module flow_timestep_module implicit none private public flow save contains subroutine flow(s,par) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Copyright (C) 2007 UNESCO-IHE, WL|Delft Hydraulics and Delft University ! ! Dano Roelvink, Ap van Dongeren, Ad Reniers, Jamie Lescinski, ! ! Jaap van Thiel de Vries, Robert McCall ! ! ! ! d.roelvink@unesco-ihe.org ! ! UNESCO-IHE Institute for Water Education ! ! P.O. Box 3015 ! ! 2601 DA Delft ! ! The Netherlands ! ! ! ! This library is free software; you can redistribute it and/or ! ! modify it under the terms of the GNU Lesser General Public ! ! License as published by the Free Software Foundation; either ! ! version 2.1 of the License, or (at your option) any later version. ! ! ! ! This library 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 ! ! Lesser General Public License for more details. ! ! ! ! You should have received a copy of the GNU Lesser General Public ! ! License along with this library; if not, write to the Free Software ! ! Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 ! ! USA ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! use params, only: parameters use spaceparamsdef, only: manage_lowx, manage_highx, manage_lowy, manage_highy, spacepars use xmpi_module, only: xmpi_shift_ee use boundaryconditions, only: flow_lat_bc, discharge_boundary_h, discharge_boundary_v use flow_secondorder_module, only: flow_secondorder_huhv, flow_secondorder_advuv use nonh_module, only: nonh_cor use bedroughness_module, only: bedroughness_init, bedroughness_update use vsm_u_xb_module, only: vsm_u_XB use spaceparamsdef, only: imin_uu, imax_uu, imin_vv, imax_vv , & & imin_zs, imax_zs, jmin_uu, jmax_uu , & & jmin_vv, jmax_vv, jmin_zs, jmax_zs use paramsconst IMPLICIT NONE type(spacepars),target :: s type(parameters) :: par integer :: i integer :: j,j1,jp1,jm1 real*8,dimension(:,:),allocatable,save :: vv_old !Velocity at previous timestep real*8,dimension(:,:),allocatable,save :: uu_old !Velocity at previous timestep real*8,dimension(:,:),allocatable,save :: zs_old real*8,dimension(:,:),allocatable,save :: vsu,usu,vsv,usv,veu,uev real*8,dimension(:,:),allocatable,save :: dudx,dvdy real*8,dimension(:,:),allocatable,save :: us,vs real*8 :: nuh1,nuh2 real*8 :: dudx1,dudx2,dudy1,dudy2 real*8 :: dvdy1,dvdy2,dvdx1,dvdx2 !Jaap real*8 :: dalfa !difference in grid angles real*8 :: uin,vin !s%u resp s%v-velocity corrected for grid angle change real*8 :: qin !specific discharge entering cell real*8,save :: fc real*8,dimension(:,:),allocatable,save :: sinthm,costhm real*8 :: fcvisc=0.1d0,facdel=5.d0,facdf=1.d0,ks real*8 :: tauw,tauwx,tauwy integer :: jmax,swglm=0 if (.not. allocated(vsu) ) then