+beta*(pk-omega*apk)
count=count+1
enddo
case(2)
do while(sqrt(total_resi/total_source).gt.error.and.count.le.hc_max)
alphau=0.0d0;alphad=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
apk(i,j,k)=matrix(i,j,k,1)*pk(i,j,k) &
+matrix(i,j,k,2)*pk(i-1,j,k)+matrix(i,j,k,3)*pk(i+1,j,k) &
+matrix(i,j,k,4)*pk(i,j-1,k)+matrix(i,j,k,5)*pk(i,j+1,k) &
+matrix(i,j,k,6)*pk(i-1,j-1,k)+matrix(i,j,k,7)*pk(i+1,j-1,k) &
+matrix(i,j,k,8)*pk(i-1,j+1,k)+matrix(i,j,k,9)*pk(i+1,j+1,k)
alphau=alphau+(residual(i,j,k)*r0(i,j,k))
alphad=alphad+(r0(i,j,k)*apk(i,j,k))
enddo;
enddo;enddo
alpha=alphau/alphad
! print *,count,total_resi,total_source,alphau,alphad,alpha
tkp=residual-alpha*apk
omegau=0.0d0;omegad=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
atk=matrix(i,j,k,1)*tkp(i,j,k) &
+matrix(i,j,k,2)*tkp(i-1,j,k)+matrix(i,j,k,3)*tkp(i+1,j,k) &
+matrix(i,j,k,4)*tkp(i,j-1,k)+matrix(i,j,k,5)*tkp(i,j+1,k) &
+matrix(i,j,k,6)*tkp(i-1,j-1,k)+matrix(i,j,k,7)*tkp(i+1,j-1,k)&
+matrix(i,j,k,8)*tkp(i-1,j+1,k)+matrix(i,j,k,9)*tkp(i+1,j+1,k)
omegau=omegau+tkp(i,j,k)*atk
omegad=omegad+atk*atk
enddo;enddo;enddo
omega=omegau/omegad
te=te+alpha*pk+omega*tkp
betau=0.0d0;betad=0.0d0;total_resi=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
residual(i,j,k)=source(i,j,k)-( &
matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k) &
+matrix(i,j,k,6)*te(i-1,j-1,k)+matrix(i,j,k,7)*te(i+1,j-1,k) &
+matrix(i,j,k,8)*te(i-1,j+1,k)+matrix(i,j,k,9)*te(i+1,j+1,k))
betau=betau+r0(i,j,k)*residual(i,j,k)
total_resi=total_resi+residual(i,j,k)*residual(i,j,k)
enddo;enddo;enddo
beta=betau/alphau*alpha/omega
pk=residual+beta*(pk-omega*apk)
count=count+1
! print *,count,total_resi,alpha,omega,beta,betau
enddo
! stop
end select
end subroutine BiCGstab
subroutine BiCGstabMPI(matrix,te,source,count)
integer,intent(inout)::count
double precision,intent(in)::matrix(ix,jx,kx,n_hc)
double precision,intent(inout)::te(ix,jx,kx),source(ix,jx,kx)
double precision residual(ix,jx,kx)
integer i,j,k,n
double precision total_resi,total_source,tmp
double precision alpha,alphas(2),g_alphas(2)
double precision beta,betas(2),g_betas(2)
double precision omega,omegas(2),g_omegas(2)
double precision pk(ix,jx,kx),r0(ix,jx,kx),Apk(ix,jx,kx),tkp(ix,jx,kx)
double precision atk,g_total_resi,g_total_source
integer,parameter::g_margin=1
! residual(is:ie,js:je,ks:ke)=source(is:ie,js:je,ks:ke)
residual=source
do n=1,n_hc
residual(is:ie,js:je,ks:ke)=residual(is:ie,js:je,ks:ke) &
-matrix(is:ie,js:je,ks:ke,n)* &
te(is+di(n):ie+di(n),js+dj(n):je+dj(n),ks+dk(n):ke:dk(n))
! print *,n,matrix(is:ie,js:js,ks:ke,n)
enddo
total_resi=sum(residual(is:ie,js:je,ks:ke)**2)
total_source=sum(source(is:ie,js:je,ks:ke)**2)
if(total_prc.ge.2) then
call mpi_allreduce(total_resi,g_total_resi,1,mpi_double_precision, &
MPI_SUM,mpi_comm_world,ierr)
call mpi_allreduce(total_source,g_total_source,1,mpi_double_precision, &
MPI_SUM,mpi_comm_world,ierr)
call mpiBND(residual,g_margin)
endif
count=0
r0=residual
pk=r0
apk=0
select case(hc_split)
case(1)
do while(sqrt(g_total_resi/g_total_source).gt.error.and.count.le.hc_max)
alphas(:)=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
