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turbulence_models.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 compact_filter(Uvel,Vvel,Wvel,Ru,Rp,dr,phiv,dz,i1,j1,k1,ib,ie,jb,je,kb,ke,rank,px,a,
& tmax_inPpunt,i_inPpunt,j_inPpunt,tmax_inUpunt,i_inUpunt,j_inUpunt,tmax_inVpunt,i_inVpunt,j_inVpunt,kjet)
implicit none
include 'mpif.h'
real Uvel(0:i1,0:j1,0:k1),Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1)
integer i1,j1,k1,ib,ie,jb,je,kb,ke,rank,px
real dr(0:i1),phiv(0:j1),dz,Ru(0:i1),Rp(0:i1),a
integer i,j,k
integer ileng,ierr,itag,status(MPI_STATUS_SIZE)
real aax_1ie(1:ie),bbx_1ie(1:ie),ccx_1ie(1:ie),ddx_1ie(1:ie)
real aaz_1ke(1:ke),bbz_1ke(1:ke),ccz_1ke(1:ke),ddz_1ke(1:ke)
real aay_1jepx(1:je*px),bby_1jepx(1:je*px),ccy_1jepx(1:je*px),ddy_1jepx(1:je*px)
real var(0:i1,1:je,0:k1),filt_var(1:ie,1:je,1:ke)
real Uvel_T(1:ie,0:je*px+1,1:ke/px),Vvel_T(1:ie,1:je*px,1:ke/px),Wvel_T(1:ie,0:je*px+1,1:ke/px)
real var_T(1:ie,0:je*px+1,1:ke/px),filt_var_T(1:ie,1:je*px,1:ke/px)
real Uvel2(0:i1,0:j1,0:k1),Vvel2(0:i1,0:j1,0:k1),Wvel2(0:i1,0:j1,0:k1)
integer tmax_inPpunt,tmax_inVpunt,tmax_inUpunt
integer*2 i_inUpunt(i1*j1),j_inUpunt(i1*j1),i_inVpunt(i1*j1),j_inVpunt(i1*j1),i_inPpunt(i1*j1),j_inPpunt(i1*j1)
integer kjet,t
bbx_1ie=1.
aax_1ie=a
aax_1ie(1)=0.
aax_1ie(ie)=0.
ccx_1ie=a
ccx_1ie(1)=0.
ccx_1ie(ie)=0.
bbz_1ke=1.
aaz_1ke=a
aaz_1ke(1)=0.
aaz_1ke(ke)=0.
ccz_1ke=a
ccz_1ke(1)=0.
ccz_1ke(ke)=0.
bby_1jepx=1.
aay_1jepx=a
aay_1jepx(1)=0.
aay_1jepx(je*px)=0.
ccy_1jepx=a
ccy_1jepx(1)=0.
ccy_1jepx(je*px)=0.
!! Set boundary conditions jet in:
Uvel2=Uvel
Vvel2=Vvel
Wvel2=Wvel
var(0:i1,1:je,1:ke)=Uvel(0:i1,1:je,1:ke)
do j=jb,je
do k=kb,ke
! ddx_1ie(1)=(0.0625*a+0.9375)*var(1,j,k)+(0.25+0.75*a)*var(2,j,k)
! & -0.375*(1-a)*var(3,j,k)+0.25*(1-a)*var(4,j,k)-0.0625*(1-a)*var(5,j,k)
! ddx_1ie(ie)=(0.0625*a+0.9375)*var(ie,j,k)+(0.25+0.75*a)*var(ie-1,j,k)
! & -0.375*(1-a)*var(ie-2,j,k)+0.25*(1-a)*var(ie-3,j,k)-0.0625*(1-a)*var(ie-4,j,k)
ddx_1ie(1)=var(1,j,k)
ddx_1ie(ie)=var(ie,j,k)
! ddx_1ie(2)=(0.0625+0.875*a)*var(1,j,k)+(0.75+0.5*a)*var(2,j,k)
! & +(0.375+0.25*a)*var(3,j,k)-0.5*(0.5-a)*var(4,j,k)+0.125*(0.5-a)*var(5,j,k)
! ddx_1ie(ie-1)=(0.0625+0.875*a)*var(ie,j,k)+(0.75+0.5*a)*var(ie-1,j,k)
! & +(0.375+0.25*a)*var(ie-2,j,k)-0.5*(0.5-a)*var(ie-3,j,k)+0.125*(0.5-a)*var(ie-4,j,k)
do i=2,ie-1
ddx_1ie(i)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i+1,j,k)+var(i-1,j,k))
& +(-0.125+0.25*a )*(var(i+2,j,k)+var(i-2,j,k))
enddo
CALL solve_tridiag(filt_var(1:ie,j,k),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie)
enddo
enddo
Uvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
var(0:i1,1:je,1:ke)=Vvel(0:i1,1:je,1:ke)
do j=jb,je
do k=kb,ke
! ddx_1ie(1)=(0.0625*a+0.9375)*var(1,j,k)+(0.25+0.75*a)*var(2,j,k)
! & -0.375*(1-a)*var(3,j,k)+0.25*(1-a)*var(4,j,k)-0.0625*(1-a)*var(5,j,k)
! ddx_1ie(ie)=(0.0625*a+0.9375)*var(ie,j,k)+(0.25+0.75*a)*var(ie-1,j,k)
! & -0.375*(1-a)*var(ie-2,j,k)+0.25*(1-a)*var(ie-3,j,k)-0.0625*(1-a)*var(ie-4,j,k)
ddx_1ie(1)=var(1,j,k)
ddx_1ie(ie)=var(ie,j,k)
! ddx_1ie(2)=(0.0625+0.875*a)*var(1,j,k)+(0.75+0.5*a)*var(2,j,k)
! & +(0.375+0.25*a)*var(3,j,k)-0.5*(0.5-a)*var(4,j,k)+0.125*(0.5-a)*var(5,j,k)
! ddx_1ie(ie-1)=(0.0625+0.875*a)*var(ie,j,k)+(0.75+0.5*a)*var(ie-1,j,k)
! & +(0.375+0.25*a)*var(ie-2,j,k)-0.5*(0.5-a)*var(ie-3,j,k)+0.125*(0.5-a)*var(ie-4,j,k)
do i=2,ie-1
ddx_1ie(i)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i+1,j,k)+var(i-1,j,k))
& +(-0.125+0.25*a )*(var(i+2,j,k)+var(i-2,j,k))
enddo
CALL solve_tridiag(filt_var(1:ie,j,k),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie)
enddo
enddo
Vvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
var(0:i1,1:je,1:ke)=Wvel(0:i1,1:je,1:ke)
do j=jb,je
do k=kb,ke
! ddx_1ie(1)=(0.0625*a+0.9375)*var(1,j,k)+(0.25+0.75*a)*var(2,j,k)
! & -0.375*(1-a)*var(3,j,k)+0.25*(1-a)*var(4,j,k)-0.0625*(1-a)*var(5,j,k)
! ddx_1ie(ie)=(0.0625*a+0.9375)*var(ie,j,k)+(0.25+0.75*a)*var(ie-1,j,k)
! & -0.375*(1-a)*var(ie-2,j,k)+0.25*(1-a)*var(ie-3,j,k)-0.0625*(1-a)*var(ie-4,j,k)
ddx_1ie(1)=var(1,j,k)
ddx_1ie(ie)=var(ie,j,k)
! ddx_1ie(2)=(0.0625+0.875*a)*var(1,j,k)+(0.75+0.5*a)*var(2,j,k)
! & +(0.375+0.25*a)*var(3,j,k)-0.5*(0.5-a)*var(4,j,k)+0.125*(0.5-a)*var(5,j,k)
