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filter.f90
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!################################################################################
!This file is part of Incompact3d.
!
!Incompact3d
!Copyright (c) 2012 Eric Lamballais and Sylvain Laizet
!eric.lamballais@univ-poitiers.fr / sylvain.laizet@gmail.com
!
! Incompact3d is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation.
!
! Incompact3d is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with the code. If not, see <http://www.gnu.org/licenses/>.
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------
! We kindly request that you cite Incompact3d in your publications and
! presentations. The following citations are suggested:
!
! 1-Laizet S. & Lamballais E., 2009, High-order compact schemes for
! incompressible flows: a simple and efficient method with the quasi-spectral
! accuracy, J. Comp. Phys., vol 228 (15), pp 5989-6015
!
! 2-Laizet S. & Li N., 2011, Incompact3d: a powerful tool to tackle turbulence
! problems with up to 0(10^5) computational cores, Int. J. of Numerical
! Methods in Fluids, vol 67 (11), pp 1735-1757
!################################################################################
!*********************************************************************
!
subroutine filx(tx,ux,rx,sx,vx,fiffx,fifx,ficx,fibx,fibbx,filax,fiz1x,&
fiz2x,nx,ny,nz,npaire)
!
!*********************************************************************
USE param
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) :: sx,vx
real(mytype), dimension(nx) :: fiffx, fifx,ficx,fibx,fibbx,fiz1x,fiz2x
real(mytype), dimension(nx,2) :: filax
real(mytype) :: xcoef
if (nclx==0) then
do k=1,nz
do j=1,ny
rx(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(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(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))
enddo
enddo
do i=4,nx-3
do k=1,nz
do j=1,ny
rx(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
enddo
enddo
do k=1,nz
do j=1,ny
rx(nx,j,k)=fiaix*ux(nx,j,k)+&
fibix*(ux(1,j,k)+ux(nx-1,j,k))+&
ficix*(ux(2,j,k)+ux(nx-2,j,k))+&
fidix*(ux(3,j,k)+ux(nx-3,j,k))
rx(nx-1,j,k)=fiaix*ux(nx-1,j,k)+&
fibix*(ux(nx,j,k)+ux(nx-2,j,k))+&
ficix*(ux(1,j,k)+ux(nx-3,j,k))+&
fidix*(ux(2,j,k)+ux(nx-4,j,k))
rx(nx-2,j,k)=fiaix*ux(nx-2,j,k)+&
fibix*(ux(nx-1,j,k)+ux(nx-3,j,k))+&
ficix*(ux(nx,j,k)+ux(nx-4,j,k))+&
fidix*(ux(1,j,k)+ux(nx-5,j,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx-2
rx(i+1,j,k)=rx(i+1,j,k)-filax(i,1)*rx(i,j,k)
rx(i+2,j,k)=rx(i+2,j,k)-filax(i,2)*rx(i,j,k)
enddo
enddo
enddo
do k=1,nz
do j=1,ny
rx(nx,j,k)=rx(nx,j,k)-filax(nx-1,1)*rx(nx-1,j,k)
enddo
enddo
do k=1,nz
do j=1,ny
rx(nx,j,k)=rx(nx,j,k)*fiffx(nx)
rx(nx-1,j,k)=(rx(nx-1,j,k)-fifx(nx-1)*rx(nx,j,k))*&
fiffx(nx-1)
rx(nx-2,j,k)=(rx(nx-2,j,k)-fifx(nx-2)*rx(nx-1,j,k)-&
