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AMSS-NCKU/AMSS_NCKU_source/lopsidediff.f90
CGH0S7 714c6e90c6 Add OpenMP parallelization to Fortran compute kernels 
Add !$omp parallel do collapse(2) directives to all triple-loop
stencil kernels (fderivs, fdderivs, fdx/fdy/fdz, kodis, lopsided,
enforce_ag/enforce_ga) across all ghost_width variants. Add !$omp
parallel workshare to RK4/ICN/Euler whole-array update routines.

Build system: add -qopenmp to compile and link flags, switch MKL
from sequential to threaded (-lmkl_intel_thread -liomp5).

Runtime: set OMP_NUM_THREADS=96, OMP_STACKSIZE=16M, OMP_PROC_BIND=close,
OMP_PLACES=cores for 96-core server target.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
2026-02-10 23:40:17 +08:00

907 lines
37 KiB
Fortran
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! Compute advection terms in right hand sides of field equations
#include "macrodef.fh"
! we need only distinguish different finite difference order
! Vertex or Cell is distinguished in routine symmetry_bd which locates in
! file "fmisc.f90"
#if (ghost_width == 2)
! second order code
!-----------------------------------------------------------------------------
! v
! D f = ------[ - 3 f + 4 f - f ]
! i 2dx i i+v i+2v
!
! where
!
! i
! |B |
! v = -----
! i
! B
!
!-----------------------------------------------------------------------------
subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
implicit none
!~~~~~~> Input parameters:
integer, intent(in) :: ex(1:3),Symmetry
real*8, intent(in) :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
real*8,dimension(ex(1),ex(2),ex(3)),intent(in) :: f,Sfx,Sfy,Sfz
real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
real*8,dimension(3),intent(in) ::SoA
!~~~~~~> local variables:
! note index -1,0, so we have 2 extra points
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: dX,dY,dZ
real*8 :: d2dx,d2dy,d2dz
real*8, parameter :: ZEO=0.d0,ONE=1.d0,TWO=2.d0,THR=3.d0,FOUR=4.d0
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
call symmetry_bd(2,ex,f,fh,SoA)
! upper bound set ex-1 only for efficiency,
! the loop body will set ex 0 also
!$omp parallel do collapse(2) private(i,j,k)
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(Sfx(i,j,k) >= ZEO)then
if( i+2 <= imax .and. i >= imin)then
! v
! D f = ------[ - 3 f + 4 f - f ]
! i 2dx i i+v i+2v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i >= imin)then
! v
! D f = ------[ - f + f ]
! i dx i i+v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i+1,j,k))
endif
elseif(Sfx(i,j,k) <= ZEO)then
if( i-2 >= imin .and. i <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d2dx*(-THR*fh(i,j,k)+FOUR*fh(i-1,j,k)-fh(i-2,j,k))
elseif(i-1 >= imin .and. i <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d2dx*(-fh(i,j,k)+fh(i-1,j,k))
endif
! set imax and imin 0
endif
! y direction
if(Sfy(i,j,k) >= ZEO)then
if( j+2 <= jmax .and. j >= jmin)then
! v
! D f = ------[ - 3 f + 4 f - f ]
! i 2dx i i+v i+2v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j >= jmin)then
! v
! D f = ------[ - f + f ]
! i dx i i+v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j+1,k))
endif
elseif(Sfy(i,j,k) <= ZEO)then
if( j-2 >= jmin .and. j <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d2dy*(-THR*fh(i,j,k)+FOUR*fh(i,j-1,k)-fh(i,j-2,k))
elseif(j-1 >= jmin .and. j <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d2dy*(-fh(i,j,k)+fh(i,j-1,k))
endif
! set jmin and jmax 0
endif
!! z direction
if(Sfz(i,j,k) >= ZEO)then
if( k+2 <= kmax .and. k >= kmin)then
! v
! D f = ------[ - 3 f + 4 f - f ]
! i 2dx i i+v i+2v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k >= kmin)then
! v
! D f = ------[ - f + f ]
! i dx i i+v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k+1))
endif
elseif(Sfz(i,j,k) <= ZEO)then
if( k-2 >= kmin .and. k <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d2dz*(-THR*fh(i,j,k)+FOUR*fh(i,j,k-1)-fh(i,j,k-2))
elseif(k-1 >= kmin .and. k <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d2dz*(-fh(i,j,k)+fh(i,j,k-1))
endif
! set kmin and kmax 0
endif
enddo
enddo
enddo
return
end subroutine lopsided
#elif (ghost_width == 3)
! fourth order code
!-----------------------------------------------------------------------------
!