! ddx_1ie(ie-1)=(0.0625+0.875*a)*var(ie,j,k)+(0.75+0.5*a)*var(ie-1,j,k)
! & +(0.375+0.25*a)*var(ie-2,j,k)-0.5*(0.5-a)*var(ie-3,j,k)+0.125*(0.5-a)*var(ie-4,j,k)
do i=2,ie-1
ddx_1ie(i)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i+1,j,k)+var(i-1,j,k))
& +(-0.125+0.25*a )*(var(i+2,j,k)+var(i-2,j,k))
enddo
CALL solve_tridiag(filt_var(1:ie,j,k),aax_1ie,bbx_1ie,ccx_1ie,ddx_1ie,ie)
enddo
enddo
Wvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
var(1:ie,1:je,0:k1)=Uvel(1:ie,1:je,0:k1)
do j=jb,je
do i=ib,ie
! ddz_1ke(1)=(0.0625*a+0.9375)*var(i,j,1)+(0.25+0.75*a)*var(i,j,2)
! & -0.375*(1-a)*var(i,j,3)+0.25*(1-a)*var(i,j,4)-0.0625*(1-a)*var(i,j,5)
! ddz_1ke(ke)=(0.0625*a+0.9375)*var(i,j,ke)+(0.25+0.75*a)*var(i,j,ke-1)
! & -0.375*(1-a)*var(i,j,ke-2)+0.25*(1-a)*var(i,j,ke-3)-0.0625*(1-a)*var(i,j,ke-4)
ddz_1ke(1)=var(i,j,1)
ddz_1ke(ke)=var(i,j,ke)
do k=2,ke-1
ddz_1ke(k)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i,j,k+1)+var(i,j,k-1))
& +(-0.125+0.25*a )*(var(i,j,k+2)+var(i,j,k-2))
enddo
CALL solve_tridiag(filt_var(i,j,1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke)
enddo
enddo
Uvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
var(1:ie,1:je,0:k1)=Vvel(1:ie,1:je,0:k1)
do j=jb,je
do i=ib,ie
! ddz_1ke(1)=(0.0625*a+0.9375)*var(i,j,1)+(0.25+0.75*a)*var(i,j,2)
! & -0.375*(1-a)*var(i,j,3)+0.25*(1-a)*var(i,j,4)-0.0625*(1-a)*var(i,j,5)
! ddz_1ke(ke)=(0.0625*a+0.9375)*var(i,j,ke)+(0.25+0.75*a)*var(i,j,ke-1)
! & -0.375*(1-a)*var(i,j,ke-2)+0.25*(1-a)*var(i,j,ke-3)-0.0625*(1-a)*var(i,j,ke-4)
ddz_1ke(1)=var(i,j,1)
ddz_1ke(ke)=var(i,j,ke)
do k=2,ke-1
ddz_1ke(k)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i,j,k+1)+var(i,j,k-1))
& +(-0.125+0.25*a )*(var(i,j,k+2)+var(i,j,k-2))
enddo
CALL solve_tridiag(filt_var(i,j,1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke)
enddo
enddo
Vvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
var(1:ie,1:je,1:ke)=Wvel(1:ie,1:je,1:ke)
do j=jb,je
do i=ib,ie
! ddz_1ke(1)=(0.0625*a+0.9375)*var(i,j,1)+(0.25+0.75*a)*var(i,j,2)
! & -0.375*(1-a)*var(i,j,3)+0.25*(1-a)*var(i,j,4)-0.0625*(1-a)*var(i,j,5)
! ddz_1ke(ke)=(0.0625*a+0.9375)*var(i,j,ke)+(0.25+0.75*a)*var(i,j,ke-1)
! & -0.375*(1-a)*var(i,j,ke-2)+0.25*(1-a)*var(i,j,ke-3)-0.0625*(1-a)*var(i,j,ke-4)
ddz_1ke(1)=var(i,j,1)
ddz_1ke(ke)=var(i,j,ke)
ddz_1ke(2)=(0.0625+0.875*a)*var(i,j,1)+(0.75+0.5*a)*var(i,j,2)
& +(0.375+0.25*a)*var(i,j,3)-0.5*(0.5-a)*var(i,j,4)+0.125*(0.5-a)*var(i,j,5)
ddz_1ke(ke-1)=(0.0625+0.875*a)*var(i,j,ke)+(0.75+0.5*a)*var(i,j,ke-1)
& +(0.375+0.25*a)*var(i,j,ke-2)-0.5*(0.5-a)*var(i,j,ke-3)+0.125*(0.5-a)*var(i,j,ke-4)
do k=3,ke-2
ddz_1ke(k)= ( 0.625+0.75*a )*var(i,j,k)
& +( 0.25 +0.5 *a )*(var(i,j,k+1)+var(i,j,k-1))
& +(-0.125+0.25*a )*(var(i,j,k+2)+var(i,j,k-2))
enddo
CALL solve_tridiag(filt_var(i,j,1:ke),aaz_1ke,bbz_1ke,ccz_1ke,ddz_1ke,ke)
enddo
enddo
Wvel(1:ie,1:je,1:ke)=filt_var(1:ie,1:je,1:ke)
!! first swap u,v,w -> u_T,v_T,w_T
call t2np(Uvel(1:ie,1:je,1:ke),Uvel_T(1:ie,1:je*px,1:ke/px))
call t2np(Vvel(1:ie,1:je,1:ke),Vvel_T(1:ie,1:je*px,1:ke/px))
call t2np(Wvel(1:ie,1:je,1:ke),Wvel_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(Uvel(1:ie,0,i*ke/px+1:(i+1)*ke/px),ie*ke/px,MPI_REAL8,i,i+200,MPI_COMM_WORLD,status,ierr)
call mpi_send(Wvel(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
Uvel_T(1:ie,0,1:ke/px)=Uvel(1:ie,0,1:ke/px)
Wvel_T(1:ie,0,1:ke/px)=Wvel(1:ie,0,1:ke/px)
else
call mpi_recv(Uvel_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+200,MPI_COMM_WORLD,status,ierr)
call mpi_recv(Wvel_T(1:ie,0,1:ke/px),ie*ke/px,MPI_REAL8,0,rank+201,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(Uvel(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)
call mpi_send(Wvel(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
Uvel_T(1:ie,je*px+1,1:ke/px)=Uvel(1:ie,je+1,rank*ke/px+1:(rank+1)*ke/px)
Wvel_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(Uvel_T(1:ie,je*px+1,1:ke/px),ie*ke/px,MPI_REAL8,px-1,rank+400,MPI_COMM_WORLD,status,ierr)
call mpi_recv(Wvel_T(1:ie,je*px+1,1:ke/px),ie*ke/px,MPI_REAL8,px-1,rank+401,MPI_COMM_WORLD,status,ierr)
endif
var_T(1:ie,0:je*px+1,1:ke/px)=Uvel_T(1:ie,0:je*px+1,1:ke/px)
do i=ib,ie
do k=kb,ke/px
! ddy_1jepx(1)=(0.0625*a+0.9375)*var_T(i,1,k)+(0.25+0.75*a)*var_T(i,2,k)
