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filters.f90
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subroutine filter(af)
USE decomp_2d
USE param
USE parfiX
USE parfiY
USE parfiZ
!=================================================
! Discrete low-pass filter according to
!=================================================
implicit none
real(mytype),intent(in) :: af
real(mytype) :: af1,afn
integer :: i,j,k
! Set the coefficient for the discrete filter following
! the tridiagonal filtering of Motheau and Abraham, JCP 2016
! Filter should be -0.5<filax<0.5
! General Case (entire points)
! alpha*fhat(i-1)+fhat(i)+alpha*fhat(i+1)=af(i)+b/2*[f(i+1)+f(i-1)] + ...
! Coefficients are calculated according to the report of Gaitonde & Visbal, 1998,
! "High-order schemes for Navier-Stokes equations: Algorithm and implementation into FDL3DI"
!========================================
! Define filter coefficients for X-pencil
!========================================
fialx=af ! alpha_f
!Interior points
fiaix=(11. + 10.*af)/16. ! a
fibix=0.5*(15. + 34.*af)/32. ! b/2
ficix=0.5*(-3. + 6.*af)/16. ! c/2
fidix=0.5*(1. - 2.*af)/32. ! d/2
! Explicit third-order filters near the boundaries!
!Boundary point 1
af1=0.
fia1x=7./8.+af/8. ! a1/2
fib1x=3./8.+5.*af/8. ! b1/2
fic1x=-3./8.+3./8.*af ! c1/2
fid1x=1./8.-1./8.*af ! d1/2
!Boundary point 2 (Third order)
fia2x=1./8.+3./4.*af ! a2
fib2x=5./8.+3./4.*af ! b2/2
fic2x=3./8.+af/4. ! c2/2
fid2x=-1./8.+af/4. ! d2/2
!Boundary point 3 (Fifth order)
fia3x= -1./32.+af/16. ! a3
fib3x= 5./32.+11./16.*af ! b3/2
fic3x= 11./16.+5.*af/8. ! c3/2
fid3x= 5./16.+3.*af/8. ! d3/2
fie3x=-5./32.+5.*af/16. ! e3/2
fif3x=1./32.-af/16. ! f3/2
!Boundary point n
afn=0.
fianx=7./8.+af/8. ! a1/2
fibnx=3./8.+5.*af/8. ! b1/2
ficnx=-3./8.+3./8.*af ! c1/2
fidnx=1./8.-1./8.*af ! d1/2
!Boundary point m=n-1
fiamx=1./8.+3./4.*af ! a2
fibmx=5./8.+3./4.*af ! b2/2
ficmx=3./8.+af/4. ! c2/2
fidmx=-1./8.+af/4. ! d2/2
!Boundary point p=n-2 (Fifth order)
fiapx= -1./32.+af/16. ! a3
fibpx= 5./32.+11./16.*af ! b3/2
ficpx= 11./16.+5.*af/8. ! c3/2
fidpx= 5./16.+3.*af/8. ! d3/2
fiepx=-5./32.+5.*af/16. ! e3/2
fifpx=1./32.-af/16. ! f3/2
! Set the coefficients for the matrix A
! Periodic case
if (nclx.eq.0) then
fiffx(1) =af
fiffx(2) =af
fiffx(nx-2)=af
fiffx(nx-1)=af
fiffx(nx) =0.
fifcx(1) =2.
fifcx(2) =1.
fifcx(nx-2)=1.
fifcx(nx-1)=1.
fifcx(nx )=1.+af*af
fifbx(1) =af
fifbx(2) =af
fifbx(nx-2)=af
fifbx(nx-1)=af
fifbx(nx )=0.
do i=3,nx-3
fiffx(i)=af
fifcx(i)=1.
fifbx(i)=af
enddo
endif
if (nclx.eq.1) then
fiffx(1) =af1
fiffx(2) =af
fiffx(ny-2)=af
fiffx(ny-1)=af
fiffy(ny) =0.
fifcx(1) =1.
fifcx(2) =1.
fifcx(nx-2)=1.
fifcx(nx-1)=1.
fifcx(nx )=1.
fifbx(1) =af
fifbx(2) =af
fifbx(nx-2)=af
fifbx(nx-1)=afn
fifbx(nx )=0.
do i=3,nx-3
fiffy(i)=af
fifcy(i)=1.
fifby(i)=af
enddo
endif
if (nclx.eq.2) then
fiffx(1) =af1
fiffx(2) =af
fiffx(nx-2)=af
fiffx(nx-1)=af
fiffx(nx) =0.
fifcx(1) =1.
fifcx(2) =1.
fifcx(nx-2)=1.
fifcx(nx-1)=1.
fifcx(nx )=1.
fifbx(1) =af
fifbx(2) =af
fifbx(nx-2)=af
fifbx(nx-1)=afn
fifbx(nx )=0.
