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advec_compact4knikker.f
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advec_compact4knikker.f
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! Part of Dflow3d a 3D Navier Stokes solver with variable density for
! simulations of near field dredge plume mixing
! Copyright (C) 2012 Lynyrd de Wit
! This program 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, either version 3 of the License, or
! (at your option) any later version.
! This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
subroutine advecu_COM4(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,phivt,dz,
+ i1,j1,k1,ib,ie,jb,je,kb,ke,rank,px)
implicit none
include 'mpif.h'
c
c********************************************************************
c
c advecu calculates the advection of the u-velocity, which is
c the velocity in the radial direction.
c
c In formula:
c
c 1 d(ruu) 1 d(uv) d(uw) vv
c - ( - ------ + - ----- + ----- - -- )
c r dr r dphi dz r
c
c on input :
c
c putout : "empty" (initialised to zero)
c Uvel,Vvel,Wvel : contain velocities at former timestep
c Utmp : contains velocity at oldest timestep
c dr,phiv,dz : grid spacing in r, phi and z-direction
c i1,j1,k1 : parameters for array-dimensions
c ib,ie,jb,je,kb,ke : range of gridpoints for which the
c advection has to be calculated
c Ru,Rp : radial positions of the U-velocity
c component and the pressure location
c respectively
c
c on output :
c
c putout : advection part
c other parameters : all unchanged
c
c********************************************************************
integer i,j,k,im,ip,jm,jp,km,kp,i1,j1,k1,ib,ie,jb,je,kb,ke
integer rank,px
real putout(0:i1,0:j1,0:k1),Uvel(0:i1,0:j1,0:k1),
+ Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),
+ dr(0:i1),phivt(0:je*px+1),dz,Ru(0:i1),Rp(0:i1)
real rho(0:i1,0:j1,0:k1),uu(0:i1,0:j1,0:k1)
real rhoip,rhoim,rhojp,rhojm,rhokp,rhokm
real wall_value
! real aax_0i1(0:i1),bbx_0i1(0:i1),ccx_0i1(0:i1),ddx_0i1(0:i1)
real aax2_0ie(0:ie),bbx2_0ie(0:ie),ccx2_0ie(0:ie),ddx2_0ie(0:ie)
real aax_0ie(0:ie),bbx_0ie(0:ie),ccx_0ie(0:ie),ddx_0ie(0:ie)
! real aax_1i1(1:i1),bbx_1i1(1:i1),ccx_1i1(1:i1),ddx_1i1(1:i1)
real aax_1ie(1:ie),bbx_1ie(1:ie),ccx_1ie(1:ie),ddx_1ie(1:ie)
! real aax_0ie1(0:i1),bbx_0ie1(0:i1),ccx_0ie1(0:i1),ddx_0ie1(0:i1),dfx1(0:i1)
real aaz_0ke(0:ke),bbz_0ke(0:ke),ccz_0ke(0:ke),ddz_0ke(0:ke)
real aaz_1ke(1:ke),bbz_1ke(1:ke),ccz_1ke(1:ke),ddz_1ke(1:ke)
real ruu(0:i1),u_r(0:i1),dfx(0:ie),ru_u(0:ie,0:j1,0:k1),w_II(0:ie,0:j1,0:k1)
real ru_II(0:ke),ruw(0:ke),dfz(1:ke)
real v_I(0:ie,0:j1,0:k1)
real putout_T(1:ie,1:je*px,1:ke/px),v_I_T(1:ie,0:je*px+1,1:ke/px),ru_u_T(1:ie,0:je*px+1,1:ke/px)
real putouty(1:ie,1:je,1:ke)
real dfy_T(1:je*px),ru_I_T(0:je*px),ruv_I_T(0:je*px)
real aay_0jepx(0:je*px),bby_0jepx(0:je*px),ccy_0jepx(0:je*px),ddy_0jepx(0:je*px)
real aay_1jepx(1:je*px),bby_1jepx(1:je*px),ccy_1jepx(1:je*px),ddy_1jepx(1:je*px)
integer ileng,ierr,itag,status(MPI_STATUS_SIZE)
real const_1_6,const_1_22,const_12_11,const_2_3
putout=0.
const_1_6=1./6.
const_1_22=1./22.
const_12_11=12./11.
const_2_3=2./3.
bbx_1ie=1.
aax_1ie=const_1_6 !3./10.
aax_1ie(1)=0.
aax_1ie(ie)=0. !0. !1. !0.
ccx_1ie=const_1_6 !3./10.
ccx_1ie(1)=0. !0. !0. !1. !0. !1.
ccx_1ie(ie)=0.
bbx2_0ie=1.
aax2_0ie=const_1_6 !3./10.
aax2_0ie(0)=0.
aax2_0ie(ie)=0. !5. !0.
ccx2_0ie=const_1_6 !3./10.
ccx2_0ie(0)=0. !5. !0.
ccx2_0ie(ie)=0.
bbx_0ie=1.
aax_0ie=const_1_22 !9./62.
aax_0ie(0)=0.
aax_0ie(ie)=3.!*3./8. !331./15. !23. !0. !const_1_22 !0. !1./23. ! 1./23. !0. !2. !15.
ccx_0ie=const_1_22 !9./62.
ccx_0ie(0)=3.!*3./8. !331./15. !23. !const_1_22 !23. !0. !1./23. !1./23. !0. !2. !15.
ccx_0ie(ie)=0.
