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schemes.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 schemes()
!
!********************************************************************
USE param
USE derivX
USE derivY
USE derivZ
USE variables
USE var
implicit none
integer :: i,j,k
real(mytype) :: fpi2
alfa1x= 2.
af1x =-(5./2. )/dx
bf1x = ( 2. )/dx
cf1x = (1./2. )/dx
df1x = 0.
alfa2x= 1./4.
af2x = (3./4. )/dx
alfanx= 2.
afnx =-(5./2. )/dx
bfnx = ( 2. )/dx
cfnx = (1./2. )/dx
dfnx = 0.
alfamx= 1./4.
afmx = (3./4. )/dx
alfaix= 1./3.
afix = (7./9. )/dx
bfix = (1./36. )/dx
alsa1x= 11.
as1x = (13. )/dx2
bs1x =-(27. )/dx2
cs1x = (15. )/dx2
ds1x =-(1. )/dx2
alsa2x= 1./10.
as2x = (6./5. )/dx2
alsa3x= 2./11.
as3x = (12./11.)/dx2
bs3x = (3./44. )/dx2
alsanx= 11.
asnx = (13. )/dx2
bsnx =-(27. )/dx2
csnx = (15. )/dx2
dsnx =-(1. )/dx2
alsamx= 1./10.
asmx = (6./5. )/dx2
alsatx= 2./11.
astx = (12./11.)/dx2
bstx = (3./44. )/dx2
!alsaix= 2./11.
!asix = (12./11.)/dx2
!bsix = (3./44. )/dx2
!csix = 0.
!NUMERICAL DISSIPATION (see publications for help)
fpi2=4.
! fpi2=(48./7)/(pi*pi)
alsaix=(45.*fpi2*pi*pi-272.)/(2.*(45.*fpi2*pi*pi-208.))
asix =((6.-9.*alsaix)/4.)/dx2
bsix =((-3.+24*alsaix)/5.)/(4.*dx2)
csix =((2.-11.*alsaix)/20.)/(9.*dx2)
! stop
!if (nrank==0) then
! write(*,*) '=== derxx ==='
! write(*,*) alsaix
! write(*,*) asix*dx2
! write(*,*) bsix*4*dx2
! write(*,*) csix*9*dx2
! write(*,*) '============='
alfa1y= 2.
af1y =-(5./2. )/dy
bf1y = ( 2. )/dy
cf1y = (1./2. )/dy
df1y = 0.
alfa2y= 1./4.
af2y = (3./4. )/dy
alfany= 2.
afny =-(5./2. )/dy
bfny = ( 2. )/dy
cfny = (1./2. )/dy
dfny = 0.
alfamy= 1./4.
afmy = (3./4. )/dy
alfajy= 1./3.
afjy = (7./9. )/dy
bfjy = (1./36. )/dy
alsa1y= 11.
as1y = (13. )/dy2
bs1y =-(27. )/dy2
cs1y = (15. )/dy2
ds1y =-(1. )/dy2
alsa2y= 1./10.
as2y = (6./5. )/dy2
alsa3y= 2./11.
as3y = (12./11.)/dy2
bs3y = (3./44. )/dy2
alsany= 11.
asny = (13. )/dy2
bsny =-(27. )/dy2
csny = (15. )/dy2
dsny =-(1. )/dy2
alsamy= 1./10.
asmy = (6./5. )/dy2
alsaty= 2./11.
asty = (12./11.)/dy2
bsty = (3./44. )/dy2
!alsajy= 2./11.