ficx(nx-2)*rx(nx,j,k))*fiffx(nx-2)
rx(nx-3,j,k)=(rx(nx-3,j,k)-fifx(nx-3)*rx(nx-2,j,k)-&
ficx(nx-3)*rx(nx-1,j,k)-&
fibx(nx-3)*rx(nx,j,k))*fiffx(nx-3)
enddo
enddo
do k=1,nz
do j=1,ny
do i=nx-4,1,-1
rx(i,j,k)=(rx(i,j,k)-fifx(i)*rx(i+1,j,k)-&
ficx(i)*rx(i+2,j,k)-&
fibx(i)*rx(i+3,j,k)-&
fibbx(i)*rx(i+4,j,k))*fiffx(i)
enddo
enddo
enddo
xcoef=1._mytype/2._mytype
do k=1,nz
do j=1,ny
sx(j,k)=fih1x*(-fibex*rx(1,j,k)+fibex*rx(nx-1,j,k)*xcoef+&
fialx*rx(nx,j,k)*xcoef)+&
fih2x*(fialx*rx(1,j,k)*xcoef+fibex*rx(2,j,k)*xcoef-&
fibex*rx(nx,j,k))
vx(j,k)=fih3x*(-fibex*rx(1,j,k)+fibex*rx(nx-1,j,k)*xcoef+&
fialx*rx(nx,j,k)*xcoef)+&
fih4x*(fialx*rx(1,j,k)*xcoef+fibex*rx(2,j,k)*xcoef-&
fibex*rx(nx,j,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx
tx(i,j,k)=rx(i,j,k)-fiz1x(i)*sx(j,k)-fiz2x(i)*vx(j,k)
enddo
enddo
enddo
endif
if (nclx==1) then
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=fiaix*ux(1,j,k)+&
fibix*(ux(2,j,k)+ux(2,j,k))+&
ficix*(ux(3,j,k)+ux(3,j,k))+&
fidix*(ux(4,j,k)+ux(4,j,k))
tx(2,j,k)=fiaix*ux(2,j,k)+&
fibix*(ux(3,j,k)+ux(1,j,k))+&
ficix*(ux(4,j,k)+ux(2,j,k))+&
fidix*(ux(5,j,k)+ux(3,j,k))
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(2,j,k))
enddo
enddo
do i=4,nx-3
do k=1,nz
do j=1,ny
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
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=fiaix*ux(nx,j,k)+&
fibix*(ux(nx-1,j,k)+ux(nx-1,j,k))+&
ficix*(ux(nx-2,j,k)+ux(nx-2,j,k))+&
fidix*(ux(nx-3,j,k)+ux(nx-3,j,k))
tx(nx-1,j,k)=fiaix*ux(nx-1,j,k)+&
fibix*(ux(nx,j,k)+ux(nx-2,j,k))+&
ficix*(ux(nx-1,j,k)+ux(nx-3,j,k))+&
fidix*(ux(nx-2,j,k)+ux(nx-4,j,k))
tx(nx-2,j,k)=fiaix*ux(nx-2,j,k)+&
fibix*(ux(nx-1,j,k)+ux(nx-3,j,k))+&
ficix*(ux(nx,j,k)+ux(nx-4,j,k))+&
fidix*(ux(nx-1,j,k)+ux(nx-5,j,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx-2
tx(i+1,j,k)=tx(i+1,j,k)-filax(i,1)*tx(i,j,k)
tx(i+2,j,k)=tx(i+2,j,k)-filax(i,2)*tx(i,j,k)
enddo
tx(nx,j,k)=tx(nx,j,k)-filax(nx-1,1)*tx(nx-1,j,k)
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=tx(nx,j,k)*fiffx(nx)
tx(nx-1,j,k)=(tx(nx-1,j,k)-fifx(nx-1)*tx(nx,j,k))*&
fiffx(nx-1)
tx(nx-2,j,k)=(tx(nx-2,j,k)-fifx(nx-2)*tx(nx-1,j,k)-&
ficx(nx-2)*tx(nx,j,k))*fiffx(nx-2)
tx(nx-3,j,k)=(tx(nx-3,j,k)-fifx(nx-3)*tx(nx-2,j,k)-&
ficx(nx-3)*tx(nx-1,j,k)-&
fibx(nx-3)*tx(nx,j,k))*fiffx(nx-3)
do i=nx-4,1,-1
tx(i,j,k)=(tx(i,j,k)-fifx(i)*tx(i+1,j,k)-&
ficx(i)*tx(i+2,j,k)-&
fibx(i)*tx(i+3,j,k)-&
fibbx(i)*tx(i+4,j,k))*fiffx(i)
enddo
enddo
enddo
endif
if (npaire==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(2,j,k))+&
ficix*(ux(3,j,k)-ux(3,j,k))+&
fidix*(ux(4,j,k)-ux(4,j,k))
tx(2,j,k)=fiaix*ux(2,j,k)+&
fibix*(ux(3,j,k)+ux(1,j,k))+&
ficix*(ux(4,j,k)-ux(2,j,k))+&
fidix*(ux(5,j,k)-ux(3,j,k))
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(2,j,k))
enddo
enddo
do i=4,nx-3
do k=1,nz
do j=1,ny
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
