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advec_upw1.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/>.
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecu_UPW1(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!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,dphi,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
!!! 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),dphi,dz,Ru(0:i1),Rp(0:i1)
!!! real rho(0:i1,0:j1,0:k1)
!!! real rhoip,rhoim,rhojp,rhojm,rhokp,rhokm
!!! do k=kb,ke
!!! kp=k+1
!!! km=k-1
!!! do j=jb,je
!!! jp=j+1
!!! jm=j-1
!!! do i=ib,ie
!!! ip=i+1
!!! im=i-1
!!! rhojp =0.25*(rho(i,j,k)+rho(i,jp,k)+rho(ip,j,k)+rho(ip,jp,k))
!!! rhojm =0.25*(rho(i,j,k)+rho(i,jm,k)+rho(ip,j,k)+rho(ip,jm,k))
!!! rhokp =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(ip,j,k)+rho(ip,j,kp))
!!! rhokm =0.25*(rho(i,j,k)+rho(i,j,km)+rho(ip,j,k)+rho(ip,j,km))
!!! putout(i,j,k) = 0.0
!!! putout(i,j,k) = - 0.25 * (
!!! 1 (Rp(ip)*(Uvel(i,j,k)+Uvel(ip,j,k))*(Uvel(i,j,k)+Uvel(ip,j,k))*rho(ip,j,k) -
!!! 1 Rp(i )*(Uvel(i,j,k)+Uvel(im,j,k))*(Uvel(i,j,k)+Uvel(im,j,k))*rho(i ,j,k) )
!!! 1 / ( Ru(i) * ( Rp(ip)-Rp(i) ) )
!!! + +
!!! 2 ( (Vvel(i,j,k) +Vvel(ip,j,k) )*(Uvel(i,j,k)+Uvel(i,jp,k))*rhojp -
!!! 2 (Vvel(i,jm,k)+Vvel(ip,jm,k))*(Uvel(i,j,k)+Uvel(i,jm,k))*rhojm )
!!! 2 / ( Ru(i) * dphi )
!!! + +
!!! 3 ( (Wvel(i,j,k) +Wvel(ip,j,k) )*(Uvel(i,j,k)+Uvel(i,j,kp))*rhokp -
!!! 3 (Wvel(i,j,km)+Wvel(ip,j,km))*(Uvel(i,j,k)+Uvel(i,j,km))*rhokm )
!!! 3 / ( dz )
!!! + -
!!! 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
!!!
!!!
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecv_CDS2(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!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,dphi,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
!!! 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),dphi,dz,Ru(0:i1),Rp(0:i1)
!!! real rho(0:i1,0:j1,0:k1)
!!! real rhoip,rhoim,rhojp,rhojm,rhokp,rhokm
!!! do k=kb,ke
!!! kp=k+1
!!! km=k-1
!!! do j=jb,je
!!! jp=j+1
!!! jm=j-1
!!! do i=ib,ie
!!! ip=i+1
!!! im=i-1
!!! rhoip =0.25*(rho(i,j,k)+rho(ip,j,k)+rho(i,jp,k)+rho(ip,jp,k))
!!! rhoim =0.25*(rho(i,j,k)+rho(im,j,k)+rho(i,jp,k)+rho(im,jp,k))
!!! rhojp =rho(i,jp,k)
!!! rhojm =rho(i,j,k )
!!! rhokp =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(i,jp,k)+rho(i,jp,kp))
!!! rhokm =0.25*(rho(i,j,k)+rho(i,j,km)+rho(i,jp,k)+rho(i,jp,km))
!!! putout(i,j,k) = 0.0
!!! putout(i,j,k) = - 0.25 * (
!!! 1 ( Ru(i ) * Ru(i ) *rhoip*
!!! 1 (Uvel(i,j,k) +Uvel(i,jp,k) )*(Vvel(i,j,k)+Vvel(ip,j,k)) -
!!! 1 Ru(im) * Ru(im) *rhoim*
!!! 1 (Uvel(im,j,k)+Uvel(im,jp,k))*(Vvel(i,j,k)+Vvel(im,j,k)) )
!!! 1 / ( Rp(i) * Rp(i) * dr(i) )
!!! + +
!!! 2 ( (Vvel(i,j,k) +Vvel(i,jp,k) )*(Vvel(i,j,k)+Vvel(i,jp,k))*rhojp -
!!! 2 (Vvel(i,jm,k)+Vvel(i,j,k) )*(Vvel(i,j,k)+Vvel(i,jm,k))*rhojm )
!!! 2 / ( Rp(i) * dphi )
!!! + +
!!! 3 ( (Wvel(i,j,k) +Wvel(i,jp,k) )*(Vvel(i,j,k)+Vvel(i,j,kp))*rhokp -
!!! 3 (Wvel(i,j,km)+Wvel(i,jp,km))*(Vvel(i,j,k)+Vvel(i,j,km))*rhokm )
!!! 3 / ( dz )
!!! + )
!!! enddo
!!! enddo
!!! enddo
!!! return
!!! end
!!!
