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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 derx_00(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivX
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
real(mytype), dimension(nx):: ffx,fsx,fwx
if(ilag.eq.1) call lagpolx(ux)
do k=1,nz
do j=1,ny
tx(1,j,k)=afix*(ux(2,j,k)-ux(nx,j,k))&
+bfix*(ux(3,j,k)-ux(nx-1,j,k))
rx(1,j,k)=-one
tx(2,j,k)=afix*(ux(3,j,k)-ux(1,j,k))&
+bfix*(ux(4,j,k)-ux(nx,j,k))
rx(2,j,k)=zero
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
rx(i,j,k)=zero
enddo
tx(nx-1,j,k)=afix*(ux(nx,j,k)-ux(nx-2,j,k))&
+bfix*(ux(1,j,k)-ux(nx-3,j,k))
rx(nx-1,j,k)=zero
tx(nx,j,k)=afix*(ux(1,j,k)-ux(nx-1,j,k))&
+bfix*(ux(2,j,k)-ux(nx-2,j,k))
rx(nx,j,k)=alfaix
do i=2, nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
rx(i,j,k)=rx(i,j,k)-rx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
rx(nx,j,k)=rx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
rx(i,j,k)=(rx(i,j,k)-ffx(i)*rx(i+1,j,k))*fwx(i)
enddo
sx(j,k)=(tx(1,j,k)-alfaix*tx(nx,j,k))&
/(one+rx(1,j,k)-alfaix*rx(nx,j,k))
do i=1,nx
tx(i,j,k)=tx(i,j,k)-sx(j,k)*rx(i,j,k)
enddo
enddo
enddo
return
end subroutine derx_00
!********************************************************************
!
subroutine derx_11(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivX
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
real(mytype), dimension(nx):: ffx,fsx,fwx
if(ilag.eq.1) call lagpolx(ux)
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=zero
tx(2,j,k)=afix*(ux(3,j,k)-ux(1,j,k))&
+bfix*(ux(4,j,k)-ux(2,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afix*(ux(nx,j,k)-ux(nx-2,j,k))&
+bfix*(ux(nx-1,j,k)-ux(nx-3,j,k))
tx(nx,j,k)=zero
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=afix*(ux(2,j,k)+ux(2,j,k))&
+bfix*(ux(3,j,k)+ux(3,j,k))
tx(2,j,k)=afix*(ux(3,j,k)-ux(1,j,k))&
+bfix*(ux(4,j,k)+ux(2,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afix*(ux(nx,j,k)-ux(nx-2,j,k))&
+bfix*((-ux(nx-1,j,k))-ux(nx-3,j,k))
tx(nx,j,k)=afix*((-ux(nx-1,j,k))-ux(nx-1,j,k))&
+bfix*((-ux(nx-2,j,k))-ux(nx-2,j,k))
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
return
end subroutine derx_11
!********************************************************************
!
subroutine derx_12(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivX
implicit none
integer :: nx,ny,nz,i,j,k,npaire
real(mytype), dimension(nx,ny,nz) :: tx,ux,rx
real(mytype), dimension(ny,nz):: sx
real(mytype), dimension(nx):: ffx,fsx,fwx
if(ilag.eq.1) call lagpolx(ux)
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=zero
tx(2,j,k)=afix*(ux(3,j,k)-ux(1,j,k))&
+bfix*(ux(4,j,k)-ux(2,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afmx*(ux(nx,j,k)-ux(nx-2,j,k))
tx(nx,j,k)=(-afnx*ux(nx,j,k))-bfnx*ux(nx-1,j,k)-cfnx*ux(nx-2,j,k)
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=afix*(ux(2,j,k)+ux(2,j,k))&
+bfix*(ux(3,j,k)+ux(3,j,k))
tx(2,j,k)=afix*(ux(3,j,k)-ux(1,j,k))&
+bfix*(ux(4,j,k)+ux(2,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afmx*(ux(nx,j,k)-ux(nx-2,j,k))
tx(nx,j,k)=(-afnx*ux(nx,j,k))-bfnx*ux(nx-1,j,k)-cfnx*ux(nx-2,j,k)
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
return
end subroutine derx_12
!********************************************************************
!