do i=3,nx-3
fiffx(i)=af
fifcx(i)=1.
fifbx(i)=af
enddo
endif
! Prepare coefficients to be used in the Thomas Algorithm
do i=1,nx
fiffxp(i)=fiffx(i)
enddo
call prepare (fifbx,fifcx,fiffx,fifsx,fifwx,nx)
call prepare (fifbx,fifcx,fiffxp,fifsxp,fifwxp,nx)
if (nclx.eq.1) then
fiffx(1)=0.0_mytype
fifbx(nx-1)=0.0_mytype
call prepare (fifbx,fifcx,fiffx,fifsx,fifwx,nx)
endif
!========================================
! Define filter coefficients for Y-pencil
!========================================
fialy=af ! alpha_f
!Interior points
fiajy=(11. + 10.*af)/16. ! a
fibjy=0.5*(15. + 34.*af)/32. ! b/2
ficjy=0.5*(-3. + 6.*af)/16. ! c/2
fidjy=0.5*(1. - 2.*af)/32. ! d/2
! Explicit third-order filters near the boundaries!
!Boundary point 1
af1=0.
fia1y=7./8.+af/8. ! a1/2
fib1y=3./8.+5.*af/8. ! b1/2
fic1y=-3./8.+3./8.*af ! c1/2
fid1y=1./8.-1./8.*af ! d1/2
!Boundary point 2 (Third order)
fia2y=1./8.+3./4.*af ! a2
fib2y=5./8.+3./4.*af ! b2/2
fic2y=3./8.+af/4. ! c2/2
fid2y=-1./8.+af/4. ! d2/2
!Boundary point 3 (Fifth order)
fia3y= -1./32.+af/16. ! a3
fib3y= 5./32.+11./16.*af ! b3/2
fic3y= 11./16.+5.*af/8. ! c3/2
fid3y= 5./16.+3.*af/8. ! d3/2
fie3y=-5./32.+5.*af/16. ! e3/2
fif3y=1./32.-af/16. ! f3/2
!Boundary point n
afn=0.
fiany=7./8.+af/8. ! a1/2
fibny=3./8.+5.*af/8. ! b1/2
ficny=-3./8.+3./8.*af ! c1/2
fidny=1./8.-1./8.*af ! d1/2
!Boundary point m=n-1
fiamy=1./8.+3./4.*af ! a2
fibmy=5./8.+3./4.*af ! b2/2
ficmy=3./8.+af/4. ! c2/2
fidmy=-1./8.+af/4. ! d2/2
!Boundary point p=n-2 (Fifth order)
fiapy= -1./32.+af/16. ! a3
fibpy= 5./32.+11./16.*af ! b3/2
ficpy= 11./16.+5.*af/8. ! c3/2
fidpy= 5./16.+3.*af/8. ! d3/2
fiepy=-5./32.+5.*af/16. ! e3/2
fifpy=1./32.-af/16. ! f3/2
! Define coefficients
if (ncly.eq.0) then
fiffy(1) =af
fiffy(2) =af
fiffy(ny-2)=af
fiffy(ny-1)=af
fiffy(ny) =0.
fifcy(1) =2.
fifcy(2) =1.
fifcy(ny-2)=1.
fifcy(ny-1)=1.
fifcy(ny )=1.+af*af
fifby(1) =af
fifby(2) =af
fifby(ny-2)=af
fifby(ny-1)=af
fifby(ny )=0.
do j=3,ny-3
fiffy(j)=af
fifcy(j)=1.
fifby(j)=af
enddo
endif
if (ncly.eq.1) then
fiffy(1) =af+af
fiffy(2) =af
fiffy(ny-2)=af
fiffy(ny-1)=af
fiffy(ny) =0.0_mytype
fifcy(1) =1.0_mytype
fifcy(2) =1.0_mytype
fifcy(ny-2)=1.0_mytype
fifcy(ny-1)=1.0_mytype
fifcy(ny )=1.0_mytype
fifby(1) =af
fifby(2) =af
fifby(ny-2)=af
fifby(ny-1)=af+af
fifby(ny )=0.0_mytype
do j=3,ny-3
fiffy(j)=af
fifcy(j)=1.0_mytype
fifby(j)=af
enddo
endif
if (ncly.eq.2) then
fiffy(1) =af1
fiffy(2) =af
fiffy(ny-2)=af
fiffy(ny-1)=af
fiffy(ny) =0.0_mytype
fifcy(1) =1.0_mytype
fifcy(2) =1.0_mytype
fifcy(ny-2)=1.0_mytype
fifcy(ny-1)=1.0_mytype
fifcy(ny )=1.0_mytype
fifby(1) =af
fifby(2) =af
fifby(ny-2)=af
fifby(ny-1)=afn
fifby(ny )=0.0_mytype
do j=3,ny-3
fiffy(j)=af
fifcy(j)=1.0_mytype
fifby(j)=af
enddo
endif
do j=1,ny
fiffyp(j)=fiffy(j)
enddo
call prepare (fifby,fifcy,fiffy,fifsy,fifwy,ny)
call prepare (fifby,fifcy,fiffyp,fifsyp,fifwyp,ny)
if (ncly.eq.1) then
fiffy(1)=0.0_mytype
fifby(ny-1)=0.0_mytype
call prepare (fifby,fifcy,fiffy,fifsy,fifwy,ny)
endif
!========================================
! Define filter coefficients for Z-pencil
!========================================
fialz=af ! alpha_f
fiakz=(11. + 10.*af)/16. ! a
fibkz=0.5*(15. + 34.*af)/32. ! b/2
fickz=0.5*(-3. + 6.*af)/16. ! c/2
fidkz=0.5*(1. - 2.*af)/32. ! d/2
! Explicit third-order filters near the boundaries!