do k=0,k1 !kb,ke
do j=0,j1
! !! interpolate_x rho -> u-loc
ddx2_0ie(0)=0.5*(rho(0,j,k)+rho(1,j,k))
ddx2_0ie(ie)=0.5*(rho(ie,j,k)+rho(i1,j,k))
do i=1,ie-1
ddx2_0ie(i)=const_2_3*(rho(i+1,j,k)+rho(i,j,k))
enddo
CALL solve_tridiag(ru_u(0:ie,j,k),aax2_0ie,bbx2_0ie,ccx2_0ie,ddx2_0ie,i1) ! interpolate rho -> u-loc -> 0:i1
ru_u(0:ie,j,k)=ru_u(0:ie,j,k)*Uvel(0:ie,j,k)
enddo
enddo
uu=Uvel
do k=kb,ke
do j=jb,je
! !! interpolate_x u -> rho-loc
ddx_1ie(1)=0.5*(uu(0,j,k)+uu(1,j,k))
ddx_1ie(ie)=0.5*(uu(ie-1,j,k)+uu(ie,j,k))
do i=2,ie-1
ddx_1ie(i)=const_2_3*(uu(i-1,j,k)+uu(i,j,k))
enddo
CALL solve_tridiag(u_r(1:ie),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie)
! derivative d(Rrhouu)Rdr
ruu(1:ie)=Rp(1:ie)*u_r(1:ie)*u_r(1:ie)*rho(1:ie,j,k)
ddx_0ie(0)=8./3.*(-Ru(0)*uu(0,j,k)*uu(0,j,k)*rho(0,j,k)+ruu(2))/(Ru(0)*(Rp(1)-Rp(0)))
ddx_0ie(ie)=8./3.*(Ru(ie)*uu(ie,j,k)*uu(ie,j,k)*rho(i1,j,k)-ruu(ie-1))/(Ru(ie)*(Rp(i1)-Rp(ie)))
do i=1,ie-1
ddx_0ie(i)=const_12_11*(ruu(i+1)-ruu(i))/(Ru(i)*(Rp(i+1)-Rp(i)))
enddo
CALL solve_tridiag(dfx(0:ie),aax_0ie,bbx_0ie,ccx_0ie,ddx_0ie,ie+1) ! df on Uvel(i,j,k) location -> 1:ie
putout(1:ie,j,k)=putout(1:ie,j,k)-dfx(1:ie) ! derivative: d(ruu)/rdr
enddo
enddo
do k=0,ke ! for correct bc on w_II also k=0 is included
do j=jb,je
!! interpolate_x Wvel -> II-loc
ddx2_0ie(0)=0.5*(Wvel(0,j,k)+Wvel(1,j,k))
ddx2_0ie(ie)=0.5*(Wvel(ie,j,k)+Wvel(i1,j,k))
do i=1,ie-1
ddx2_0ie(i)=const_2_3*(Wvel(i+1,j,k)+Wvel(i,j,k))
enddo
CALL solve_tridiag(w_II(0:ie,j,k),aax2_0ie,bbx2_0ie,ccx2_0ie,ddx2_0ie,i1) ! interpolate W -> II-loc -> 0:i1 (with i1 as not used value)
enddo
enddo
bbz_0ke=1.
aaz_0ke=const_1_6 !3./10.
aaz_0ke(0)=0.
aaz_0ke(ke)=0. !5. !0.
ccz_0ke=const_1_6 !3./10.
ccz_0ke(0)=0. !5. !0.
ccz_0ke(ke)=0.
bbz_1ke=1.
aaz_1ke=const_1_22 !9./62.
aaz_1ke(1)=0.
aaz_1ke(ke)=-1. !-1.!*26./24. !0. !const_1_22 !1./11.
ccz_1ke=const_1_22 !9./62.
ccz_1ke(1)=-1. !-1.!*26./24. !0. !const_1_22 !1./11.
ccz_1ke(ke)=0.
do i=ib,ie
do j=jb,je
! interpolate_z ru_u -> II-loc
ddz_0ke(0)=0.5*(ru_u(i,j,0)+ru_u(i,j,1))
ddz_0ke(ke)=0.5*(ru_u(i,j,ke)+ru_u(i,j,k1))
do k=1,ke-1
ddz_0ke(k)=const_2_3*(ru_u(i,j,k+1)+ru_u(i,j,k))
enddo
CALL solve_tridiag(ru_II(0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,ke+1) ! ru_II -> II-loc 0:ke
ruw(0:ke)=ru_II(0:ke)*w_II(i,j,0:ke)
ddz_1ke(1)=(-ruw(0)+2.*ruw(1)-ruw(2))/dz
ddz_1ke(ke)=(+ruw(ke)-2.*ruw(ke-1)+ruw(ke-2))/dz
do k=2,ke-1
ddz_1ke(k)=const_12_11*(ruw(k)-ruw(k-1))/dz
enddo
CALL solve_tridiag(dfz(1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke) ! dfz on Uvel(i,j,k) location -> 1:ke
putout(i,j,1:ke)=putout(i,j,1:ke)-dfz(1:ke)
enddo
enddo
!! interpolate_x Vvel -> I-loc
do k=kb,ke ! for correct bc on v_I also j=0 is included
do j=0,je
!! interpolate_x Vvel -> I-loc
ddx2_0ie(0)=0.5*(Vvel(0,j,k)+Vvel(1,j,k))
ddx2_0ie(ie)=0.5*(Vvel(ie,j,k)+Vvel(i1,j,k))
do i=1,ie-1
ddx2_0ie(i)=const_2_3*(Vvel(i+1,j,k)+Vvel(i,j,k))
enddo
CALL solve_tridiag(v_I(0:ie,j,k),aax2_0ie,bbx2_0ie,ccx2_0ie,ddx2_0ie,i1) ! interpolate_x V -> I-loc -> 0:i1 (with 0 and i1 as not used value)
enddo
enddo
call t2np(ru_u(1:ie,1:je,1:ke),ru_u_T(1:ie,1:je*px,1:ke/px))
call t2np(v_I(1:ie,1:je,1:ke),v_I_T(1:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send(v_I(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i,MPI_COMM_WORLD,status,ierr)
call mpi_send(ru_u(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+100,MPI_COMM_WORLD,status,ierr)
enddo
v_I_T(1:ie,0,1:ke/px)=v_I(1:ie,0,1:ke/px)
ru_u_T(1:ie,0,1:ke/px)=ru_u(1:ie,0,1:ke/px)
else
call mpi_recv(v_I_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank,MPI_COMM_WORLD,status,ierr)
call mpi_recv(ru_u_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+100,MPI_COMM_WORLD,status,ierr)
endif
!! also pass over boundaries at j=jmax+1 :
IF (rank.eq.px-1) THEN
do i=0,px-2
call mpi_send(ru_u(1:ie,je+1,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+200,MPI_COMM_WORLD,status,ierr)
enddo
ru_u_T(1:ie,je*px+1,1:ke/px)=ru_u(1:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
else
call mpi_recv(ru_u_T(1:ie,je*px+1,1:ke/px),ie*ke/px,MPI_REAL8,px-1,rank+200,MPI_COMM_WORLD,status,ierr)
endif
bby_0jepx=1.
aay_0jepx=const_1_6 !3./10.
aay_0jepx(0)=0.
aay_0jepx(je*px)=0. !5. !0.
ccy_0jepx=const_1_6 !3./10.
ccy_0jepx(0)=0. !5. !0.
ccy_0jepx(je*px)=0.
bby_1jepx=1.
aay_1jepx=const_1_22 !9./62.
aay_1jepx(1)=0.
aay_1jepx(je*px)=-1. !-1.!*26./24. !0. !const_1_22 !0. !const_1_22 !0.! -1.