!asjy = (12./11.)/dy2
!bsjy = (3./44. )/dy2
!csjy = 0.
alsajy=(45.*fpi2*pi*pi-272.)/(2.*(45.*fpi2*pi*pi-208.))
asjy =((6.-9.*alsajy)/4.)/dy2
bsjy =((-3.+24*alsajy)/5.)/(4.*dy2)
csjy =((2.-11.*alsajy)/20.)/(9.*dy2)
!if (nrank==0) then
! write(*,*) '=== deryy ==='
! write(*,*) alsajy
! write(*,*) asjy*dy2
! write(*,*) bsjy*4*dy2
! write(*,*) csjy*9*dy2
! write(*,*) '============='
!endif
alcaix6=9./62.
acix6=(63./62.)/dx
bcix6=(17./62.)/3./dx
cfx6(1)=alcaix6
cfx6(2)=alcaix6
cfx6(nxm-2)=alcaix6
cfx6(nxm-1)=alcaix6
cfx6(nxm)=0.
if (nclx==0) ccx6(1)=2.
if (nclx==1) ccx6(1)=1. + alcaix6
if (nclx==2) ccx6(1)=1. + alcaix6
ccx6(2)=1.
ccx6(nxm-2)=1.
ccx6(nxm-1)=1.
if (nclx==0) ccx6(nxm)=1. + alcaix6*alcaix6
if (nclx==1) ccx6(nxm)=1. + alcaix6
if (nclx==2) ccx6(nxm)=1. + alcaix6
cbx6(1)=alcaix6
cbx6(2)=alcaix6
cbx6(nxm-2)=alcaix6
cbx6(nxm-1)=alcaix6
cbx6(nxm)=0.
do i=3,nxm-3
cfx6(i)=alcaix6
ccx6(i)=1.
cbx6(i)=alcaix6
enddo
cfi6(1)=alcaix6 + alcaix6
cfi6(2)=alcaix6
cfi6(nx-2)=alcaix6
cfi6(nx-1)=alcaix6
cfi6(nx)=0.
cci6(1)=1.
cci6(2)=1.
cci6(nx-2)=1.
cci6(nx-1)=1.
cci6(nx)=1.
cbi6(1)=alcaix6
cbi6(2)=alcaix6
cbi6(nx-2)=alcaix6
cbi6(nx-1)=alcaix6 + alcaix6
cbi6(nx)=0.
do i=3,nx-3
cfi6(i)=alcaix6
cci6(i)=1.
cbi6(i)=alcaix6
enddo
ailcaix6=3./10.
aicix6=1./128.*(75.+70.*ailcaix6)
bicix6=1./256.*(126.*ailcaix6-25.)
cicix6=1./256.*(-10.*ailcaix6+3.)
if (nrank==0) print *,'New coef Inter X',aicix6,bicix6,cicix6
cifx6(1)=ailcaix6
cifx6(2)=ailcaix6
cifx6(nxm-2)=ailcaix6
cifx6(nxm-1)=ailcaix6
cifx6(nxm)=0.
if (nclx==0) cicx6(1)=2.
if (nclx==1) cicx6(1)=1. + ailcaix6
if (nclx==2) cicx6(1)=1. + ailcaix6
cicx6(2)=1.
cicx6(nxm-2)=1.
cicx6(nxm-1)=1.
if (nclx==0) cicx6(nxm)=1. + ailcaix6*ailcaix6
if (nclx==1) cicx6(nxm)=1. + ailcaix6
if (nclx==2) cicx6(nxm)=1. + ailcaix6
cibx6(1)=ailcaix6
cibx6(2)=ailcaix6
cibx6(nxm-2)=ailcaix6
cibx6(nxm-1)=ailcaix6
cibx6(nxm)=0.
do i=3,nxm-3
cifx6(i)=ailcaix6
cicx6(i)=1.
cibx6(i)=ailcaix6
enddo
cifi6(1)=ailcaix6 + ailcaix6
cifi6(2)=ailcaix6
cifi6(nx-2)=ailcaix6
cifi6(nx-1)=ailcaix6
cifi6(nx)=0.
cici6(1)=1.
cici6(2)=1.
cici6(nx-2)=1.
cici6(nx-1)=1.
cici6(nx)=1.
cibi6(1)=ailcaix6
cibi6(2)=ailcaix6
cibi6(nx-2)=ailcaix6
cibi6(nx-1)=ailcaix6 + ailcaix6
cibi6(nx)=0.