!Boundary point 1
af1=0.
fia1z=7./8.+af/8. ! a1/2
fib1z=3./8.+5.*af/8. ! b1/2
fic1z=-3./8.+3./8.*af ! c1/2
fid1z=1./8.-1./8.*af ! d1/2
!Boundary point 2 (Third order)
fia2z=1./8.+3./4.*af ! a2
fib2z=5./8.+3./4.*af ! b2/2
fic2z=3./8.+af/4. ! c2/2
fid2z=-1./8.+af/4. ! d2/2
!Boundary point 3 (Fifth order)
fia3z= -1./32.+af/16. ! a3
fib3z= 5./32.+11./16.*af ! b3/2
fic3z= 11./16.+5.*af/8. ! c3/2
fid3z= 5./16.+3.*af/8. ! d3/2
fie3z=-5./32.+5.*af/16. ! e3/2
fif3z=1./32.-af/16. ! f3/2
!Boundary point n
afn=0.
fianz=7./8.+af/8. ! a1/2
fibnz=3./8.+5.*af/8. ! b1/2
ficnz=-3./8.+3./8.*af ! c1/2
fidnz=1./8.-1./8.*af ! d1/2
!Boundary point m=n-1
fiamz=1./8.+3./4.*af ! a2
fibmz=5./8.+3./4.*af ! b2/2
ficmz=3./8.+af/4. ! c2/2
fidmz=-1./8.+af/4. ! d2/2
!Boundary point p=n-2 (Fifth order)
fiapz= -1./32.+af/16. ! a3
fibpz= 5./32.+11./16.*af ! b3/2
ficpz= 11./16.+5.*af/8. ! c3/2
fidpz= 5./16.+3.*af/8. ! d3/2
fiepz=-5./32.+5.*af/16. ! e3/2
fifpz=1./32.-af/16. ! f3/2
if (nclz.eq.0) then
fiffz(1) =af
fiffz(2) =af
fiffz(nz-2)=af
fiffz(nz-1)=af
fiffz(nz) =0.
fifcz(1) =2.
fifcz(2) =1.
fifcz(nz-2)=1.
fifcz(nz-1)=1.
fifcz(nz )=1.+af*af
fifbz(1) =af
fifbz(2) =af
fifbz(nz-2)=af
fifbz(nz-1)=af
fifbz(nz )=0.
do k=3,nz-3
fiffz(k)=af
fifcz(k)=1.
fifbz(k)=af
enddo
endif
if (nclz.eq.1) then
fiffz(1) =af+af
fiffz(2) =af
fiffz(nz-2)=af
fiffz(nz-1)=af
fiffz(nz) =0.0_mytype
fifcz(1) =1.0_mytype
fifcz(2) =1.0_mytype
fifcz(nz-2)=1.0_mytype
fifcz(nz-1)=1.0_mytype
fifcz(nz )=1.0_mytype
fifbz(1) =af
fifbz(2) =af
fifbz(nz-2)=af
fifbz(nz-1)=af+af
fifbz(nz )=0.0_mytype
do k=3,nz-3
fiffz(k)=af
fifcz(k)=1.0_mytype
fifbz(k)=af
enddo
endif
if (nclz.eq.2) then
fiffz(1) =af1
fiffz(2) =af
fiffz(nz-2)=af
fiffz(nz-1)=af
fiffz(nz) =0.
fifcz(1) =1.
fifcz(2) =1.
fifcz(nz-2)=1.
fifcz(nz-1)=1.
fifcz(nz )=1.
fifbz(1) =af
fifbz(2) =af
fifbz(nz-2)=af
fifbz(nz-1)=afn
fifbz(nz )=0.
do k=3,nz-3
fiffz(k)=af
fifcz(k)=1.