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=fiaix*ux(nx,j,k)+&
fibix*(ux(nx-1,j,k)-ux(nx-1,j,k))+&
ficix*(ux(nx-2,j,k)-ux(nx-2,j,k))+&
fidix*(ux(nx-3,j,k)-ux(nx-3,j,k))
tx(nx-1,j,k)=fiaix*ux(nx-1,j,k)+&
fibix*(ux(nx,j,k)+ux(nx-2,j,k))+&
ficix*(-ux(nx-1,j,k)+ux(nx-3,j,k))+&
fidix*(-ux(nx-2,j,k)+ux(nx-4,j,k))
tx(nx-2,j,k)=fiaix*ux(nx-2,j,k)+&
fibix*(ux(nx-1,j,k)+ux(nx-3,j,k))+&
ficix*(ux(nx,j,k)+ux(nx-4,j,k))+&
fidix*(-ux(nx-1,j,k)+ux(nx-5,j,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx-2
tx(i+1,j,k)=tx(i+1,j,k)-filax(i,1)*tx(i,j,k)
tx(i+2,j,k)=tx(i+2,j,k)-filax(i,2)*tx(i,j,k)
enddo
tx(nx,j,k)=tx(nx,j,k)-filax(nx-1,1)*tx(nx-1,j,k)
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=tx(nx,j,k)*fiffx(nx)
tx(nx-1,j,k)=(tx(nx-1,j,k)-fifx(nx-1)*tx(nx,j,k))*&
fiffx(nx-1)
tx(nx-2,j,k)=(tx(nx-2,j,k)-fifx(nx-2)*tx(nx-1,j,k)-&
ficx(nx-2)*tx(nx,j,k))*fiffx(nx-2)
tx(nx-3,j,k)=(tx(nx-3,j,k)-fifx(nx-3)*tx(nx-2,j,k)-&
ficx(nx-3)*tx(nx-1,j,k)-&
fibx(nx-3)*tx(nx,j,k))*fiffx(nx-3)
do i=nx-4,1,-1
tx(i,j,k)=(tx(i,j,k)-fifx(i)*tx(i+1,j,k)-&
ficx(i)*tx(i+2,j,k)-&
fibx(i)*tx(i+3,j,k)-&
fibbx(i)*tx(i+4,j,k))*fiffx(i)
enddo
enddo
enddo
endif
endif
if (nclx==2) then
do k=1,nz
do j=1,ny
tx(1,j,k)=fia1x*ux(1,j,k)+fib1x*ux(2,j,k)+&
fic1x*ux(3,j,k)+fid1x*ux(4,j,k)+&
fie1x*ux(5,j,k)
tx(2,j,k)=fia2x*ux(2,j,k)+fib2x*ux(1,j,k)+&
fic2x*ux(3,j,k)+fid2x*ux(4,j,k)+&
fie2x*ux(5,j,k)
tx(3,j,k)=fia3x*ux(3,j,k)+fib3x*ux(1,j,k)+&
fic3x*ux(2,j,k)+fid3x*ux(4,j,k)+&
fie3x*ux(5,j,k)
enddo
enddo
do i=4,nx-3
do k=1,nz
do j=1,ny
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
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=fianx*ux(nx,j,k)+fibnx*ux(nx-1,j,k)+&
ficnx*ux(nx-2,j,k)+fidnx*ux(nx-3,j,k)+&
fienx*ux(nx-4,j,k)
tx(nx-1,j,k)=fiamx*ux(nx-1,j,k)+fibmx*ux(nx,j,k)+&
ficmx*ux(nx-2,j,k)+fidmx*ux(nx-3,j,k)+&
fiemx*ux(nx-4,j,k)
tx(nx-2,j,k)=fiapx*ux(nx-2,j,k)+fibpx*ux(nx,j,k)+&
ficpx*ux(nx-1,j,k)+fidpx*ux(nx-3,j,k)+&
fiepx*ux(nx-4,j,k)
enddo
enddo
do i=1,nx-2
do k=1,nz
do j=1,ny
tx(i+1,j,k)=tx(i+1,j,k)-filax(i,1)*tx(i,j,k)
tx(i+2,j,k)=tx(i+2,j,k)-filax(i,2)*tx(i,j,k)
enddo
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=tx(nx,j,k)-filax(nx-1,1)*tx(nx-1,j,k)
enddo
enddo
do k=1,nz
do j=1,ny
tx(nx,j,k)=tx(nx,j,k)*fiffx(nx)
tx(nx-1,j,k)=(tx(nx-1,j,k)-fifx(nx-1)*tx(nx,j,k))*&
fiffx(nx-1)
tx(nx-2,j,k)=(tx(nx-2,j,k)-fifx(nx-2)*tx(nx-1,j,k)-&
ficx(nx-2)*tx(nx,j,k))*fiffx(nx-2)
tx(nx-3,j,k)=(tx(nx-3,j,k)-fifx(nx-3)*tx(nx-2,j,k)-&
ficx(nx-3)*tx(nx-1,j,k)-&
fibx(nx-3)*tx(nx,j,k))*fiffx(nx-3)
enddo
enddo
do i=nx-4,1,-1
do k=1,nz
do j=1,ny
tx(i,j,k)=(tx(i,j,k)-fifx(i)*tx(i+1,j,k)-&
ficx(i)*tx(i+2,j,k)-&
fibx(i)*tx(i+3,j,k)-&
fibbx(i)*tx(i+4,j,k))*fiffx(i)
enddo
enddo
enddo
endif
return
end subroutine filx
!*********************************************************************
!
subroutine fily(ty,uy,ry,sy,vy,fiffy,fify,ficy,fiby,fibby,filay,fiz1y,&