apk(i,j,k)=matrix(i,j,k,1)*pk(i,j,k) &
+matrix(i,j,k,2)*pk(i-1,j,k)+matrix(i,j,k,3)*pk(i+1,j,k) &
+matrix(i,j,k,4)*pk(i,j-1,k)+matrix(i,j,k,5)*pk(i,j+1,k)
alphas(1)=alphas(1)+(residual(i,j,k)*r0(i,j,k))
alphas(2)=alphas(2)+(r0(i,j,k)*apk(i,j,k))
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpi_allreduce(alphas,g_alphas,2,mpi_double_precision,&
mpi_sum,mpi_comm_world,ierr)
call mpiBND(apk,g_margin)
endif
alpha=g_alphas(2)/g_alphas(1)
tkp=residual-alpha*apk
omegas(:)=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
atk=matrix(i,j,k,1)*tkp(i,j,k) &
+matrix(i,j,k,2)*tkp(i-1,j,k)+matrix(i,j,k,3)*tkp(i+1,j,k) &
+matrix(i,j,k,4)*tkp(i,j-1,k)+matrix(i,j,k,5)*tkp(i,j+1,k)
omegas(1)=omegas(1)+tkp(i,j,k)*atk
omegas(2)=omegas(2)+atk*atk
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpi_allreduce(omegas,g_omegas,2,mpi_double_precision,&
mpi_sum,mpi_comm_world,ierr)
! call mpiBND(atk,2)
endif
omega=omegas(2)/omegas(1)
te=te+alpha*pk+omega*tkp
if(total_prc.ge.2) then
call mpiBND(te,g_margin)
endif
betas(:)=0.0d0;total_resi=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
residual(i,j,k)=source(i,j,k)-( &
matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k))
betas(1)=betas(1)+r0(i,j,k)*residual(i,j,k)
total_resi=total_resi+residual(i,j,k)*residual(i,j,k)
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpiBND(residual,g_margin)
call mpi_allreduce(betas,g_betas,2,mpi_double_precision,mpi_sum &
,mpi_comm_world,ierr)
call mpi_allreduce(total_resi,g_total_resi,1, &
mpi_double_precision,mpi_sum,mpi_comm_world,ierr)
endif
beta=g_betas(1)/g_alphas(1)*alpha/omega
pk=residual+beta*(pk-omega*apk)
count=count+1
enddo
case(2)
do while(sqrt(g_total_resi/g_total_source).gt.error.and.count.le.hc_max)
alphas(:)=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
apk(i,j,k)=matrix(i,j,k,1)*pk(i,j,k) &
+matrix(i,j,k,2)*pk(i-1,j,k)+matrix(i,j,k,3)*pk(i+1,j,k) &
+matrix(i,j,k,4)*pk(i,j-1,k)+matrix(i,j,k,5)*pk(i,j+1,k) &
+matrix(i,j,k,6)*pk(i-1,j-1,k)+matrix(i,j,k,7)*pk(i+1,j-1,k) &
+matrix(i,j,k,8)*pk(i-1,j+1,k)+matrix(i,j,k,9)*pk(i+1,j+1,k)
alphas(1)=alphas(1)+(residual(i,j,k)*r0(i,j,k))
alphas(2)=alphas(2)+(r0(i,j,k)*apk(i,j,k))
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpi_allreduce(alphas,g_alphas,2,mpi_double_precision,&
mpi_sum,mpi_comm_world,ierr)
call mpiBND(apk,2)
endif
alpha=g_alphas(1)/g_alphas(2)
tkp=residual-alpha*apk
omegas(:)=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
atk=matrix(i,j,k,1)*tkp(i,j,k) &
+matrix(i,j,k,2)*tkp(i-1,j,k)+matrix(i,j,k,3)*tkp(i+1,j,k) &
+matrix(i,j,k,4)*tkp(i,j-1,k)+matrix(i,j,k,5)*tkp(i,j+1,k) &
+matrix(i,j,k,6)*tkp(i-1,j-1,k)+matrix(i,j,k,7)*tkp(i+1,j-1,k)&
+matrix(i,j,k,8)*tkp(i-1,j+1,k)+matrix(i,j,k,9)*tkp(i+1,j+1,k)
omegas(1)=omegas(1)+tkp(i,j,k)*atk
omegas(2)=omegas(2)+atk*atk
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpi_allreduce(omegas,g_omegas,2,mpi_double_precision,&
mpi_sum,mpi_comm_world,ierr)
endif
omega=omegas(1)/omegas(2)
te=te+alpha*pk+omega*tkp
if(total_prc.ge.2) then
call mpiBND(te,2)
endif
betas(:)=0.0d0;total_resi=0.0d0
do k=ks,ke; do j=js,je; do i=is,ie
residual(i,j,k)=source(i,j,k)-( &