fifbz(k)=af
enddo
endif
do k=1,nz
fiffzp(k)=fiffz(k)
enddo
call prepare (fifbz,fifcz,fiffz,fifsz,fifwz,nz)
call prepare (fifbz,fifcz,fiffzp,fifszp,fifwzp,nz)
if (nclz.eq.1) then
fiffz(1)=0.0_mytype
fifbz(nz-1)=0.0_mytype
call prepare (fifbz,fifcz,fiffz,fifsz,fifwz,nz)
endif
return
end subroutine filter
subroutine filx(tx,ux,rx,fisx,fiffx,fifsx,fifwx,nx,ny,nz,npaire)
USE param, only: nclx, ncly, nclz
USE parfiX
implicit none
integer :: nx,ny,nz,npaire,i,j,k
real(mytype), dimension(nx,ny,nz) :: tx,ux,rx
real(mytype), dimension(ny,nz) :: fisx
real(mytype), dimension(nx) :: fiffx,fifsx,fifwx
! This is for periodic boundary conditions
if (nclx==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=fiaix*ux(1,j,k)+fibix*(ux(2,j,k)+ux(nx,j,k))&
+ficix*(ux(3,j,k)+ux(nx-1,j,k))&
+fidix*(ux(4,j,k)+ux(nx-2,j,k))
rx(1,j,k)=-1.
tx(2,j,k)=fiaix*ux(2,j,k)+fibix*(ux(3,j,k)+ux(1,j,k))&
+ficix*(ux(4,j,k)+ux(nx,j,k))&
+fidix*(ux(5,j,k)+ux(nx-1,j,k))
rx(2,j,k)=0.
tx(3,j,k)=fiaix*ux(3,j,k)+fibix*(ux(4,j,k)+ux(2,j,k))&
+ficix*(ux(5,j,k)+ux(1,j,k))&
+fidix*(ux(6,j,k)+ux(nx,j,k))
rx(3,j,k)=0.
do i=4,nx-3
tx(i,j,k)=fiaix*ux(i,j,k)+fibix*(ux(i+1,j,k)+ux(i-1,j,k))&
+ficix*(ux(i+2,j,k)+ux(i-2,j,k))&
+fidix*(ux(i+3,j,k)+ux(i-3,j,k))
rx(i,j,k)=0.
enddo
tx(nx-2,j,k)=fiaix*ux(nx-2,j,k)+fibix*(ux(nx-3,j,k)+ux(nx-1,j,k))&
+ficix*(ux(nx-4,j,k)+ux(nx,j,k))&
+fidix*(ux(nx-5,j,k)+ux(1,j,k))
rx(nx-2,j,k)=0.
tx(nx-1,j,k)=fiaix*ux(nx-1,j,k)+fibix*(ux(nx-2,j,k)+ux(nx,j,k))&
+ficix*(ux(nx-3,j,k)+ux(1,j,k))&
+fidix*(ux(nx-4,j,k)+ux(2,j,k))
rx(nx-1,j,k)=0.
tx(nx,j,k)=fiaix*ux(nx,j,k)+fibix*(ux(nx-1,j,k)+ux(1,j,k))&
+ficix*(ux(nx-2,j,k)+ux(2,j,k))&
+fidix*(ux(nx-3,j,k)+ux(3,j,k))
rx(nx,j,k)=fialx
do i=2, nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fifsx(i)
rx(i,j,k)=rx(i,j,k)-rx(i-1,j,k)*fifsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fifwx(nx)
rx(nx,j,k)=rx(nx,j,k)*fifwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-fiffx(i)*tx(i+1,j,k))*fifwx(i)
rx(i,j,k)=(rx(i,j,k)-fiffx(i)*rx(i+1,j,k))*fifwx(i)
enddo
fisx(j,k)=(tx(1,j,k)-fialx*tx(nx,j,k))&
/(1.+rx(1,j,k)-fialx*rx(nx,j,k))
do i=1,nx
tx(i,j,k)=tx(i,j,k)-fisx(j,k)*rx(i,j,k)
enddo
enddo
enddo
endif
if (nclx==2) then
do k=1,nz
do j=1,ny
tx(1,j,k)=ux(1,j,k)
tx(2,j,k)=fia2x*ux(1,j,k)+fib2x*ux(2,j,k)+fic2x*ux(3,j,k)+&
fid2x*ux(4,j,k)
tx(3,j,k)=fia3x*ux(1,j,k)+fib3x*ux(2,j,k)+fic3x*ux(3,j,k)+&
fid3x*ux(4,j,k)+fie3x*ux(5,j,k)+fif3x*ux(6,j,k)
do i=4,nx-3
tx(i,j,k)=fiaix*ux(i,j,k)+fibix*(ux(i+1,j,k)+ux(i-1,j,k))&
+ficix*(ux(i+2,j,k)+ux(i-2,j,k))&
+fidix*(ux(i+3,j,k)+ux(i-3,j,k))
enddo
tx(nx,j,k)=ux(nx,j,k)
tx(nx-1,j,k)=fiamx*ux(nx,j,k)+fibmx*ux(nx-1,j,k)+ficmx*ux(nx-2,j,k)+&
fidmx*ux(nx-3,j,k)
tx(nx-2,j,k)=fiapx*ux(nx,j,k)+fibpx*ux(nx-1,j,k)+ficpx*ux(nx-2,j,k)+&
fidpx*ux(nx-3,j,k)+fiepx*ux(nx-4,j,k)+fifpx*ux(nx-5,j,k)
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fifsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fifwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-fiffx(i)*tx(i+1,j,k))*fifwx(i)
enddo
enddo
enddo
endif
return
end subroutine filx
!********************************************************************
!