allocate ( vsu(s%nx+1,s%ny+1)) allocate ( usu(s%nx+1,s%ny+1)) allocate ( vsv(s%nx+1,s%ny+1)) allocate ( usv(s%nx+1,s%ny+1)) allocate ( veu(s%nx+1,s%ny+1)) allocate ( uev(s%nx+1,s%ny+1)) allocate ( dudx(s%nx+1,s%ny+1)) allocate ( dvdy(s%nx+1,s%ny+1)) allocate ( us(s%nx+1,s%ny+1)) allocate ( vs(s%nx+1,s%ny+1)) allocate (sinthm(s%nx+1,s%ny+1)) allocate (costhm(s%nx+1,s%ny+1)) ! if (par%secorder == 1 .or. par%wavemodel==WAVEMODEL_NONH) then allocate(vv_old(s%nx+1,s%ny+1)); vv_old = s%vv allocate(uu_old(s%nx+1,s%ny+1)); uu_old = s%uu allocate(zs_old(s%nx+1,s%ny+1)); zs_old = s%zs endif s%vu = 0.d0 vsu = 0.d0 usu = 0.d0 vsv = 0.d0 usv = 0.d0 s%uv = 0.d0 veu = 0.d0 uev = 0.d0 s%ueu = 0.d0 s%vev = 0.d0 dudx = 0.d0 s%ududx = 0.d0 dvdy = 0.d0 s%vdvdy = 0.d0 s%udvdx = 0.d0 s%vdudy = 0.d0 s%viscu = 0.d0 s%viscv = 0.d0 us = 0.d0 vs = 0.d0 s%u = 0.d0 s%v = 0.d0 s%ue = 0.d0 s%ve = 0.d0 fc = 2.d0*par%wearth*sin(par%lat) call bedroughness_init(s,par) ! note, this is not yet designed for initialisation ! on sglobal, so don't call from initialize.F90 endif ! Super fast 1D if (s%ny==0) then j1 = 1 else j1 = 2 endif ! Add vertical discharges call discharge_boundary_v(s,par) ! ! s%zs=s%zs*s%wetz ! Water level slopes do j=1,s%ny+1 do i=2,s%nx s%dzsdx(i,j)=(s%zs(i+1,j)+s%ph(i+1,j)-s%zs(i,j)-s%ph(i,j))/s%dsu(i,j) end do end do ! do j=2,ny do j=1,s%ny ! Dano need to get correct slope on boundary s%y=0 do i=1,s%nx+1 s%dzsdy(i,j)=(s%zs(i,j+1)+s%ph(i,j+1)-s%zs(i,j)-s%ph(i,j))/s%dnv(i,j) end do end do ! ! Compute velocity gradients for viscosity terms. ! Robert: Check whether should be same gradients as advection terms? do j=j1,max(s%ny,1) do i=2,s%nx+1 dudx(i,j) = (s%uu(i,j)-s%uu(i-1,j))/s%dsz(i,j) enddo enddo ! wwvv: added: manage_lowx if (manage_lowx) then dudx(1,:) = 0.d0 ! Robert: by defintion of Neumann boundary endif if (s%ny>2) then do j=2,s%ny+1 do i=1,s%nx+1 dvdy(i,j) = (s%vv(i,j)-s%vv(i,j-1))/s%dnz(i,j) enddo enddo ! wwvv: added: manage_lowy if (manage_lowy) then dvdy(:,1) = 0.d0 ! Robert: by defintion of Neumann boundary endif else dvdy = 0.d0 ! Robert: by definition of 1D model endif ! Update bed roughness coefficient call bedroughness_update(s,par) !cf = cfu : Robert: cf is not used anymore ! ! Advection x-direction ! do j=j1,max(s%ny,1) do i=2,s%nx s%ududx(i,j) = 0.d0 qin = .5d0*(s%qx(i,j)+s%qx(i-1,j)) if (qin>0) then dalfa = s%alfau(i,j)-s%alfau(i-1,j) uin = s%uu(i-1,j)*cos(dalfa) + s%vu(i-1,j)*sin(dalfa) if ((s%uu(i,j)-s%uu(i-1,j))>par%eps_sd) then ! Conservation of energy head s%ududx(i,j) = s%ududx(i,j) + 0.5d0*(s%uu(i-1,j)+s%uu(i,j))*(s%uu(i,j)-uin)*s%dnz(i,j)*s%dsdnui(i,j) else ! Conservation of momentum