ccy_1jepx=const_1_22 !9./62.
ccy_1jepx(1)=-1. !-1.!*26./24. !0. !const_1_22 !0. !const_1_22 !0. !-1.
ccy_1jepx(je*px)=0.
do i=ib,ie
do k=1,ke/px
!! interpolate_y ru_u_T -> I-loc
ddy_0jepx(0)= 0.5*(ru_u_T(i,0,k)+ru_u_T(i,1,k))
ddy_0jepx(je*px)=0.5*(ru_u_T(i,je*px,k)+ru_u_T(i,je*px+1,k))
do j=1,je*px-1
ddy_0jepx(j)=const_2_3*(ru_u_T(i,j+1,k)+ru_u_T(i,j,k))
enddo
CALL solve_tridiag(ru_I_T(0:je*px),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) !interpolate ru_u_T -> I-loc -> 0:je*px
ruv_I_T(0:je*px)=ru_I_T(0:je*px)*v_I_T(i,0:je*px,k)
ddy_1jepx(1)=(-ruv_I_T(0)+2.*ruv_I_T(1)-ruv_I_T(2))/(Ru(i)*(phivt(1)-phivt(0))) !no idea wether indices of phivt are correct, LdW 17-11-2015
ddy_1jepx(je*px)=(ruv_I_T(je*px)-2.*ruv_I_T(je*px-1)+ruv_I_T(je*px-2))/(Ru(i)*(phivt(je*px)-phivt(je*px-1)))
do j=2,je*px-1
ddy_1jepx(j)=const_12_11*(ruv_I_T(j)-ruv_I_T(j-1))/(Ru(i)*(phivt(j)-phivt(j-1)))
enddo
CALL solve_tridiag(dfy_T(1:je*px),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px) !dfy on Uvel(i,j,k) location -> 1:je*px
putout_T(i,1:je*px,k)=-dfy_T(1:je*px)
enddo
enddo
call t2fp(putout_T(ib:ie,1:je*px,kb:ke/px),putouty(ib:ie,jb:je,kb:ke))
putout(ib:ie,jb:je,kb:ke)=putout(ib:ie,jb:je,kb:ke)+putouty(ib:ie,jb:je,kb:ke)
do k=kb,ke
do j=jb,je
jp=j+1
jm=j-1
do i=ib,ie
ip=i+1
im=i-1
putout(i,j,k) = putout(i,j,k) + 0.25 * (
4 0.5*(rho(i,j,k)+rho(ip,j,k))*( Vvel(i,j,k) + Vvel(ip,j,k) + Vvel(i,jm,k) + Vvel(ip,jm,k) )**2
4 / ( 4.0 * Ru(i) )
+ )
enddo
enddo
enddo
return
end
subroutine advecv_COM4(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,phivt,dz,
+ i1,j1,k1,ib,ie,jb,je,kb,ke,rank,px)
implicit none
include 'mpif.h'
c
c********************************************************************
c
c advecv calculates the advection of the v-velocity, which is
c the velocity in the tangential direction.
c
c In formula:
c
c 1 d(ruv) 1 d(vv) d(vw) uv
c - ( - ------ + - ----- + ----- + -- )
c r dr r dphi dz r
c
c on input :
c
c putout : "empty" (initialised to zero)
c Uvel,Vvel,Wvel : contain velocities at former timestep
c Vtmp : contains velocity at oldest timestep
c dr,phivt,dz : grid spacing in r, phi and z-direction
c i1,j1,k1 : parameters for array-dimensions
c ib,ie,jb,je,kb,ke : range of gridpoints for which the
c advection has to be calculated
c Ru,Rp : radial positions of the U-velocity
c component and the pressure location
c respectively
c
c on output :
c
c putout : advection part
c other parameters : all unchanged
c
c********************************************************************
integer i,j,k,im,ip,jm,jp,km,kp,i1,j1,k1,ib,ie,jb,je,kb,ke
integer rank,px
real putout(0:i1,0:j1,0:k1),Uvel(0:i1,0:j1,0:k1),
+ Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),
+ dr(0:i1),phivt(0:je*px+1),dz,Ru(0:i1),Rp(0:i1)
real rho(0:i1,0:j1,0:k1)
real rhoip,rhoim,rhojp,rhojm,rhokp,rhokm
real aax_0ie(0:ie),bbx_0ie(0:ie),ccx_0ie(0:ie),ddx_0ie(0:ie)
real aax_1ie(1:ie),bbx_1ie(1:ie),ccx_1ie(1:ie),ddx_1ie(1:ie)
! real ruu(0:i1),u_r(0:i1),ru_u(0:i1,0:j1,0:k1)
real u_I(0:ie,1:je,1:ke)
real v_I_T(0:ie,0:je*px+1,1:ke/px)
real rvu(0:ie),dfx(1:ie),u_I_T(0:ie,0:je*px,1:ke)
real rv_I(0:ie)
real rho_T(0:ie,0:je*px+1,1:ke/px),rho_v_T(0:ie,0:je*px,1:ke/px),rv_v(0:ie,1:je,1:ke)
! real rho_T(1:ie,0:je*px+1,0:ke/px+1),rho_v_T(1:ie,0:je*px,0:ke/px+1),rv_v(1:ie,1:je,0:ke+1)
real u_T(0:ie,0:je*px+1,1:ke/px),v_T(1:ie,0:je*px,1:ke/px),w_T(1:ie,0:je*px+1,1:ke/px)
real rvv_T(1:je*px),dfy_T(1:ie,0:je*px,1:ke/px),putouty(1:ie,1:je,1:ke)
real aay_0jepx(0:je*px),bby_0jepx(0:je*px),ccy_0jepx(0:je*px),ddy_0jepx(0:je*px)
real aay_1jepx(1:je*px),bby_1jepx(1:je*px),ccy_1jepx(1:je*px),ddy_1jepx(1:je*px)
real w_II(1:ie,1:je,0:ke),dfz(1:ke),rvw(0:ke),rv_II(0:ke),w_II_T(1:ie,0:je*px,1:ke/px)
real aaz_0ke(0:ke),bbz_0ke(0:ke),ccz_0ke(0:ke),ddz_0ke(0:ke)
real aaz_1ke(1:ke),bbz_1ke(1:ke),ccz_1ke(1:ke),ddz_1ke(1:ke)
integer ileng,ierr,itag,status(MPI_STATUS_SIZE)
real const_1_6,const_1_22,const_12_11,const_2_3
putout=0.
const_1_6=1./6.
const_1_22=1./22.
const_12_11=12./11.
const_2_3=2./3.
bbx_0ie=1.
aax_0ie=const_1_6 !3./10.
aax_0ie(0)=0.
aax_0ie(ie)=0.
ccx_0ie=const_1_6 !3./10.
ccx_0ie(0)=0.
ccx_0ie(ie)=0.
bbx_1ie=1.
aax_1ie=const_1_22 !9./62.
aax_1ie(1)=0.
aax_1ie(ie)=-1. !-1.!*26./24. !-1. !const_1_22 !-1. !0. !const_1_22 !0. ! 1./23. !0. !2. !15.
ccx_1ie=const_1_22 !9./62.
ccx_1ie(1)=-1. !-1.!*26./24. !-1. !const_1_22 !-1. !0. !const_1_22 !1./23. !0. !2. !15.
ccx_1ie(ie)=0.