subroutine fily(ty,uy,ry,fisy,fiffy,fifsy,fifwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only: ncly, istret
USE parfiY
implicit none
integer :: nx,ny,nz,i,j,k,npaire
real(mytype), dimension(nx,ny,nz) :: ty,uy
real(mytype), dimension(nx,ny,nz) :: ry
real(mytype), dimension(nx,nz) :: fisy
real(mytype), dimension(ny) :: fiffy,fifsy,fifwy,ppy
if (ncly==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=fiajy*uy(i,1,k)+fibjy*(uy(i,2,k)+uy(i,nx,k))&
+ficjy*(uy(i,3,k)+uy(i,nx-1,k))&
+fidjy*(uy(i,4,k)+uy(i,nx-2,k))
ry(i,1,k)=-1.
ty(i,2,k)=fiajy*uy(i,2,k)+fibjy*(uy(i,3,k)+uy(i,1,k))&
+ficjy*(uy(i,4,k)+uy(i,nx,k))&
+fidjy*(uy(i,5,k)+uy(i,nx-1,k))
ry(i,2,k)=0.
ty(i,3,k)=fiajy*uy(i,3,k)+fibjy*(uy(i,4,k)+uy(i,2,k))&
+ficjy*(uy(i,5,k)+uy(i,1,k))&
+fidjy*(uy(i,6,k)+uy(i,nx,k))
ry(i,3,k)=0.
do j=4,ny-3
ty(i,j,k)=fiajy*uy(i,j,k)+fibjy*(uy(i,j+1,k)+uy(i,j-1,k))&
+ficjy*(uy(i,j+2,k)+uy(i,j-2,k))&
+fidjy*(uy(i,j+3,k)+uy(i,j-3,k))
ry(i,j,k)=0.
enddo
ty(i,ny-2,k)=fiajy*uy(i,ny-2,k)+fibjy*(uy(i,ny-3,k)+uy(i,ny-1,k))&
+ficjy*(uy(i,ny-4,k)+uy(i,ny,k))&
+fidjy*(uy(i,ny-5,k)+uy(i,1,k))
ry(i,ny-2,k)=0.
ty(i,ny-1,k)=fiajy*uy(i,ny-1,k)+fibjy*(uy(i,ny-2,k)+uy(i,ny,k))&
+ficjy*(uy(i,ny-3,k)+uy(i,1,k))&
+fidjy*(uy(i,ny-4,k)+uy(i,2,k))
ry(i,ny-1,k)=0.
ty(i,ny,k)=fiajy*uy(i,ny,k)+fibjy*(uy(i,ny-1,k)+uy(i,1,k))&
+ficjy*(uy(i,ny-2,k)+uy(i,2,k))&
+fidjy*(uy(i,ny-3,k)+uy(i,3,k))
ry(i,ny,k)=fialy
do j=2, ny
ty(i,j,k)=ty(i,j,k)-ty(i,j-1,k)*fifsy(j)
ry(i,j,k)=ry(i,j,k)-ry(i,j-1,k)*fifsy(j)
enddo
ty(i,ny,k)=ty(i,ny,k)*fifwy(ny)
ry(i,ny,k)=ry(i,ny,k)*fifwy(ny)
do j=ny-1,1,-1
ty(i,j,k)=(ty(i,j,k)-fiffy(j)*ty(i,j+1,k))*fifwy(j)
ry(i,j,k)=(ry(i,j,k)-fiffy(j)*ry(i,j+1,k))*fifwy(j)
enddo
fisy(i,k)=(ty(i,1,k)-fialy*ty(i,ny,k))&
/(1.+ry(i,1,k)-fialy*ry(i,ny,k))
do j=1,ny
ty(i,j,k)=ty(i,j,k)-fisy(i,k)*ry(i,j,k)
enddo
enddo
enddo
endif
if (ncly==1) then
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=fiajy*uy(i,1,k)+fibjy*(uy(i,2,k)+uy(i,2,k))&
+ficjy*(uy(i,3,k)+uy(i,3,k))&
+fidjy*(uy(i,4,k)+uy(i,4,k))