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecw_CDS2(putout,Uvel,Vvel,Wvel,RHO,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!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,dphi,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
!!! 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),dphi,dz,Ru(0:i1),Rp(0:i1)
!!! real rho(0:i1,0:j1,0:k1)
!!! real rhoip,rhoim,rhojp,rhojm
!!! do k=kb,ke
!!! kp=k+1
!!! km=k-1
!!! do j=jb,je
!!! jp=j+1
!!! jm=j-1
!!! do i=ib,ie
!!! ip=i+1
!!! im=i-1
!!! rhoip =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(ip,j,k)+rho(ip,j,kp))
!!! rhoim =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(im,j,k)+rho(im,j,kp))
!!! rhojp =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(i,jp,k)+rho(i,jp,kp))
!!! rhojm =0.25*(rho(i,j,k)+rho(i,j,kp)+rho(i,jm,k)+rho(i,jm,kp))
!!! putout(i,j,k) = 0.0
!!! putout(i,j,k) = - 0.25 * (
!!! 1 (Ru(i )*(Uvel(i,j,k) +Uvel(i,j,kp) )*(Wvel(i,j,k)+Wvel(ip,j,k))*rhoip -
!!! 1 Ru(im)*(Uvel(im,j,k)+Uvel(im,j,kp))*(Wvel(i,j,k)+Wvel(im,j,k))*rhoim )
!!! 1 / ( Rp(i) * dr(i) )
!!! + +
!!! 2 ( (Vvel(i,j,k) +Vvel(i,j,kp) )*(Wvel(i,j,k)+Wvel(i,jp,k))*rhojp -
!!! 2 (Vvel(i,jm,k)+Vvel(i,jm,kp))*(Wvel(i,j,k)+Wvel(i,jm,k))*rhojm )
!!! 2 / ( Rp(i) * dphi )
!!! + +
!!! 3 ( (Wvel(i,j,k) +Wvel(i,j,kp) )*(Wvel(i,j,k)+Wvel(i,j,kp))*rho(i,j,kp) -
!!! 3 (Wvel(i,j,k) +Wvel(i,j,km) )*(Wvel(i,j,k)+Wvel(i,j,km))*rho(i,j,k ) )
!!! 3 / ( dz )
!!! + )
!!! enddo
!!! enddo
!!! enddo
!!! return
!!! end
!!!
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecc(putout,putin,Uvel,Vvel,Wvel,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!c
!!!c********************************************************************
!!!c
!!!c advecc calculates the advection for a scalar variable, which is
!!!c situated in the center point of the grid cell.
