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derive.f90
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!###############################################################################
!This file is part of Incompact3d.
!
!Incompact3d
!Copyright (c) 2012 Eric Lamballais and Sylvain Laizet
!
! 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(tx,ux,rx,sx,ffx,fsx,fwx,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only:nclx
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 (nclx==0) then
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)=-1.
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)=0.
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)=0.
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)=0.
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))&
/(1.+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
endif
if (nclx==1) then
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=0.
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)=0.
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
endif
if (nclx==2) 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)=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
!********************************************************************
!
subroutine dery(ty,uy,ry,sy,ffy,fsy,fwy,ppy,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only: ncly, istret
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 (ncly==0) then
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)=-1.
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)=0.
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)=0.
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)=0.
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
endif
if (ncly==1) then
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=0.
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)=0.
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
endif
if (ncly==2) 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)=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
!********************************************************************
!
subroutine derz(tz,uz,rz,sz,ffz,fsz,fwz,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only: nclz
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 (nclz==0) then
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)=-1.
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)=0.
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)=0.
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)=0.
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
endif
if (nclz==1) then
if (npaire==1) then
do j=1,ny
do i=1,nx
tz(i,j,1)=0.
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 )=0.
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
do i=1,nx
tz(i,j,1)=afkz*(uz(i,j,2)+uz(i,j,2))&
+bfkz*(uz(i,j,3)+uz(i,j,3))
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 )=afkz*(-uz(i,j,nz-1)-uz(i,j,nz-1))&
+bfkz*(-uz(i,j,nz-2)-uz(i,j,nz-2))
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
endif
if (nclz==2) then
do j=1,ny
do i=1,nx
tz(i,j,1)=af1z*uz(i,j,1)+bf1z*uz(i,j,2)&
+cf1z*uz(i,j,3)
tz(i,j,2)=af2z*(uz(i,j,3)-uz(i,j,1))
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)= afmz*(uz(i,j,nz)-uz(i,j,nz-2))
tz(i,j,nz )=-afnz*uz(i,j,nz)-bfnz*uz(i,j,nz-1)&
-cfnz*uz(i,j,nz-2)
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
return
end subroutine derz
!********************************************************************
!
subroutine derxx(tx,ux,rx,sx,sfx,ssx,swx,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only:nclx
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):: sfx,ssx,swx
if (nclx==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=asix*(ux(2,j,k)-ux(1 ,j,k)&
-ux(1,j,k)+ux(nx ,j,k))&
+bsix*(ux(3,j,k)-ux(1 ,j,k)&
-ux(1,j,k)+ux(nx-1,j,k))&
+csix*(ux(4,j,k)-ux(1 ,j,k)&
-ux(1,j,k)+ux(nx-2,j,k))
rx(1,j,k)=-1.
tx(2,j,k)=asix*(ux(3,j,k)-ux(2 ,j,k)&
-ux(2,j,k)+ux(1 ,j,k))&
+bsix*(ux(4,j,k)-ux(2 ,j,k)&
-ux(2,j,k)+ux(nx ,j,k))&
+csix*(ux(5,j,k)-ux(2 ,j,k)&
-ux(2,j,k)+ux(nx-1,j,k))
rx(2,j,k)=0.
tx(3,j,k)=asix*(ux(4,j,k)-ux(3 ,j,k)&
-ux(3,j,k)+ux(2 ,j,k))&
+bsix*(ux(5,j,k)-ux(3 ,j,k)&
-ux(3,j,k)+ux(1 ,j,k))&
+csix*(ux(6,j,k)-ux(3 ,j,k)&
-ux(3,j,k)+ux(nx,j,k))
rx(3,j,k)=0.
do i=4,nx-3
tx(i,j,k)=asix*(ux(i+1,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-1,j,k))&
+bsix*(ux(i+2,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-2,j,k))&
+csix*(ux(i+3,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-3,j,k))
rx(i,j,k)=0.
enddo
tx(nx-2,j,k)=asix*(ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-3,j,k))&
+bsix*(ux(nx ,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-4,j,k))&
+csix*(ux(1 ,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-5,j,k))
rx(nx-2,j,k)=0.