matrix(i,j,k,1)*te(i,j,k) &
+matrix(i,j,k,2)*te(i-1,j,k)+matrix(i,j,k,3)*te(i+1,j,k) &
+matrix(i,j,k,4)*te(i,j-1,k)+matrix(i,j,k,5)*te(i,j+1,k) &
+matrix(i,j,k,6)*te(i-1,j-1,k)+matrix(i,j,k,7)*te(i+1,j-1,k) &
+matrix(i,j,k,8)*te(i-1,j+1,k)+matrix(i,j,k,9)*te(i+1,j+1,k))
betas(1)=betas(1)+r0(i,j,k)*residual(i,j,k)
total_resi=total_resi+residual(i,j,k)*residual(i,j,k)
enddo;enddo;enddo
if(total_prc.ge.2) then
call mpiBND(residual,2)
call mpi_allreduce(betas,g_betas,2,mpi_double_precision,mpi_sum &
,mpi_comm_world,ierr)
call mpi_allreduce(total_resi,g_total_resi,1, &
mpi_double_precision,mpi_sum,mpi_comm_world,ierr)
endif
beta=g_betas(1)/g_alphas(1)*alpha/omega
pk=residual+beta*(pk-omega*apk)
count=count+1
! if(my_rank.eq.0)print*,count,g_total_resi,alpha,omega,beta,g_betas(1)
enddo
end select
! stop
end subroutine BiCGstabMPI
subroutine set_matrix_boundary(matrix)
double precision,intent(inout):: matrix(ix,jx,kx,n_hc)
select case(ndim)
case(1)
case(2)
select case(hc_split)
case(1)
if(neighbor(1).eq.-1) then
matrix(is,:,:,1)=matrix(is,:,:,2)+matrix(is,:,:,1)
matrix(is,:,:,2)=0.0d0
matrix(ie,:,:,1)=matrix(ie,:,:,3)+matrix(ie,:,:,1)
matrix(ie,:,:,3)=0.0d0
endif
if(neighbor(2).eq.-1) then
matrix(:,js,:,1)=matrix(:,js,:,4)+matrix(:,js,:,1)
matrix(:,js,:,4)=0.0d0
matrix(:,je,:,1)=matrix(:,je,:,5)+matrix(:,je,:,1)
matrix(:,je,:,5)=0.0d0
endif
case(2)
!x-minus
if(neighbor(1).eq.-1) then
matrix(is,:,:,1)=matrix(is,:,:,2)+matrix(is,:,:,1)
matrix(is,:,:,2)=0.0d0
matrix(is,:,:,4)=matrix(is,:,:,4)+matrix(is,:,:,6)
matrix(is,:,:,6)=0.0d0
matrix(is,:,:,5)=matrix(is,:,:,5)+matrix(is,:,:,8)
matrix(is,:,:,8)=0.0d0
endif
!x-plus
if(neighbor(2).eq.-1) then
matrix(ie,:,:,1)=matrix(ie,:,:,3)+matrix(ie,:,:,1)
matrix(ie,:,:,3)=0.0d0
matrix(ie,:,:,4)=matrix(ie,:,:,4)+matrix(ie,:,:,7)
matrix(ie,:,:,7)=0.0d0
matrix(ie,:,:,5)=matrix(ie,:,:,5)+matrix(ie,:,:,9)
matrix(ie,:,:,9)=0.0d0
endif
!y-minus
if(neighbor(3).eq.-1) then
matrix(:,js,:,1)=matrix(:,js,:,4)+matrix(:,js,:,1)
matrix(:,js,:,4)=0.0d0
matrix(:,js,:,2)=matrix(:,js,:,6)+matrix(:,js,:,2)
matrix(:,js,:,6)=0.0d0
matrix(:,js,:,3)=matrix(:,js,:,7)+matrix(:,js,:,3)
matrix(:,js,:,7)=0.0d0
endif
if(neighbor(4).eq.-1) then
matrix(:,je,:,1)=matrix(:,je,:,5)+matrix(:,je,:,1)
matrix(:,je,:,5)=0.0d0
matrix(:,je,:,2)=matrix(:,je,:,2)+matrix(:,je,:,8)
matrix(:,je,:,8)=0.0d0
matrix(:,je,:,3)=matrix(:,je,:,3)+matrix(:,je,:,9)
matrix(:,je,:,9)=0.0d0
endif
end select
case(3)
end select
end subroutine set_matrix_boundary
subroutine test_matrix(matrix,source,te)
double precision,intent(inout):: matrix(ix,jx,n_hc),source(ix,jx),te(ix,jx)
double precision eta
character*2 c_sch
character*4 c_ome
integer i,j
write(c_sch,"(i2.2)")hc_sch
write(c_ome,"(f4.2)")sor_omega
open(hc_unit,file=trim("tmp_hc_"//c_sch//"_"//c_ome//".txt"), &
status="replace",form="formatted")
eta=-kapper
! eta=1.5d0
do j=js,je
do i=is,ie
matrix(i,j,2)=eta*2
matrix(i,j,3)=eta*2
matrix(i,j,4)=eta
matrix(i,j,5)=eta
matrix(i,j,1)=1.0d0-matrix(i,j,2)-matrix(i,j,3)-matrix(i,j,4)-matrix(i,j,5)
source(i,j)=1.0d0+10.0d0*exp(-((x(i)**2)/0.1d0))
te(i,j)=1.0d0
enddo
enddo
end subroutine test_matrix