!! swap rho -> rho_T & u -> u_T
call t2np_i1(rho(0:ie,1:je,1:ke),rho_T(0:ie,1:je*px,1:ke/px))
call t2np_i1(Uvel(0:ie,1:je,1:ke),u_T(0:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send( rho(0:ie,0,i*ke/px+1:(i+1)*ke/px),i1*ke/px,MPI_REAL8,i,i+100,MPI_COMM_WORLD,status,ierr)
call mpi_send(Uvel(0:ie,0,i*ke/px+1:(i+1)*ke/px),i1*ke/px,MPI_REAL8,i,i+200,MPI_COMM_WORLD,status,ierr)
enddo
u_T (0:ie,0,1:ke/px)=Uvel(0:ie,0,1:ke/px)
rho_T(0:ie,0,1:ke/px)= rho(0:ie,0,1:ke/px)
else
call mpi_recv(rho_T(0:ie,0,1:ke/px),i1*ke/px,MPI_REAL8,0,rank+100,MPI_COMM_WORLD,status,ierr)
call mpi_recv( u_T(0:ie,0,1:ke/px),i1*ke/px,MPI_REAL8,0,rank+200,MPI_COMM_WORLD,status,ierr)
endif
!! also pass over boundaries at j=jmax+1 :
IF (rank.eq.px-1) THEN
do i=0,px-2
call mpi_send( rho(0:ie,je+1,i*ke/px+1:(i+1)*ke/px),i1*ke/px,MPI_REAL8,i,i+300,MPI_COMM_WORLD,status,ierr)
call mpi_send(Uvel(0:ie,je+1,i*ke/px+1:(i+1)*ke/px),i1*ke/px,MPI_REAL8,i,i+400,MPI_COMM_WORLD,status,ierr)
enddo
rho_T(0:ie,je*px+1,1:ke/px)= rho(0:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
u_T(0:ie,je*px+1,1:ke/px)=Uvel(0:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
else
call mpi_recv(rho_T(0:ie,je*px+1,1:ke/px),i1*ke/px,MPI_REAL8,px-1,rank+300,MPI_COMM_WORLD,status,ierr)
call mpi_recv( u_T(0:ie,je*px+1,1:ke/px),i1*ke/px,MPI_REAL8,px-1,rank+400,MPI_COMM_WORLD,status,ierr)
endif
bby_0jepx=1.
aay_0jepx=const_1_6 !3./10.
aay_0jepx(0)=0.
aay_0jepx(je*px)=0.
ccy_0jepx=const_1_6 !3./10.
ccy_0jepx(0)=0.
ccy_0jepx(je*px)=0.
do i=0,ie
do k=1,ke/px !k=0,ke/px+1
!! interpolate_y rho_T -> v-loc
ddy_0jepx(0)=0.5*(rho_T(i,0,k)+rho_T(i,1,k))
ddy_0jepx(je*px)=0.5*(rho_T(i,je*px,k)+rho_T(i,je*px+1,k))
do j=1,je*px-1
ddy_0jepx(j)=const_2_3*(rho_T(i,j+1,k)+rho_T(i,j,k))
enddo
CALL solve_tridiag(rho_v_T(i,0:je*px,k),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) ! interpolate rho_T -> v-loc -> 0:je*px
enddo
enddo
do i=0,ie
do k=1,ke/px
!! interpolate_y u_T -> I-loc
ddy_0jepx(0)=0.5*(u_T(i,0,k)+u_T(i,1,k))
ddy_0jepx(je*px)=0.5*(u_T(i,je*px,k)+u_T(i,je*px+1,k))
do j=1,je*px-1
ddy_0jepx(j)=const_2_3*(u_T(i,j+1,k)+u_T(i,j,k))
enddo
CALL solve_tridiag(u_I_T(i,0:je*px,k),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) ! interpolate_y u_T -> I-loc -> 0:je*px
enddo
enddo
! swap back
call t2fp_0ie(rho_v_T(0:ie,1:je*px,1:ke/px),rv_v(0:ie,1:je,1:ke))
call t2fp_0ie(u_I_T(0:ie,1:je*px,kb:ke/px),u_I(0:ie,1:je,1:ke))
rv_v(0:ie,1:je,1:ke)=rv_v(0:ie,1:je,1:ke)*Vvel(0:ie,1:je,1:ke)
do k=kb,ke !kb,ke
do j=jb,je
!! interpolate_x rv_v -> I-loc
ddx_0ie(0)=0.5*(rv_v(0,j,k)+rv_v(1,j,k))
ddx_0ie(ie)=rv_v(ie,j,k)
do i=1,ie-1
ddx_0ie(i)=const_2_3*(rv_v(i+1,j,k)+rv_v(i,j,k))
enddo
CALL solve_tridiag(rv_I(0:ie),aax_0ie,bbx_0ie,ccx_0ie,ddx_0ie,i1) ! interpolate_x rv -> I-loc -> 0:ie
!! derivative d(Rrhovu)Rdr
rvu(0:ie)=rv_I(0:ie)*u_I(0:ie,j,k)*Ru(0:ie)
ddx_1ie(1)=(2.*rvu(1)-rvu(0)-rvu(2))/ ( Rp(1) * dr(1) )
ddx_1ie(ie)=(-2.*rvu(ie-1)+rvu(ie)+rvu(ie-2))/ ( Rp(ie) * dr(ie) )
do i=2,ie-1
ddx_1ie(i)=const_12_11*(rvu(i)-rvu(i-1))/ ( Rp(i) * dr(i) )
enddo
CALL solve_tridiag(dfx(1:ie),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie) ! df on Uvel(i,j,k) location -> 1:ie
putout(1:ie,j,k)=putout(1:ie,j,k)-dfx(1:ie) ! derivative: d(rvu)/rdr
enddo
enddo
call t2np(Vvel(1:ie,1:je,1:ke),v_T(1:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send(Vvel(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+100,MPI_COMM_WORLD,status,ierr)
v_T(1:ie,0,1:ke/px)=Vvel(1:ie,0,1:ke/px)
enddo
else
call mpi_recv(v_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+100,MPI_COMM_WORLD,status,ierr)
endif
bby_0jepx=1.