! Compute advection terms in right hand sides of field equations
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
!
! where
!
! i
! |B |
! v = -----
! i
! B
!
!-----------------------------------------------------------------------------
subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
implicit none
!~~~~~~> Input parameters:
integer, intent(in) :: ex(1:3),Symmetry
real*8, intent(in) :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
real*8,dimension(ex(1),ex(2),ex(3)),intent(in) :: f,Sfx,Sfy,Sfz
real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
real*8,dimension(3),intent(in) ::SoA
!~~~~~~> local variables:
! note index -2,-1,0, so we have 3 extra points
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: dX,dY,dZ
real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F3=3.d0
real*8, parameter :: TWO=2.d0,F6=6.0d0,F18=1.8d1
real*8, parameter :: F12=1.2d1, F10=1.d1,EIT=8.d0
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
call symmetry_bd(3,ex,f,fh,SoA)
! upper bound set ex-1 only for efficiency,
! the loop body will set ex 0 also
!$omp parallel do collapse(2) private(i,j,k)
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
#if 0
!! old code
! x direction
if(Sfx(i,j,k) >= ZEO .and. i+3 <= imax .and. i-1 >= imin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
-F6*fh(i+2,j,k)+ fh(i+3,j,k))
elseif(Sfx(i,j,k) <= ZEO .and. i-3 >= imin .and. i+1 <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
-F6*fh(i-2,j,k)+ fh(i-3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(Sfy(i,j,k) >= ZEO .and. j+3 <= jmax .and. j-1 >= jmin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
-F6*fh(i,j+2,k)+ fh(i,j+3,k))
elseif(Sfy(i,j,k) <= ZEO .and. j-3 >= jmin .and. j+1 <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
-F6*fh(i,j-2,k)+ fh(i,j-3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmin and jmax 0
endif
!! z direction
if(Sfz(i,j,k) >= ZEO .and. k+3 <= kmax .and. k-1 >= kmin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
-F6*fh(i,j,k+2)+ fh(i,j,k+3))
elseif(Sfz(i,j,k) <= ZEO .and. k-3 >= kmin .and. k+1 <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
-F6*fh(i,j,k-2)+ fh(i,j,k-3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmin and kmax 0
endif
#else
!! new code, 2012dec27, based on bam
! x direction
if(Sfx(i,j,k) > ZEO)then
if(i+3 <= imax)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
-F6*fh(i+2,j,k)+ fh(i+3,j,k))
elseif(i+2 <= imax)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
-F6*fh(i-2,j,k)+ fh(i-3,j,k))
! set imax and imin 0
endif
elseif(Sfx(i,j,k) < ZEO)then
if(i-3 >= imin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d12dx*(-F3*fh(i+1,j,k)-F10*fh(i,j,k)+F18*fh(i-1,j,k) &
-F6*fh(i-2,j,k)+ fh(i-3,j,k))
elseif(i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i-1 >= imin)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(-F3*fh(i-1,j,k)-F10*fh(i,j,k)+F18*fh(i+1,j,k) &
-F6*fh(i+2,j,k)+ fh(i+3,j,k))
! set imax and imin 0
endif
endif
! y direction
if(Sfy(i,j,k) > ZEO)then
if(j+3 <= jmax)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
-F6*fh(i,j+2,k)+ fh(i,j+3,k))
elseif(j+2 <= jmax)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
-F6*fh(i,j-2,k)+ fh(i,j-3,k))
! set imax and imin 0
endif
elseif(Sfy(i,j,k) < ZEO)then
if(j-3 >= jmin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j+1,k)-F10*fh(i,j,k)+F18*fh(i,j-1,k) &
-F6*fh(i,j-2,k)+ fh(i,j-3,k))
elseif(j-2 >= jmin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j-1 >= jmin)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(-F3*fh(i,j-1,k)-F10*fh(i,j,k)+F18*fh(i,j+1,k) &
-F6*fh(i,j+2,k)+ fh(i,j+3,k))
! set jmax and jmin 0
endif
endif
! z direction
if(Sfz(i,j,k) > ZEO)then
if(k+3 <= kmax)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
-F6*fh(i,j,k+2)+ fh(i,j,k+3))
elseif(k+2 <= kmax)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
-F6*fh(i,j,k-2)+ fh(i,j,k-3))
! set imax and imin 0
endif
elseif(Sfz(i,j,k) < ZEO)then
if(k-3 >= kmin)then
! v
! D f = ------[ - 3f - 10f + 18f - 6f + f ]
! i 12dx i-v i i+v i+2v i+3v
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k+1)-F10*fh(i,j,k)+F18*fh(i,j,k-1) &
-F6*fh(i,j,k-2)+ fh(i,j,k-3))
elseif(k-2 >= kmin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k-1 >= kmin)then
! v
! D f = ------[ 3f + 10f - 18f + 6f - f ]
! i 12dx i+v i i-v i-2v i-3v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(-F3*fh(i,j,k-1)-F10*fh(i,j,k)+F18*fh(i,j,k+1) &
-F6*fh(i,j,k+2)+ fh(i,j,k+3))
! set kmax and kmin 0
endif
endif
#endif
enddo
enddo
enddo
return
end subroutine lopsided
#elif (ghost_width == 4)
! sixth order code
! Compute advection terms in right hand sides of field equations
! v
! D f = ------[ 2f - 24f - 35f + 80f - 30f + 8f - f ]
! i 60dx i-2v i-v i i+v i+2v i+3v i+4v
!