subroutine set_matrix_source_1D(matrix,source,ro,te)
double precision,intent(inout):: matrix(ix,n_hc),source(ix)
double precision,intent(in)::ro(ix),te(ix)
double precision eta
integer i
source=te
do i=is,ie
eta=kapper*dt*(gm-1.0d0)/ro(i)/dxc(i)
matrix(i,2)=-eta*(0.5d0*(te(i-1)+te(i)))**2.5/dx(i-1)
matrix(i,3)=-eta*(0.5d0*(te(i+1)+te(i)))**2.5/dx(i)
matrix(i,1)=1.0d0-matrix(i,2)-matrix(i,3)
enddo
end subroutine set_matrix_source_1D
subroutine set_matrix_source_2D(matrix,source,ro,te)
double precision,intent(inout):: matrix(ix,jx,n_hc),source(ix,jx)
double precision,intent(in)::ro(ix,jx),te(ix,jx)
double precision eta
integer i,j
source=te
do j=js,je;do i=is,ie
! eta=dt/(dx(i)*dx(i)*kapper
eta=kapper*dt*(gm-1.0d0)/ro(i,j)*gm
matrix(i,j,2)=-eta*(0.5d0*(te(i-1,j)+te(i,j)))**2.5/(dx(i-1)*dxc(i))
matrix(i,j,3)=-eta*(0.5d0*(te(i+1,j)+te(i,j)))**2.5/(dx(i)*dxc(i))
matrix(i,j,4)=-eta*(0.5d0*(te(i,j-1)+te(i,j)))**2.5/(dy(j-1)*dyc(j))
matrix(i,j,5)=-eta*(0.5d0*(te(i,j+1)+te(i,j)))**2.5/(dy(j)*dyc(j))
matrix(i,j,1)=1.0d0-matrix(i,j,2)-matrix(i,j,3)&
-matrix(i,j,4)-matrix(i,j,5)
enddo;enddo
end subroutine set_matrix_source_2D
subroutine set_matrix_source_MHD2D5(matrix,source,ro,te,bx,by,bz)
double precision,intent(inout):: matrix(ix,jx,n_hc),source(ix,jx)
double precision,intent(in)::ro(ix,jx),te(ix,jx)
double precision,intent(in)::bx(ix,jx),by(ix,jx),bz(ix,jx)
double precision bypx,bymx,bxpy,bxmy,bxp,byp,bxm,bym,b2n,b2e,b2s,b2w,eta
integer i,j
!set matrix and source term-----------------------------------------
eta=gm*(gm-1.0d0)*dt*kapper
do j=js,je ; do i=is,ie
! bypx=(by(i,j-1)+by(i,j)+by(i+1,j)+by(i+1,j-1))/4.0d0
! bymx=(by(i-1,j-1)+by(i-1,j)+by(i,j)+by(i,j-1))/4.0d0
! bxpy=(bx(i-1,j)+bx(i,j)+bx(i,j+1)+bx(i-1,j+1))/4.0d0
! bxmy=(bx(i-1,j-1)+bx(i,j-1)+bx(i,j)+bx(i-1,j))/4.0d0
! bxp=bx(i,j) ; bxm=bx(i-1,j)
! byp=by(i,j) ; bym=by(i,j-1)
bxp=0.5d0*(bx(i,j)+bx(i+1,j))
bxm=0.5d0*(bx(i-1,j)+bx(i,j))
bxpy=0.5d0*(bx(i,j+1)+bx(i,j))
bxmy=0.5d0*(bx(i,j-1)+bx(i,j))
bypx=0.5d0*(by(i,j)+by(i+1,j))
bymx=0.5d0*(by(i,j)+by(i-1,j))
byp=0.5d0*(by(i,j)+by(i,j+1))
bym=0.5d0*(by(i,j-1)+by(i,j))
b2n=byp**2+bxpy**2+((bz(i,j)+bz(i,j+1))/2.0d0)**2+epsi
b2e=bxp**2+bypx**2+((bz(i,j)+bz(i+1,j))/2.0d0)**2+epsi
b2s=bym**2+bxmy**2+((bz(i,j)+bz(i,j-1))/2.0d0)**2+epsi
b2w=bxm**2+bymx**2+((bz(i,j)+bz(i-1,j))/2.0d0)**2+epsi
source(i,j)=te(i,j)+eta/ro(i,j)/dxc(i)/dyc(j)*( &
((te(i+1,j)+te(i,j))/2.0)**2.5*bxp*bypx/b2e* &
((te(i,j+1)+te(i+1,j+1)-te(i,j-1)-te(i+1,j-1))/4.0d0) - &
(((te(i,j)+te(i-1,j))/2.0)**2.5*bxm*bymx/b2w* &
((te(i-1,j+1)+te(i,j+1)-te(i-1,j-1)-te(i,j-1))/4.0d0)) + &
((te(i,j+1)+te(i,j))/2.0)**2.5*byp*bxpy/b2n* &
((te(i+1,j)+te(i+1,j+1)-te(i-1,j)-te(i-1,j+1))/4.0d0) - &
(((te(i,j)+te(i,j-1))/2.0)**2.5*bym*bxmy/b2s* &
((te(i+1,j-1)+te(i+1,j)-te(i-1,j-1)-te(i-1,j))/4.0d0)))
!set Matrix
matrix(i,j,2)=-eta/(dx(i-1)*dxc(i))/ro(i,j) &
*((te(i-1,j)+te(i,j))/2)**2.5d0*bxm**2/b2w
matrix(i,j,3)=-eta/(dx(i)*dxc(i))/ro(i,j) &
*((te(i+1,j)+te(i,j))/2)**2.5d0*bxp**2/b2e
matrix(i,j,4)=-eta/(dy(j-1)*dyc(j))/ro(i,j) &
*((te(i,j)+te(i,j-1))/2)**2.5d0*bym**2/b2s
matrix(i,j,5)=-eta*dt/(dy(j)*dyc(j))/ro(i,j) &