aay_0jepx=const_1_22 !9./62.
aay_0jepx(0)=0.
aay_0jepx(je*px)=3.!*3./8. !0. !1./23. !2. !0. !2. !1./15. !1./23.
ccy_0jepx=const_1_22 !9./62.
ccy_0jepx(0)=3.!*3./8. !0. !1./23. !2. !0. !2. !1./15. !1./23.
ccy_0jepx(je*px)=0.
bby_1jepx=1.
aay_1jepx=const_1_6 !3./10.
aay_1jepx(1)=0.
aay_1jepx(je*px)=0. !1. !0. !1.
ccy_1jepx=const_1_6 !3./10.
ccy_1jepx(je*px)=0.
ccy_1jepx(1)=0. !1. !0. !1.
do i=ib,ie
do k=1,ke/px
!! interpolate_y v_T -> rho-loc
ddy_1jepx(1)=0.5*(v_T(i,0,k)+v_T(i,1,k)) !
ddy_1jepx(je*px)=0.5*(v_T(i,je*px,k)+v_T(i,je*px-1,k)) !
do j=2,je*px-1
ddy_1jepx(j)=const_2_3*(v_T(i,j,k)+v_T(i,j-1,k))
enddo
CALL solve_tridiag(rvv_T(1:je*px),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px) ! interpolate v_T -> rho-loc -> 1:je*px
rvv_T(1:je*px)=rvv_T(1:je*px)*rvv_T(1:je*px)*rho_T(i,1:je*px,k)
! ddy_0jepx(0)=0.
! ddy_0jepx(je*px)=0.
! ddy_0jepx(0)=(-25.*rvv_T(1)+26.*rvv_T(2)-rvv_T(3))/(Rp(i)*(phivt(1)-phivt(0)))
! ddy_0jepx(je*px)=(+25.*rvv_T(je*px)-26.*rvv_T(je*px-1)+rvv_T(je*px-2))/(Rp(i)*(phivt(j)-phivt(jm)))
ddy_0jepx(0)=8./3.*(-v_T(i,0,k)**2*0.5*(rho_T(i,0,k)+rho_T(i,1,k))+rvv_T(2))/(Rp(i)*(phivt(1)-phivt(0))) !no idea wether phivt indices are correct, LdW 17/11/2015
ddy_0jepx(je*px)=8./3.*(v_T(i,je*px,k)**2*0.5*(rho_T(i,je*px,k)+rho_T(i,je*px+1,k))-rvv_T(je*px-1))
& /(Rp(i)*(phivt(je*px)-phivt(je*px-1)))
do j=1,je*px-1
ddy_0jepx(j)=const_12_11*(rvv_T(j+1)-rvv_T(j))/(Rp(i)*(phivt(j+1)-phivt(j)))
enddo
CALL solve_tridiag(dfy_T(i,0:je*px,k),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) ! dfy on Uvel(i,j,k) location -> 1:je*px
enddo
enddo
call t2fp(dfy_T(1:ie,1:je*px,1:ke/px),putouty(ib:ie,jb:je,kb:ke))
putout(ib:ie,jb:je,kb:ke)=putout(ib:ie,jb:je,kb:ke)-putouty(ib:ie,jb:je,kb:ke)
!!!!!!!!
call t2np(Wvel(1:ie,1:je,1:ke),w_T(1:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send(Wvel(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+200,MPI_COMM_WORLD,status,ierr)
enddo
w_T(1:ie,0,1:ke/px)=Wvel(1:ie,0,1:ke/px)
else
call mpi_recv(w_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+200,MPI_COMM_WORLD,status,ierr)
endif
!! also pass over boundaries at j=jmax+1 :
IF (rank.eq.px-1) THEN
do i=0,px-2
call mpi_send(Wvel(1:ie,je+1,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+400,MPI_COMM_WORLD,status,ierr)
enddo
w_T(1:ie,je*px+1,1:ke/px)=Wvel(1:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
else
call mpi_recv(w_T(1:ie,je*px+1,1:ke/px),ie*ke/px,MPI_REAL8,px-1,rank+400,MPI_COMM_WORLD,status,ierr)
endif
bby_0jepx=1.
aay_0jepx=const_1_6 !3./10.
aay_0jepx(0)=0.
aay_0jepx(je*px)=0.
ccy_0jepx=const_1_6 !3./10.
ccy_0jepx(0)=0.
ccy_0jepx(je*px)=0.
do i=ib,ie
do k=1,ke/px
!! interpolate_y w_T -> II-loc
ddy_0jepx(0)=0.5*(w_T(i,0,k)+w_T(i,1,k))
ddy_0jepx(je*px)=0.5*(w_T(i,je*px,k)+w_T(i,je*px+1,k))
do j=1,je*px-1
ddy_0jepx(j)=const_2_3*(w_T(i,j+1,k)+w_T(i,j,k))
enddo
CALL solve_tridiag(w_II_T(i,0:je*px,k),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) ! interpolate w_T -> II-loc -> 0:je*px
enddo
enddo
call t2fp(w_II_T(1:ie,1:je*px,1:ke/px),w_II(1:ie,1:je,1:ke))
w_II(ib:ie,jb:je,0)=0.5*(Wvel(ib:ie,jb:je,0)+Wvel(ib:ie,jb+1:je+1,0)) !non compact interpolation, no problem -> W(i,j,0)=0.
bbz_0ke=1.
aaz_0ke=const_1_6 !3./10.
aaz_0ke(0)=0.
aaz_0ke(ke)=0.
ccz_0ke=const_1_6 !3./10.
ccz_0ke(0)=0.
ccz_0ke(ke)=0.
bbz_1ke=1.
aaz_1ke=const_1_22 !9./62.
aaz_1ke(1)=0.
aaz_1ke(ke)=-1. !-1.!*26./24. !0. !const_1_22 !1./11. !! met aanpassing voor k=0 en k=ke ontploft hij, zowel van Lele, als van Hokpunna 2010
aaz_1ke(2)=const_1_22!*21./24.
aaz_1ke(ke-1)=const_1_22!*21./24.
ccz_1ke=const_1_22 !9./62.