do i=3,nx-3
cifi6(i)=ailcaix6
cici6(i)=1.
cibi6(i)=ailcaix6
enddo
alcaiy6=9./62.
aciy6=(63./62.)/dy
bciy6=(17./62.)/3./dy
cfy6(1)=alcaiy6
cfy6(2)=alcaiy6
cfy6(nym-2)=alcaiy6
cfy6(nym-1)=alcaiy6
cfy6(nym)=0.
if (ncly==0) ccy6(1)=2.
if (ncly==1) ccy6(1)=1. + alcaiy6
if (ncly==2) ccy6(1)=1. + alcaiy6
ccy6(2)=1.
ccy6(nym-2)=1.
ccy6(nym-1)=1.
if (ncly==0) ccy6(nym)=1. + alcaiy6*alcaiy6
if (ncly==1) ccy6(nym)=1. + alcaiy6
if (ncly==2) ccy6(nym)=1. + alcaiy6
cby6(1)=alcaiy6
cby6(2)=alcaiy6
cby6(nym-2)=alcaiy6
cby6(nym-1)=alcaiy6
cby6(nym)=0.
do j=3,nym-3
cfy6(j)=alcaiy6
ccy6(j)=1.
cby6(j)=alcaiy6
enddo
cfi6y(1)=alcaiy6 + alcaiy6
cfi6y(2)=alcaiy6
cfi6y(ny-2)=alcaiy6
cfi6y(ny-1)=alcaiy6
cfi6y(ny)=0.
cci6y(1)=1.
cci6y(2)=1.
cci6y(ny-2)=1.
cci6y(ny-1)=1.
cci6y(ny)=1.
cbi6y(1)=alcaiy6
cbi6y(2)=alcaiy6
cbi6y(ny-2)=alcaiy6
cbi6y(ny-1)=alcaiy6 + alcaiy6
cbi6y(ny)=0.
do j=3,ny-3
cfi6y(j)=alcaiy6
cci6y(j)=1.
cbi6y(j)=alcaiy6
enddo
ailcaiy6=3./10.
aiciy6=1./128.*(75.+70.*ailcaiy6)
biciy6=1./256.*(126.*ailcaiy6-25.)
ciciy6=1./256.*(-10.*ailcaiy6+3.)
if (nrank==0) print *,'New coef Inter Y',aiciy6,biciy6,ciciy6
cify6(1)=ailcaiy6
cify6(2)=ailcaiy6
cify6(nym-2)=ailcaiy6
cify6(nym-1)=ailcaiy6
cify6(nym)=0.
if (ncly==0) cicy6(1)=2.
if (ncly==1) cicy6(1)=1. + ailcaiy6
if (ncly==2) cicy6(1)=1. + ailcaiy6
cicy6(2)=1.
cicy6(nym-2)=1.
cicy6(nym-1)=1.
if (ncly==0) cicy6(nym)=1. + ailcaiy6*ailcaiy6
if (ncly==1) cicy6(nym)=1. + ailcaiy6
if (ncly==2) cicy6(nym)=1. + ailcaiy6
ciby6(1)=ailcaiy6
ciby6(2)=ailcaiy6
ciby6(nym-2)=ailcaiy6
ciby6(nym-1)=ailcaiy6
ciby6(nym)=0.
do j=3,nym-3
cify6(j)=ailcaiy6
cicy6(j)=1.
ciby6(j)=ailcaiy6
enddo
cifi6y(1)=ailcaiy6 + ailcaiy6
cifi6y(2)=ailcaiy6
cifi6y(ny-2)=ailcaiy6
cifi6y(ny-1)=ailcaiy6
cifi6y(ny)=0.
cici6y(1)=1.
cici6y(2)=1.
cici6y(ny-2)=1.
cici6y(ny-1)=1.
cici6y(ny)=1.
cibi6y(1)=ailcaiy6
cibi6y(2)=ailcaiy6
cibi6y(ny-2)=ailcaiy6
cibi6y(ny-1)=ailcaiy6 + ailcaiy6
cibi6y(ny)=0.