*((te(i,j)+te(i,j+1))/2)**2.5d0*byp**2/b2n
matrix(i,j,1)=1.0-(matrix(i,j,2)+matrix(i,j,3)+matrix(i,j,4)+matrix(i,j,5))
enddo;enddo
!--------------------------------------------------------------------
end subroutine set_matrix_source_MHD2D5
subroutine set_matrix_source_MHD2D9(matrix,source,ro,te,bx,by,bz)
double precision,intent(inout):: matrix(ix,jx,kx,n_hc),source(ix,jx,kx)
double precision,intent(in)::ro(ix,jx,kx),te(ix,jx,kx)
double precision,intent(in)::bx(ix,jx,kx),by(ix,jx,kx),bz(ix,jx,kx)
double precision ::bxl,bxr,bxd,bxu,byl,byr,byd,byu,tnorm,nyl,nyr,nyu,nyd
double precision ::bxxl,bxxr,byyd,byyu,bxyl,bxyr,byxd,byxu,nxl,nxr,nxu,nxd
double precision ::bzl,bzr,bzd,bzu,res0,eta
double precision ::te_xm,te_xp,te_ym,te_yp
double precision ::te_xm25,te_xp25,te_ym25,te_yp25
integer i,j,k
!set matrix and source term-----------------------------------------
source=te
do k=ks,ke;do j=js,je ;do i=is,ie
eta=kapper*dt*(gm-1.0d0)/ro(i,j,k)*gm
! bxl=bx(i-1,j,k) ; bxr=bx(i,j,k)
! bxd=(bx(i-1,j-1,k)+bx(i,j-1,k)+bx(i-1,j,k)+bx(i,j,k))/4.0d0
! bxu=(bx(i-1,j,k)+bx(i,j,k)+bx(i-1,j+1,k)+bx(i,j+1,k))/4.0d0
! byl=(by(i-1,j-1,k)+by(i,j-1,k)+by(i-1,j,k)+by(i,j,k))/4.0d0
! byr=(by(i,j-1,k)+by(i+1,j-1,k)+by(i,j,k)+by(i+1,j,k))/4.0d0
! byd=by(i,j-1,k) ; byu=by(i,j,k)
bxl=(bx(i-1,j,k)+bx(i,j,k))/2.0d0
bxr=(bx(i+1,j,k)+bx(i,j,k))/2.0d0
bxd=(bx(i,j-1,k)+bx(i,j,k))/2.0d0
bxu=(bx(i,j+1,k)+bx(i,j,k))/2.0d0
byl=(by(i-1,j,k)+by(i,j,k))/2.0d0
byr=(by(i+1,j,k)+by(i,j,k))/2.0d0
byd=(by(i,j-1,k)+by(i,j,k))/2.0d0
byu=(by(i,j+1,k)+by(i,j,k))/2.0d0
bzl=(bz(i-1,j,k)+bz(i,j,k))/2.0d0
bzr=(bz(i+1,j,k)+bz(i,j,k))/2.0d0
bzd=(bz(i,j-1,k)+bz(i,j,k))/2.0d0
bzu=(bz(i,j+1,k)+bz(i,j,k))/2.0d0
nxl=bxl/(max(sqrt(bxl**2+byl**2+bzl**2),epsi))
nxr=bxr/(max(sqrt(bxr**2+byr**2+bzr**2),epsi))
nxd=bxd/(max(sqrt(bxd**2+byd**2+bzd**2),epsi))
nxu=bxu/(max(sqrt(bxu**2+byu**2+bzu**2),epsi))
nyl=byl/(max(sqrt(bxl**2+byl**2+bzl**2),epsi))
nyr=byr/(max(sqrt(bxr**2+byr**2+bzr**2),epsi))
nyd=byd/(max(sqrt(bxd**2+byd**2+bzd**2),epsi))
nyu=byu/(max(sqrt(bxu**2+byu**2+bzu**2),epsi))
te_xm=0.5d0*(te(i,j,k)+te(i-1,j,k))
te_xp=0.5d0*(te(i,j,k)+te(i+1,j,k))
te_ym=0.5d0*(te(i,j,k)+te(i,j-1,k))
te_yp=0.5d0*(te(i,j,k)+te(i,j+1,k))
te_xm25=te_xm*te_xm*sqrt(te_xm)
te_xp25=te_xp*te_xp*sqrt(te_xp)
te_ym25=te_ym*te_ym*sqrt(te_ym)
te_yp25=te_yp*te_yp*sqrt(te_yp)
bxxl=-eta*te_xm25*nxl*nxl/dxc(i)/dx(i-1)
bxxr=-eta*te_xp25*nxr*nxr/dxc(i)/dx(i)
byyd=-eta*te_ym25*nyd*nyd/dyc(j)/dy(j-1)
byyu=-eta*te_yp25*nyu*nyu/dyc(j)/dy(j)
bxyl=-eta/4.0d0/dxc(i)/dyc(j)*nxl*nyl*te_xm25
bxyr=-eta/4.0d0/dxc(i)/dyc(j)*nxr*nyr*te_xp25
byxd=-eta/4.0d0/dxc(i)/dyc(j)*nyd*nxd*te_ym25
byxu=-eta/4.0d0/dxc(i)/dyc(j)*nyu*nxu*te_yp25
! bxxl=-eta*(0.5d0*(te(i,j,k)+te(i-1,j,k))* &
! (0.5d0*(te(i,j,k)+te(i-1,j,k)))* &
! sqrt(0.5d0*(te(i,j,k)+te(i-1,j,k)))) &
! *nxl*nxl/dxc(i)/dx(i-1)
! bxxr=-eta*(0.5d0*(te(i,j,k)+te(i+1,j,k)))**2.5d0*nxr**2/dxc(i)/dx(i)
! byyd=-eta*(0.5d0*(te(i,j,k)+te(i,j-1,k)))**2.5d0*nyd**2/dyc(j)/dy(j-1)
! byyu=-eta*(0.5d0*(te(i,j,k)+te(i,j+1,k)))**2.5d0*nyu**2/dyc(j)/dy(j)
! bxyl=-eta/4.0d0/dxc(i)/dyc(j)*nxl*nyl*(0.5d0*(te(i,j,k)+te(i-1,j,k)))**2.5d0