subroutine derx_21(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivX
implicit none
integer :: nx,ny,nz,i,j,k,npaire
real(mytype), dimension(nx,ny,nz) :: tx,ux,rx
real(mytype), dimension(ny,nz):: sx
real(mytype), dimension(nx):: ffx,fsx,fwx
if(ilag.eq.1) call lagpolx(ux)
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=af1x*ux(1,j,k)+bf1x*ux(2,j,k)+cf1x*ux(3,j,k)
tx(2,j,k)=af2x*(ux(3,j,k)-ux(1,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afix*(ux(nx,j,k)-ux(nx-2,j,k))&
+bfix*(ux(nx-1,j,k)-ux(nx-3,j,k))
tx(nx,j,k)=zero
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=af1x*ux(1,j,k)+bf1x*ux(2,j,k)+cf1x*ux(3,j,k)
tx(2,j,k)=af2x*(ux(3,j,k)-ux(1,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afix*(ux(nx,j,k)-ux(nx-2,j,k))&
+bfix*((-ux(nx-1,j,k))-ux(nx-3,j,k))
tx(nx,j,k)=afix*((-ux(nx-1,j,k))-ux(nx-1,j,k))&
+bfix*((-ux(nx-2,j,k))-ux(nx-2,j,k))
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
endif
return
end subroutine derx_21
!********************************************************************
!
subroutine derx_22(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivX
implicit none
integer :: nx,ny,nz,i,j,k,npaire
real(mytype), dimension(nx,ny,nz) :: tx,ux,rx
real(mytype), dimension(ny,nz):: sx
real(mytype), dimension(nx):: ffx,fsx,fwx
if(ilag.eq.1) call lagpolx(ux)
do k=1,nz
do j=1,ny
tx(1,j,k)=af1x*ux(1,j,k)+bf1x*ux(2,j,k)+cf1x*ux(3,j,k)
tx(2,j,k)=af2x*(ux(3,j,k)-ux(1,j,k))
do i=3,nx-2
tx(i,j,k)=afix*(ux(i+1,j,k)-ux(i-1,j,k))&
+bfix*(ux(i+2,j,k)-ux(i-2,j,k))
enddo
tx(nx-1,j,k)=afmx*(ux(nx,j,k)-ux(nx-2,j,k))
tx(nx,j,k)=(-afnx*ux(nx,j,k))-bfnx*ux(nx-1,j,k)-cfnx*ux(nx-2,j,k)
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*fsx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*fwx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-ffx(i)*tx(i+1,j,k))*fwx(i)
enddo
enddo
enddo
return
end subroutine derx_22
!********************************************************************
!
subroutine dery_00(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivY
implicit none
integer :: nx,ny,nz,npaire,i,j,k
real(mytype), dimension(nx,ny,nz) :: ty,uy
real(mytype), dimension(nx,ny,nz) :: ry
real(mytype), dimension(nx,nz) :: sy
real(mytype), dimension(ny) :: ffy,fsy,fwy,ppy
if(ilag.eq.1) call lagpoly(uy)
do k=1,nz
do i=1,nx
ty(i,1,k)=afjy*(uy(i,2,k)-uy(i,ny,k))&
+bfjy*(uy(i,3,k)-uy(i,ny-1,k))
ry(i,1,k)=-one
ty(i,2,k)=afjy*(uy(i,3,k)-uy(i,1,k))&
+bfjy*(uy(i,4,k)-uy(i,ny,k))
ry(i,2,k)=zero
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
ry(i,j,k)=zero
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afjy*(uy(i,ny,k)-uy(i,ny-2,k))&
+bfjy*(uy(i,1,k)-uy(i,ny-3,k))
ry(i,ny-1,k)=zero
ty(i,ny,k)=afjy*(uy(i,1,k)-uy(i,ny-1,k))&
+bfjy*(uy(i,2,k)-uy(i,ny-2,k))
ry(i,ny,k)=alfajy
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)*fsy(j)
ry(i,j,k)=ry(i,j,k)-ry(i,j-1,k)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(ny)
ry(i,ny,k)=ry(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
ry(i,j,k)=(ry(i,j,k)-ffy(j)*ry(i,j+1,k))*fwy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
sy(i,k)=(ty(i,1,k)-alfajy*ty(i,ny,k))&
/(1.+ry(i,1,k)-alfajy*ry(i,ny,k))
enddo
enddo
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)-sy(i,k)*ry(i,j,k)
enddo
enddo
enddo
if (istret.ne.0) then
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)*ppy(j)
enddo
enddo
enddo
endif
return
end subroutine dery_00
!********************************************************************
!