! & -0.375*(1-a)*var_T(i,3,k)+0.25*(1-a)*var_T(i,4,k)-0.0625*(1-a)*var_T(i,5,k)
! ddy_1jepx(je*px)=(0.0625*a+0.9375)*var_T(i,je*px,k)+(0.25+0.75*a)*var_T(i,je*px-1,k)
! & -0.375*(1-a)*var_T(i,je*px-2,k)+0.25*(1-a)*var_T(i,je*px-3,k)-0.0625*(1-a)*var_T(i,je*px-4,k)
ddy_1jepx(1)=var_T(i,1,k)
ddy_1jepx(je*px)=var_T(i,je*px,k)
! ddy_1jepx(2)=(0.0625+0.875*a)*var_T(i,1,k)+(0.75+0.5*a)*var_T(i,2,k)
! & +(0.375+0.25*a)*var_T(i,3,k)-0.5*(0.5-a)*var_T(i,4,k)+0.125*(0.5-a)*var_T(i,5,k)
! ddy_1jepx(je*px-1)=(0.0625+0.875*a)*var_T(i,je*px,k)+(0.75+0.5*a)*var_T(i,je*px-1,k)
! & +(0.375+0.25*a)*var_T(i,je*px-2,k)-0.5*(0.5-a)*var_T(i,je*px-3,k)+0.125*(0.5-a)*var_T(i,je*px-4,k)
do j=2,je*px-1
ddy_1jepx(j)= ( 0.625+0.75*a )*var_T(i,j,k)
& +( 0.25 +0.5 *a )*(var_T(i,j+1,k)+var_T(i,j-1,k))
& +(-0.125+0.25*a )*(var_T(i,j+2,k)+var_T(i,j-2,k))
enddo
CALL solve_tridiag(filt_var_T(i,1:je*px,k),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px)
enddo
enddo
Uvel_T(1:ie,1:je*px,1:ke/px)=filt_var_T(1:ie,1:je*px,1:ke/px)
var_T(1:ie,1:je*px,1:ke/px)=Vvel_T(1:ie,1:je*px,1:ke/px)
do i=ib,ie
do k=kb,ke/px
! ddy_1jepx(1)=(0.0625*a+0.9375)*var_T(i,1,k)+(0.25+0.75*a)*var_T(i,2,k)
! & -0.375*(1-a)*var_T(i,3,k)+0.25*(1-a)*var_T(i,4,k)-0.0625*(1-a)*var_T(i,5,k)
ddy_1jepx(2)=(0.0625+0.875*a)*var_T(i,1,k)+(0.75+0.5*a)*var_T(i,2,k)
& +(0.375+0.25*a)*var_T(i,3,k)-0.5*(0.5-a)*var_T(i,4,k)+0.125*(0.5-a)*var_T(i,5,k)
! ddy_1jepx(je*px)=(0.0625*a+0.9375)*var_T(i,je*px,k)+(0.25+0.75*a)*var_T(i,je*px-1,k)
! & -0.375*(1-a)*var_T(i,je*px-2,k)+0.25*(1-a)*var_T(i,je*px-3,k)-0.0625*(1-a)*var_T(i,je*px-4,k)
ddy_1jepx(je*px-1)=(0.0625+0.875*a)*var_T(i,je*px,k)+(0.75+0.5*a)*var_T(i,je*px-1,k)
& +(0.375+0.25*a)*var_T(i,je*px-2,k)-0.5*(0.5-a)*var_T(i,je*px-3,k)+0.125*(0.5-a)*var_T(i,je*px-4,k)
ddy_1jepx(1)=var_T(i,1,k)
ddy_1jepx(je*px)=var_T(i,je*px,k)
do j=3,je*px-2
ddy_1jepx(j)= ( 0.625+0.75*a )*var_T(i,j,k)
& +( 0.25 +0.5 *a )*(var_T(i,j+1,k)+var_T(i,j-1,k))
& +(-0.125+0.25*a )*(var_T(i,j+2,k)+var_T(i,j-2,k))
enddo
CALL solve_tridiag(filt_var_T(i,1:je*px,k),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px)
enddo
enddo
Vvel_T(1:ie,1:je*px,1:ke/px)=filt_var_T(1:ie,1:je*px,1:ke/px)
var_T(1:ie,0:je*px+1,1:ke/px)=Wvel_T(1:ie,0:je*px+1,1:ke/px)
do i=ib,ie
do k=kb,ke/px
! ddy_1jepx(1)=(0.0625*a+0.9375)*var_T(i,1,k)+(0.25+0.75*a)*var_T(i,2,k)
! & -0.375*(1-a)*var_T(i,3,k)+0.25*(1-a)*var_T(i,4,k)-0.0625*(1-a)*var_T(i,5,k)
! ddy_1jepx(je*px)=(0.0625*a+0.9375)*var_T(i,je*px,k)+(0.25+0.75*a)*var_T(i,je*px-1,k)
! & -0.375*(1-a)*var_T(i,je*px-2,k)+0.25*(1-a)*var_T(i,je*px-3,k)-0.0625*(1-a)*var_T(i,je*px-4,k)
ddy_1jepx(1)=var_T(i,1,k)
ddy_1jepx(je*px)=var_T(i,je*px,k)
! ddy_1jepx(2)=(0.0625+0.875*a)*var_T(i,1,k)+(0.75+0.5*a)*var_T(i,2,k)
! & +(0.375+0.25*a)*var_T(i,3,k)-0.5*(0.5-a)*var_T(i,4,k)+0.125*(0.5-a)*var_T(i,5,k)
! ddy_1jepx(je*px-1)=(0.0625+0.875*a)*var_T(i,je*px,k)+(0.75+0.5*a)*var_T(i,je*px-1,k)
! & +(0.375+0.25*a)*var_T(i,je*px-2,k)-0.5*(0.5-a)*var_T(i,je*px-3,k)+0.125*(0.5-a)*var_T(i,je*px-4,k)
do j=2,je*px-1
ddy_1jepx(j)= ( 0.625+0.75*a )*var_T(i,j,k)
& +( 0.25 +0.5 *a )*(var_T(i,j+1,k)+var_T(i,j-1,k))
& +(-0.125+0.25*a )*(var_T(i,j+2,k)+var_T(i,j-2,k))
enddo
CALL solve_tridiag(filt_var_T(i,1:je*px,k),aay_1jepx,bby_1jepx,ccy_1jepx,ddy_1jepx,je*px)
enddo
enddo
Wvel_T(1:ie,1:je*px,1:ke/px)=filt_var_T(1:ie,1:je*px,1:ke/px)
call t2fp(Uvel_T(1:ie,1:je*px,1:ke/px),Uvel(1:ie,1:je,1:ke))
call t2fp(Vvel_T(1:ie,1:je*px,1:ke/px),Vvel(1:ie,1:je,1:ke))
call t2fp(Wvel_T(1:ie,1:je*px,1:ke/px),Wvel(1:ie,1:je,1:ke))
end
subroutine LES_smagorinsky(Uvel,Vvel,Wvel,rr)
USE nlist
implicit none
! include 'param.txt'
! include 'common.txt'
!include 'mpif.h'
real shear
real xx,yy,f,dzi,uu,vv,absU,ust,z0,yplus
integer n,t,tel,kt,n2
real ebb(0:i1,0:k1)
real ebf(0:i1,0:k1)
real Lm2,dRpp_i,dRp_i,divergentie
real Uvel(0:i1,0:j1,0:k1),
+ Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),rr(0:i1,0:j1,0:k1)
real ekm2(0:i1,0:j1,0:k1)
integer im,ip,jm,jp,km,kp
real ctot,cref,pwr,tauu,tauv
integer fracs_included(nfr_sand+nfr_silt)
! real shr(1:imax,1:jmax,1:kmax),ekm1(1:imax,1:jmax,1:kmax),ekm2(1:imax,1:jmax,1:kmax)
! real shr_T(1:imax,1:jmax*px,1:kmax/px),ekm2_T(1:imax,1:jmax*px,1:kmax/px),ekm2y(1:imax,1:jmax,1:kmax)
shear = 0.