! bxyr=-eta/4.0d0/dxc(i)/dyc(j)*nxr*nyr*(0.5d0*(te(i,j,k)+te(i+1,j,k)))**2.5d0
! byxd=-eta/4.0d0/dxc(i)/dyc(j)*nyd*nxd*(0.5d0*(te(i,j,k)+te(i,j-1,k)))**2.5d0
! byxu=-eta/4.0d0/dxc(i)/dyc(j)*nyu*nxu*(0.5d0*(te(i,j,k)+te(i,j+1,k)))**2.5d0
matrix(i,j,k,2)=bxxl-(byxu-byxd)
matrix(i,j,k,3)=bxxr+(byxu-byxd)
matrix(i,j,k,4)=byyd-(bxyr-bxyl)
matrix(i,j,k,5)=byyu+(bxyr-bxyl)
matrix(i,j,k,6)=bxyl+byxd
matrix(i,j,k,7)=-(bxyr+byxd)
matrix(i,j,k,8)=-(bxyl+byxu)
matrix(i,j,k,9)=bxyr+byxu
matrix(i,j,k,1)=1.0-(matrix(i,j,k,2)+matrix(i,j,k,3)+matrix(i,j,k,4)+matrix(i,j,k,5))
enddo;enddo;enddo
!--------------------------------------------------------------------
end subroutine set_matrix_source_MHD2D9
subroutine set_matrix_source_MHD2D9_limiter(matrix,source,ro,te,bx,by,bz)
double precision,intent(inout):: matrix(ix,jx,kx,n_hc),source(ix,jx,kx)
double precision,intent(in)::ro(ix,jx,kx),te(ix,jx,kx)
double precision,intent(in)::bx(ix,jx,kx),by(ix,jx,kx),bz(ix,jx,kx)
double precision ::bxl,bxr,bxd,bxu,byl,byr,byd,byu,tnorm,nyl,nyr,nyu,nyd
double precision ::bxxl,bxxr,byyd,byyu,bxyl,bxyr,byxd,byxu,nxl,nxr,nxu,nxd
double precision ::bzl,bzr,bzd,bzu,res0,eta
double precision ::te_xm,te_xp,te_ym,te_yp
double precision ::te_xm25,te_xp25,te_ym25,te_yp25
double precision ::lim_l,lim_r,lim_d,lim_u
double precision ::F_l,F_r,F_d,F_u
double precision ::F_sat_l,F_sat_r,F_sat_d,F_sat_u
double precision ::dTdx_l,dTdx_r,dTdx_d,dTdx_u
double precision ::dTdy_l,dTdy_r,dTdy_d,dTdy_u
integer i,j,k
!set matrix and source term-----------------------------------------
source=te
do k=ks,ke;do j=js,je ;do i=is,ie
eta=kapper*dt*(gm-1.0d0)/ro(i,j,k)*gm
bxl=(bx(i-1,j,k)+bx(i,j,k))/2.0d0
bxr=(bx(i+1,j,k)+bx(i,j,k))/2.0d0
bxd=(bx(i,j-1,k)+bx(i,j,k))/2.0d0
bxu=(bx(i,j+1,k)+bx(i,j,k))/2.0d0
byl=(by(i-1,j,k)+by(i,j,k))/2.0d0
byr=(by(i+1,j,k)+by(i,j,k))/2.0d0
byd=(by(i,j-1,k)+by(i,j,k))/2.0d0
byu=(by(i,j+1,k)+by(i,j,k))/2.0d0
bzl=(bz(i-1,j,k)+bz(i,j,k))/2.0d0
bzr=(bz(i+1,j,k)+bz(i,j,k))/2.0d0
bzd=(bz(i,j-1,k)+bz(i,j,k))/2.0d0
bzu=(bz(i,j+1,k)+bz(i,j,k))/2.0d0
nxl=bxl/(max(sqrt(bxl**2+byl**2+bzl**2),epsi))
nxr=bxr/(max(sqrt(bxr**2+byr**2+bzr**2),epsi))
nxd=bxd/(max(sqrt(bxd**2+byd**2+bzd**2),epsi))
nxu=bxu/(max(sqrt(bxu**2+byu**2+bzu**2),epsi))
nyl=byl/(max(sqrt(bxl**2+byl**2+bzl**2),epsi))
nyr=byr/(max(sqrt(bxr**2+byr**2+bzr**2),epsi))
nyd=byd/(max(sqrt(bxd**2+byd**2+bzd**2),epsi))
nyu=byu/(max(sqrt(bxu**2+byu**2+bzu**2),epsi))
te_xm=0.5d0*(te(i,j,k)+te(i-1,j,k))
te_xp=0.5d0*(te(i,j,k)+te(i+1,j,k))
te_ym=0.5d0*(te(i,j,k)+te(i,j-1,k))
te_yp=0.5d0*(te(i,j,k)+te(i,j+1,k))
! kc_sat = 5.d0*ro*te*sqrt(te) !! for saturation flux (defined at i,j,k)
F_sat_l=2.5d0*(ro(i-1,j,k)+ro(i,j,k))*te_xm*sqrt(te_xm)
F_sat_r=2.5d0*(ro(i+1,j,k)+ro(i,j,k))*te_xp*sqrt(te_xp)
F_sat_d=2.5d0*(ro(i,j-1,k)+ro(i,j,k))*te_ym*sqrt(te_ym)
F_sat_u=2.5d0*(ro(i,j+1,k)+ro(i,j,k))*te_yp*sqrt(te_yp)
te_xm25=te_xm*te_xm*sqrt(te_xm)
te_xp25=te_xp*te_xp*sqrt(te_xp)
te_ym25=te_ym*te_ym*sqrt(te_ym)
te_yp25=te_yp*te_yp*sqrt(te_yp)
dTdx_l=(te(i,j,k)-te(i-1,j,k))/dx(i-1)
dTdx_r=(te(i+1,j,k)-te(i,j,k))/dx(i)
dTdx_d=(te(i+1,j-1,k)+te(i+1,j,k)-te(i-1,j-1,k)-te(i-1,j,k))/(4.0d0*dxc(i))