! where
!
! i
! |B |
! v = -----
! i
! B
!
!-----------------------------------------------------------------------------
subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
implicit none
!~~~~~~> Input parameters:
integer, intent(in) :: ex(1:3),Symmetry
real*8, intent(in) :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
real*8,dimension(ex(1),ex(2),ex(3)),intent(in) :: f,Sfx,Sfy,Sfz
real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
real*8,dimension(3),intent(in) ::SoA
!~~~~~~> local variables:
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: dX,dY,dZ
real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,F24=2.4d1,F35=3.5d1,F80=8.d1,F30=3.d1,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
real*8, parameter :: F10=1.d1,F77=7.7d1,F150=1.5d2,F100=1.d2,F50=5.d1,F15=1.5d1
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
d60dx = ONE/F60/dX
d60dy = ONE/F60/dY
d60dz = ONE/F60/dZ
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
call symmetry_bd(4,ex,f,fh,SoA)
! upper bound set ex-1 only for efficiency,
! the loop body will set ex 0 also
!$omp parallel do collapse(2) private(i,j,k)
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(Sfx(i,j,k) >= ZEO .and. i+4 <= imax .and. i-2 >= imin)then
! v
! D f = ------[ 2f - 24f - 35f + 80f - 30f + 8f - f ]
! i 60dx i-2v i-v i i+v i+2v i+3v i+4v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d60dx*(TWO*fh(i-2,j,k)-F24*fh(i-1,j,k)-F35*fh(i,j,k)+F80*fh(i+1,j,k) &
-F30*fh(i+2,j,k)+EIT*fh(i+3,j,k)- fh(i+4,j,k))
elseif(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-1 >= imin)then
! v
! D f = ------[-10f - 77f + 150f - 100f + 50f -15f + 2f ]
! i 60dx i-v i i+v i+2v i+3v i+4v i+5v
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d60dx*(-F10*fh(i-1,j,k)-F77*fh(i ,j,k)+F150*fh(i+1,j,k)-F100*fh(i+2,j,k) &
+F50*fh(i+3,j,k)-F15*fh(i+4,j,k)+ TWO*fh(i+5,j,k))
elseif(Sfx(i,j,k) <= ZEO .and. i-4 >= imin .and. i+2 <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d60dx*(TWO*fh(i+2,j,k)-F24*fh(i+1,j,k)-F35*fh(i,j,k)+F80*fh(i-1,j,k) &
-F30*fh(i-2,j,k)+EIT*fh(i-3,j,k)- fh(i-4,j,k))
elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+1 <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d60dx*(-F10*fh(i+1,j,k)-F77*fh(i ,j,k)+F150*fh(i-1,j,k)-F100*fh(i-2,j,k) &
+F50*fh(i-3,j,k)-F15*fh(i-4,j,k)+ TWO*fh(i-5,j,k))
elseif(i+3 <= imax .and. i-3 >= imin)then
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(Sfy(i,j,k) >= ZEO .and. j+4 <= jmax .and. j-2 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d60dy*(TWO*fh(i,j-2,k)-F24*fh(i,j-1,k)-F35*fh(i,j,k)+F80*fh(i,j+1,k) &
-F30*fh(i,j+2,k)+EIT*fh(i,j+3,k)- fh(i,j+4,k))
elseif(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-1 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d60dy*(-F10*fh(i,j-1,k)-F77*fh(i,j ,k)+F150*fh(i,j+1,k)-F100*fh(i,j+2,k) &
+F50*fh(i,j+3,k)-F15*fh(i,j+4,k)+ TWO*fh(i,j+5,k))
elseif(Sfy(i,j,k) <= ZEO .and. j-4 >= jmin .and. j+2 <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d60dy*(TWO*fh(i,j+2,k)-F24*fh(i,j+1,k)-F35*fh(i,j,k)+F80*fh(i,j-1,k) &
-F30*fh(i,j-2,k)+EIT*fh(i,j-3,k)- fh(i,j-4,k))
elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+1 <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d60dy*(-F10*fh(i,j+1,k)-F77*fh(i,j ,k)+F150*fh(i,j-1,k)-F100*fh(i,j-2,k) &