do j=3,ny-3
cifi6y(j)=ailcaiy6
cici6y(j)=1.
cibi6y(j)=ailcaiy6
enddo
#ifndef TWOD
alcaiz6=9./62.
aciz6=(63./62.)/dz
bciz6=(17./62.)/3./dz
cfz6(1)=alcaiz6
cfz6(2)=alcaiz6
cfz6(nzm-2)=alcaiz6
cfz6(nzm-1)=alcaiz6
cfz6(nzm)=0.
if (nclz==0) ccz6(1)=2.
if (nclz==1) ccz6(1)=1. + alcaiz6
if (nclz==2) ccz6(1)=1. + alcaiz6
ccz6(2)=1.
ccz6(nzm-2)=1.
ccz6(nzm-1)=1.
if (nclz==0) ccz6(nzm)=1. + alcaiz6*alcaiz6
if (nclz==1) ccz6(nzm)=1. + alcaiz6
if (nclz==2) ccz6(nzm)=1. + alcaiz6
cbz6(1)=alcaiz6
cbz6(2)=alcaiz6
cbz6(nzm-2)=alcaiz6
cbz6(nzm-1)=alcaiz6
cbz6(nzm)=0.
do k=3,nzm-3
cfz6(k)=alcaiz6
ccz6(k)=1.
cbz6(k)=alcaiz6
enddo
cfi6z(1)=alcaiz6 + alcaiz6
cfi6z(2)=alcaiz6
cfi6z(nz-2)=alcaiz6
cfi6z(nz-1)=alcaiz6
cfi6z(nz)=0.
cci6z(1)=1.
cci6z(2)=1.
cci6z(nz-2)=1.
cci6z(nz-1)=1.
cci6z(nz)=1.
cbi6z(1)=alcaiz6
cbi6z(2)=alcaiz6
cbi6z(nz-2)=alcaiz6
cbi6z(nz-1)=alcaiz6 + alcaiz6
cbi6z(nz)=0.
do k=3,nz-3
cfi6z(k)=alcaiz6
cci6z(k)=1.
cbi6z(k)=alcaiz6
enddo
ailcaiz6=3./10.
aiciz6=1./128.*(75.+70.*ailcaiz6)
biciz6=1./256.*(126.*ailcaiz6-25.)
ciciz6=1./256.*(-10.*ailcaiz6+3.)
if (nrank==0) print *,'New coef Inter Z',aiciz6,biciz6,ciciz6
cifz6(1)=ailcaiz6
cifz6(2)=ailcaiz6
cifz6(nzm-2)=ailcaiz6
cifz6(nzm-1)=ailcaiz6
cifz6(nzm)=0.
if (nclz==0) cicz6(1)=2.
if (nclz==1) cicz6(1)=1. + ailcaiz6
if (nclz==2) cicz6(1)=1. + ailcaiz6
cicz6(2)=1.
cicz6(nzm-2)=1.
cicz6(nzm-1)=1.
if (nclz==0) cicz6(nzm)=1. + ailcaiz6*ailcaiz6
if (nclz==1) cicz6(nzm)=1. + ailcaiz6
if (nclz==2) cicz6(nzm)=1. + ailcaiz6
cibz6(1)=ailcaiz6
cibz6(2)=ailcaiz6
cibz6(nzm-2)=ailcaiz6
cibz6(nzm-1)=ailcaiz6
cibz6(nzm)=0.
do k=3,nzm-3
cifz6(k)=ailcaiz6
cicz6(k)=1.
cibz6(k)=ailcaiz6
enddo
cifi6z(1)=ailcaiz6 + ailcaiz6
cifi6z(2)=ailcaiz6
cifi6z(nz-2)=ailcaiz6
cifi6z(nz-1)=ailcaiz6
cifi6z(nz)=0.
cici6z(1)=1.
cici6z(2)=1.
cici6z(nz-2)=1.