!!!c
!!!c In formula:
!!!c
!!!c 1 d(ruC) 1 d(vC) d(wC)
!!!c - ( - ------ + - ----- + ----- )
!!!c r dr r dphi dz
!!!c
!!!c on input :
!!!c
!!!c putout : "empty" (initialised to zero)
!!!c putin : variable for which the advection has
!!!c to be calculated
!!!c Uvel,Vvel,Wvel : contain velocities at former timestep
!!!c putinn : contains subgrid energy at oldest timestep
!!!c dr,dphi,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
!!! real putout(0:i1,0:j1,0:k1),putin(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),dphi,dz,Ru(0:i1),Rp(0:i1)
!!!c
!!!c -------------------------------------------start k-loop
!!! do 100 k=kb,ke
!!!c
!!! kp=k+1
!!! km=k-1
!!!c
!!!c -------------------------------------------start j-loop
!!! do 200 j=jb,je
!!!c
!!! jp=j+1
!!! jm=j-1
!!!c
!!!c -------------------------------------------start i-loop
!!! do 300 i=ib,ie
!!!c
!!! ip=i+1
!!! im=i-1
!!!c
!!!c
!!! putout(i,j,k) = - 0.5 * (
!!! 1 ( Ru(i) * Uvel(i,j,k) * ( putin(i,j,k) + putin(ip,j,k) ) -
!!! 1 Ru(im) * Uvel(im,j,k) * ( putin(i,j,k) + putin(im,j,k) ) )
!!! 1 / ( Rp(i) * dr(i) )
!!! + +
!!! 2 ( Vvel(i,j,k) * ( putin(i,j,k) + putin(i,jp,k) ) -
!!! 2 Vvel(i,jm,k) * ( putin(i,j,k) + putin(i,jm,k) ) )
!!! 2 / ( Rp(i) * dphi )
!!! + +
!!! 3 ( Wvel(i,j,k) * ( putin(i,j,k) + putin(i,j,kp) ) -
!!! 3 Wvel(i,j,km) * ( putin(i,j,k) + putin(i,j,km) ) )
!!! 3 / ( dz )
!!! + )
!!!c
!!!300 continue
!!!c -------------------------------------------end i-loop
!!!200 continue
!!!c -------------------------------------------end j-loop
!!!100 continue
!!!c -------------------------------------------end k-loop
!!!c
!!! return
!!! end
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecc_TVD(putout,putin,Uvel,Vvel,Wvel,rho,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!c
!!!c********************************************************************
!!!c
!!!c advecc calculates the advection for a scalar variable, which is
!!!c situated in the center point of the grid cell.
!!!c
!!!c In formula:
!!!c
!!!c 1 d(ruC) 1 d(vC) d(wC)
!!!c - ( - ------ + - ----- + ----- )
!!!c r dr r dphi dz
!!!c
!!!c on input :
!!!c
!!!c putout : "empty" (initialised to zero)
!!!c putin : variable for which the advection has
!!!c to be calculated
!!!c Uvel,Vvel,Wvel : contain velocities at former timestep
!!!c putinn : contains subgrid energy at oldest timestep
!!!c dr,dphi,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
!!! real putout(0:i1,0:j1,0:k1),putin(0:i1,0:j1,0:k1),
!!! + Uvel(0:i1,0:j1,0:k1),rho(0:i1,0:j1,0:k1),
!!! + Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),
!!! + dr(0:i1),dphi,dz,Ru(0:i1),Rp(0:i1),
!!! + noemer,rRpos,rRneg,rLpos,rLneg,cRpos,cRneg,cLpos,cLneg,limiter,
!!! + rho_p,rho_m
!!! integer kmm,kpp,imm,ipp,jmm,jpp
!!! real dz_i,Rpdr_i,Rpdphi_i,var_grid_Rpos,var_grid_Rneg,var_grid_Lpos,var_grid_Lneg
!!!
!!!
!!! dz_i=1./dz
!!!
!!!c
!!!c -------------------------------------------start i-loop
!!! do 100 i=ib,ie
!!!c
!!! ip=i+1
!!! im=i-1
!!! imm=im
!!! ipp=ip
!!! if (i.eq.1) imm=i
!!! if (i.eq.ie) ipp=i
!!! var_grid_Rpos=(Rp(ip)-Rp(i))/(Rp(i)-Rp(im))
!!! var_grid_Rneg=(Rp(ipp)-Rp(i))/(Rp(ipp+1)-Rp(ipp))
!!! var_grid_Lpos=(Rp(i)-Rp(imm))/(Rp(imm)-Rp(imm-1))
!!! var_grid_Lneg=(Rp(i)-Rp(im))/(Rp(ip)-Rp(i))
!!! Rpdr_i=1./(Rp(i)*dr(i))
!!! Rpdphi_i=1./(Rp(i)*dphi)
!!!
!!!c -------------------------------------------start j-loop
!!! do 200 j=jb,je
!!!c
!!! jp=j+1
!!! jm=j-1
!!! jmm=jm
!!! jpp=jp
!!! if (j.eq.1) jmm=j
!!! if (j.eq.je) jpp=j
!!!