fiz2y,nx,ny,nz,npaire)
!
!*********************************************************************
USE param
USE parfiY
implicit none
integer :: nx,ny,nz,i,j,k,npaire
real(mytype), dimension(nx,ny,nz) :: ty,uy,ry
real(mytype), dimension(nx,nz) :: sy,vy
real(mytype), dimension(ny) :: fiffy,fify,ficy,fiby,fibby,fiz1y,fiz2y
real(mytype), dimension(ny,2) :: filay
real(mytype) :: xcoef
if (ncly==0) then
do k=1,nz
do i=1,nx
ry(i,1,k)=fiaiy*uy(i,1,k)+&
fibiy*(uy(i,2,k)+uy(i,ny,k))+&
ficiy*(uy(i,3,k)+uy(i,ny-1,k))+&
fidiy*(uy(i,4,k)+uy(i,ny-2,k))
ry(i,2,k)=fiaiy*uy(i,2,k)+&
fibiy*(uy(i,3,k)+uy(i,1,k))+&
ficiy*(uy(i,4,k)+uy(i,ny,k))+ &
fidiy*(uy(i,5,k)+uy(i,ny-1,k))
ry(i,3,k)=fiaiy*uy(i,3,k)+&
fibiy*(uy(i,4,k)+uy(i,2,k))+&
ficiy*(uy(i,5,k)+uy(i,1,k))+&
fidiy*(uy(i,6,k)+uy(i,ny,k))
enddo
enddo
do j=4,ny-3
do k=1,nz
do i=1,nx
ry(i,j,k)=fiaiy*uy(i,j,k)+&
fibiy*(uy(i,j+1,k)+uy(i,j-1,k))+&
ficiy*(uy(i,j+2,k)+uy(i,j-2,k))+&
fidiy*(uy(i,j+3,k)+uy(i,j-3,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ry(i,ny,k)=fiaiy*uy(i,ny,k)+&
fibiy*(uy(i,1,k)+uy(i,ny-1,k))+&
ficiy*(uy(i,2,k)+uy(i,ny-2,k))+&
fidiy*(uy(i,3,k)+uy(i,ny-3,k))
ry(i,ny-1,k)=fiaiy*uy(i,ny-1,k)+&
fibiy*(uy(i,ny,k)+uy(i,ny-2,k))+&
ficiy*(uy(i,1,k)+uy(i,ny-3,k))+&
fidiy*(uy(i,2,k)+uy(i,ny-4,k))
ry(i,ny-2,k)=fiaiy*uy(i,ny-2,k)+&
fibiy*(uy(i,ny-1,k)+uy(i,ny-3,k))+&
ficiy*(uy(i,ny,k)+uy(i,ny-4,k))+&
fidiy*(uy(i,1,k)+uy(i,ny-5,k))
enddo
enddo
do k=1,nz
do i=1,nx
do j=1,ny-2
ry(i,j+1,k)=ry(i,j+1,k)-filay(j,1)*ry(i,j,k)
ry(i,j+2,k)=ry(i,j+2,k)-filay(j,2)*ry(i,j,k)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ry(i,ny,k)=ry(i,ny,k)-filay(ny-1,1)*ry(i,ny-1,k)
enddo
enddo
do k=1,nz
do i=1,nx
ry(i,ny,k)=ry(i,ny,k)*fiffy(ny)
ry(i,ny-1,k)=(ry(i,ny-1,k)-fify(ny-1)*ry(i,ny,k))*&
fiffy(ny-1)
ry(i,ny-2,k)=(ry(i,ny-2,k)-fify(ny-2)*ry(i,ny-1,k)-&
ficy(ny-2)*ry(i,ny,k))*fiffy(ny-2)
ry(i,ny-3,k)=(ry(i,ny-3,k)-fify(ny-3)*ry(i,ny-2,k)-&
ficy(ny-3)*ry(i,ny-1,k)-&
fiby(ny-3)*ry(i,ny,k))*fiffy(ny-3)
enddo
enddo
do k=1,nz
do i=1,nx
do j=ny-4,1,-1
ry(i,j,k)=(ry(i,j,k)-fify(j)*ry(i,j+1,k)-&
ficy(j)*ry(i,j+2,k)-&
fiby(j)*ry(i,j+3,k)-&
fibby(j)*ry(i,j+4,k))*fiffy(j)
enddo
enddo
enddo
xcoef=1._mytype/2._mytype
do k=1,nz
do i=1,nx
sy(i,k)=fih1y*(-fibey*ry(i,1,k)+fibey*ry(i,ny-1,k)*xcoef+&
fialy*ry(i,ny,k)*xcoef)+&
fih2y*(fialy*ry(i,1,k)*xcoef+fibey*ry(i,2,k)*xcoef-&
fibey*ry(i,ny,k))
vy(i,k)=fih3y*(-fibey*ry(i,1,k)+fibey*ry(i,ny-1,k)*xcoef+&
fialy*ry(i,ny,k)*xcoef)+&
fih4y*(fialy*ry(i,1,k)*xcoef+fibey*ry(i,2,k)*xcoef-&
fibey*ry(i,ny,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ry(i,j,k)-fiz1y(j)*sy(i,k)-fiz2y(j)*vy(i,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)=fiaiy*uy(i,1,k)+&
fibiy*(uy(i,2,k)+uy(i,2,k))+&
ficiy*(uy(i,3,k)+uy(i,3,k))+&
fidiy*(uy(i,4,k)+uy(i,4,k))
ty(i,2,k)=fiaiy*uy(i,2,k)+&
fibiy*(uy(i,3,k)+uy(i,1,k))+&
ficiy*(uy(i,4,k)+uy(i,2,k))+&