cici6z(nz-1)=1.
cici6z(nz)=1.
cibi6z(1)=ailcaiz6
cibi6z(2)=ailcaiz6
cibi6z(nz-2)=ailcaiz6
cibi6z(nz-1)=ailcaiz6 + ailcaiz6
cibi6z(nz)=0.
do k=3,nz-3
cifi6z(k)=ailcaiz6
cici6z(k)=1.
cibi6z(k)=ailcaiz6
enddo
alfa1z= 2.
af1z =-(5./2. )/dz
bf1z = ( 2. )/dz
cf1z = (1./2. )/dz
df1z = 0.
alfa2z= 1./4.
af2z = (3./4. )/dz
alfanz= 2.
afnz =-(5./2. )/dz
bfnz = ( 2. )/dz
cfnz = (1./2. )/dz
dfnz = 0.
alfamz= 1./4.
afmz = (3./4. )/dz
alfakz= 1./3.
afkz = (7./9. )/dz
bfkz = (1./36. )/dz
alsa1z= 11.
as1z = (13. )/dz2
bs1z =-(27. )/dz2
cs1z = (15. )/dz2
ds1z =-(1. )/dz2
alsa2z= 1./10.
as2z = (6./5. )/dz2
alsa3z= 2./11.
as3z = (12./11.)/dz2
bs3z = (3./44. )/dz2
alsanz= 11.
asnz = (13. )/dz2
bsnz =-(27. )/dz2
csnz = (15. )/dz2
dsnz =-(1. )/dz2
alsamz= 1./10.
asmz = (6./5. )/dz2
alsatz= 2./11.
astz = (12./11.)/dz2
bstz = (3./44. )/dz2
! alsakz= 2./11.
! askz = (12./11.)/dz2
! bskz = (3./44. )/dz2
! cskz = 0.
alsakz=(45.*fpi2*pi*pi-272.)/(2.*(45.*fpi2*pi*pi-208.))
askz =((6.-9.*alsakz)/4.)/dz2
bskz =((-3.+24*alsakz)/5.)/(4.*dz2)
cskz =((2.-11.*alsakz)/20.)/(9.*dz2)
!if (nrank==0) then
! write(*,*) '=== derzz ==='
! write(*,*) alsakz
! write(*,*) askz*dz2
! write(*,*) bskz*4*dz2
! write(*,*) cskz*9*dz2
! write(*,*) '============='
!endif
#endif
if (nclx.eq.0) then
ffx(1) =alfaix
ffx(2) =alfaix
ffx(nx-2)=alfaix
ffx(nx-1)=alfaix
ffx(nx) =0.
fcx(1) =2.
fcx(2) =1.
fcx(nx-2)=1.
fcx(nx-1)=1.
fcx(nx )=1.+alfaix*alfaix
fbx(1) =alfaix
fbx(2) =alfaix
fbx(nx-2)=alfaix
fbx(nx-1)=alfaix
fbx(nx )=0.
do i=3,nx-3
ffx(i)=alfaix
fcx(i)=1.
fbx(i)=alfaix
enddo
endif
if (nclx.eq.1) then
ffx(1) =alfaix+alfaix
ffx(2) =alfaix
ffx(nx-2)=alfaix
ffx(nx-1)=alfaix
ffx(nx) =0.
fcx(1) =1.
fcx(2) =1.
fcx(nx-2)=1.
fcx(nx-1)=1.
fcx(nx )=1.
fbx(1) =alfaix
fbx(2) =alfaix
fbx(nx-2)=alfaix
fbx(nx-1)=alfaix+alfaix
fbx(nx )=0.
do i=3,nx-3
ffx(i)=alfaix
fcx(i)=1.
fbx(i)=alfaix
enddo
endif
if (nclx.eq.2) then
ffx(1) =alfa1x
ffx(2) =alfa2x
ffx(nx-2)=alfaix
ffx(nx-1)=alfamx
ffx(nx) =0.
fcx(1) =1.
fcx(2) =1.