+F50*fh(i,j-3,k)-F15*fh(i,j-4,k)+ TWO*fh(i,j-5,k))
elseif(j+3 <= jmax .and. j-3 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmin and jmax 0
endif
!! z direction
if(Sfz(i,j,k) >= ZEO .and. k+4 <= kmax .and. k-2 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k-2)-F24*fh(i,j,k-1)-F35*fh(i,j,k)+F80*fh(i,j,k+1) &
-F30*fh(i,j,k+2)+EIT*fh(i,j,k+3)- fh(i,j,k+4))
elseif(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-1 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k-1)-F77*fh(i,j,k )+F150*fh(i,j,k+1)-F100*fh(i,j,k+2) &
+F50*fh(i,j,k+3)-F15*fh(i,j,k+4)+ TWO*fh(i,j,k+5))
elseif(Sfz(i,j,k) <= ZEO .and. k-4 >= kmin .and. k+2 <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d60dz*(TWO*fh(i,j,k+2)-F24*fh(i,j,k+1)-F35*fh(i,j,k)+F80*fh(i,j,k-1) &
-F30*fh(i,j,k-2)+EIT*fh(i,j,k-3)- fh(i,j,k-4))
elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+1 <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d60dz*(-F10*fh(i,j,k+1)-F77*fh(i,j,k )+F150*fh(i,j,k-1)-F100*fh(i,j,k-2) &
+F50*fh(i,j,k-3)-F15*fh(i,j,k-4)+ TWO*fh(i,j,k-5))
elseif(k+3 <= kmax .and. k-3 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmin and kmax 0
endif
enddo
enddo
enddo
return
end subroutine lopsided
#elif (ghost_width == 5)
! eighth order code
!-----------------------------------------------------------------------------
! PRD 77, 024034 (2008)
! Compute advection terms in right hand sides of field equations
! v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
! D f = --------------------------------------------------------------------------------------------------------------------------
! i 840 dx
!
! where
!
! i
! |B |
! v = -----
! i
! B
!
!-----------------------------------------------------------------------------
subroutine lopsided(ex,X,Y,Z,f,f_rhs,Sfx,Sfy,Sfz,Symmetry,SoA)
implicit none
!~~~~~~> Input parameters:
integer, intent(in) :: ex(1:3),Symmetry
real*8, intent(in) :: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3))
real*8,dimension(ex(1),ex(2),ex(3)),intent(in) :: f,Sfx,Sfy,Sfz
real*8,dimension(ex(1),ex(2),ex(3)),intent(inout):: f_rhs
real*8,dimension(3),intent(in) ::SoA
!~~~~~~> local variables:
real*8,dimension(-4:ex(1),-4:ex(2),-4:ex(3)) :: fh
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: dX,dY,dZ
real*8 :: d840dx,d840dy,d840dz,d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,F30=3.d1,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1,F140=1.4d2,THR=3.d0
real*8, parameter :: F840=8.4d2,F5=5.d0,F420=4.2d2,F378=3.78d2,F1050=1.05d3
real*8, parameter :: F32=3.2d1,F168=1.68d2,F672=6.72d2
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
d840dx = ONE/F840/dX
d840dy = ONE/F840/dY
d840dz = ONE/F840/dZ
d60dx = ONE/F60/dX
d60dy = ONE/F60/dY
d60dz = ONE/F60/dZ
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -4
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -4
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -4
call symmetry_bd(5,ex,f,fh,SoA)
! upper bound set ex-1 only for efficiency,
! the loop body will set ex 0 also
!$omp parallel do collapse(2) private(i,j,k)
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(Sfx(i,j,k) >= ZEO .and. i+5 <= imax .and. i-3 >= imin)then