ty(i,2,k)=fiajy*uy(i,2,k)+fibjy*(uy(i,3,k)+uy(i,1,k))&
+ficjy*(uy(i,4,k)+uy(i,2,k))&
+fidjy*(uy(i,5,k)+uy(i,3,k))
ty(i,3,k)=fiajy*uy(i,3,k)+fibjy*(uy(i,4,k)+uy(i,2,k))&
+ficjy*(uy(i,5,k)+uy(i,1,k))&
+fidjy*(uy(i,6,k)+uy(i,2,k))
enddo
enddo
do k=1,nz
do j=4,ny-3
do i=1,nx
ty(i,j,k)=fiajy*uy(i,j,k)+fibjy*(uy(i,j+1,k)+uy(i,j-1,k))&
+ficjy*(uy(i,j+2,k)+uy(i,j-2,k))&
+fidjy*(uy(i,j+3,k)+uy(i,j-3,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=fiajy*uy(i,ny,k)+fibjy*(uy(i,ny-1,k)+uy(i,ny-1,k))&
+ficjy*(uy(i,ny-2,k)+uy(i,ny-2,k))&
+fidjy*(uy(i,ny-3,k)+uy(i,ny-3,k))
ty(i,ny-1,k)=fiajy*uy(i,ny-1,k)+fibjy*(uy(i,ny,k) +uy(i,ny-2,k))&
+ficjy*(uy(i,ny-1,k)+uy(i,ny-3,k))&
+fidjy*(uy(i,ny-2,k)+uy(i,ny-4,k))
ty(i,ny-2,k)=fiajy*uy(i,ny-2,k)+fibjy*(uy(i,ny-1,k)+uy(i,ny-3,k))&
+ficjy*(uy(i,ny,k)+uy(i,ny-4,k))&
+fidjy*(uy(i,ny-1,k)+uy(i,ny-5,k))
enddo
enddo
do k=1,nz
do j=2,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)-ty(i,j-1,k)*fifsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fifwy(ny)
enddo
enddo
do k=1,nz
do j=ny-1,1,-1
do i=1,nx
ty(i,j,k)=(ty(i,j,k)-fiffy(j)*ty(i,j+1,k))*fifwy(j)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=fiajy*uy(i,1,k)
ty(i,2,k)=fiajy*uy(i,2,k)+fibjy*(uy(i,3,k)+uy(i,1,k))&
+ficjy*(uy(i,4,k)-uy(i,2,k))&
+fidjy*(uy(i,5,k)-uy(i,3,k))
ty(i,3,k)=fiajy*uy(i,3,k)+fibjy*(uy(i,4,k)+uy(i,2,k))&
+ficjy*(uy(i,5,k)+uy(i,1,k))&
+fidjy*(uy(i,6,k)-uy(i,2,k))
enddo
enddo
do k=1,nz
do j=4,ny-3
do i=1,nx
ty(i,j,k)=fiajy*uy(i,j,k)+fibjy*(uy(i,j+1,k)+uy(i,j-1,k))&
+ficjy*(uy(i,j+2,k)+uy(i,j-2,k))&
+fidjy*(uy(i,j+3,k)+uy(i,j-3,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=fiajy*uy(i,ny,k)
ty(i,ny-1,k)=fiajy*uy(i,ny-1,k)+fibjy*(uy(i,ny,k)+uy(i,ny-2,k))&
+ficjy*(-uy(i,ny-1,k)+uy(i,ny-3,k))&
+fidjy*(-uy(i,ny-2,k)+uy(i,ny-4,k))
ty(i,ny-2,k)=fiajy*uy(i,ny-2,k)+fibjy*(uy(i,ny-1,k)+uy(i,ny-3,k))&
+ficjy*(uy(i,ny,k)+uy(i,ny-4,k))&
+fidjy*(-uy(i,ny-1,k)+uy(i,ny-5,k))
enddo
enddo
do k=1,nz
do j=2,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)-ty(i,j-1,k)*fifsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fifwy(ny)