fcx(nx-2)=1.
fcx(nx-1)=1.
fcx(nx )=1.
fbx(1) =alfa2x
fbx(2) =alfaix
fbx(nx-2)=alfamx
fbx(nx-1)=alfanx
fbx(nx )=0.
do i=3,nx-3
ffx(i)=alfaix
fcx(i)=1.
fbx(i)=alfaix
enddo
endif
if (ncly.eq.0) then
ffy(1) =alfajy
ffy(2) =alfajy
ffy(ny-2)=alfajy
ffy(ny-1)=alfajy
ffy(ny) =0.
fcy(1) =2.
fcy(2) =1.
fcy(ny-2)=1.
fcy(ny-1)=1.
fcy(ny )=1.+alfajy*alfajy
fby(1) =alfajy
fby(2) =alfajy
fby(ny-2)=alfajy
fby(ny-1)=alfajy
fby(ny )=0.
do j=3,ny-3
ffy(j)=alfajy
fcy(j)=1.
fby(j)=alfajy
enddo
endif
if (ncly.eq.1) then
ffy(1) =alfajy+alfajy
ffy(2) =alfajy
ffy(ny-2)=alfajy
ffy(ny-1)=alfajy
ffy(ny) =0.
fcy(1) =1.
fcy(2) =1.
fcy(ny-2)=1.
fcy(ny-1)=1.
fcy(ny )=1.
fby(1) =alfajy
fby(2) =alfajy
fby(ny-2)=alfajy
fby(ny-1)=alfajy+alfajy
fby(ny )=0.
do j=3,ny-3
ffy(j)=alfajy
fcy(j)=1.
fby(j)=alfajy
enddo
endif
if (ncly.eq.2) then
ffy(1) =alfa1y
ffy(2) =alfa2y
ffy(ny-2)=alfajy
ffy(ny-1)=alfamy
ffy(ny) =0.
fcy(1) =1.
fcy(2) =1.
fcy(ny-2)=1.
fcy(ny-1)=1.
fcy(ny )=1.
fby(1) =alfa2y
fby(2) =alfajy
fby(ny-2)=alfamy
fby(ny-1)=alfany
fby(ny )=0.
do j=3,ny-3
ffy(j)=alfajy
fcy(j)=1.
fby(j)=alfajy
enddo
endif
#ifndef TWOD
if (nclz.eq.0) then
ffz(1) =alfakz
ffz(2) =alfakz
ffz(nz-2)=alfakz
ffz(nz-1)=alfakz
ffz(nz) =0.
fcz(1) =2.
fcz(2) =1.
fcz(nz-2)=1.
fcz(nz-1)=1.
fcz(nz )=1.+alfakz*alfakz
fbz(1) =alfakz
fbz(2) =alfakz
fbz(nz-2)=alfakz
fbz(nz-1)=alfakz
fbz(nz )=0.
do k=3,nz-3
ffz(k)=alfakz
fcz(k)=1.
fbz(k)=alfakz
enddo
endif
if (nclz.eq.1) then
ffz(1) =alfakz+alfakz
ffz(2) =alfakz
ffz(nz-2)=alfakz
ffz(nz-1)=alfakz
ffz(nz) =0.
fcz(1) =1.
fcz(2) =1.
fcz(nz-2)=1.
fcz(nz-1)=1.
fcz(nz )=1.
fbz(1) =alfakz
fbz(2) =alfakz
fbz(nz-2)=alfakz
fbz(nz-1)=alfakz+alfakz
fbz(nz )=0.
do k=3,nz-3
ffz(k)=alfakz
fcz(k)=1.
fbz(k)=alfakz
enddo
endif
if (nclz.eq.2) then
ffz(1) =alfa1z
ffz(2) =alfa2z
ffz(nz-2)=alfakz
ffz(nz-1)=alfamz
ffz(nz) =0.
fcz(1) =1.
fcz(2) =1.
fcz(nz-2)=1.
fcz(nz-1)=1.
fcz(nz )=1.