! v [ - 5 f(i-3v) + 60 f(i-2v) - 420 f(i-v) - 378 f(i) + 1050 f(i+v) - 420 f(i+2v) + 140 f(i+3v) - 30 f(i+4v) + 3 f(i+5v)]
! D f = --------------------------------------------------------------------------------------------------------------------------
! i 840 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d840dx*(-F5*fh(i-3,j,k)+F60 *fh(i-2,j,k)-F420*fh(i-1,j,k)-F378*fh(i ,j,k) &
+F1050*fh(i+1,j,k)-F420*fh(i+2,j,k)+F140*fh(i+3,j,k)-F30 *fh(i+4,j,k)+THR*fh(i+5,j,k))
elseif(Sfx(i,j,k) <= ZEO .and. i-5 >= imin .and. i+3 <= imax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfx(i,j,k)*d840dx*(-F5*fh(i+3,j,k)+F60 *fh(i+2,j,k)-F420*fh(i+1,j,k)-F378*fh(i ,j,k) &
+F1050*fh(i-1,j,k)-F420*fh(i-2,j,k)+F140*fh(i-3,j,k)- F30*fh(i-4,j,k)+THR*fh(i-5,j,k))
elseif(i+4 <= imax .and. i-4 >= imin)then
! 3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
! fx(i) = -------------------------------------------------------------------------------------------------
! 840 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+ &
F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
elseif(i+3 <= imax .and. i-3 >= imin)then
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfx(i,j,k)*d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfx(i,j,k)*d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(Sfy(i,j,k) >= ZEO .and. j+5 <= jmax .and. j-3 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d840dy*(-F5*fh(i,j-3,k)+F60 *fh(i,j-2,k)-F420*fh(i,j-1,k)-F378*fh(i,j ,k) &
+F1050*fh(i,j+1,k)-F420*fh(i,j+2,k)+F140*fh(i,j+3,k)-F30 *fh(i,j+4,k)+THR*fh(i,j+5,k))
elseif(Sfy(i,j,k) <= ZEO .and. j-5 >= jmin .and. j+3 <= jmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfy(i,j,k)*d840dy*(-F5*fh(i,j+3,k)+F60 *fh(i,j+2,k)-F420*fh(i,j+1,k)-F378*fh(i,j ,k) &
+F1050*fh(i,j-1,k)-F420*fh(i,j-2,k)+F140*fh(i,j-3,k)- F30*fh(i,j-4,k)+THR*fh(i,j-5,k))
elseif(j+4 <= jmax .and. j-4 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+ &
F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
elseif(j+3 <= jmax .and. j-3 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfy(i,j,k)*d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
f_rhs(i,j,k)=f_rhs(i,j,k) + Sfy(i,j,k)*d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmin and jmax 0
endif
!! z direction
if(Sfz(i,j,k) >= ZEO .and. k+5 <= kmax .and. k-3 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k-3)+F60 *fh(i,j,k-2)-F420*fh(i,j,k-1)-F378*fh(i,j,k ) &
+F1050*fh(i,j,k+1)-F420*fh(i,j,k+2)+F140*fh(i,j,k+3)-F30 *fh(i,j,k+4)+THR*fh(i,j,k+5))
elseif(Sfz(i,j,k) <= ZEO .and. k-5 >= kmin .and. k+3 <= kmax)then
f_rhs(i,j,k)=f_rhs(i,j,k)- &
Sfz(i,j,k)*d840dz*(-F5*fh(i,j,k+3)+F60 *fh(i,j,k+2)-F420*fh(i,j,k+1)-F378*fh(i,j,k ) &
+F1050*fh(i,j,k-1)-F420*fh(i,j,k-2)+F140*fh(i,j,k-3)- F30*fh(i,j,k-4)+THR*fh(i,j,k-5))
elseif(k+4 <= kmax .and. k-4 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+ &
F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
elseif(k+3 <= kmax .and. k-3 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+ &
Sfz(i,j,k)*d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
f_rhs(i,j,k)=f_rhs(i,j,k)+Sfz(i,j,k)*d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmin and kmax 0
endif
enddo
enddo
enddo
return
end subroutine lopsided
#endif
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