fidiy*(uy(i,5,k)+uy(i,3,k))
ty(i,3,k)=fiaiy*uy(i,3,k)+&
fibiy*(uy(i,4,k)+uy(i,2,k))+&
ficiy*(uy(i,5,k)+uy(i,1,k))+&
fidiy*(uy(i,6,k)+uy(i,2,k))
enddo
enddo
do j=4,ny-3
do k=1,nz
do i=1,nx
ty(i,j,k)=fiaiy*uy(i,j,k)+&
fibiy*(uy(i,j+1,k)+uy(i,j-1,k))+&
ficiy*(uy(i,j+2,k)+uy(i,j-2,k))+&
fidiy*(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)=fiaiy*uy(i,ny,k)+&
fibiy*(uy(i,ny-1,k)+uy(i,ny-1,k))+&
ficiy*(uy(i,ny-2,k)+uy(i,ny-2,k))+&
fidiy*(uy(i,ny-3,k)+uy(i,ny-3,k))
ty(i,ny-1,k)=fiaiy*uy(i,ny-1,k)+&
fibiy*(uy(i,ny,k)+uy(i,ny-2,k))+&
ficiy*(uy(i,ny-1,k)+uy(i,ny-3,k))+&
fidiy*(uy(i,ny-2,k)+uy(i,ny-4,k))
ty(i,ny-2,k)=fiaiy*uy(i,ny-2,k)+&
fibiy*(uy(i,ny-1,k)+uy(i,ny-3,k))+&
ficiy*(uy(i,ny,k)+uy(i,ny-4,k))+&
fidiy*(uy(i,ny-1,k)+uy(i,ny-5,k))
enddo
enddo
do k=1,nz
do i=1,nx
do j=1,ny-2
ty(i,j+1,k)=ty(i,j+1,k)-filay(j,1)*ty(i,j,k)
ty(i,j+2,k)=ty(i,j+2,k)-filay(j,2)*ty(i,j,k)
enddo
ty(i,ny,k)=ty(i,ny,k)-filay(ny-1,1)*ty(i,ny-1,k)
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fiffy(ny)
ty(i,ny-1,k)=(ty(i,ny-1,k)-fify(ny-1)*ty(i,ny,k))*&
fiffy(ny-1)
ty(i,ny-2,k)=(ty(i,ny-2,k)-fify(ny-2)*ty(i,ny-1,k)-&
ficy(ny-2)*ty(i,ny,k))*fiffy(ny-2)
ty(i,ny-3,k)=(ty(i,ny-3,k)-fify(ny-3)*ty(i,ny-2,k)-&
ficy(ny-3)*ty(i,ny-1,k)-&
fiby(ny-3)*ty(i,ny,k))*fiffy(ny-3)
do j=ny-4,1,-1
ty(i,j,k)=(ty(i,j,k)-fify(j)*ty(i,j+1,k)-&
ficy(j)*ty(i,j+2,k)-&
fiby(j)*ty(i,j+3,k)-&
fibby(j)*ty(i,j+4,k))*fiffy(j)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=fiaiy*uy(i,1,k)+&
fibiy*(uy(i,2,k)-uy(i,2,k))+&
ficiy*(uy(i,3,k)-uy(i,3,k))+&
fidiy*(uy(i,4,k)-uy(i,4,k))
ty(i,2,k)=fiaiy*uy(i,2,k)+&
fibiy*(uy(i,3,k)+uy(i,1,k))+&
ficiy*(uy(i,4,k)-uy(i,2,k))+&
fidiy*(uy(i,5,k)-uy(i,3,k))
ty(i,3,k)=fiaiy*uy(i,3,k)+&
fibiy*(uy(i,4,k)+uy(i,2,k))+&
ficiy*(uy(i,5,k)+uy(i,1,k))+&
fidiy*(uy(i,6,k)-uy(i,2,k))
enddo
enddo
do j=4,ny-3
do k=1,nz
do i=1,nx
ty(i,j,k)=fiaiy*uy(i,j,k)+&
fibiy*(uy(i,j+1,k)+uy(i,j-1,k))+&
ficiy*(uy(i,j+2,k)+uy(i,j-2,k))+&
fidiy*(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)=fiaiy*uy(i,ny,k)+&
fibiy*(uy(i,ny-1,k)-uy(i,ny-1,k))+&
ficiy*(uy(i,ny-2,k)-uy(i,ny-2,k))+&
fidiy*(uy(i,ny-3,k)-uy(i,ny-3,k))
ty(i,ny-1,k)=fiaiy*uy(i,ny-1,k)+&
fibiy*(uy(i,ny,k)+uy(i,ny-2,k))+&
ficiy*(-uy(i,ny-1,k)+uy(i,ny-3,k))+&
fidiy*(-uy(i,ny-2,k)+uy(i,ny-4,k))
ty(i,ny-2,k)=fiaiy*uy(i,ny-2,k)+&
fibiy*(uy(i,ny-1,k)+uy(i,ny-3,k))+&
ficiy*(uy(i,ny,k)+uy(i,ny-4,k))+&
fidiy*(-uy(i,ny-1,k)+uy(i,ny-5,k))
enddo
enddo
do k=1,nz
do i=1,nx
do j=1,ny-2
ty(i,j+1,k)=ty(i,j+1,k)-filay(j,1)*ty(i,j,k)
ty(i,j+2,k)=ty(i,j+2,k)-filay(j,2)*ty(i,j,k)
enddo
ty(i,ny,k)=ty(i,ny,k)-filay(ny-1,1)*ty(i,ny-1,k)
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fiffy(ny)
ty(i,ny-1,k)=(ty(i,ny-1,k)-fify(ny-1)*ty(i,ny,k))*&
fiffy(ny-1)
ty(i,ny-2,k)=(ty(i,ny-2,k)-fify(ny-2)*ty(i,ny-1,k)-&
ficy(ny-2)*ty(i,ny,k))*fiffy(ny-2)
ty(i,ny-3,k)=(ty(i,ny-3,k)-fify(ny-3)*ty(i,ny-2,k)-&