dzi=1./dz
do i=1,imax
dRpp_i=1./(Rp(i+1)-Rp(i))
dRp_i=1./(Rp(i)-Rp(i-1))
do j=1,jmax
Lm2=Lmix2(i,j)*Cs*Cs
do k=1,kmax
shear = 2.0*(
1 ((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i))*((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i)) +
1 ((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1))) + 0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i))*
1 ((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1))) + 0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i)) +
1 ((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi)*((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi) )
shear = shear + 0.25*(
1 ((Uvel(i ,j+1,k )-Uvel(i ,j ,k ))/(Ru(i)*(phip(j+1)-phip(j))) +
2 ( Vvel(i+1,j ,k )/Rp(i+1)-Vvel(i ,j ,k )/Rp(i))*dRpp_i*Ru(i) )**2 +
1 ((Uvel(i ,j ,k )-Uvel(i ,j-1,k ))/(Ru(i)*(phip(j)-phip(j-1))) +
2 ( Vvel(i+1,j-1,k )/Rp(i+1)-Vvel(i ,j-1,k )/Rp(i))*dRpp_i*Ru(i) )**2 +
1 ((Uvel(i-1,j+1,k )-Uvel(i-1,j ,k ))/(Ru(i-1)*(phip(j+1)-phip(j))) +
2 ( Vvel(i ,j ,k )/Rp(i)-Vvel(i-1,j ,k )/Rp(i-1))*dRp_i*Ru(i-1) )**2 +
1 ((Uvel(i-1,j ,k )-Uvel(i-1,j-1,k ))/(Ru(i-1)*(phip(j)-phip(j-1))) +
2 ( Vvel(i ,j-1,k )/Rp(i)-Vvel(i-1,j-1,k )/Rp(i-1))*dRp_i*Ru(i-1) )**2
e )
shear = shear + 0.25*(
1 ((Uvel(i ,j ,k+1)-Uvel(i ,j ,k ))*dzi +
2 ( Wvel(i+1,j ,k )-Wvel(i ,j ,k ))*dRpp_i)**2 +
1 ((Uvel(i ,j ,k )-Uvel(i ,j ,k-1))*dzi +
2 ( Wvel(i+1,j ,k-1)-Wvel(i ,j ,k-1))*dRpp_i)**2 +
1 ((Uvel(i-1,j ,k+1)-Uvel(i-1,j ,k ))*dzi +
2 ( Wvel(i ,j ,k )-Wvel(i-1,j ,k ))*dRp_i)**2 +
1 ((Uvel(i-1,j ,k )-Uvel(i-1,j ,k-1))*dzi +
2 ( Wvel(i ,j ,k-1)-Wvel(i-1,j ,k-1))*dRp_i)**2
e )
shear = shear + 0.25*(
1 ((Vvel(i ,j ,k+1)-Vvel(i ,j ,k ))*dzi +
2 ( Wvel(i ,j+1,k )-Wvel(i ,j ,k ))/(Rp(i)*(phip(j+1)-phip(j))) )**2 +
1 ((Vvel(i ,j ,k )-Vvel(i ,j ,k-1))*dzi +
2 ( Wvel(i ,j+1,k-1)-Wvel(i ,j ,k-1))/(Rp(i)*(phip(j+1)-phip(j))) )**2 +
1 ((Vvel(i ,j-1,k+1)-Vvel(i ,j-1,k ))*dzi +
2 ( Wvel(i ,j ,k )-Wvel(i ,j-1,k ))/(Rp(i)*(phip(j)-phip(j-1))) )**2 +
1 ((Vvel(i ,j-1,k )-Vvel(i ,j-1,k-1))*dzi +
2 ( Wvel(i ,j ,k-1)-Wvel(i ,j-1,k-1))/(Rp(i)*(phip(j)-phip(j-1))) )**2
e )
!!
divergentie= 2./3.*(( Ru(i)*Uvel(i,j,k) - Ru(i-1)*Uvel(i-1,j,k) ) / ( Rp(i)*dr(i) )
+ +
2 ( Vvel(i,j,k) - Vvel(i,j-1,k) ) / ( Rp(i)*(phiv(j)-phiv(j-1)) )
+ +
3 ( Wvel(i,j,k) - Wvel(i,j,k-1) ) / ( dz ))
shear = shear
+ +1.5*divergentie*divergentie
+ -divergentie*2.*((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i))
+ -divergentie*2.*((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1)))+0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i))
+ -divergentie*2.*((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi)
ekm(i,j,k) = rr(i,j,k) * Lm2 * sqrt(shear) ! Smagorinsky
enddo
enddo
enddo
c*************************************************************
c Van Driest damping of sgs viscosity
c Determine ust, then yplus and adjust
c mu_t with mu_t = mu_t * (1 - exp(-y+/A))
c A = 26 cf. Modeling and simulation of turbulent flows (Schiestel 2008) & Pope (2000) p.304
c*************************************************************
! ust=0.1*U_b
! do i=1,10
! z0=0.11*1e-6/ust+kn/30.