!!!c
!!!c -------------------------------------------start k-loop
!!! do 300 k=kb,ke
!!!c
!!! kp=k+1
!!! km=k-1
!!! kmm=km
!!! kpp=kp
!!! if (k.eq.1) kmm=k
!!! if (k.eq.ke) kpp=k
!!!c
!!!c
!!! noemer = putin(ip,j,k)-putin(i,j,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!!
!!!
!!! rRpos = (putin(i,j,k)-putin(im,j,k))/noemer *var_grid_Rpos
!!! rRneg = (putin(ipp+1,j,k)-putin(ip,j,k))/noemer *var_grid_Rneg
!!! noemer = putin(i,j,k)-putin(im,j,k)
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!
!!! rLneg = (putin(ip,j,k)-putin(i,j,k))/noemer *var_grid_Lneg
!!! rLpos = (putin(im,j,k)-putin(imm-1,j,k))/noemer *var_grid_Lpos
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(ip,j,k) - putin(i ,j,k))
!!! cLpos = putin(im,j,k) + 0.5*limiter(rLpos)*(putin( i,j,k) - putin(im,j,k))
!!! cRneg = putin(ip,j,k) + 0.5*limiter(rRneg)*(putin( i,j,k) - putin(ip,j,k))
!!! cLneg = putin(i ,j,k) + 0.5*limiter(rLneg)*(putin(im,j,k) - putin(i ,j,k))
!!!
!!!
!!! putout(i,j,k) = - (
!!! & Ru(i) * ( 0.5*(Uvel(i ,j,k)+ABS(Uvel(i ,j,k)))*cRpos + 0.5*(Uvel(i ,j,k)-ABS(Uvel(i ,j,k)))*cRneg ) -
!!! & Ru(im) * ( 0.5*(Uvel(im,j,k)+ABS(Uvel(im,j,k)))*cLpos + 0.5*(Uvel(im,j,k)-ABS(Uvel(im,j,k)))*cLneg ) )
!!! & *Rpdr_i !/ ( Rp(i) * dr(i) )
!!!
!!! noemer = putin(i,jp,k)-putin(i,j,k)
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!
!!! rRpos = (putin(i,j,k)-putin(i,jm,k))/noemer
!!! rRneg = (putin(i,jpp+1,k)-putin(i,jp,k))/noemer
!!!
!!! noemer = putin(i,j,k)-putin(i,jm,k)
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!
!!!
!!! rLneg = (putin(i,jp,k)-putin(i,j,k))/noemer
!!! rLpos = (putin(i,jm,k)-putin(i,jmm-1,k))/noemer
!!!
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(i,jp,k) - putin(i ,j,k))
!!! cLpos = putin(i,jm,k) + 0.5*limiter(rLpos)*(putin( i,j,k) - putin(i,jm,k))
!!! cRneg = putin(i,jp,k) + 0.5*limiter(rRneg)*(putin( i,j,k) - putin(i,jp,k))
!!! cLneg = putin(i,j ,k) + 0.5*limiter(rLneg)*(putin(i,jm,k) - putin(i,j ,k))
!!!
!!!
!!! putout(i,j,k) = putout(i,j,k) - (
!!! & ( 0.5*(Vvel(i,j ,k)+ABS(Vvel(i,j ,k)))*cRpos + 0.5*(Vvel(i,j ,k)-ABS(Vvel(i,j ,k)))*cRneg ) -
!!! & ( 0.5*(Vvel(i,jm,k)+ABS(Vvel(i,jm,k)))*cLpos + 0.5*(Vvel(i,jm,k)-ABS(Vvel(i,jm,k)))*cLneg ) )
!!! & *Rpdphi_i !/ ( Rp(i) * dphi )
!!!
!!! noemer = putin(i,j,kp)-putin(i,j,k)
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!
!!! rRpos = (putin(i,j,k)-putin(i,j,km))/noemer
!!! rRneg = (putin(i,j,kpp+1)-putin(i,j,kp))/noemer
!!!
!!! noemer = putin(i,j,k)-putin(i,j,km)
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!