s%ududx(i,j) = s%ududx(i,j) + qin/s%hum(i,j) *(s%uu(i,j)-uin)*s%dnz(i,j)*s%dsdnui(i,j) endif endif qin = -.5d0*(s%qx(i,j)+s%qx(i+1,j)) if (qin>0) then dalfa = s%alfau(i,j)-s%alfau(i+1,j) uin = s%uu(i+1,j)*cos(dalfa) + s%vu(i+1,j)*sin(dalfa) if ((s%uu(i+1,j)-s%uu(i,j))>par%eps_sd) then ! Conservation of energy head s%ududx(i,j) = s%ududx(i,j) - 0.5d0*(s%uu(i+1,j)+s%uu(i,j))*(s%uu(i,j)-uin)*s%dnz(i+1,j)*s%dsdnui(i,j) else ! Conservation of momentum s%ududx(i,j) = s%ududx(i,j) + qin/s%hum(i,j) *(s%uu(i,j)-uin)*s%dnz(i+1,j)*s%dsdnui(i,j) endif endif end do end do do j=2,s%ny do i=1,s%nx s%vdudy(i,j) = 0.d0 qin = .5d0*(s%qy(i,j-1)+s%qy(i+1,j-1)) if (qin>0) then dalfa = s%alfau(i,j)-s%alfau(i,j-1) uin = s%uu(i,j-1)*cos(dalfa) + s%vu(i,j-1)*sin(dalfa) if ((s%vv(i,j)-s%vv(i,j-1))>par%eps_sd) then ! Conservation of energy head s%vdudy(i,j) = s%vdudy(i,j) + 0.5d0*(s%vv(i,j-1)+s%vv(i+1,j-1))*(s%uu(i,j)-uin)*s%dsc(i,j-1)*s%dsdnui(i,j) else ! Conservation of momentum s%vdudy(i,j) = s%vdudy(i,j) + qin/s%hum(i,j) *(s%uu(i,j)-uin)*s%dsc(i,j-1)*s%dsdnui(i,j) endif endif qin = -.5d0*(s%qy(i,j)+s%qy(i+1,j)) if (qin>0) then dalfa = s%alfau(i,j)-s%alfau(i,j+1) uin = s%uu(i,j+1)*cos(dalfa) + s%vu(i,j+1)*sin(dalfa) if ((s%vv(i,j+1)-s%vv(i,j))>par%eps_sd) then ! Conservation of energy head s%vdudy(i,j) = s%vdudy(i,j) - 0.5d0*(s%vv(i,j)+s%vv(i+1,j))*(s%uu(i,j)-uin)*s%dsc(i,j)*s%dsdnui(i,j) else ! Conservation of momentum s%vdudy(i,j) = s%vdudy(i,j) + qin/s%hum(i,j) *(s%uu(i,j)-uin)*s%dsc(i,j)*s%dsdnui(i,j) endif endif end do end do ! ! Advection y-direction if (manage_highy .and. s%ny>0) then ! no such condition needed for _lowy, because s%vdvdy(:,1) not needed in mpi subdomain jmax = s%ny-1 elseif (manage_highy .and. s%ny==0) then jmax = 1 else jmax = s%ny endif s%vdvdy=0.d0 ! calculate true vdvdy up to ny in central domains and up to ny-1 on manage_highy do j=2,jmax do i=2,s%nx qin = .5d0*(s%qy(i,j)+s%qy(i,j-1)) if (qin>0) then dalfa = s%alfav(i,j)-s%alfav(i,j-1) vin = s%vv(i,j-1)*cos(dalfa) - s%uv(i,j-1)*sin(dalfa) if ((s%vv(i,j)-s%vv(i,j-1))>par%eps_sd) then ! Conservation of energy head s%vdvdy(i,j) = s%vdvdy(i,j) + 0.5d0*(s%vv(i,j-1)+s%vv(i,j))*(s%vv(i,j)-vin)*s%dsz(i,j)*s%dsdnvi(i,j) else ! Conservation of momentum s%vdvdy(i,j) = s%vdvdy(i,j) + qin/s%hvm(i,j) *(s%vv(i,j)-vin)*s%dsz(i,j)*s%dsdnvi(i,j) endif endif qin = -.5d0*(s%qy(i,j)+s%qy(i,j+1)) if (qin>0) then dalfa = s%alfav(i,j)-s%alfav(i,j+1) vin = s%vv(i,j+1)*cos(dalfa) - s%uv(i,j+1)*sin(dalfa) if ((s%vv(i,j+1)-s%vv(i,j))>par%eps_sd) then ! Conservation of energy head s%vdvdy(i,j) = s%vdvdy(i,j) - 0.5d0*(s%vv(i,j+1)+s%vv(i,j))*(s%vv(i,j)-vin)*s%dsz(i,j+1)*s%dsdnvi(i,j) else ! Conservation of momentum