dTdx_u=(te(i+1,j+1,k)+te(i+1,j,k)-te(i-1,j+1,k)-te(i-1,j,k))/(4.0d0*dxc(i))
dTdy_l=(te(i-1,j+1,k)+te(i,j+1,k)-te(i-1,j-1,k)-te(i,j-1,k))/(4.0d0*dyc(j))
dTdy_r=(te(i+1,j+1,k)+te(i,j+1,k)-te(i+1,j-1,k)-te(i,j-1,k))/(4.0d0*dyc(j))
dTdy_d=(te(i,j,k)-te(i,j-1,k))/dy(j-1)
dTdy_u=(te(i,j+1,k)-te(i,j,k))/dy(j)
F_l=te_xm25*kapper*sqrt(dTdx_l**2+dTdy_l**2)
F_r=te_xp25*kapper*sqrt(dTdx_r**2+dTdy_r**2)
F_d=te_ym25*kapper*sqrt(dTdx_d**2+dTdy_d**2)
F_u=te_yp25*kapper*sqrt(dTdx_u**2+dTdy_u**2)
lim_l=max(0.0d0,min(1.0d0,1.0d0-0.5d0*F_l/F_sat_l))
lim_r=max(0.0d0,min(1.0d0,1.0d0-0.5d0*F_r/F_sat_r))
lim_d=max(0.0d0,min(1.0d0,1.0d0-0.5d0*F_d/F_sat_d))
lim_u=max(0.0d0,min(1.0d0,1.0d0-0.5d0*F_u/F_sat_u))
F_sat_l=F_sat_l*sign(1.0d0,-nxl*dTdx_l-nyl*dTdy_l)
F_sat_r=F_sat_r*sign(1.0d0,-nxr*dTdx_r-nyr*dTdy_r)
F_sat_d=F_sat_d*sign(1.0d0,-nxd*dTdx_d-nyd*dTdy_d)
F_sat_u=F_sat_u*sign(1.0d0,-nxu*dTdx_u-nyu*dTdy_u)
source(i,j,k)=source(i,j,k)&
-dt*(((1.0d0-lim_r)*F_sat_r*nxr-(1.0d0-lim_l)*F_sat_l*nxl)/dxc(i) &
+((1.0d0-lim_u)*F_sat_u*nyu-(1.0d0-lim_d)*F_sat_d*nyd)/dyc(j))
bxxl=-eta*te_xm25*nxl*nxl/dxc(i)/dx(i-1)*lim_l
bxxr=-eta*te_xp25*nxr*nxr/dxc(i)/dx(i)*lim_r
byyd=-eta*te_ym25*nyd*nyd/dyc(j)/dy(j-1)*lim_d
byyu=-eta*te_yp25*nyu*nyu/dyc(j)/dy(j)*lim_u
bxyl=-eta/4.0d0/dxc(i)/dyc(j)*nxl*nyl*te_xm25*lim_l
bxyr=-eta/4.0d0/dxc(i)/dyc(j)*nxr*nyr*te_xp25*lim_r
byxd=-eta/4.0d0/dxc(i)/dyc(j)*nyd*nxd*te_ym25*lim_d
byxu=-eta/4.0d0/dxc(i)/dyc(j)*nyu*nxu*te_yp25*lim_u
matrix(i,j,k,2)=bxxl-(byxu-byxd)
matrix(i,j,k,3)=bxxr+(byxu-byxd)
matrix(i,j,k,4)=byyd-(bxyr-bxyl)
matrix(i,j,k,5)=byyu+(bxyr-bxyl)
matrix(i,j,k,6)=bxyl+byxd
matrix(i,j,k,7)=-(bxyr+byxd)
matrix(i,j,k,8)=-(bxyl+byxu)
matrix(i,j,k,9)=bxyr+byxu
matrix(i,j,k,1)=1.0-(matrix(i,j,k,2)+matrix(i,j,k,3)+matrix(i,j,k,4)+matrix(i,j,k,5))
enddo;enddo;enddo
!--------------------------------------------------------------------
end subroutine set_matrix_source_MHD2D9_limiter
subroutine mpiBND(var,n_margin)
integer,intent(in)::n_margin
double precision,intent(inout)::var(ix,jx,kx)
double precision recvx(n_margin,jx,kx),sendx(n_margin,jx,kx)
double precision recvy(ix,n_margin,kx),sendy(ix,n_margin,kx)
double precision recvz(ix,jx,n_margin),sendz(ix,jx,n_margin)
integer nsend,nrecv,xcount,ycount,zcount
xcount=jx*kx*n_margin
ycount=ix*kx*n_margin
zcount=ix*jx*n_margin
!x-direction
if(mpi_siz(1).gt.1) then
!x-plus
sendx=var(ix-margin(1)-n_margin+1:ix-margin(1),:,:)
nsend=neighbor(2)
nrecv=neighbor(1)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendx,xcount,mpi_double_precision,nsend,0, &
recvx,xcount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(1).ne.-1) then
var(margin(1)-n_margin+1:margin(1),:,:)=recvx
endif
!x-minus
sendx=var(margin(1)+1:margin(1)+n_margin,:,:)
nsend=neighbor(1)
nrecv=neighbor(2)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendx,xcount,mpi_double_precision,nsend,0, &
recvx,xcount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(2).ne.-1) then
var(ix-margin(1)+1:ix-margin(1)+n_margin,:,:)=recvx
endif
endif
!y-direction
if(mpi_siz(2).gt.1) then
!=============================================================
!y-plus
sendy=var(:,jx-margin(2)-n_margin+1:jx-margin(2),:)