!!! rLneg = (putin(i,j,kp)-putin(i,j,k))/noemer
!!! rLpos = (putin(i,j,km)-putin(i,j,kmm-1))/noemer
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(i,j,kp) - putin(i ,j,k))
!!! cLpos = putin(i,j,km) + 0.5*limiter(rLpos)*(putin(i,j, k) - putin(i,j,km))
!!! cRneg = putin(i,j,kp) + 0.5*limiter(rRneg)*(putin(i,j, k) - putin(i,j,kp))
!!! cLneg = putin(i,j,k ) + 0.5*limiter(rLneg)*(putin(i,j,km) - putin(i,j, k))
!!!
!!! putout(i,j,k) = putout(i,j,k) - (
!!! & ( 0.5*(Wvel(i,j,k )+ABS(Wvel(i,j,k )))*cRpos + 0.5*(Wvel(i,j,k )-ABS(Wvel(i,j,k )))*cRneg ) -
!!! & ( 0.5*(Wvel(i,j,km)+ABS(Wvel(i,j,km)))*cLpos + 0.5*(Wvel(i,j,km)-ABS(Wvel(i,j,km)))*cLneg ) )
!!! & *dz_i !/ ( dz )
!!!
!!!c
!!!300 continue
!!!c -------------------------------------------end i-loop
!!!200 continue
!!!c -------------------------------------------end j-loop
!!!100 continue
!!!c -------------------------------------------end k-loop
!!!c
!!! return
!!! end
!!! dphi is not constant in lateral dir anymore; this subroutine is not used anymore:
!!! subroutine advecc_TVD_rho(putout,putin,Uvel,Vvel,Wvel,rho,Ru,Rp,dr,dphi,dz,
!!! + i1,j1,k1,ib,ie,jb,je,kb,ke)
!!! implicit none
!!!c
!!!c********************************************************************
!!!c
!!!c advecc calculates the advection for a scalar variable, which is
!!!c situated in the center point of the grid cell.
!!!c
!!!c In formula:
!!!c
!!!c 1 d(ruC) 1 d(vC) d(wC)
!!!c - ( - ------ + - ----- + ----- )
!!!c r dr r dphi dz
!!!c
!!!c on input :
!!!c
!!!c putout : "empty" (initialised to zero)
!!!c putin : variable for which the advection has
!!!c to be calculated
!!!c Uvel,Vvel,Wvel : contain velocities at former timestep
!!!c putinn : contains subgrid energy at oldest timestep
!!!c dr,dphi,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
!!! real putout(0:i1,0:j1,0:k1),putin(0:i1,0:j1,0:k1),
!!! + Uvel(0:i1,0:j1,0:k1),rho(0:i1,0:j1,0:k1),
!!! + Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),
!!! + dr(0:i1),dphi,dz,Ru(0:i1),Rp(0:i1),
!!! + noemer,rRpos,rRneg,rLpos,rLneg,cRpos,cRneg,cLpos,cLneg,limiter,
!!! + rho_p,rho_m
!!! integer kmm,kpp,imm,ipp,jmm,jpp
!!! real dz_i,Rpdr_i,Rpdphi_i,var_grid_Rpos,var_grid_Rneg,var_grid_Lpos,var_grid_Lneg
!!!
!!!
!!! dz_i=1./dz
!!!
!!!c
!!!c -------------------------------------------start i-loop
!!! do 100 i=ib,ie
!!!c
!!! ip=i+1
!!! im=i-1
!!! imm=im
!!! ipp=ip
!!! if (i.eq.1) imm=i
!!! if (i.eq.ie) ipp=i
!!! var_grid_Rpos=(Rp(ip)-Rp(i))/(Rp(i)-Rp(im))
!!! var_grid_Rneg=(Rp(ipp)-Rp(i))/(Rp(ipp+1)-Rp(ipp))
!!! var_grid_Lpos=(Rp(i)-Rp(imm))/(Rp(imm)-Rp(imm-1))
!!! var_grid_Lneg=(Rp(i)-Rp(im))/(Rp(ip)-Rp(i))
!!! Rpdr_i=1./(Rp(i)*dr(i))
!!! Rpdphi_i=1./(Rp(i)*dphi)
!!!
!!!c -------------------------------------------start j-loop
!!! do 200 j=jb,je
!!!c
!!! jp=j+1
!!! jm=j-1
!!! jmm=jm
!!! jpp=jp
!!! if (j.eq.1) jmm=j
!!! if (j.eq.je) jpp=j
!!!