! ust=U_b*kappa/(log(((depth-bc_obst_h)-bc_obst_h)/z0)-1);
! enddo
if (slip_bot.ge.1) then
ekm2=ekm
do i=1,imax
do j=1,jmax
kp=MIN(kbedt(i,j)+1,k1)
uu=0.5*(Uvel(i,j,kp)+Uvel(i-1,j,kp))
vv=0.5*(Vvel(i,j,kp)+Vvel(i,j-1,kp))
absU=sqrt(uu*uu+vv*vv)
IF (slip_bot.ge.3) THEN
tauu=0.5*(tau_fl_Uold(i,j)+tau_fl_Uold(i-1,j))
tauv=0.5*(tau_fl_Vold(i,j)+tau_fl_Vold(i,j-1))
ust = ((tauu/rr(i,j,kp))**2+(tauv/rr(i,j,kp))**2)**0.25
ust = MIN(0.5*absU,ust) !ust maximal 0.5*absU
ELSE
ust=0.1*absU
do tel=1,10 ! 10 iter is more than enough
z0=kn/30+0.11*nu_mol/MAX(ust,1.e-6)
ust=absU/MAX(1./kappa*log(0.5*dz/z0),2.) !ust maximal 0.5*absU
enddo
yplus=MAX(0.5*dz*ust/nu_mol,1e-12)
if (yplus<11.225) then !viscous sublayer uplus=yplus
ust=sqrt(absU*nu_mol/(0.5*dz))
endif
ENDIF
! write(*,*) 'ust van Driest damping',ust
do k=1,10 ! first 10 grid layers from wall are adjusted
yplus=MAX((REAL(k)-0.5)*dz*ust/nu_mol,1e-12)
ekm(i,j,k)=ekm(i,j,k) * (1. - exp(-yplus/26.))
enddo
enddo
enddo
!! Set ekm jet back:
do t=1,tmax_inPpunt
i=i_inPpunt(t)
j=j_inPpunt(t)
do k=k1-kjet+1,k1
ekm(i,j,k)=ekm2(i,j,k)
enddo
enddo
endif
ekm=ekm+ekm_mol
!! Boundary conditions Neumann
call shiftf(ekm,ebf)
call shiftb(ekm,ebb)
if (periodicy.eq.0.or.periodicy.eq.2) then
if (rank.eq.0) then ! boundaries in j-direction
do k=1,kmax
do i=1,imax
ekm(i,0,k) = ekm(i,1,k)
ekm(i,j1,k)= ebb(i,k)
enddo
enddo
elseif (rank.eq.px-1) then
do k=1,kmax
do i=1,imax
ekm(i,0,k) = ebf(i,k)
ekm(i,j1,k)= ekm(i,jmax,k)
enddo
enddo
else
do k=1,kmax
do i=1,imax
ekm(i,0,k) = ebf(i,k)
ekm(i,j1,k) =ebb(i,k)
enddo
enddo
endif
else
do k=1,kmax
do i=1,imax
ekm(i,0,k) = ebf(i,k)
ekm(i,j1,k) =ebb(i,k)
enddo
enddo
endif
if (periodicx.eq.0.or.periodicx.eq.2) then
do k=1,kmax ! boundaries in i-direction
do j=0,j1
ekm(0,j,k) = ekm(1,j,k)
ekm(i1,j,k) = ekm(imax,j,k)
enddo
enddo
else
do k=1,kmax ! boundaries in i-direction
do j=0,j1
ekm(0,j,k) = ekm(imax,j,k)
ekm(i1,j,k) = ekm(1,j,k)
enddo
enddo
endif
do i=0,i1 ! boundaries in k-direction
do j=0,j1
ekm(i,j,0) = ekm(i,j,1)
ekm(i,j,k1) = ekm(i,j,kmax)
enddo
enddo
ekm2=ekm
if (LOA>0.and.kn_TSHD>0.) then
do t=1,tmax_inUpunt_tauTSHD
i=i_inUpunt_tauTSHD(t)
j=j_inUpunt_tauTSHD(t)
k=k_inUpunt_tauTSHD(t)
uu=0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))
vv=0.5*(Vvel(i,j,k)+Vvel(i,j-1,k))
absU=sqrt(uu*uu+vv*vv)
ust=0.1*absU
do tel=1,10 ! 10 iter is more than enough
z0=kn/30+0.11*nu_mol/MAX(ust,1.e-6)
ust=absU/MAX(1./kappa*log(0.5*dz/z0),2.) !ust maximal 0.5*absU
enddo
yplus=MAX(0.5*dz*ust/nu_mol,1e-12)
if (yplus<11.225) then !viscous sublayer uplus=yplus
ust=sqrt(absU*nu_mol/(0.5*dz))
endif
! write(*,*) 'ust van Driest damping',ust
do kt=k,k-10,-1 ! first 10 grid layers from wall are adjusted
yplus=MAX((REAL(kmax-kjet-kt)+0.5)*dz*ust/nu_mol,1e-12)
ekm(i,j,kt)=ekm(i,j,kt) * (1. - exp(-yplus/26.))
enddo
enddo
endif
do k=kmax-kjet-2,k1 ! laat ekm in buisje ongemoeid
do t=1,tmax_inPpunt
i=i_inPpunt(t)
j=j_inPpunt(t)
ekm(i,j,k)=ekm2(i,j,k)
enddo
enddo
Diffcof=ekm/Sc/rr
do k=kmax-kjet+1,k1 ! maak Diffcof rand buisje nul
do t=1,tmax_inPpuntrand
i=i_inPpuntrand(t)
j=j_inPpuntrand(t)
Diffcof(i,j,k)=0.
enddo
enddo
! IF (LOA>0.or.nobst>0) THEN ! ship:
! do t=1,tmax_inPpuntTSHD
! i=i_inPpuntTSHD(t)
! j=j_inPpuntTSHD(t)
! k=k_inPpuntTSHD(t)
! !ekm(i,j,k)=0.
! Diffcof(i,j,k)=0.
! im=MAX(0,i-1)
! ip=MIN(i1,i+1)
! jm=MAX(0,j-1)
! jp=MIN(j1,j+1)
! km=MAX(0,k-1)
! kp=MIN(k1,k+1)
! Diffcof(im,j,k)=0.
! Diffcof(ip,j,k)=0.
! Diffcof(i,jm,k)=0.
! Diffcof(i,jp,k)=0.
! Diffcof(i,j,km)=0.
! Diffcof(i,j,kp)=0.
! enddo
! ELSEIF(kjet>0) THEN
IF (kjet>0) THEN
!ekm(0:i1,0:j1,kmax-kjet+1:k1)=0. !maak ekm in zone rondom buisje nul
Diffcof(0:i1,0:j1,kmax-kjet+1:k1)=0.
ENDIF
! ! no diffusion allowed into bed:
! DO i=0,i1
! DO j=0,j1
! DO k=0,kbed(i,j)
! im=MAX(0,i-1)
! ip=MIN(i1,i+1)
! jm=MAX(0,j-1)
! jp=MIN(j1,j+1)
! km=MAX(0,k-1)
! kp=MIN(k1,k+1)
! Diffcof(im,j,k)=0.
! Diffcof(ip,j,k)=0.
! Diffcof(i,jm,k)=0.
! Diffcof(i,jp,k)=0.
! Diffcof(i,j,k)=0.
! Diffcof(i,j,kp)=0.
! ENDDO
! ENDDO
! ENDDO
IF (extra_mix_visc.eq.'Krie') THEN !apply Krieger mixing viscosity only on ekm (momentum diffusivity) and not on Diffcof (concentration diffusivity)
pwr=-2.5*cfixedbed
cref=1.001*cfixedbed !max ekm_mix is 3e4*ekm_mol
tel=0
DO n=1,nfr_silt
tel=tel+1
fracs_included(tel)=nfrac_silt(n)
ENDDO
DO n=1,nfr_sand
tel=tel+1
fracs_included(tel)=nfrac_sand(n)
ENDDO
DO i=0,i1 !1,imax
DO j=0,j1 !1,jmax
DO k=0,k1 !1,kmax
!ctot=SUM(cnew(fracs_included,i,j,k))
ctot=0.