ficy(ny-3)*ty(i,ny-1,k)-&
fiby(ny-3)*ty(i,ny,k))*fiffy(ny-3)
do j=ny-4,1,-1
ty(i,j,k)=(ty(i,j,k)-fify(j)*ty(i,j+1,k)-&
ficy(j)*ty(i,j+2,k)-&
fiby(j)*ty(i,j+3,k)-&
fibby(j)*ty(i,j+4,k))*fiffy(j)
enddo
enddo
enddo
endif
endif
if (ncly.eq.2) then
do k=1,nz
do i=1,nx
ty(i,1,k)=fia1y*uy(i,1,k)+fib1y*uy(i,2,k)+&
fic1y*uy(i,3,k)+fid1y*uy(i,4,k)+&
fie1y*uy(i,5,k)
ty(i,2,k)=fia2y*uy(i,2,k)+fib2y*uy(i,1,k)+&
fic2y*uy(i,3,k)+fid2y*uy(i,4,k)+&
fie2y*uy(i,5,k)
ty(i,3,k)=fia3y*uy(i,3,k)+fib3y*uy(i,1,k)+&
fic3y*uy(i,2,k)+fid3y*uy(i,4,k)+&
fie3y*uy(i,5,k)
enddo
enddo
do j=4,ny-3
do k=1,nz
do i=1,nx
ty(i,j,k)=fiaiy*uy(i,j,k)+&
fibiy*(uy(i,j+1,k)+uy(i,j-1,k))+&
ficiy*(uy(i,j+2,k)+uy(i,j-2,k))+&
fidiy*(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)=fiany*uy(i,ny,k)+fibny*uy(i,ny-1,k)+&
ficny*uy(i,ny-2,k)+fidny*uy(i,ny-3,k)+&
fieny*uy(i,ny-4,k)
ty(i,ny-1,k)=fiamy*uy(i,ny-1,k)+fibmy*uy(i,ny,k)+&
ficmy*uy(i,ny-2,k)+fidmy*uy(i,ny-3,k)+&
fiemy*uy(i,ny-4,k)
ty(i,ny-2,k)=fiapy*uy(i,ny-2,k)+fibpy*uy(i,ny,k)+&
ficpy*uy(i,ny-1,k)+fidpy*uy(i,ny-3,k)+&
fiepy*uy(i,ny-4,k)
enddo
enddo
do k=1,nz
do i=1,nx
do j=1,ny-2
ty(i,j+1,k)=ty(i,j+1,k)-filay(j,1)*ty(i,j,k)
ty(i,j+2,k)=ty(i,j+2,k)-filay(j,2)*ty(i,j,k)
enddo
ty(i,ny,k)=ty(i,ny,k)-filay(ny-1,1)*ty(i,ny-1,k)
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fiffy(ny)
ty(i,ny-1,k)=(ty(i,ny-1,k)-fify(ny-1)*ty(i,ny,k))*&
fiffy(ny-1)
ty(i,ny-2,k)=(ty(i,ny-2,k)-fify(ny-2)*ty(i,ny-1,k)-&
ficy(ny-2)*ty(i,ny,k))*fiffy(ny-2)
ty(i,ny-3,k)=(ty(i,ny-3,k)-fify(ny-3)*ty(i,ny-2,k)-&
ficy(ny-3)*ty(i,ny-1,k)-&
fiby(ny-3)*ty(i,ny,k))*fiffy(ny-3)
do j=ny-4,1,-1
ty(i,j,k)=(ty(i,j,k)-fify(j)*ty(i,j+1,k)-&
ficy(j)*ty(i,j+2,k)-&
fiby(j)*ty(i,j+3,k)-&
fibby(j)*ty(i,j+4,k))*fiffy(j)
enddo
enddo
enddo
endif
return
end subroutine fily
!*********************************************************************
!
subroutine filz(tz,uz,rz,sz,vz,fiffz,fifz,ficz,fibz,fibbz,filaz,fiz1z,&
fiz2z,nx,ny,nz,npaire)
!
!*********************************************************************
USE param
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) :: sz,vz
real(mytype), dimension(nz) :: fiffz,fifz,ficz,fibz,fibbz,fiz1z,fiz2z
real(mytype), dimension(nz,2) :: filaz
real(mytype) :: xcoef
if (nclz==0) then
do j=1,ny
do i=1,nx
rz(i,j,1)=fiaiz*uz(i,j,1)+&
fibiz*(uz(i,j,2)+uz(i,j,nz))+&
ficiz*(uz(i,j,3)+uz(i,j,nz-1))+&
fidiz*(uz(i,j,4)+uz(i,j,nz-2))
rz(i,j,2)=fiaiz*uz(i,j,2)+&
fibiz*(uz(i,j,3)+uz(i,j,1))+ &
ficiz*(uz(i,j,4)+uz(i,j,nz))+&
fidiz*(uz(i,j,5)+uz(i,j,nz-1))
rz(i,j,3)=fiaiz*uz(i,j,3)+&
fibiz*(uz(i,j,4)+uz(i,j,2))+&
ficiz*(uz(i,j,5)+uz(i,j,1))+&
fidiz*(uz(i,j,6)+uz(i,j,nz))
enddo
enddo
do k=4,nz-3
do j=1,ny
do i=1,nx
rz(i,j,k)=fiaiz*uz(i,j,k)+&
fibiz*(uz(i,j,k+1)+uz(i,j,k-1))+&
ficiz*(uz(i,j,k+2)+uz(i,j,k-2))+&
fidiz*(uz(i,j,k+3)+uz(i,j,k-3))
enddo
enddo
enddo
do j=1,ny
do i=1,nx
rz(i,j,nz)=fiaiz*uz(i,j,nz)+&