!!!c
!!!c -------------------------------------------start k-loop
!!! do 300 k=kb,ke
!!!c
!!! kp=k+1
!!! km=k-1
!!! kmm=km
!!! kpp=kp
!!! if (k.eq.1) kmm=k
!!! if (k.eq.ke) kpp=k
!!!c
!!!c
!!! noemer = putin(ip,j,k)-putin(i,j,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!!
!!!
!!! rRpos = (putin(i,j,k)-putin(im,j,k))/noemer *var_grid_Rpos
!!!! & (Rp(ip)-Rp(i))/(Rp(i)-Rp(im))
!!!
!!!! if (i.ne.ie) then
!!!! rRneg = (putin(ip+1,j,k)-putin(ip,j,k))/noemer *
!!!! & (Rp(ip)-Rp(i))/(Rp(ip+1)-Rp(ip))
!!!! else
!!!! rRneg = 0.
!!!! endif
!!! rRneg = (putin(ipp+1,j,k)-putin(ip,j,k))/noemer *var_grid_Rneg
!!!! & (Rp(ipp)-Rp(i))/(Rp(ipp+1)-Rp(ipp))
!!!
!!! noemer = putin(i,j,k)-putin(im,j,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!! rLneg = (putin(ip,j,k)-putin(i,j,k))/noemer *var_grid_Lneg
!!!! & (Rp(i)-Rp(im))/(Rp(ip)-Rp(i))
!!!
!!!! if (im.ne.0) then
!!!! rLpos = (putin(im,j,k)-putin(im-1,j,k))/noemer *
!!!! & (Rp(i)-Rp(im))/(Rp(im)-Rp(im-1))
!!!! else
!!!! rLpos = 0.
!!!! endif
!!! rLpos = (putin(im,j,k)-putin(imm-1,j,k))/noemer *var_grid_Lpos
!!!! & (Rp(i)-Rp(imm))/(Rp(imm)-Rp(imm-1))
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(ip,j,k) - putin(i ,j,k))
!!! cLpos = putin(im,j,k) + 0.5*limiter(rLpos)*(putin( i,j,k) - putin(im,j,k))
!!! cRneg = putin(ip,j,k) + 0.5*limiter(rRneg)*(putin( i,j,k) - putin(ip,j,k))
!!! cLneg = putin(i ,j,k) + 0.5*limiter(rLneg)*(putin(im,j,k) - putin(i ,j,k))
!!!
!!!
!!! rho_p = 0.5*(rho(i,j,k)+rho(ip,j,k))
!!! rho_m = 0.5*(rho(i,j,k)+rho(im,j,k))
!!! putout(i,j,k) = - (
!!! & rho_p*Ru(i) * ( 0.5*(Uvel(i ,j,k)+ABS(Uvel(i ,j,k)))*cRpos + 0.5*(Uvel(i ,j,k)-ABS(Uvel(i ,j,k)))*cRneg ) -
!!! & rho_m*Ru(im) * ( 0.5*(Uvel(im,j,k)+ABS(Uvel(im,j,k)))*cLpos + 0.5*(Uvel(im,j,k)-ABS(Uvel(im,j,k)))*cLneg ) )
!!! & *Rpdr_i !/ ( Rp(i) * dr(i) )
!!!
!!! noemer = putin(i,jp,k)-putin(i,j,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!! rRpos = (putin(i,j,k)-putin(i,jm,k))/noemer
!!!
!!!! if (j.ne.je) then
!!!! rRneg = (putin(i,jp+1,k)-putin(i,jp,k))/noemer
!!!! else
!!!! rRneg = 0.
!!!! endif
!!! rRneg = (putin(i,jpp+1,k)-putin(i,jp,k))/noemer
!!!
!!! noemer = putin(i,j,k)-putin(i,jm,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!! rLneg = (putin(i,jp,k)-putin(i,j,k))/noemer
!!!
!!!! if (jm.ne.0) then
!!!! rLpos = (putin(i,jm,k)-putin(i,jm-1,k))/noemer
!!!! else
!!!! rLpos = 0.
!!!! endif
!!! rLpos = (putin(i,jm,k)-putin(i,jmm-1,k))/noemer
!!!