enddo
enddo
do k=1,nz
do j=ny-1,1,-1
do i=1,nx
ty(i,j,k)=(ty(i,j,k)-fiffy(j)*ty(i,j+1,k))*fifwy(j)
enddo
enddo
enddo
endif
endif
if (ncly==2) then
do k=1,nz
do i=1,nx
ty(i,1,k)=uy(i,1,k)
ty(i,2,k)=fia2y*uy(i,1,k)+fib2y*uy(i,2,k)+fic2y*uy(i,3,k)+&
fid2y*uy(i,4,k)
do j=3,ny-2
ty(i,j,k)=fiajy*uy(i,j,k)+fibjy*(uy(i,j+1,k)+uy(i,j-1,k))&
+ficjy*(uy(i,j+2,k)+uy(i,j-2,k))&
+fidjy*(uy(i,j+3,k)+uy(i,j-3,k))
enddo
ty(i,ny,k)=uy(i,ny,k)
ty(i,ny-1,k)=fiamy*uy(i,ny,k)+fibmy*uy(i,ny-1,k)+ficmy*uy(i,ny-2,k)+&
fidmy*uy(i,ny-3,k)
do j=2,ny
ty(i,j,k)=ty(i,j,k)-ty(i,j-1,k)*fifsy(j)
enddo
ty(i,ny,k)=ty(i,ny,k)*fifwy(ny)
do j=ny-1,1,-1
ty(i,j,k)=(ty(i,j,k)-fiffy(j)*ty(i,j+1,k))*fifwy(j)
enddo
enddo
enddo
endif
end subroutine fily
subroutine filz(tz,uz,rz,fisz,fiffz,fifsz,fifwz,nx,ny,nz,npaire)
USE param, only: nclz
USE parfiZ
implicit none
integer :: nx,ny,nz,npaire,i,j,k
real(mytype), dimension(nx,ny,nz) :: tz,uz,rz
real(mytype), dimension(nx,ny) :: fisz
real(mytype), dimension(nz) :: fiffz,fifsz,fifwz
! This is for periodic boundary conditions
if (nclz==0) then
do j=1,ny
do i=1,nx
tz(i,j,1)=fiakz*uz(i,j,1)+fibkz*(uz(i,j,2)+uz(i,j,nz))&
+fickz*(uz(i,j,3)+uz(i,j,nz-1))&
+fidkz*(uz(i,j,4)+uz(i,j,nz-2))
rz(i,j,1)=-1.
tz(i,j,2)=fiakz*uz(i,j,2)+fibkz*(uz(i,j,3)+uz(i,j,1))&
+fickz*(uz(i,j,4)+uz(i,j,nz))&
+fidkz*(uz(i,j,5)+uz(i,j,nz-1))
rz(i,j,2)=0.
tz(i,j,3)=fiakz*uz(i,j,3)+fibkz*(uz(i,j,4)+uz(i,j,2))&
+fickz*(uz(i,j,5)+uz(i,j,1))&
+fidkz*(uz(i,j,6)+uz(i,j,nz))
rz(i,j,3)=0.
enddo
enddo
do k=4,nz-3
do j=1,ny
do i=1,nx
tz(i,j,k)=fiakz*uz(i,j,k)+fibkz*(uz(i,j,k+1)+uz(i,j,k-1))&
+fickz*(uz(i,j,k+2)+uz(i,j,k-2))&
+fidkz*(uz(i,j,k+3)+uz(i,j,k-3))
rz(i,j,k)=0.
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz-2)=fiakz*uz(i,j,nz-2)+fibkz*(uz(i,j,nz-3)+uz(i,j,nz-1))&
+fickz*(uz(i,j,nz-4)+uz(i,j,nz))&
+fidkz*(uz(i,j,nz-5)+uz(i,j,1))
rz(i,j,nz-2)=0.
tz(i,j,nz-1)=fiakz*uz(i,j,nz-1)+fibkz*(uz(i,j,nz-2)+uz(i,j,nz))&
+fickz*(uz(i,j,nz-3)+uz(i,j,1))&
+fidkz*(uz(i,j,nz-4)+uz(i,j,2))
rz(i,j,nz-1)=0.