subroutine dery_11(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivY
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) :: sy
real(mytype), dimension(ny) :: ffy,fsy,fwy,ppy
if(ilag.eq.1) call lagpoly(uy)
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=zero
ty(i,2,k)=afjy*(uy(i,3,k)-uy(i,1,k))&
+bfjy*(uy(i,4,k)-uy(i,2,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afjy*(uy(i,ny,k)-uy(i,ny-2,k))&
+bfjy*(uy(i,ny-1,k)-uy(i,ny-3,k))
ty(i,ny,k)=zero
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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=afjy*(uy(i,2,k)+uy(i,2,k))&
+bfjy*(uy(i,3,k)+uy(i,3,k))
ty(i,2,k)=afjy*(uy(i,3,k)-uy(i,1,k))&
+bfjy*(uy(i,4,k)+uy(i,2,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afjy*(uy(i,ny,k)-uy(i,ny-2,k))&
+bfjy*((-uy(i,ny-1,k))-uy(i,ny-3,k))
ty(i,ny,k)=afjy*((-uy(i,ny-1,k))-uy(i,ny-1,k))&
+bfjy*((-uy(i,ny-2,k))-uy(i,ny-2,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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (istret.ne.0) then
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)*ppy(j)
enddo
enddo
enddo
endif
return
end subroutine dery_11
!********************************************************************
!
subroutine dery_12(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivY
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) :: sy
real(mytype), dimension(ny) :: ffy,fsy,fwy,ppy
if(ilag.eq.1) call lagpoly(uy)
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=zero
ty(i,2,k)=afjy*(uy(i,3,k)-uy(i,1,k))&
+bfjy*(uy(i,4,k)-uy(i,2,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afmy*(uy(i,ny,k)-uy(i,ny-2,k))
ty(i,ny,k)=-afny*uy(i,ny,k)-bfny*uy(i,ny-1,k)-cfny*uy(i,ny-2,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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=afjy*(uy(i,2,k)+uy(i,2,k))&
+bfjy*(uy(i,3,k)+uy(i,3,k))
ty(i,2,k)=afjy*(uy(i,3,k)-uy(i,1,k))&
+bfjy*(uy(i,4,k)+uy(i,2,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afmy*(uy(i,ny,k)-uy(i,ny-2,k))
ty(i,ny,k)=-afny*uy(i,ny,k)-bfny*uy(i,ny-1,k)-cfny*uy(i,ny-2,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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (istret.ne.0) then
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)*ppy(j)
enddo
enddo
enddo
endif
return
end subroutine dery_12
!********************************************************************
!
subroutine dery_21(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivY
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) :: sy
real(mytype), dimension(ny) :: ffy,fsy,fwy,ppy
if(ilag.eq.1) call lagpoly(uy)
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=af1y*uy(i,1,k)+bf1y*uy(i,2,k)+cf1y*uy(i,3,k)
ty(i,2,k)=af2y*(uy(i,3,k)-uy(i,1,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afjy*(uy(i,ny,k)-uy(i,ny-2,k))&
+bfjy*(uy(i,ny-1,k)-uy(i,ny-3,k))
ty(i,ny,k)=zero
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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=af1y*uy(i,1,k)+bf1y*uy(i,2,k)+cf1y*uy(i,3,k)
ty(i,2,k)=af2y*(uy(i,3,k)-uy(i,1,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afjy*(uy(i,ny,k)-uy(i,ny-2,k))&
+bfjy*((-uy(i,ny-1,k))-uy(i,ny-3,k))
ty(i,ny,k)=afjy*((-uy(i,ny-1,k))-uy(i,ny-1,k))&
+bfjy*((-uy(i,ny-2,k))-uy(i,ny-2,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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
endif
if (istret.ne.0) then
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)*ppy(j)
enddo
enddo
enddo
endif
return
end subroutine dery_21
!********************************************************************
!