s%vdvdy(i,j) = s%vdvdy(i,j) + qin/s%hvm(i,j) *(s%vv(i,j)-vin)*s%dsz(i,j+1)*s%dsdnvi(i,j) endif endif enddo enddo if (s%ny>0) then ! Global boundary conditions for vdvdy(:,1) and vdvdy(:,ny), global vdvdy(:,ny+1) not needed anywhere if (manage_lowy) then ! (vv(:,1)-vv(:,0))/dy == 0 so only second part of the vdvdy equation: do i=2,s%nx qin = -.5d0*(s%qy(i,1)+s%qy(i,2)) if (qin>0) then dalfa = s%alfav(i,1)-s%alfav(i,2) vin = s%vv(i,2)*cos(dalfa) - s%uv(i,2)*sin(dalfa) s%vdvdy(i,1) = s%vdvdy(i,1) + qin*(s%vv(i,1)-vin)*s%dsz(i,2)/s%hvm(i,1)*s%dsdnvi(i,1) endif enddo endif if (manage_highy) then ! (vv(:,ny+1)-vv(:,ny))/dy == 0 so only first part of the vdvdy equation: do i=2,s%nx qin = .5d0*(s%qy(i,s%ny)+s%qy(i,s%ny-1)) if (qin>0) then dalfa = s%alfav(i,s%ny)-s%alfav(i,s%ny-1) vin = s%vv(i,s%ny-1)*cos(dalfa) - s%uv(i,s%ny-1)*sin(dalfa) s%vdvdy(i,s%ny) = s%vdvdy(i,s%ny) + qin*(s%vv(i,s%ny)-vin)*s%dsz(i,s%ny)/s%hvm(i,s%ny)*s%dsdnvi(i,s%ny) endif enddo endif endif s%udvdx=0.d0 if (s%ny>0) then ! Robert: udvdx not usually needed at j = 1 do j=1,s%ny !1,s%ny instead of 2,s%ny do i=2,s%nx qin = .5d0*(s%qx(i-1,j)+s%qx(i-1,j+1)) if (qin>0) then dalfa = s%alfav(i,j)-s%alfav(i-1,j) vin = s%vv(i-1,j)*cos(dalfa) - s%uv(i-1,j)*sin(dalfa) if ((s%uu(i,j)-s%uu(i-1,j))>par%eps_sd) then ! Conservation of energy head s%udvdx(i,j) = s%udvdx(i,j) + 0.5d0*(s%uu(i-1,j)+s%uu(i-1,j+1))*(s%vv(i,j)-vin)*s%dnc(i-1,j)*s%dsdnvi(i,j) else ! Conservation of momentum s%udvdx(i,j) = s%udvdx(i,j) + qin/s%hvm(i,j) *(s%vv(i,j)-vin)*s%dnc(i-1,j)*s%dsdnvi(i,j) endif endif qin = -.5d0*(s%qx(i,j)+s%qx(i,j+1)) if (qin>0) then dalfa = s%alfav(i,j)-s%alfav(i+1,j) vin = s%vv(i+1,j)*cos(dalfa) - s%uv(i+1,j)*sin(dalfa) if ((s%uu(i+1,j)-s%uu(i,j))>par%eps_sd) then ! Conservation of energy head s%udvdx(i,j) = s%udvdx(i,j) - 0.5d0*(s%uu(i,j)+s%uu(i,j+1))*(s%vv(i,j)-vin)*s%dnc(i,j)*s%dsdnvi(i,j) else ! Conservation of momentum s%udvdx(i,j) = s%udvdx(i,j) + qin/s%hvm(i,j) *(s%vv(i,j)-vin)*s%dnc(i,j)*s%dsdnvi(i,j) endif endif end do end do else do i=2,s%nx qin = s%qx(i-1,1) if (qin>0) then dalfa = s%alfav(i,1)-s%alfav(i-1,1) vin = s%vv(i-1,1)*cos(dalfa) - s%uv(i-1,1)*sin(dalfa) s%udvdx(i,1) = s%udvdx(i,1) + qin*(s%vv(i,1)-vin)*s%dnc(i-1,1)/s%hvm(i,1)*s%dsdnvi(i,1) endif qin = -s%qx(i,1) if (qin>0) then dalfa = s%alfav(i,1)-s%alfav(i+1,1) vin = s%vv(i+1,1)*cos(dalfa) - s%uv(i+1,1)*sin(dalfa) s%udvdx(i,1) = s%udvdx(i,1) + qin*(s%vv(i,1)-vin)*s%dnc(i,1)/s%hvm(i,1)*s%dsdnvi(i,1) endif enddo endif ! ! ! There is a possibility to turn viscosity off ! if (par%viscosity==0) then ! Dano: put it here so it actualy saves a lot of computation time s%nuh = 0.d0 s%viscu = 0.d0 else ! Jaap: Slightly changes approach; 1) background viscosity is user defined