fibiz*(uz(i,j,1)+uz(i,j,nz-1))+&
ficiz*(uz(i,j,2)+uz(i,j,nz-2))+&
fidiz*(uz(i,j,3)+uz(i,j,nz-3))
rz(i,j,nz-1)=fiaiz*uz(i,j,nz-1)+&
fibiz*(uz(i,j,nz)+uz(i,j,nz-2))+&
ficiz*(uz(i,j,1)+uz(i,j,nz-3))+&
fidiz*(uz(i,j,2)+uz(i,j,nz-4))
rz(i,j,nz-2)=fiaiz*uz(i,j,nz-2)+&
fibiz*(uz(i,j,nz-1)+uz(i,j,nz-3))+&
ficiz*(uz(i,j,nz)+uz(i,j,nz-4))+&
fidiz*(uz(i,j,1)+uz(i,j,nz-5))
enddo
enddo
do j=1,ny
do i=1,nx
do k=1,nz-2
rz(i,j,k+1)=rz(i,j,k+1)-filaz(k,1)*rz(i,j,k)
rz(i,j,k+2)=rz(i,j,k+2)-filaz(k,2)*rz(i,j,k)
enddo
rz(i,j,nz)=rz(i,j,nz)-filaz(nz-1,1)*rz(i,j,nz-1)
enddo
enddo
do j=1,ny
do i=1,nx
rz(i,j,nz)=rz(i,j,nz)*fiffz(nz)
rz(i,j,nz-1)=(rz(i,j,nz-1)-fifz(nz-1)*rz(i,j,nz))*&
fiffz(nz-1)
rz(i,j,nz-2)=(rz(i,j,nz-2)-fifz(nz-2)*rz(i,j,nz-1)-&
ficz(nz-2)*rz(i,j,nz))*fiffz(nz-2)
rz(i,j,nz-3)=(rz(i,j,nz-3)-fifz(nz-3)*rz(i,j,nz-2)-&
ficz(nz-3)*rz(i,j,nz-1)-&
fibz(nz-3)*rz(i,j,nz))*fiffz(nz-3)
enddo
enddo
do j=1,ny
do i=1,nx
do k=nz-4,1,-1
rz(i,j,k)=(rz(i,j,k)-fifz(k)*rz(i,j,k+1)-&
ficz(k)*rz(i,j,k+2)-&
fibz(k)*rz(i,j,k+3)-&
fibbz(k)*rz(i,j,k+4))*fiffz(k)
enddo
enddo
enddo
xcoef=1._mytype/2._mytype
do j=1,ny
do i=1,nx
sz(i,j)=fih1z*(-fibez*rz(i,j,1)+fibez*rz(i,j,nz-1)*xcoef+&
fialz*rz(i,j,nz)*xcoef)+&
fih2z*(fialz*rz(i,j,1)*xcoef+fibez*rz(i,j,2)*xcoef-&
fibez*rz(i,j,nz))
vz(i,j)=fih3z*(-fibez*rz(i,j,1)+fibez*rz(i,j,nz-1)*xcoef+&
fialz*rz(i,j,nz)*xcoef)+&
fih4z*(fialz*rz(i,j,1)*xcoef+fibez*rz(i,j,2)*xcoef-&
fibez*rz(i,j,nz))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx
tz(i,j,k)=rz(i,j,k)-fiz1z(k)*sz(i,j)-fiz2z(k)*vz(i,j)
enddo
enddo
enddo
endif
if (nclz==1) then
if (npaire==1) then
do j=1,ny
do i=1,nx
tz(i,j,1)=fiaiz*uz(i,j,1)+&
fibiz*(uz(i,j,2)+uz(i,j,2))+&
ficiz*(uz(i,j,3)+uz(i,j,3))+&
fidiz*(uz(i,j,4)+uz(i,j,4))
tz(i,j,2)=fiaiz*uz(i,j,2)+&
fibiz*(uz(i,j,3)+uz(i,j,1))+&
ficiz*(uz(i,j,4)+uz(i,j,2))+&
fidiz*(uz(i,j,5)+uz(i,j,3))
tz(i,j,3)=fiaiz*uz(i,j,3)+&
fibiz*(uz(i,j,4)+uz(i,j,2))+&
ficiz*(uz(i,j,5)+uz(i,j,1))+&
fidiz*(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)=fiaiz*uz(i,j,k)+&
fibiz*(uz(i,j,k+1)+uz(i,j,k-1))+&
ficiz*(uz(i,j,k+2)+uz(i,j,k-2))+&
fidiz*(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)=fiaiz*uz(i,j,nz)+&
fibiz*(uz(i,j,nz-1)+uz(i,j,nz-1))+&
ficiz*(uz(i,j,nz-2)+uz(i,j,nz-2))+&
fidiz*(uz(i,j,nz-3)+uz(i,j,nz-3))
tz(i,j,nz-1)=fiaiz*uz(i,j,nz-1)+&
fibiz*(uz(i,j,nz)+uz(i,j,nz-2))+&
ficiz*(uz(i,j,nz-1)+uz(i,j,nz-3))+&
fidiz*(uz(i,j,nz-2)+uz(i,j,nz-4))
tz(i,j,nz-2)=fiaiz*uz(i,j,nz-2)+&
fibiz*(uz(i,j,nz-1)+uz(i,j,nz-3))+&
ficiz*(uz(i,j,nz)+uz(i,j,nz-4))+&
fidiz*(uz(i,j,nz-1)+uz(i,j,nz-5))
enddo
enddo
do j=1,ny
do i=1,nx
do k=1,nz-2
tz(i,j,k+1)=tz(i,j,k+1)-filaz(k,1)*tz(i,j,k)
tz(i,j,k+2)=tz(i,j,k+2)-filaz(k,2)*tz(i,j,k)
enddo
tz(i,j,nz)=tz(i,j,nz)-filaz(nz-1,1)*tz(i,j,nz-1)
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fiffz(nz)
tz(i,j,nz-1)=(tz(i,j,nz-1)-fifz(nz-1)*tz(i,j,nz))*&