tx(nx-1,j,k)=asix*(ux(nx ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-2,j,k))&
+bsix*(ux(1 ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-3,j,k))&
+csix*(ux(2 ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-4,j,k))
rx(nx-1,j,k)=0.
tx(nx ,j,k)=asix*(ux(1 ,j,k)-ux(nx ,j,k)&
-ux(nx,j,k)+ux(nx-1,j,k))&
+bsix*(ux(2 ,j,k)-ux(nx ,j,k)&
-ux(nx,j,k)+ux(nx-2,j,k))&
+csix*(ux(3 ,j,k)-ux(nx ,j,k)&
-ux(nx,j,k)+ux(nx-3,j,k))
rx(nx ,j,k)=alsaix
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*ssx(i)
rx(i,j,k)=rx(i,j,k)-rx(i-1,j,k)*ssx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*swx(nx)
rx(nx,j,k)=rx(nx,j,k)*swx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-sfx(i)*tx(i+1,j,k))*swx(i)
rx(i,j,k)=(rx(i,j,k)-sfx(i)*rx(i+1,j,k))*swx(i)
enddo
sx(j,k)=( tx(1,j,k)-alsaix*tx(nx,j,k))/&
(1.+rx(1,j,k)-alsaix*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
endif
if (nclx==1) then
if (npaire==1) then
do k=1,nz
do j=1,ny
tx(1,j,k)=asix*(ux(2,j,k)-ux(1,j,k)&
-ux(1,j,k)+ux(2,j,k))&
+bsix*(ux(3,j,k)-ux(1,j,k)&
-ux(1,j,k)+ux(3,j,k))&
+csix*(ux(4,j,k)-ux(1,j,k)&
-ux(1,j,k)+ux(4,j,k))
tx(2,j,k)=asix*(ux(3,j,k)-ux(2,j,k)&
-ux(2,j,k)+ux(1,j,k))&
+bsix*(ux(4,j,k)-ux(2,j,k)&
-ux(2,j,k)+ux(2,j,k))&
+csix*(ux(5,j,k)-ux(2,j,k)&
-ux(2,j,k)+ux(3,j,k))
tx(3,j,k)=asix*(ux(4,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(2,j,k))&
+bsix*(ux(5,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(1,j,k))&
+csix*(ux(6,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(2,j,k))
do i=4,nx-3
tx(i,j,k)=asix*(ux(i+1,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-1,j,k))&
+bsix*(ux(i+2,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-2,j,k))&
+csix*(ux(i+3,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-3,j,k))
enddo
tx(nx-2,j,k)=asix*(ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-3,j,k))&
+bsix*(ux(nx ,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-4,j,k))&
+csix*(ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-5,j,k))
tx(nx-1,j,k)=asix*(ux(nx ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-2,j,k))&
+bsix*(ux(nx-1,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-3,j,k))&
+csix*(ux(nx-2,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-4,j,k))
tx(nx ,j,k)=asix*(ux(nx-1,j,k)-ux(nx ,j,k)&
-ux(nx ,j,k)+ux(nx-1,j,k))&
+bsix*(ux(nx-2,j,k)-ux(nx ,j,k)&
-ux(nx ,j,k)+ux(nx-2,j,k))&
+csix*(ux(nx-3,j,k)-ux(nx ,j,k)&
-ux(nx ,j,k)+ux(nx-3,j,k))
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*ssx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*swx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-sfx(i)*tx(i+1,j,k))*swx(i)
enddo
enddo
enddo
endif
if (npaire==0) then
do k=1,nz
do j=1,ny
tx(1,j,k)=0.