or obtained from Smagorinsky, 2) nuh = max(nuh,roller induced viscosity) if (par%smag == 1) then !Use smagorinsky subgrid model call visc_smagorinsky(s,par) else s%nuh = par%nuh endif ! ! Add viscosity for wave breaking effects if (par%swave == 1) then do j=j1,max(s%ny,1) do i=2,s%nx s%nuh(i,j) = max(s%nuh(i,j),par%nuhfac*s%hh(i,j)*(s%DR(i,j)/par%rho)**(1.0d0/3.0d0)) ! Ad: change to max end do end do elseif (par%swave==0 .and. par%wavemodel==WAVEMODEL_NONH) then select case (par%nhbreaker) case (1) where (s%breaking/=0) s%nuh = par%breakviscfac*s%nuh endwhere case (2) where (s%breaking==1) s%nuh = s%nuh + (par%nuh*par%breakvisclen*s%hh)**2*sqrt(dudx**2+dvdy**2) endwhere case (3) ! Ad en Arnold: Battjes 1975 formulation to smoothen front of lf wave bore in the swash ! compute (long) wave turbulence due to breaking !nuh = max(par%nuh, par%avis*hloc*sqrt(kturb)) case default ! do nothing to increase viscosity end select endif ! do j=jmin_uu,jmax_uu do i=imin_uu,imax_uu dudx1 = s%nuh(i+1,j)*s%hh(i+1,j)*(s%uu(i+1,j)-s%uu(i,j))/s%dsz(i+1,j) dudx2 = s%nuh(i,j) *s%hh(i ,j)*(s%uu(i,j)-s%uu(i-1,j))/s%dsz(i,j) s%viscu(i,j) = (1.0d0/s%hum(i,j))*( 2*(dudx1-dudx2)/(s%dsz(i,j)+s%dsz(i+1,j)) ) end do end do if (par%smag == 1) then ! ! For non constant eddy viscosity the stress terms read: ! ! d d d d d ! -- [ 2* mu -- (U) ] + --[ mu --(U) +mu --(V) ] ! dx dx dy dy dx ! ! d d ! Only when -- [mu] = --[mu] = 0 we have (for incompressible flow) ! dx dy ! ! 2 2 ! d d ! mu --2 [U] + mu --2 [U] ! dx dy ! s%viscu = 2.0d0*s%viscu endif do j=jmin_uu,jmax_uu jp1=min(j+1,1) jm1=max(j-1,1) do i=imin_uu,imax_uu !Nuh is defined at eta points, interpolate from four surrounding points nuh1 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jp1)+s%nuh(i,jp1)) nuh2 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jm1)+s%nuh(i,jm1)) dudy1 = nuh1 *.5d0*(s%hvm(i,j )+s%hvm(i+1,j ))*(s%uu(i,jp1)-s%uu(i,j))/s%dnc(i,j) dudy2 = nuh2 *.5d0*(s%hvm(i,jm1)+s%hvm(i+1,jm1))*(s%uu(i,j)-s%uu(i,jm1))/s%dnc(i,jm1) s%viscu(i,j) = s%viscu(i,j) + (1.0d0/s%hum(i,j))* & ( 2.0d0*(dudy1-dudy2)/(s%dnc(i,j)+s%dnc(i,jm1)) )*s%wetu(i,jp1)*s%wetu(i,jm1) end do end do if (par%smag == 1) then do j=jmin_uu,jmax_uu jp1=min(j+1,1) jm1=max(j-1,1) do i=imin_uu,imax_uu !Nuh is defined at eta points, interpolate from four surrounding points nuh1 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jp1)+s%nuh(i,jp1)) nuh2 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jm1)+s%nuh(i,jm1)) dvdx1 = nuh1*.5d0*(s%hvm(i,j )+s%hvm(i+1,j ))*(s%vv(i+1,j )-s%vv(i,j ))/s%dsc(i,j) dvdx2 = nuh2*.5d0*(s%hvm(i,jm1)+s%hvm(i+1,jm1))*(s%vv(i+1,jm1)-s%vv(i,jm1))/s%dsc(i,jm1) s%viscu(i,j) = s%viscu(i,j) + (1.d0/s%hum(i,j))*(dvdx1-dvdx2)/s%dnz(i,j)*real(s%wetv(i+1,j) & * s%wetv(i,j)*s%wetv(i+1,jm1)*s%wetv(i,jm1),8) enddo