subroutine dery_22(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivY
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) :: sy
real(mytype), dimension(ny) :: ffy,fsy,fwy,ppy
if(ilag.eq.1) call lagpoly(uy)
do k=1,nz
do i=1,nx
ty(i,1,k)=af1y*uy(i,1,k)+bf1y*uy(i,2,k)+cf1y*uy(i,3,k)
ty(i,2,k)=af2y*(uy(i,3,k)-uy(i,1,k))
enddo
enddo
do k=1,nz
do j=3,ny-2
do i=1,nx
ty(i,j,k)=afjy*(uy(i,j+1,k)-uy(i,j-1,k))&
+bfjy*(uy(i,j+2,k)-uy(i,j-2,k))
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-1,k)=afmy*(uy(i,ny,k)-uy(i,ny-2,k))
ty(i,ny,k)=-afny*uy(i,ny,k)-bfny*uy(i,ny-1,k)-cfny*uy(i,ny-2,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)*fsy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*fwy(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)-ffy(j)*ty(i,j+1,k))*fwy(j)
enddo
enddo
enddo
if (istret.ne.0) then
do k=1,nz
do j=1,ny
do i=1,nx
ty(i,j,k)=ty(i,j,k)*ppy(j)
enddo
enddo
enddo
endif
return
end subroutine dery_22
!********************************************************************
!
subroutine derz_00(tz,uz,rz,sz,ffz,fsz,fwz,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivZ
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
real(mytype), dimension(nz) :: ffz,fsz,fwz
if(ilag.eq.1) call lagpolz(uz)
do j=1,ny
do i=1,nx
tz(i,j,1)=afkz*(uz(i,j,2)-uz(i,j,nz ))&
+bfkz*(uz(i,j,3)-uz(i,j,nz-1))
rz(i,j,1)=-one
tz(i,j,2)=afkz*(uz(i,j,3)-uz(i,j,1 ))&
+bfkz*(uz(i,j,4)-uz(i,j,nz))
rz(i,j,2)=zero
enddo
enddo
do k=3,nz-2
do j=1,ny
do i=1,nx
tz(i,j,k)=afkz*(uz(i,j,k+1)-uz(i,j,k-1))&
+bfkz*(uz(i,j,k+2)-uz(i,j,k-2))
rz(i,j,k)=zero
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz-1)=afkz*(uz(i,j,nz)-uz(i,j,nz-2))&
+bfkz*(uz(i,j,1 )-uz(i,j,nz-3))
rz(i,j,nz-1)=zero
tz(i,j,nz )=afkz*(uz(i,j,1)-uz(i,j,nz-1))&
+bfkz*(uz(i,j,2)-uz(i,j,nz-2))
rz(i,j,nz )=alfakz
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)*fsz(k)
rz(i,j,k)=rz(i,j,k)-rz(i,j,k-1)*fsz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fwz(nz)
rz(i,j,nz)=rz(i,j,nz)*fwz(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)-ffz(k)*tz(i,j,k+1))*fwz(k)
rz(i,j,k)=(rz(i,j,k)-ffz(k)*rz(i,j,k+1))*fwz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
sz(i,j)=( tz(i,j,1)-alfakz*tz(i,j,nz))/&
(1.+rz(i,j,1)-alfakz*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)-sz(i,j)*rz(i,j,k)
enddo
enddo
enddo
return
end subroutine derz_00
!********************************************************************
!
subroutine derz_11(tz,uz,rz,sz,ffz,fsz,fwz,nx,ny,nz,npaire)
!
!********************************************************************
USE param
USE derivZ
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
real(mytype), dimension(nz) :: ffz,fsz,fwz
if(ilag.eq.1) call lagpolz(uz)
if (npaire==1) then
do j=1,ny
do i=1,nx
tz(i,j,1)=zero
tz(i,j,2)=afkz*(uz(i,j,3)-uz(i,j,1))&
+bfkz*(uz(i,j,4)-uz(i,j,2))
enddo
enddo
do k=3,nz-2
do j=1,ny
do i=1,nx
tz(i,j,k)=afkz*(uz(i,j,k+1)-uz(i,j,k-1))&
+bfkz*(uz(i,j,k+2)-uz(i,j,k-2))
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz-1)=afkz*(uz(i,j,nz )-uz(i,j,nz-2))&
+bfkz*(uz(i,j,nz-1)-uz(i,j,nz-3))
tz(i,j,nz )=zero
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)*fsz(k)
enddo
enddo
enddo
do j=1,ny
do i=1,nx
tz(i,j,nz)=tz(i,j,nz)*fwz(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)-ffz(k)*tz(i,j,k+1))*fwz(k)
enddo
enddo
enddo
endif
if (npaire==0) then
do j=1,ny