ccz_1ke(1)=-1. !-1.!*26./24. !0. !const_1_22 !1./11.
ccz_1ke(ke)=0.
ccz_1ke(2)=const_1_22!*21./24.
ccz_1ke(ke-1)=const_1_22!*21./24.
do i=ib,ie
do j=jb,je
!! interpolate_z rv_v -> II-loc
! ddz_0ke(0)=0.125*(Vvel(i,j,0)+Vvel(i,j,1))*(rho(i,j,0)+rho(i,j,1)+rho(i,j+1,0)+rho(i,j+1,1))
! ddz_0ke(ke)=0.125*(Vvel(i,j,k1)+Vvel(i,j,ke))*(rho(i,j,k1)+rho(i,j,ke)+rho(i,j+1,k1)+rho(i,j+1,ke))
ddz_0ke(0)=rv_v(i,j,1) !0.5*(rv_v(i,j,1)+rv_v(i,j,0))
ddz_0ke(ke)=rv_v(i,j,ke) !0.5*(rv_v(i,j,ke+1)+rv_v(i,j,ke))
do k=1,ke-1
ddz_0ke(k)=const_2_3*(rv_v(i,j,k+1)+rv_v(i,j,k))
enddo
CALL solve_tridiag(rv_II(0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,k1) ! interpolate_z rv_v -> II-loc -> 0:ke
!! derivative d(rhovw)dz
rvw(0:ke)=rv_II(0:ke)*w_II(i,j,0:ke)
ddz_1ke(1)=(-rvw(0)+2.*rvw(1)-rvw(2))/ dz
ddz_1ke(ke)=(+rvw(ke)-2.*rvw(ke-1)+rvw(ke-2))/ dz
do k=2,ke-1
ddz_1ke(k)=const_12_11*(rvw(k)-rvw(k-1))/ dz
enddo
CALL solve_tridiag(dfz(1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke) ! df on Uvel(i,j,k) location -> 1:ke
putout(i,j,1:ke)=putout(i,j,1:ke)-dfz(1:ke) ! derivative: d(rvw)/dz
enddo
enddo
do k=kb,ke
do j=jb,je
jp=j+1
jm=j-1
do i=ib,ie
ip=i+1
im=i-1
putout(i,j,k) = putout(i,j,k)- 0.25 * (
4 0.5*(rho(i,j,k)+rho(i,jp,k))*((Uvel(i,j,k)+Uvel(i,jp,k)+Uvel(im,j,k)+Uvel(im,jp,k))*Vvel(i,j,k))/Rp(i)
4 )
enddo
enddo
enddo
return
end
subroutine advecw_COM4(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,phivt,dz,
+ i1,j1,k1,ib,ie,jb,je,kb,ke,rank,px)
implicit none
include 'mpif.h'
c
c********************************************************************
c
c advecw calculates the advection of the w-velocity, which is
c the velocity in the axial direction.
c
c In formula:
c
c 1 d(ruw) 1 d(wv) d(ww)
c - ( - ------ + - ----- + ----- )
c r dr r dphi dz
c
c on input :
c
c putout : "empty" (initialised to zero)
c Uvel,Vvel,Wvel : contain velocities at former timestep
c Wtmp : contains velocity at oldest timestep
c dr,phivt,dz : grid spacing in r, phi and z-direction
c i1,j1,k1 : parameters for array-dimensions
c ib,ie,jb,je,kb,ke : range of gridpoints for which the
c advection has to be calculated
c Ru,Rp : radial positions of the U-velocity
c component and the pressure location
c respectively
c
c on output :
c
c putout : advection part
c other parameters : all unchanged
c
c********************************************************************
integer i,j,k,im,ip,jm,jp,km,kp,i1,j1,k1,ib,ie,jb,je,kb,ke
integer rank,px
real putout(0:i1,0:j1,0:k1),Uvel(0:i1,0:j1,0:k1),
+ Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),
+ dr(0:i1),phivt(0:je*px+1),dz,Ru(0:i1),Rp(0:i1)
real rho(0:i1,0:j1,0:k1)
real rhoip,rhoim,rhojp,rhojm
real rw_w(0:ie,0:j1,0:ke),u_I(0:ie,jb:je,0:ke),rwu_I(0:ie),rw_I(0:ie)
real dfx(1:ie),dfy_T(ib:ie,jb:je*px,kb:ke/px),putouty(ib:ie,jb:je,kb:ke),dfz(0:ke)
real rw_w_T(ib:ie,0:je*px+1,1:ke/px),v_II(ib:ie,0:je,0:ke),v_II_T(ib:ie,0:je*px,1:ke/px)
real rw_II_T(0:je*px),rwv_II_T(0:je*px),w_r(1:ke),rww_r(1:ke),rww_r2(0:k1)
real ww(0:i1,0:j1,0:k1)
real aax_0ie(0:ie),bbx_0ie(0:ie),ccx_0ie(0:ie),ddx_0ie(0:ie)
real aax_1ie(1:ie),bbx_1ie(1:ie),ccx_1ie(1:ie),ddx_1ie(1:ie)
real aay_0jepx(0:je*px),bby_0jepx(0:je*px),ccy_0jepx(0:je*px),ddy_0jepx(0:je*px)
real aay_1jepx(1:je*px),bby_1jepx(1:je*px),ccy_1jepx(1:je*px),ddy_1jepx(1:je*px)
real aaz_0ke(0:ke),bbz_0ke(0:ke),ccz_0ke(0:ke),ddz_0ke(0:ke)
real aaz_1ke(1:ke),bbz_1ke(1:ke),ccz_1ke(1:ke),ddz_1ke(1:ke)
integer ileng,ierr,itag,status(MPI_STATUS_SIZE)
real const_1_6,const_1_22,const_12_11,const_2_3
putout=0.
const_1_6=1./6.
const_1_22=1./22.
const_12_11=12./11.
const_2_3=2./3.
bbz_0ke=1.
aaz_0ke=const_1_6 !3./10.
aaz_0ke(0)=0.
aaz_0ke(ke)=0.
ccz_0ke=const_1_6 !3./10.
ccz_0ke(0)=0.
ccz_0ke(ke)=0.
bbx_0ie=1.
aax_0ie=const_1_6 !3./10.
aax_0ie(0)=0.
aax_0ie(ie)=0.
ccx_0ie=const_1_6 !3./10.
ccx_0ie(0)=0.
ccx_0ie(ie)=0.
bbx_1ie=1.
aax_1ie=const_1_22 !9./62.
aax_1ie(1)=0.