DO n2=1,tel
n=fracs_included(n2)
ctot = ctot + cnew(n,i,j,k)*frac(n)%dfloc/frac(n)%dpart
ctot = MIN(cfixedbed,ctot)
ENDDO
ekm(i,j,k)=ekm(i,j,k)+ekm_mol*(1.-ctot/cref)**pwr-ekm_mol
ENDDO
ENDDO
ENDDO
ENDIF
end
subroutine LES_mixinglengthdamped(Uvel,Vvel,Wvel,rr)
USE nlist
implicit none
! include 'param.txt'
! include 'common.txt'
!include 'mpif.h'
real shear
real xx,yy,f,dzi,uu,vv,absU,ust,z0,yplus,ww,tauw,tauv,tauu
integer n,t,tel,kt,n2
real ebb(0:i1,0:k1)
real ebf(0:i1,0:k1)
real Lm2,dRpp_i,dRp_i,divergentie
real Uvel(0:i1,0:j1,0:k1),
+ Vvel(0:i1,0:j1,0:k1),Wvel(0:i1,0:j1,0:k1),rr(0:i1,0:j1,0:k1)
real ekm2(0:i1,0:j1,0:k1)
real z,Ri,dudz,dvdz,drdz,Diffcof2(0:i1,0:j1,0:k1),Lm2_Bak,MuAn_factor
integer im,ip,jm,jp,km,kp
real ctot,cref,pwr,zb_C,distance_to_bed,nu_t,factor,absU2,gvector
integer fracs_included(nfr_sand+nfr_silt)
! real shr(1:imax,1:jmax,1:kmax),ekm1(1:imax,1:jmax,1:kmax),ekm2(1:imax,1:jmax,1:kmax)
! real shr_T(1:imax,1:jmax*px,1:kmax/px),ekm2_T(1:imax,1:jmax*px,1:kmax/px),ekm2y(1:imax,1:jmax,1:kmax)
shear = 0.
MuAn_factor=0.
gvector=sqrt(gx**2+gy**2+gz**2)
if (damping_drho_dz.eq.'MuAn') then
MuAn_factor=1.
endif
dzi=1./dz
do i=1,imax
dRpp_i=1./(Rp(i+1)-Rp(i))
dRp_i=1./(Rp(i)-Rp(i-1))
do j=1,jmax
Lm2=Lmix2(i,j)*Cs*Cs
do k=1,kmax
shear = 2.0*(
1 ((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i))*((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i)) +
1 ((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1))) + 0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i))*
1 ((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1))) + 0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i)) +
1 ((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi)*((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi) )
shear = shear + 0.25*(
1 ((Uvel(i ,j+1,k )-Uvel(i ,j ,k ))/(Ru(i)*(phip(j+1)-phip(j))) +
2 ( Vvel(i+1,j ,k )/Rp(i+1)-Vvel(i ,j ,k )/Rp(i))*dRpp_i*Ru(i) )**2 +
1 ((Uvel(i ,j ,k )-Uvel(i ,j-1,k ))/(Ru(i)*(phip(j)-phip(j-1))) +
2 ( Vvel(i+1,j-1,k )/Rp(i+1)-Vvel(i ,j-1,k )/Rp(i))*dRpp_i*Ru(i) )**2 +
1 ((Uvel(i-1,j+1,k )-Uvel(i-1,j ,k ))/(Ru(i-1)*(phip(j+1)-phip(j))) +
2 ( Vvel(i ,j ,k )/Rp(i)-Vvel(i-1,j ,k )/Rp(i-1))*dRp_i*Ru(i-1) )**2 +
1 ((Uvel(i-1,j ,k )-Uvel(i-1,j-1,k ))/(Ru(i-1)*(phip(j)-phip(j-1))) +
2 ( Vvel(i ,j-1,k )/Rp(i)-Vvel(i-1,j-1,k )/Rp(i-1))*dRp_i*Ru(i-1) )**2
e )
shear = shear + 0.25*(
1 ((Uvel(i ,j ,k+1)-Uvel(i ,j ,k ))*dzi +
2 ( Wvel(i+1,j ,k )-Wvel(i ,j ,k ))*dRpp_i)**2 +
1 ((Uvel(i ,j ,k )-Uvel(i ,j ,k-1))*dzi +
2 ( Wvel(i+1,j ,k-1)-Wvel(i ,j ,k-1))*dRpp_i)**2 +
1 ((Uvel(i-1,j ,k+1)-Uvel(i-1,j ,k ))*dzi +
2 ( Wvel(i ,j ,k )-Wvel(i-1,j ,k ))*dRp_i)**2 +
1 ((Uvel(i-1,j ,k )-Uvel(i-1,j ,k-1))*dzi +
2 ( Wvel(i ,j ,k-1)-Wvel(i-1,j ,k-1))*dRp_i)**2
e )
shear = shear + 0.25*(
1 ((Vvel(i ,j ,k+1)-Vvel(i ,j ,k ))*dzi +
2 ( Wvel(i ,j+1,k )-Wvel(i ,j ,k ))/(Rp(i)*(phip(j+1)-phip(j))) )**2 +
1 ((Vvel(i ,j ,k )-Vvel(i ,j ,k-1))*dzi +
2 ( Wvel(i ,j+1,k-1)-Wvel(i ,j ,k-1))/(Rp(i)*(phip(j+1)-phip(j))) )**2 +
1 ((Vvel(i ,j-1,k+1)-Vvel(i ,j-1,k ))*dzi +
2 ( Wvel(i ,j ,k )-Wvel(i ,j-1,k ))/(Rp(i)*(phip(j)-phip(j-1))) )**2 +
1 ((Vvel(i ,j-1,k )-Vvel(i ,j-1,k-1))*dzi +
2 ( Wvel(i ,j ,k-1)-Wvel(i ,j-1,k-1))/(Rp(i)*(phip(j)-phip(j-1))) )**2
e )
!!
divergentie = 0.