fiffz(nz-1)
tz(i,j,nz-2)=(tz(i,j,nz-2)-fifz(nz-2)*tz(i,j,nz-1)-&
ficz(nz-2)*tz(i,j,nz))*fiffz(nz-2)
tz(i,j,nz-3)=(tz(i,j,nz-3)-fifz(nz-3)*tz(i,j,nz-2)-&
ficz(nz-3)*tz(i,j,nz-1)-&
fibz(nz-3)*tz(i,j,nz))*fiffz(nz-3)
do k=nz-4,1,-1
tz(i,j,k)=(tz(i,j,k)-fifz(k)*tz(i,j,k+1)-&
ficz(k)*tz(i,j,k+2)-&
fibz(k)*tz(i,j,k+3)-&
fibbz(k)*tz(i,j,k+4))*fiffz(k)
enddo
enddo
enddo
endif
if (npaire==0) then
do j=1,ny
do i=1,nx
tz(i,j,1)=fiaiz*uz(i,j,1)+&
fibiz*(uz(i,j,2)-uz(i,j,2))+&
ficiz*(uz(i,j,3)-uz(i,j,3))+&
fidiz*(uz(i,j,4)-uz(i,j,4))
tz(i,j,2)=fiaiz*uz(i,j,2)+&
fibiz*(uz(i,j,3)+uz(i,j,1))+&
ficiz*(uz(i,j,4)-uz(i,j,2))+&
fidiz*(uz(i,j,5)-uz(i,j,3))
tz(i,j,3)=fiaiz*uz(i,j,3)+&
fibiz*(uz(i,j,4)+uz(i,j,2))+&
ficiz*(uz(i,j,5)+uz(i,j,1))+&
fidiz*(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)=fiaiz*uz(i,j,k)+&
fibiz*(uz(i,j,k+1)+uz(i,j,k-1))+&
ficiz*(uz(i,j,k+2)+uz(i,j,k-2))+&
fidiz*(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)=fiaiz*uz(i,j,nz)+&
fibiz*(uz(i,j,nz-1)-uz(i,j,nz-1))+&
ficiz*(uz(i,j,nz-2)-uz(i,j,nz-2))+&
fidiz*(uz(i,j,nz-3)-uz(i,j,nz-3))
tz(i,j,nz-1)=fiaiz*uz(i,j,nz-1)+&
fibiz*(uz(i,j,nz)+uz(i,j,nz-2))+&
ficiz*(-uz(i,j,nz-1)+uz(i,j,nz-3))+&
fidiz*(-uz(i,j,nz-2)+uz(i,j,nz-4))
tz(i,j,nz-2)=fiaiz*uz(i,j,nz-2)+&
fibiz*(uz(i,j,nz-1)+uz(i,j,nz-3))+&
ficiz*(uz(i,j,nz)+uz(i,j,nz-4))+&
fidiz*(-uz(i,j,nz-1)+uz(i,j,nz-5))
enddo
enddo
do j=1,ny
do i=1,nx
do k=1,nz-2
tz(i,j,k+1)=tz(i,j,k+1)-filaz(k,1)*tz(i,j,k)
tz(i,j,k+2)=tz(i,j,k+2)-filaz(k,2)*tz(i,j,k)
enddo
tz(i,j,nz)=tz(i,j,nz)-filaz(nz-1,1)*tz(i,j,nz-1)
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fiffz(nz)
tz(i,j,nz-1)=(tz(i,j,nz-1)-fifz(nz-1)*tz(i,j,nz))*&
fiffz(nz-1)
tz(i,j,nz-2)=(tz(i,j,nz-2)-fifz(nz-2)*tz(i,j,nz-1)-&
ficz(nz-2)*tz(i,j,nz))*fiffz(nz-2)
tz(i,j,nz-3)=(tz(i,j,nz-3)-fifz(nz-3)*tz(i,j,nz-2)-&
ficz(nz-3)*tz(i,j,nz-1)-&
fibz(nz-3)*tz(i,j,nz))*fiffz(nz-3)
do k=nz-4,1,-1
tz(i,j,k)=(tz(i,j,k)-fifz(k)*tz(i,j,k+1)-&
ficz(k)*tz(i,j,k+2)-&
fibz(k)*tz(i,j,k+3)-&
fibbz(k)*tz(i,j,k+4))*fiffz(k)
enddo
enddo
enddo
endif
endif
if (nclz==2) then
do j=1,ny
do i=1,nx
tz(i,j,1)=fia1z*uz(i,j,1)+fib1z*uz(i,j,2)+&
fic1z*uz(i,j,3)+fid1z*uz(i,j,4)+&
fie1z*uz(i,j,5)
tz(i,j,2)=fia2z*uz(i,j,2)+fib2z*uz(i,j,1)+&
fic2z*uz(i,j,3)+fid2z*uz(i,j,4)+&
fie2z*uz(i,j,5)
tz(i,j,3)=fia3z*uz(i,j,3)+fib3z*uz(i,j,1)+&
fic3z*uz(i,j,2)+fid3z*uz(i,j,4)+&
fie3z*uz(i,j,5)
enddo
enddo
do k=4,nz-3
do j=1,ny
do i=1,nx
tz(i,j,k)=fiaiz*uz(i,j,k)+&
fibiz*(uz(i,j,k+1)+uz(i,j,k-1))+&
ficiz*(uz(i,j,k+2)+uz(i,j,k-2))+&
fidiz*(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)=fianz*uz(i,j,nz)+fibnz*uz(i,j,nz-1)+&
ficnz*uz(i,j,nz-2)+fidnz*uz(i,j,nz-3)+&
fienz*uz(i,j,nz-4)
tz(i,j,nz-1)=fiamz*uz(i,j,nz-1)+fibmz*uz(i,j,nz)+&
ficmz*uz(i,j,nz-2)+fidmz*uz(i,j,nz-3)+&
fiemz*uz(i,j,nz-4)
tz(i,j,nz-2)=fiapz*uz(i,j,nz-2)+fibpz*uz(i,j,nz)+&
ficpz*uz(i,j,nz-1)+fidpz*uz(i,j,nz-3)+&