tz(i,j,nz)=fiakz*uz(i,j,nz)+fibkz*(uz(i,j,nz-1)+uz(i,j,1))&
+fickz*(uz(i,j,nz-2)+uz(i,j,2))&
+fidkz*(uz(i,j,nz-3)+uz(i,j,3))
rz(i,j,nz)=fialz
enddo
enddo
do k=2,nz
do j=1,ny
do i=1,nx
tz(i,j,k)=tz(i,j,k)-tz(i,j,k-1)*fifsz(k)
rz(i,j,k)=rz(i,j,k)-rz(i,j,k-1)*fifsz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fifwz(nz)
rz(i,j,nz)=rz(i,j,nz)*fifwz(nz)
enddo
enddo
do k=nz-1,1,-1
do j=1,ny
do i=1,nx
tz(i,j,k)=(tz(i,j,k)-fiffz(k)*tz(i,j,k+1))*fifwz(k)
rz(i,j,k)=(rz(i,j,k)-fiffz(k)*rz(i,j,k+1))*fifwz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
fisz(i,j)=(tz(i,j,1)-fialz*tz(i,j,nz))&
/(1.+rz(i,j,1)-fialz*rz(i,j,nz))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx
tz(i,j,k)=tz(i,j,k)-fisz(i,j)*rz(i,j,k)
enddo
enddo
enddo
endif
if (nclz==1) then
if (npaire==1) then
do j=1,ny
do i=1,nx
tz(i,j,1)=fiakz*uz(i,j,1)+fibkz*(uz(i,j,2)+uz(i,j,2))&
+fickz*(uz(i,j,3)+uz(i,j,3))&
+fidkz*(uz(i,j,4)+uz(i,j,4))
tz(i,j,2)=fiakz*uz(i,j,2)+fibkz*(uz(i,j,3)+uz(i,j,1))&
+fickz*(uz(i,j,4)+uz(i,j,2))&
+fidkz*(uz(i,j,5)+uz(i,j,3))
tz(i,j,3)=fiakz*uz(i,j,3)+fibkz*(uz(i,j,4)+uz(i,j,2))&
+fickz*(uz(i,j,5)+uz(i,j,1))&
+fidkz*(uz(i,j,6)+uz(i,j,2))
enddo
enddo
do k=4,nz-3
do j=1,ny
do i=1,nx
tz(i,j,k)=fiakz*uz(i,j,k)+fibkz*(uz(i,j,k+1)+uz(i,j,k-1))&
+fickz*(uz(i,j,k+2)+uz(i,j,k-2))&
+fidkz*(uz(i,j,k+3)+uz(i,j,k-3))
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=fiakz*uz(i,j,nz) +fibkz*(uz(i,j,nz-1)+uz(i,j,nz-1))&
+fickz*(uz(i,j,nz-2)+uz(i,j,nz-2))&
+fidkz*(uz(i,j,nz-3)+uz(i,j,nz-3))
tz(i,j,nz-1)=fiakz*uz(i,j,nz-1)+fibkz*(uz(i,j,nz)+uz(i,j,nz-2))&
+fickz*(uz(i,j,nz-1)+uz(i,j,nz-3))&
+fidkz*(uz(i,j,nz-2)+uz(i,j,nz-4))
tz(i,j,nz-2)=fiakz*uz(i,j,nz-2)+fibkz*(uz(i,j,nz-1)+uz(i,j,nz-3))&
+fickz*(uz(i,j,nz)+uz(i,j,nz-4))&
+fidkz*(uz(i,j,nz-1)+uz(i,j,nz-5))
enddo
enddo
do k=2,nz
do j=1,ny
do i=1,nx
tz(i,j,k)=tz(i,j,k)-tz(i,j,k-1)*fifsz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fifwz(nz)
enddo
enddo
do k=nz-1,1,-1
do j=1,ny
do i=1,nx
tz(i,j,k)=(tz(i,j,k)-fiffz(k)*tz(i,j,k+1))*fifwz(k)
enddo
enddo
enddo
endif
if (npaire==0) then
do j=1,ny
do i=1,nx
tz(i,j,1)=0._mytype
tz(i,j,2)=fiakz*uz(i,j,2)+fibkz*(uz(i,j,3)+uz(i,j,1))&
+fickz*(uz(i,j,4)-uz(i,j,2))&
+fidkz*(uz(i,j,5)-uz(i,j,3))
tz(i,j,3)=fiakz*uz(i,j,3)+fibkz*(uz(i,j,4)+uz(i,j,2))&
+fickz*(uz(i,j,5)+uz(i,j,1))&
+fidkz*(uz(i,j,6)-uz(i,j,2))
enddo
enddo
do k=4,nz-3
do j=1,ny
do i=1,nx
tz(i,j,k)=fiakz*uz(i,j,k)+fibkz*(uz(i,j,k+1)+uz(i,j,k-1))&
+fickz*(uz(i,j,k+2)+uz(i,j,k-2))&
+fidkz*(uz(i,j,k+3)+uz(i,j,k-3))
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz) = 0._mytype
tz(i,j,nz-1)=fiakz*uz(i,j,nz-1)+fibkz*( uz(i,j,nz) +uz(i,j,nz-2))&
+fickz*(-uz(i,j,nz-1)+uz(i,j,nz-3))&
+fidkz*(-uz(i,j,nz-2)+uz(i,j,nz-4))
tz(i,j,nz-2)=fiakz*uz(i,j,nz-2)+fibkz*( uz(i,j,nz-1)+uz(i,j,nz-3))&
+fickz*( uz(i,j,nz) +uz(i,j,nz-4))&
+fidkz*(-uz(i,j,nz-1)+uz(i,j,nz-5))
enddo
enddo
do k=2,nz
do j=1,ny
do i=1,nx
tz(i,j,k)=tz(i,j,k)-tz(i,j,k-1)*fifsz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fifwz(nz)
enddo
enddo
do k=nz-1,1,-1
do j=1,ny
do i=1,nx
tz(i,j,k)=(tz(i,j,k)-fiffz(k)*tz(i,j,k+1))*fifwz(k)
enddo
enddo
enddo
endif
endif
return
end subroutine filz