aax_1ie(ie)=-1. !-1.!*26./24. !-1. !const_1_22 !-1. !0. !const_1_22 !0. ! 1./23. !0. !2. !15.
ccx_1ie=const_1_22 !9./62.
ccx_1ie(1)=-1. !0. !-1.!*26./24. !-1. !const_1_22 !-1. !0. !const_1_22 !1./23. !0. !2. !15.
ccx_1ie(ie)=0.
do i=0,ie
do j=0,j1
!! interpolate_z rho -> w-loc
ddz_0ke(0)=0.5*(rho(i,j,0)+rho(i,j,1))
ddz_0ke(ke)=0.5*(rho(i,j,ke)+rho(i,j,k1))
do k=1,ke-1
ddz_0ke(k)=const_2_3*(rho(i,j,k+1)+rho(i,j,k))
enddo
CALL solve_tridiag(rw_w(i,j,0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,k1) ! interpolate rho -> w-loc -> 0:ke
rw_w(i,j,0:ke)=rw_w(i,j,0:ke)*Wvel(i,j,0:ke)
enddo
enddo
do i=0,ie
do j=jb,je
!! interpolate_z u -> I-loc
ddz_0ke(0)=0.5*(Uvel(i,j,0)+Uvel(i,j,1))
ddz_0ke(ke)=0.5*(Uvel(i,j,ke)+Uvel(i,j,k1))
do k=1,ke-1
ddz_0ke(k)=const_2_3*(Uvel(i,j,k+1)+Uvel(i,j,k))
enddo
CALL solve_tridiag(u_I(i,j,0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,k1) ! interpolate_z u -> I-loc -> 0:ke
enddo
enddo
do k=kb,ke !kb,ke
do j=jb,je
!! interpolate_x rw_w -> I-loc
ddx_0ie(0)=0.5*(rw_w(0,j,k)+rw_w(1,j,k))
ddx_0ie(ie)=rw_w(ie,j,k) !uitstroom is upstream interpolatie
do i=1,ie-1
ddx_0ie(i)=const_2_3*(rw_w(i+1,j,k)+rw_w(i,j,k))
enddo
CALL solve_tridiag(rw_I(0:ie),aax_0ie,bbx_0ie,ccx_0ie,ddx_0ie,i1) ! interpolate_x rw -> I-loc -> 0:ie
!! derivative d(Rrhowu)Rdr
rwu_I(0:ie)=rw_I(0:ie)*u_I(0:ie,j,k)*Ru(0:ie)
ddx_1ie(1)=(-rwu_I(0)+2.*rwu_I(1)-rwu_I(2))/ ( Rp(1) * dr(1) )
ddx_1ie(ie)=(rwu_I(ie)-2.*rwu_I(ie-1)+rwu_I(ie-2))/ ( Rp(ie) * dr(ie) )
do i=2,ie-1 !
ddx_1ie(i)=const_12_11*(rwu_I(i)-rwu_I(i-1))/ ( Rp(i) * dr(i) )
enddo
CALL solve_tridiag(dfx(1:ie),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie) ! dfx on Wvel(i,j,k) location -> 1:ie
putout(1:ie,j,k)=putout(1:ie,j,k)-dfx(1:ie) ! derivative: d(rwu)/rdr
enddo
enddo
do i=ib,ie
do j=0,je
!! interpolate_z v -> II-loc
ddz_0ke(0)=0.5*(Vvel(i,j,0)+Vvel(i,j,1))
ddz_0ke(ke)=0.5*(Vvel(i,j,ke)+Vvel(i,j,k1))
do k=1,ke-1
ddz_0ke(k)=const_2_3*(Vvel(i,j,k+1)+Vvel(i,j,k))
enddo
CALL solve_tridiag(v_II(i,j,0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,k1) ! interpolate_z v -> II-loc -> 0:ke
enddo
enddo
call t2np(v_II(1:ie,1:je,1:ke),v_II_T(1:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send(v_II(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+201,MPI_COMM_WORLD,status,ierr)
enddo
v_II_T(1:ie,0,1:ke/px)=v_II(1:ie,0,1:ke/px)
else
call mpi_recv(v_II_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+201,MPI_COMM_WORLD,status,ierr)
endif
call t2np(rw_w(1:ie,1:je,1:ke),rw_w_T(1:ie,1:je*px,1:ke/px))
!! also pass over boundaries at j=0 :
IF (rank.eq.0) THEN
do i=1,px-1
call mpi_send(rw_w(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+202,MPI_COMM_WORLD,status,ierr)
enddo
rw_w_T(1:ie,0,1:ke/px)=rw_w(1:ie,0,1:ke/px)
else
call mpi_recv(rw_w_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+202,MPI_COMM_WORLD,status,ierr)
endif
!! also pass over boundaries at j=jmax+1 :
IF (rank.eq.px-1) THEN
do i=0,px-2
call mpi_send(rw_w(1:ie,je+1,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+401,MPI_COMM_WORLD,status,ierr)
enddo
rw_w_T(1:ie,je*px+1,1:ke/px)=rw_w(1:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
else
call mpi_recv(rw_w_T(1:ie,je*px+1,1:ke/px),ie*ke/px,MPI_REAL8,px-1,rank+401,MPI_COMM_WORLD,status,ierr)
endif
bby_0jepx=1.
aay_0jepx=const_1_6 !3./10.
aay_0jepx(0)=0.
aay_0jepx(je*px)=0.
ccy_0jepx=const_1_6 !3./10.
ccy_0jepx(0)=0.
ccy_0jepx(je*px)=0.
bby_1jepx=1.
aay_1jepx=const_1_22 !9./62.
aay_1jepx(1)=0.
aay_1jepx(je*px)=-1. !-1.!*26./24. !0. !const_1_22 !0. !const_1_22 !0.! -1.
ccy_1jepx=const_1_22 !9./62.
ccy_1jepx(1)=-1. !-1.!*26./24. !0. !const_1_22 !0. !const_1_22 !0. !-1.
ccy_1jepx(je*px)=0.