fbz(1) =alfa2z
fbz(2) =alfakz
fbz(nz-2)=alfamz
fbz(nz-1)=alfanz
fbz(nz )=0.
do k=3,nz-3
ffz(k)=alfakz
fcz(k)=1.
fbz(k)=alfakz
enddo
endif
#endif
if (nclx.eq.0) then
sfx(1) =alsaix
sfx(2) =alsaix
sfx(nx-2)=alsaix
sfx(nx-1)=alsaix
sfx(nx) =0.
scx(1) =2.
scx(2) =1.
scx(nx-2)=1.
scx(nx-1)=1.
scx(nx )=1.+alsaix*alsaix
sbx(1) =alsaix
sbx(2) =alsaix
sbx(nx-2)=alsaix
sbx(nx-1)=alsaix
sbx(nx )=0.
do i=3,nx-3
sfx(i)=alsaix
scx(i)=1.
sbx(i)=alsaix
enddo
endif
if (nclx.eq.1) then
sfx(1) =alsaix+alsaix
sfx(2) =alsaix
sfx(nx-2)=alsaix
sfx(nx-1)=alsaix
sfx(nx) =0.
scx(1) =1.
scx(2) =1.
scx(nx-2)=1.
scx(nx-1)=1.
scx(nx )=1.
sbx(1) =alsaix
sbx(2) =alsaix
sbx(nx-2)=alsaix
sbx(nx-1)=alsaix+alsaix
sbx(nx )=0.
do i=3,nx-3
sfx(i)=alsaix
scx(i)=1.
sbx(i)=alsaix
enddo
endif
if (nclx.eq.2) then
sfx(1) =alsa1x
sfx(2) =alsa2x
sfx(3) =alsa3x
sfx(nx-3)=alsaix
sfx(nx-2)=alsatx
sfx(nx-1)=alsamx
sfx(nx) =0.
scx(1) =1.
scx(2) =1.
scx(3) =1.
scx(nx-3)=1.
scx(nx-2)=1.
scx(nx-1)=1.
scx(nx )=1.
sbx(1) =alsa2x
sbx(2) =alsa3x
sbx(3) =alsaix
sbx(nx-3)=alsatx
sbx(nx-2)=alsamx
sbx(nx-1)=alsanx
sbx(nx )=0.
do i=4,nx-4
sfx(i)=alsaix
scx(i)=1.
sbx(i)=alsaix
enddo
endif
if (ncly.eq.0) then
sfy(1) =alsajy
sfy(2) =alsajy
sfy(ny-2)=alsajy
sfy(ny-1)=alsajy
sfy(ny) =0.
scy(1) =2.
scy(2) =1.
scy(ny-2)=1.
scy(ny-1)=1.
scy(ny )=1.+alsajy*alsajy
sby(1) =alsajy
sby(2) =alsajy
sby(ny-2)=alsajy
sby(ny-1)=alsajy
sby(ny )=0.
do j=3,ny-3
sfy(j)=alsajy
scy(j)=1.
sby(j)=alsajy
enddo
endif
if (ncly.eq.1) then
sfy(1) =alsajy+alsajy
sfy(2) =alsajy
sfy(ny-2)=alsajy
sfy(ny-1)=alsajy
sfy(ny) =0.
scy(1) =1.
scy(2) =1.
scy(ny-2)=1.
scy(ny-1)=1.
scy(ny )=1.
sby(1) =alsajy
sby(2) =alsajy
sby(ny-2)=alsajy
sby(ny-1)=alsajy+alsajy
sby(ny )=0.
do j=3,ny-3
sfy(j)=alsajy
scy(j)=1.
sby(j)=alsajy
enddo
endif
if (ncly.eq.2) then
sfy(1) =alsa1y
sfy(2) =alsa2y
sfy(3) =alsa3y
sfy(ny-3)=alsajy
sfy(ny-2)=alsaty
sfy(ny-1)=alsamy
sfy(ny) =0.
scy(1) =1.