tx(2,j,k)=asix*(ux(3,j,k)-ux(2,j,k)&
-ux(2,j,k)+ux(1,j,k))&
+bsix*(ux(4,j,k)-ux(2,j,k)&
-ux(2,j,k)-ux(2,j,k))&
+csix*(ux(5,j,k)-ux(2,j,k)&
-ux(2,j,k)-ux(3,j,k))
tx(3,j,k)=asix*(ux(4,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(2,j,k))&
+bsix*(ux(5,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(1,j,k))&
+csix*(ux(6,j,k)-ux(3,j,k)&
-ux(3,j,k)-ux(2,j,k))
do i=4,nx-3
tx(i,j,k)=asix*(ux(i+1,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-1,j,k))&
+bsix*(ux(i+2,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-2,j,k))&
+csix*(ux(i+3,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-3,j,k))
enddo
tx(nx-2,j,k)=asix*( ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-3,j,k))&
+bsix*( ux(nx ,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-4,j,k))&
+csix*(-ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-5,j,k))
tx(nx-1,j,k)=asix*( ux(nx ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-2,j,k))&
+bsix*(-ux(nx-1,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-3,j,k))&
+csix*(-ux(nx-2,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-4,j,k))
tx(nx ,j,k)=0.
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*ssx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*swx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-sfx(i)*tx(i+1,j,k))*swx(i)
enddo
enddo
enddo
endif
endif
if (nclx==2) then
do k=1,nz
do j=1,ny
tx(1,j,k)=as1x*ux(1,j,k)+bs1x*ux(2,j,k)&
+cs1x*ux(3,j,k)+ds1x*ux(4,j,k)
tx(2,j,k)=as2x*(ux(3,j,k)-ux(2,j,k)&
-ux(2,j,k)+ux(1,j,k))
tx(3,j,k)=as3x*(ux(4,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(2,j,k))&
+bs3x*(ux(5,j,k)-ux(3,j,k)&
-ux(3,j,k)+ux(1,j,k))
do i=4,nx-3
tx(i,j,k)=asix*(ux(i+1,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-1,j,k))&
+bsix*(ux(i+2,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-2,j,k))&
+csix*(ux(i+3,j,k)-ux(i ,j,k)&
-ux(i ,j,k)+ux(i-3,j,k))
enddo
tx(nx-2,j,k)=astx*(ux(nx-1,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-3,j,k))&
+bstx*(ux(nx ,j,k)-ux(nx-2,j,k)&
-ux(nx-2,j,k)+ux(nx-4,j,k))
tx(nx-1,j,k)=asmx*(ux(nx ,j,k)-ux(nx-1,j,k)&
-ux(nx-1,j,k)+ux(nx-2,j,k))
tx(nx ,j,k)=asnx*ux(nx ,j,k)+bsnx*ux(nx-1,j,k)&
+csnx*ux(nx-2,j,k)+dsnx*ux(nx-3,j,k)
do i=2,nx
tx(i,j,k)=tx(i,j,k)-tx(i-1,j,k)*ssx(i)
enddo
tx(nx,j,k)=tx(nx,j,k)*swx(nx)
do i=nx-1,1,-1
tx(i,j,k)=(tx(i,j,k)-sfx(i)*tx(i+1,j,k))*swx(i)
enddo
enddo
enddo
endif
return
end subroutine derxx
!********************************************************************
!
subroutine deryy(ty,uy,ry,sy,sfy,ssy,swy,nx,ny,nz,npaire)
!
!********************************************************************
USE param, only:ncly, istret
USE derivY
implicit none
integer :: nx,ny,nz,npaire,i,j,k
real(mytype), dimension(nx,ny,nz) :: ty,uy,ry
real(mytype), dimension(nx,nz) :: sy
real(mytype), dimension(ny) :: sfy,ssy,swy
if (ncly==0) then
do k=1,nz
do i=1,nx
ty(i,1,k)=asjy*(uy(i,2,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,ny,k))&
+bsjy*(uy(i,3,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,ny-1,k))&
+csjy*(uy(i,4,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,ny-2,k))
ry(i,1,k)=-1.
ty(i,2,k)=asjy*(uy(i,3,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,1,k))&
+bsjy*(uy(i,4,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,ny,k))&
+csjy*(uy(i,5,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,ny-1,k))
ry(i,2,k)=0.
ty(i,3,k)=asjy*(uy(i,4,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,2,k))&
+bsjy*(uy(i,5,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,1,k))&
+csjy*(uy(i,6,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,ny,k))
ry(i,3,k)=0.
enddo
enddo
do k=1,nz
do j=4,ny-3
do i=1,nx
ty(i,j,k)=asjy*(uy(i,j+1,k)-uy(i,j,k)&
-uy(i,j,k)+uy(i,j-1,k))&
+bsjy*(uy(i,j+2,k)-uy(i,j,k)&
-uy(i,j,k)+uy(i,j-2,k))&
+csjy*(uy(i,j+3,k)-uy(i,j,k)&
-uy(i,j,k)+uy(i,j-3,k))
ry(i,j,k)=0.