do i=ib,ie
do k=kb,ke/px
!! interpolate_y rw_w_T -> II-loc
ddy_0jepx(0)=0.5*(rw_w_T(i,0,k)+rw_w_T(i,1,k))
ddy_0jepx(je*px)=0.5*(rw_w_T(i,je*px,k)+rw_w_T(i,je*px+1,k))
do j=1,je*px-1
ddy_0jepx(j)=const_2_3*(rw_w_T(i,j+1,k)+rw_w_T(i,j,k))
enddo
CALL solve_tridiag(rw_II_T(0:je*px),aay_0jepx,bby_0jepx,ccy_0jepx,ddy_0jepx,je*px+1) ! interpolate rw_w_T -> II-loc -> 0:je*px
rwv_II_T(0:je*px)=rw_II_T(0:je*px)*v_II_T(i,0:je*px,k)
!! diff_y drwv/(rdphi)
ddy_1jepx(1)=(-rwv_II_T(0)+2.*rwv_II_T(1)-rwv_II_T(2))/(Rp(i)*(phivt(1)-phivt(0))) !no idea wether indices of phivt are correct, LdW 17-11-2015
ddy_1jepx(je*px)=(rwv_II_T(je*px)-2.*rwv_II_T(je*px-1)+rwv_II_T(je*px-2))/(Rp(i)*(phivt(je*px)-phivt(je*px-1)))
do j=2,je*px-1
ddy_1jepx(j)=const_12_11*(rwv_II_T(j)-rwv_II_T(j-1))/(Rp(i)*(phivt(j)-phivt(j-1)))
enddo
CALL solve_tridiag(dfy_T(i,1:je*px,k),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px) ! diff_y -> W-loc -> 1:je*px
enddo
enddo
call t2fp(dfy_T(1:ie,1:je*px,1:ke/px),putouty(ib:ie,jb:je,kb:ke))
putout(ib:ie,jb:je,kb:ke)=putout(ib:ie,jb:je,kb:ke)-putouty(ib:ie,jb:je,kb:ke)
bbz_0ke=1.
aaz_0ke=const_1_22 !9./62.
aaz_0ke(0)=0.
aaz_0ke(ke)=3.!*3./8. !15. !23. !1./23. !1./15. !1./23.
ccz_0ke=const_1_22 !9./62.
ccz_0ke(0)=3.!*3./8. !15. !23. !0. !1./23.
ccz_0ke(ke)=0.
bbz_1ke=1.
aaz_1ke=const_1_6 !3./10.
aaz_1ke(1)=0.
aaz_1ke(ke)=0. !1. !0. !1. !0. !1.
ccz_1ke=const_1_6 !3./10.
ccz_1ke(ke)=0.
ccz_1ke(1)=0. !0. !1. !0. !1. !0. !1.
ww=Wvel
do i=ib,ie
do j=jb,je
!! interpolate_z Wvel -> rho-loc
ddz_1ke(1)=0.5*ww(i,j,0)+.5*ww(i,j,1)
ddz_1ke(ke)=0.5*ww(i,j,ke)+.5*ww(i,j,ke-1)
do k=2,ke-1
ddz_1ke(k)=const_2_3*(ww(i,j,k)+ww(i,j,k-1))
enddo
CALL solve_tridiag(w_r(1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke) ! interpolate_z Wvel -> rho-loc -> 1:ke
rww_r(1:ke)=w_r(1:ke)*w_r(1:ke)*rho(i,j,1:ke)
ddz_0ke(ke)=8./3.*(ww(i,j,ke)*ww(i,j,ke)*0.5*(rho(i,j,k1)+rho(i,j,ke))-rww_r(ke-1))/(dz)
ddz_0ke(0)=8./3.*(-ww(i,j,0)*ww(i,j,0)*0.5*(rho(i,j,1)+rho(i,j,0))+rww_r(2))/(dz)
do k=1,ke-1
ddz_0ke(k)=const_12_11*(rww_r(k+1)-rww_r(k))/dz
enddo
CALL solve_tridiag(dfz(0:ke),aaz_0ke,bbz_0ke,ccz_0ke,ddz_0ke,ke+1) ! dfz on Wvel(i,j,k) location -> 0:ke
putout(i,j,1:ke)=putout(i,j,1:ke)-dfz(1:ke)
enddo
enddo
return
end
subroutine solve_tridiag(x,a,b,c,v,n)
implicit none
! a - sub-diagonal (means it is the diagonal below the main diagonal)
! [a(1) is on line 1 of the matrix system and does not exist [give dummy value], a(end) is on end line of matrix system]
! b - the main diagonal
! c - sup-diagonal (means it is the diagonal above the main diagonal)
! [c(1) is on line 1 of the matrix system, c(end) is on end line of matrix system and does not exist [give dummy value]]
! v - right part
! x - the answer
! n - number of equations
integer,intent(in) :: n
real,dimension(n),intent(in) :: a,b,c,v
real,dimension(n),intent(out) :: x
real,dimension(n) :: bp,vp
real :: m
integer i
! Make copies of the b and v variables so that they are unaltered by this sub
bp(1) = b(1)
vp(1) = v(1)
!The first pass (setting coefficients):
do i = 2,n
m = a(i)/bp(i-1)
bp(i) = b(i) - m*c(i-1)
vp(i) = v(i) - m*vp(i-1)
end do
x(n) = vp(n)/bp(n)
!The second pass (back-substition)
do i = n-1, 1, -1
x(i) = (vp(i) - c(i)*x(i+1))/bp(i)
end do
end subroutine solve_tridiag
subroutine solve_tridiag_periodic(x,a,b,c,v,n)
implicit none
! a - sub-diagonal (means it is the diagonal below the main diagonal)
! b - the main diagonal
! c - sup-diagonal (means it is the diagonal above the main diagonal)
! v - right part
! x - the answer
! n - number of equations
integer,intent(in) :: n
real,dimension(n),intent(in) :: a,b,c,v
real,dimension(n),intent(out) :: x
real,dimension(n) :: bp,vp,bper,u,y,q,up
real :: m,corr
integer i
! Make new slightly adjusted diagonal to solve periodic system:
bper = b
bper(1) = b(1) + c(1)
bper(n) = b(n) + a(n)
! Make extra rhs:
u = 0.
u(1) = 1.
u(n) = -1.
!! Solve first system: Aper*y=v
!! Make copies of the b and v variables so that they are unaltered by this sub
bp(1) = bper(1)
vp(1) = v(1)
!The first pass (setting coefficients):
do i = 2,n
m = a(i)/bp(i-1)
bp(i) = bper(i) - m*c(i-1)
vp(i) = v(i) - m*vp(i-1)
end do
y(n) = vp(n)/bp(n)
!The second pass (back-substition)
do i = n-1, 1, -1
y(i) = (vp(i) - c(i)*y(i+1))/bp(i)
end do
!! Solve second system: Aper*q=u
!! Make copies of the b and v variables so that they are unaltered by this sub
bp(1) = bper(1)
up(1) = u(1)
!The first pass (setting coefficients):
do i = 2,n
m = a(i)/bp(i-1)
bp(i) = bper(i) - m*c(i-1)