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(i,jp,k) - putin(i ,j,k))
!!! cLpos = putin(i,jm,k) + 0.5*limiter(rLpos)*(putin( i,j,k) - putin(i,jm,k))
!!! cRneg = putin(i,jp,k) + 0.5*limiter(rRneg)*(putin( i,j,k) - putin(i,jp,k))
!!! cLneg = putin(i,j ,k) + 0.5*limiter(rLneg)*(putin(i,jm,k) - putin(i,j ,k))
!!!
!!! rho_p = 0.5*(rho(i,j,k)+rho(i,jp,k))
!!! rho_m = 0.5*(rho(i,j,k)+rho(i,jm,k))
!!!
!!! putout(i,j,k) = putout(i,j,k) - (
!!! & rho_p * ( 0.5*(Vvel(i,j ,k)+ABS(Vvel(i,j ,k)))*cRpos + 0.5*(Vvel(i,j ,k)-ABS(Vvel(i,j ,k)))*cRneg ) -
!!! & rho_m * ( 0.5*(Vvel(i,jm,k)+ABS(Vvel(i,jm,k)))*cLpos + 0.5*(Vvel(i,jm,k)-ABS(Vvel(i,jm,k)))*cLneg ) )
!!! & *Rpdphi_i !/ ( Rp(i) * dphi )
!!!
!!! noemer = putin(i,j,kp)-putin(i,j,k)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!! rRpos = (putin(i,j,k)-putin(i,j,km))/noemer
!!!
!!!! if (k.ne.ke) then
!!!! rRneg = (putin(i,j,kp+1)-putin(i,j,kp))/noemer
!!!! else
!!!! rRneg = 0.
!!!! endif
!!! rRneg = (putin(i,j,kpp+1)-putin(i,j,kp))/noemer
!!!
!!! noemer = putin(i,j,k)-putin(i,j,km)
!!!! if (abs(noemer).le.1.e-6) then
!!! noemer=MAX(ABS(noemer),1.e-6)*sign(1.,noemer)
!!!! endif
!!!
!!! rLneg = (putin(i,j,kp)-putin(i,j,k))/noemer
!!!
!!!! if (km.ne.0) then
!!!! rLpos = (putin(i,j,km)-putin(i,j,km-1))/noemer
!!!! else
!!!! rLpos = 0.
!!!! endif
!!! rLpos = (putin(i,j,km)-putin(i,j,kmm-1))/noemer
!!!
!!!
!!!
!!! cRpos = putin(i ,j,k) + 0.5*limiter(rRpos)*(putin(i,j,kp) - putin(i ,j,k))
!!! cLpos = putin(i,j,km) + 0.5*limiter(rLpos)*(putin(i,j, k) - putin(i,j,km))
!!! cRneg = putin(i,j,kp) + 0.5*limiter(rRneg)*(putin(i,j, k) - putin(i,j,kp))
!!! cLneg = putin(i,j,k ) + 0.5*limiter(rLneg)*(putin(i,j,km) - putin(i,j, k))
!!!
!!! rho_p = 0.5*(rho(i,j,k)+rho(i,j,kp))
!!! rho_m = 0.5*(rho(i,j,k)+rho(i,j,km))
!!!
!!! putout(i,j,k) = putout(i,j,k) - (
!!! & rho_p * ( 0.5*(Wvel(i,j,k )+ABS(Wvel(i,j,k )))*cRpos + 0.5*(Wvel(i,j,k )-ABS(Wvel(i,j,k )))*cRneg ) -
!!! & rho_m * ( 0.5*(Wvel(i,j,km)+ABS(Wvel(i,j,km)))*cLpos + 0.5*(Wvel(i,j,km)-ABS(Wvel(i,j,km)))*cLneg ) )
!!! & *dz_i !/ ( dz )
!!!
!!!c
!!!300 continue
!!!c -------------------------------------------end i-loop
!!!200 continue
!!!c -------------------------------------------end j-loop
!!!100 continue
!!!c -------------------------------------------end k-loop
!!!c
!!! return
!!! end
real function limiter(r)
real r
! limiter=0. !1st order upwind
! limiter=r !2nd order upwind
! limiter=(3+r)/4. !Second order QUICK
limiter=(r+ABS(r))/MAX(1.+r,1.) ! Van Leer limiter
! limiter=MAX(0.,MIN(2.*r,1.),MIN(r,2.)) ! Superbee limiter
return
end