scy(2) =1.
scy(3) =1.
scy(ny-3)=1.
scy(ny-2)=1.
scy(ny-1)=1.
scy(ny )=1.
sby(1) =alsa2y
sby(2) =alsa3y
sby(3) =alsajy
sby(ny-3)=alsaty
sby(ny-2)=alsamy
sby(ny-1)=alsany
sby(ny )=0.
do j=4,ny-4
sfy(j)=alsajy
scy(j)=1.
sby(j)=alsajy
enddo
endif
#ifndef TWOD
if (nclz.eq.0) then
sfz(1) =alsakz
sfz(2) =alsakz
sfz(nz-2)=alsakz
sfz(nz-1)=alsakz
sfz(nz) =0.
scz(1) =2.
scz(2) =1.
scz(nz-2)=1.
scz(nz-1)=1.
scz(nz )=1.+alsakz*alsakz
sbz(1) =alsakz
sbz(2) =alsakz
sbz(nz-2)=alsakz
sbz(nz-1)=alsakz
sbz(nz )=0.
do k=3,nz-3
sfz(k)=alsakz
scz(k)=1.
sbz(k)=alsakz
enddo
endif
if (nclz.eq.1) then
sfz(1) =alsakz+alsakz
sfz(2) =alsakz
sfz(nz-2)=alsakz
sfz(nz-1)=alsakz
sfz(nz) =0.
scz(1) =1.
scz(2) =1.
scz(nz-2)=1.
scz(nz-1)=1.
scz(nz )=1.
sbz(1) =alsakz
sbz(2) =alsakz
sbz(nz-2)=alsakz
sbz(nz-1)=alsakz+alsakz
sbz(nz )=0.
do k=3,nz-3
sfz(k)=alsakz
scz(k)=1.
sbz(k)=alsakz
enddo
endif
if (nclz.eq.2) then
sfz(1) =alsa1z
sfz(2) =alsa2z
sfz(3) =alsa3z
sfz(nz-3)=alsakz
sfz(nz-2)=alsatz
sfz(nz-1)=alsamz
sfz(nz) =0.
scz(1) =1.
scz(2) =1.
scz(3) =1.
scz(nz-3)=1.
scz(nz-2)=1.
scz(nz-1)=1.
scz(nz )=1.
sbz(1) =alsa2z
sbz(2) =alsa3z
sbz(3) =alsakz
sbz(nz-3)=alsatz
sbz(nz-2)=alsamz
sbz(nz-1)=alsanz
sbz(nz )=0.
do k=4,nz-4
sfz(k)=alsakz
scz(k)=1.
sbz(k)=alsakz
enddo
endif
#endif
do i=1,nx
ffxp(i)=ffx(i)
sfxp(i)=sfx(i)
enddo
do i=1,nxm
cfxp6(i)=cfx6(i)
cifxp6(i)=cifx6(i)
enddo
do i=1,nx
cifip6(i)=cifi6(i)
cfip6(i)=cfi6(i)
enddo
do j=1,ny
ffyp(j)=ffy(j)
sfyp(j)=sfy(j)
enddo
do j=1,nym
cfyp6(j)=cfy6(j)
cifyp6(j)=cify6(j)
enddo
do j=1,ny
cifip6y(j)=cifi6y(j)
cfip6y(j)=cfi6y(j)
enddo
#ifndef TWOD
do k=1,nz
ffzp(k)=ffz(k)
sfzp(k)=sfz(k)
enddo
do k=1,nzm
cfzp6(k)=cfz6(k)
cifzp6(k)=cifz6(k)
enddo
do k=1,nz
cifip6z(k)=cifi6z(k)
cfip6z(k)=cfi6z(k)
enddo
#endif
if (nclx.eq.1) then
ffxp(1)=0.
sfx (1)=0.
endif
if (ncly.eq.1) then
ffyp(1)=0.
sfy (1)=0.
endif
cfxp6(1)=0.
cfip6(1)=0.
cfyp6(1)=0.