! divergentie= 2./3.*(( Ru(i)*Uvel(i,j,k) - Ru(i-1)*Uvel(i-1,j,k) ) / ( Rp(i)*dr(i) )
! + +
! 2 ( Vvel(i,j,k) - Vvel(i,j-1,k) ) / ( Rp(i)*(phiv(j)-phiv(j-1)) )
! + +
! 3 ( Wvel(i,j,k) - Wvel(i,j,k-1) ) / ( dz ))
shear = shear
+ +1.5*divergentie*divergentie
+ -divergentie*2.*((Uvel(i,j,k)-Uvel(i-1,j,k))/dr(i))
+ -divergentie*2.*((Vvel(i,j,k)-Vvel(i,j-1,k))/(Rp(i)*(phiv(j)-phiv(j-1)))+0.5*(Uvel(i,j,k)+Uvel(i-1,j,k))/Rp(i))
+ -divergentie*2.*((Wvel(i,j,k)-Wvel(i,j,k-1))*dzi)
dudz = ((Uvel(i ,j ,k+1)-Uvel(i ,j ,k ))*dzi +
& (Uvel(i ,j ,k )-Uvel(i ,j ,k-1))*dzi +
& (Uvel(i-1,j ,k+1)-Uvel(i-1,j ,k ))*dzi +
& (Uvel(i-1,j ,k )-Uvel(i-1,j ,k-1))*dzi ) * 0.25
dvdz = ((Vvel(i ,j ,k+1)-Vvel(i ,j ,k ))*dzi +
& (Vvel(i ,j ,k )-Vvel(i ,j ,k-1))*dzi +
& (Vvel(i ,j-1,k+1)-Vvel(i ,j-1,k ))*dzi +
& (Vvel(i ,j-1,k )-Vvel(i ,j-1,k-1))*dzi ) * 0.25
drdz=0.5*(rr(i,j,k+1 )-rr(i,j,k-1))*dzi
Ri = -gvector/rr(i,j,k)*drdz/(dudz**2+dvdz**2+1.e-18)
Ri = MuAn_factor*MAX(0.,Ri)
z=MAX(0.,(k-kbed(i,j))*dz-0.5*dz)
Lm2_Bak=Cs*Cs*(kappa*z)**2*MAX(0.,1.-z/(MAX(depth-kbed(i,j)*dz,1.e-8)))
ekm(i,j,k) = rr(i,j,k) * Lm2_Bak * sqrt(shear) ! Mixing length model with Ri-damping
ekm(i,j,k) = ekm(i,j,k) * (1.+damping_a1*Ri)**damping_b1
Diffcof(i,j,k) = (ekm(i,j,k)+ekm_mol)/rr(i,j,k)/Sc * (1.+damping_a2*Ri)**damping_b2 ! damping diffusivity is by both damping functions
enddo
enddo
enddo
ekm=ekm+ekm_mol
if (slip_bot.ge.1.and.nu_minimum_wall.ge.1) then
do i=1,imax
do j=1,jmax
IF (IBMorder.eq.2) THEN
zb_C=zbed(i,j)
kp=MIN(CEILING(zb_C/dz+0.5)+1,k1) !location velocity which must be adjusted 2nd order IBM -->(0-1)*dz distance from bed
distance_to_bed=(REAL(kp)-0.5)*dz-zb_C
IF (distance_to_bed<0.1*dz) THEN
kp = MIN(k1,kp+1)
distance_to_bed=(REAL(kp)-0.5)*dz-zb_C
ENDIF
ELSE
kp = MIN(k1,kbedt(i,j)+1)
distance_to_bed = 0.5*dz
ENDIF
uu=0.5*(Uvel(i,j,kp)+Uvel(i-1,j,kp))
vv=0.5*(Vvel(i,j,kp)+Vvel(i,j-1,kp))
absU=sqrt(uu*uu+vv*vv)
IF (slip_bot.ge.3) THEN
tauu=0.5*(tau_fl_Uold(i,j)+tau_fl_Uold(i-1,j))
tauv=0.5*(tau_fl_Vold(i,j)+tau_fl_Vold(i,j-1))
ust = ((tauu/rr(i,j,kp))**2+(tauv/rr(i,j,kp))**2)**0.25
ust = MIN(0.5*absU,ust) !ust maximal 0.5*absU
ELSE
ust=0.1*absU
if (kn>0.) then !walls with rougness (log-law used which can be hydr smooth or hydr rough):
do tel=1,10 ! 10 iter is more than enough
z0=kn/30.+0.11*nu_mol/MAX(ust,1.e-9)
ust=absU/MAX(1./kappa*log(distance_to_bed/z0),2.) !ust maximal 0.5*absU
enddo
else
do tel=1,10 ! 10 iter is more than enough
yplus=MAX(distance_to_bed*ust/nu_mol,1e-12)
ust=absU/MAX((2.5*log(yplus)+5.5),2.) !ust maximal 0.5*absU
enddo
if (yplus<30.) then
do tel=1,10 ! 10 iter is more than enough
yplus=MAX(distance_to_bed*ust/nu_mol,1e-12)
ust=absU/MAX((5.*log(yplus)-3.05),2.) !ust maximal 0.5*absU
enddo
endif
if (yplus<5.) then !viscous sublayer uplus=yplus
ust=sqrt(absU*nu_mol/(distance_to_bed))
endif
endif
ENDIF
IF (nu_minimum_wall.eq.1) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = MAX(ekm(i,j,kp),nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2)
!minimum eddy viscosity is Prandtl mixing length theory including Van Driest damping (factor A=19 and power 2 is found in Van Balen 2010 dissertation p15 and Catalano et al. 2010 circular cylinder flow)
ELSEIF (nu_minimum_wall.eq.2) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = MAX(ekm(i,j,kp),nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2)
distance_to_bed=distance_to_bed+dz
kp=MIN(kp+1,k1)
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = MAX(ekm(i,j,kp),nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2)
ELSEIF (nu_minimum_wall.eq.3) THEN
kp=MIN(kp+1,k1)
uu=0.5*(Uvel(i,j,kp)+Uvel(i-1,j,kp))
vv=0.5*(Vvel(i,j,kp)+Vvel(i,j-1,kp))
absU2=sqrt(uu*uu+vv*vv)
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
IF (absU2>1.1*absU) THEN
nu_t = ust*ust/((absU2-absU)/dz)
factor = nu_t/(0.5*(ekm(i,j,kp)/rr(i,j,kp)+ekm(i,j,kp-1)/rr(i,j,kp-1)))
factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ekm(i,j,kp-1)=factor*ekm(i,j,kp-1)
ELSE
kp=kp-1
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = MAX(ekm(i,j,kp),nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2)
distance_to_bed=distance_to_bed+dz
kp=MIN(kp+1,k1)
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = MAX(ekm(i,j,kp),nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2)
ENDIF
ELSEIF (nu_minimum_wall.eq.4) THEN
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
nu_t = ust*ust/(MAX(absU,1.e-9)/distance_to_bed)
factor = nu_t/(ekm(i,j,kp)/rr(i,j,kp))
factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ELSEIF (nu_minimum_wall.eq.5) THEN
! OpenFOAM manner: tau = rho*ust*ust and ust=absU/Uplus and tau=nu_t*dUdz combined:
nu_t = ust*distance_to_bed / (MAX(absU,1.e-9)/MAX(ust,1.e-9))
factor = nu_t/(ekm(i,j,kp)/rr(i,j,kp))
factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ELSEIF (nu_minimum_wall.eq.11) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2
!minimum eddy viscosity is Prandtl mixing length theory including Van Driest damping (factor A=19 and power 2 is found in Van Balen 2010 dissertation p15 and Catalano et al. 2010 circular cylinder flow)
ELSEIF (nu_minimum_wall.eq.12) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2
distance_to_bed=distance_to_bed+dz
kp=MIN(kp+1,k1)
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2
ELSEIF (nu_minimum_wall.eq.13) THEN
kp=MIN(kp+1,k1)
uu=0.5*(Uvel(i,j,kp)+Uvel(i-1,j,kp))
vv=0.5*(Vvel(i,j,kp)+Vvel(i,j-1,kp))
absU2=sqrt(uu*uu+vv*vv)
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
IF (absU2>1.1*absU) THEN
nu_t = ust*ust/((absU2-absU)/dz)
factor = nu_t/(0.5*(ekm(i,j,kp)/rr(i,j,kp)+ekm(i,j,kp-1)/rr(i,j,kp-1)))
!factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ekm(i,j,kp-1)=factor*ekm(i,j,kp-1)
ELSE
kp=kp-1
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2
distance_to_bed=distance_to_bed+dz
kp=MIN(kp+1,k1)
yplus = distance_to_bed*ust/nu_mol
ekm(i,j,kp) = nu_mol*rr(i,j,kp)*kappa*yplus*(1-exp(-yplus/19.))**2
ENDIF
ELSEIF (nu_minimum_wall.eq.14) THEN
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
nu_t = ust*ust/(MAX(absU,1.e-9)/distance_to_bed)
factor = nu_t/(ekm(i,j,kp)/rr(i,j,kp))
!factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ELSEIF (nu_minimum_wall.eq.15) THEN
! OpenFOAM manner: tau = rho*ust*ust and ust=absU/Uplus and tau=nu_t*dUdz combined:
nu_t = ust*distance_to_bed / (MAX(absU,1.e-9)/MAX(ust,1.e-9))
factor = nu_t/(ekm(i,j,kp)/rr(i,j,kp))
!factor = MAX(factor,1.)