nsend=neighbor(4)
nrecv=neighbor(3)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendy,ycount,mpi_double_precision,nsend,0, &
recvy,ycount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(3).ne.-1) then
var(:,margin(2)-n_margin+1:margin(2),:)=recvy
endif
!=============================================================
!y-minus
sendy=var(:,margin(2)+1:margin(2)+n_margin,:)
nsend=neighbor(3)
nrecv=neighbor(4)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendy,ycount,mpi_double_precision,nsend,0, &
recvy,ycount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(4).ne.-1) then
var(:,jx-margin(2)+1:jx-margin(2)+n_margin,:)=recvy
endif
endif
!for z-direction
if(mpi_siz(3).gt.1) then
!=============================================================
!z-plus
sendz=var(:,:,kx-margin(3)-n_margin+1:kx-margin(3))
nsend=neighbor(6)
nrecv=neighbor(5)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendz,zcount,mpi_double_precision,nsend,0, &
recvz,zcount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(5).ne.-1) then
var(:,:,1+margin(3)-n_margin:margin(3))=recvz(:,:,:)
endif
!=============================================================
!right-boundary of z-direction
sendz=var(:,:,margin(3)+1:margin(3)+n_margin)
nsend=neighbor(5)
nrecv=neighbor(6)
if(nsend.eq.-1) nsend=mpi_proc_null
if(nrecv.eq.-1) nrecv=mpi_proc_null
call mpi_SendRecv(sendz,zcount,mpi_double_precision,nsend,0, &
recvz,zcount,mpi_double_precision,nrecv,0,mpi_comm_world,status,ierr)
if(neighbor(6).ne.-1) then
var(:,:,kx-margin(3)+1:kx-margin(3)+n_margin)=recvz
endif
endif
end subroutine mpiBND
!! A second-order accurate in time Super Timestepping method
!! for (anisotropic) heat conduction (Ref: Meyer+2012, MNRS)
subroutine HC_STS(U,nvar,dt,mhd,flag_sts)
double precision,intent(inout) :: U(ix,jx,kx,nvar)
double precision,intent(inout) :: dt
integer, intent(in) :: nvar,mhd,flag_sts
integer :: sub,j
double precision :: tau
double precision :: sol0(ix,jx,kx),sol1(ix,jx,kx),sol2(ix,jx,kx) &
,sol_new(ix,jx,kx)
double precision, allocatable :: b_sts(:),mu_sts(:),mut_sts(:),nu_sts(:),gmt_sts(:)
double precision :: bb(ix,jx,kx),vv(ix,jx,kx)
double precision :: ro(ix,jx,kx),vx(ix,jx,kx),vy(ix,jx,kx),vz(ix,jx,kx),pr(ix,jx,kx) &
,bx(ix,jx,kx),by(ix,jx,kx),bz(ix,jx,kx),te(ix,jx,kx)
double precision :: jd,subd,cond_func0(ix,jx,kx)
double precision :: coef_hc(ix,jx,kx,3,3),nbvec(ix,jx,kx,3)
double precision :: nbx_int(ix,jx,kx,3),nby_int(ix,jx,kx,3),nbz_int(ix,jx,kx,3)
select case(mhd)
case(0) !! HD (isotropic conduction)
call cq2pv_hd(ro,vx,vy,vz,pr,U)
te=gm*(pr/ro)
bb = 0.d0
vv = vx**2 + vy**2 + vz**2
bx = 0.d0; by = 0.d0; bz = 0.d0
case(1) !! MHD (anisotropic. Switch to isotropic cond when B is very small)
call cq2pv_mhd(ro,vx,vy,vz,pr,bx,by,bz,U)
te=gm*(pr/ro)
bb = bx**2 + by**2 + bz**2
vv = vx**2 + vy**2 + vz**2
end select
!! calculate the coefficients that depend on the magnetic field
call cal_coef_hc(coef_hc,nbvec,nbx_int,nby_int,nbz_int,bx,by,bz,bb)
!! timestep
tau = 0.5d0*dt
call cal_dt_cnd(dt_cnd,ro,te)
sub = int(0.5d0 * (sqrt(9.d0+16.d0*tau/dt_cnd)-1.d0) +1.d0) !! +1 is necessary