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny-2,k)=asjy*(uy(i,ny-1,k)-uy(i,ny-2,k)&
-uy(i,ny-2,k)+uy(i,ny-3,k))&
+bsjy*(uy(i,ny ,k)-uy(i,ny-2,k)&
-uy(i,ny-2,k)+uy(i,ny-4,k))&
+csjy*(uy(i,1 ,k)-uy(i,ny-2,k)&
-uy(i,ny-2,k)+uy(i,ny-5,k))
ry(i,ny-2,k)=0.
ty(i,ny-1,k)=asjy*(uy(i,ny ,k)-uy(i,ny-1,k)&
-uy(i,ny-1,k)+uy(i,ny-2,k))&
+bsjy*(uy(i,1 ,k)-uy(i,ny-1,k)&
-uy(i,ny-1,k)+uy(i,ny-3,k))&
+csjy*(uy(i,2 ,k)-uy(i,ny-1,k)&
-uy(i,ny-1,k)+uy(i,ny-4,k))
ry(i,ny-1,k)=0.
ty(i,ny ,k)=asjy*(uy(i,1 ,k)-uy(i,ny ,k)&
-uy(i,ny,k)+uy(i,ny-1,k))&
+bsjy*(uy(i,2 ,k)-uy(i,ny ,k)&
-uy(i,ny,k)+uy(i,ny-2,k))&
+csjy*(uy(i,3 ,k)-uy(i,ny ,k)&
-uy(i,ny,k)+uy(i,ny-3,k))
ry(i,ny ,k)=alsajy
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)*ssy(j)
ry(i,j,k)=ry(i,j,k)-ry(i,j-1,k)*ssy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
ty(i,ny,k)=ty(i,ny,k)*swy(ny)
ry(i,ny,k)=ry(i,ny,k)*swy(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)-sfy(j)*ty(i,j+1,k))*swy(j)
ry(i,j,k)=(ry(i,j,k)-sfy(j)*ry(i,j+1,k))*swy(j)
enddo
enddo
enddo
do k=1,nz
do i=1,nx
sy(i,k)=( ty(i,1,k)-alsajy*ty(i,ny,k))/&
(1.+ry(i,1,k)-alsajy*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
endif
if (ncly==1) then
if (npaire==1) then
do k=1,nz
do i=1,nx
ty(i,1,k)=asjy*(uy(i,2,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,2,k))&
+bsjy*(uy(i,3,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,3,k))&
+csjy*(uy(i,4,k)-uy(i,1,k)&
-uy(i,1,k)+uy(i,4,k))
ty(i,2,k)=asjy*(uy(i,3,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,1,k))&
+bsjy*(uy(i,4,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,2,k))&
+csjy*(uy(i,5,k)-uy(i,2,k)&
-uy(i,2,k)+uy(i,3,k))
ty(i,3,k)=asjy*(uy(i,4,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,2,k))&
+bsjy*(uy(i,5,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,1,k))&
+csjy*(uy(i,6,k)-uy(i,3,k)&
-uy(i,3,k)+uy(i,2,k))
enddo
enddo
do k=1,nz
do j=4,ny-3
do i=1,nx
ty(i,j,k)=asjy*(uy(i,j+1,k)-uy(i,j ,k)&
-uy(i,j ,k)+uy(i,j-1,k))&
+bsjy*(uy(i,j+2,k)-uy(i,j ,k)&
-uy(i,j ,k)+uy(i,j-2,k))&
+csjy*(uy(i,j+3,k)-uy(i,j ,k)&