ekm(i,j,kp)=factor*ekm(i,j,kp)
ENDIF
enddo
enddo
endif
IF (monopile.eq.1.and.nu_minimum_wall.ge.1) then ! partial slip tau based on log-wall
do k=1,kmax
do j=1,jmax
distance_to_bed = (Rp(1)-Ru(0))
ww=0.5*(Wvel(1,j,k)+Wvel(1,j,k-1))
vv=0.5*(Vvel(1,j,k)+Vvel(1,j-1,k))
absU=sqrt(ww*ww+vv*vv)
ust=0.1*absU
if (kn_mp>0.) then !walls with rougness (log-law used which can be hydr smooth or hydr rough):
do tel=1,10 ! 10 iter is more than enough
z0=kn_mp/30.+0.11*nu_mol/MAX(ust,1.e-9)
ust=absU/MAX(1./kappa*log(distance_to_bed/z0),2.) !ust maximal 0.5*absU
enddo
else
do tel=1,10 ! 10 iter is more than enough
yplus=MAX(distance_to_bed*ust/nu_mol,1e-12)
ust=absU/MAX((2.5*log(yplus)+5.5),2.) !ust maximal 0.5*absU
enddo
if (yplus<30.) then
do tel=1,10 ! 10 iter is more than enough
yplus=MAX(distance_to_bed*ust/nu_mol,1e-12)
ust=absU/MAX((5.*log(yplus)-3.05),2.) !ust maximal 0.5*absU
enddo
endif
if (yplus<5.) then !viscous sublayer uplus=yplus
ust=sqrt(absU*nu_mol/(distance_to_bed))
endif
endif
IF (nu_minimum_wall.eq.1) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = MAX(ekm(1,j,k),nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2)
!minimum eddy viscosity is Prandtl mixing length theory including Van Driest damping (factor A=19 and power 2 is found in Van Balen 2010 dissertation p15 and Catalano et al. 2010 circular cylinder flow)
ELSEIF (nu_minimum_wall.eq.2) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = MAX(ekm(1,j,k),nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2)
distance_to_bed=Rp(2)-Ru(0)
yplus = distance_to_bed*ust/nu_mol
ekm(2,j,k) = MAX(ekm(2,j,k),nu_mol*rr(2,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2)
ELSEIF (nu_minimum_wall.eq.3) THEN
kp=MIN(kp+1,k1)
ww=0.5*(Wvel(2,j,k)+Wvel(2,j,k-1))
vv=0.5*(Vvel(2,j,k)+Vvel(2,j-1,k))
absU2=sqrt(ww*ww+vv*vv)
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
IF (absU2>1.1*absU) THEN
nu_t = ust*ust/((absU2-absU)/(Rp(2)-Rp(1)))
factor = nu_t/(0.5*(ekm(1,j,k)/rr(1,j,k)+ekm(2,j,k)/rr(2,j,k)))
factor = MAX(factor,1.)
ekm(1,j,k)=factor*ekm(1,j,k)
ekm(2,j,k)=factor*ekm(2,j,k)
ELSE
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = MAX(ekm(1,j,k),nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2)
distance_to_bed=Rp(2)-Ru(0)
yplus = distance_to_bed*ust/nu_mol
ekm(2,j,k) = MAX(ekm(2,j,k),nu_mol*rr(2,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2)
ENDIF
ELSEIF (nu_minimum_wall.eq.4) THEN
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
nu_t = ust*ust/(MAX(absU,1.e-9)/distance_to_bed)
factor = nu_t/(ekm(1,j,k)/rr(1,j,k))
factor = MAX(factor,1.)
ekm(1,j,k)=factor*ekm(1,j,k)
ELSEIF (nu_minimum_wall.eq.5) THEN
! OpenFOAM manner: tau = rho*ust*ust and ust=absU/Uplus and tau=nu_t*dUdz combined:
nu_t = ust*distance_to_bed / (MAX(absU,1.e-9)/MAX(ust,1.e-9))
factor = nu_t/(ekm(1,j,k)/rr(1,j,k))
factor = MAX(factor,1.)
ekm(1,j,k)=factor*ekm(1,j,k)
ELSEIF (nu_minimum_wall.eq.11) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2
!minimum eddy viscosity is Prandtl mixing length theory including Van Driest damping (factor A=19 and power 2 is found in Van Balen 2010 dissertation p15 and Catalano et al. 2010 circular cylinder flow)
ELSEIF (nu_minimum_wall.eq.12) THEN
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2
distance_to_bed=Rp(2)-Ru(0)
yplus = distance_to_bed*ust/nu_mol
ekm(2,j,k) = nu_mol*rr(2,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2
ELSEIF (nu_minimum_wall.eq.13) THEN
kp=MIN(kp+1,k1)
ww=0.5*(Wvel(2,j,k)+Wvel(2,j,k-1))
vv=0.5*(Vvel(2,j,k)+Vvel(2,j-1,k))
absU2=sqrt(ww*ww+vv*vv)
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
IF (absU2>1.1*absU) THEN
nu_t = ust*ust/((absU2-absU)/(Rp(2)-Rp(1)))
factor = nu_t/(0.5*(ekm(1,j,k)/rr(1,j,k)+ekm(2,j,k)/rr(2,j,k)))
!factor = MAX(factor,1.)
ekm(1,j,k)=factor*ekm(1,j,k)
ekm(2,j,k)=factor*ekm(2,j,k)
ELSE
yplus = distance_to_bed*ust/nu_mol
ekm(1,j,k) = nu_mol*rr(1,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2
distance_to_bed=Rp(2)-Ru(0)
yplus = distance_to_bed*ust/nu_mol
ekm(2,j,k) = nu_mol*rr(2,j,k)*kappa*yplus*(1-exp(-yplus/19.))**2
ENDIF
ELSEIF (nu_minimum_wall.eq.14) THEN
! ust*ust = nu_t*dUdz --> nu_t = ust*ust/dUdz
nu_t = ust*ust/(MAX(absU,1.e-9)/distance_to_bed)