enddo endif !smag ==1 and s%ny>0 ! ! Viscosity y-direction ! s%viscv =0.d0 do j=jmin_vv,jmax_vv jp1=min(j+1,1) jm1=max(j-1,1) do i=imin_vv,imax_vv dvdy1 = s%nuh(i,jp1)*s%hh(i,jp1)*(s%vv(i,jp1)-s%vv(i,j))/s%dnz(i,jp1) dvdy2 = s%nuh(i,j) *s%hh(i,j )*(s%vv(i,j)-s%vv(i,jm1))/s%dnz(i,j) s%viscv(i,j) = (1.0d0/s%hvm(i,j))* 2*(dvdy1-dvdy2)/(s%dnz(i,j)+s%dnz(i,jp1))*s%wetv(i,jp1)*s%wetv(i,jm1) end do end do ! Robert: global boundary at (:,1) edge if (s%ny>0) then if (manage_lowy) then s%viscv(:,1) = s%viscv(:,2) endif if (manage_highy) then s%viscv(:,s%ny) = s%viscv(:,s%ny-1) endif endif ! ! Viscosity if (par%smag == 1) then s%viscv = 2.0d0*s%viscv endif ! s%nuh = par%nuhv*s%nuh !Robert en Ap: increase s%nuh interaction in d2v/dx2 do j=jmin_vv,jmax_vv jp1=min(j+1,1) jm1=max(j-1,1) do i=imin_vv,imax_vv !Nuh is defined at eta points, interpolate from four surrounding points nuh1 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jp1)+s%nuh(i,jp1)) nuh2 = .25d0*(s%nuh(i,j)+s%nuh(i-1,j)+s%nuh(i-1,jp1)+s%nuh(i,jp1)) dvdx1 = nuh1*.5d0*(s%hum(i ,j)+s%hum(i ,jp1))*(s%vv(i+1,j)-s%vv(i,j))/s%dsc(i,j) dvdx2 = nuh2*.5d0*(s%hum(i-1,j)+s%hum(i-1,jp1))*(s%vv(i,j)-s%vv(i-1,j))/s%dsc(i-1,j) s%viscv(i,j) = s%viscv(i,j) + (1.0d0/s%hvm(i,j))*( 2*(dvdx1-dvdx2)/(s%dsc(i-1,j)+s%dsc(i,j)) ) & *s%wetv(i+1,j)*s%wetv(i-1,j) end do end do ! if (par%smag == 1) then do j=jmin_vv,jmax_vv jp1=min(j+1,1) jm1=max(j-1,1) do i=imin_vv,imax_vv !Nuh is defined at eta points, interpolate from four surrounding points nuh1 = .25d0*(s%nuh(i,j)+s%nuh(i+1,j)+s%nuh(i+1,jp1)+s%nuh(i,jp1)) nuh2 = .25d0*(s%nuh(i,j)+s%nuh(i-1,j)+s%nuh(i-1,jp1)+s%nuh(i,jp1)) dudy1 = nuh1 *.5d0*(s%hum(i ,j)+s%hum(i ,jp1))*(s%uu(i,jp1 )-s%uu(i,j ))/s%dnc(i,j) dudy2 = nuh2 *.5d0*(s%hum(i-1,j)+s%hum(i-1,jp1))*(s%uu(i-1,jp1)-s%uu(i-1,j))/s%dnc(i-1,j) s%viscv(i,j) = s%viscv(i,j) + (1.d0/s%hvm(i,j))*(dudy1-dudy2)/s%dsz(i,j) & * real(s%wetu(i,jp1)*s%wetu(i,j)*s%wetu(i-1,jp1)*s%wetv(i-1,j),8) enddo enddo endif endif !par%viscosity==0 ! ! Bed friction term x ! where (s%wetu==1) s%taubx=s%cfu*par%rho*s%ueu*sqrt((1.16d0*s%urms)**2+s%vmageu**2) !Ruessink et al, 2001 s%taubx = s%taubx + s%taubx_add ! Account for infiltration etc. effects elsewhere s%taubx = 0.d0 endwhere ! ! ! limit bed friction term to accelerate less than realistic value where (abs(s%taubx)>100*par%g*par%rho*s%hu) s%taubx = sign(1.d0,s%taubx)*100*par%g*par%rho*s%hu endwhere ! ! Bed friction term y ! where (s%wetv==1) s%tauby=s%cfv*par%rho*s%vev*sqrt((1.16d0*s%urms)**2+s%vmagev**2) !Ruessink et al, 2001 s%tauby = s%tauby + s%tauby_add elsewhere s%tauby = 0.d0 endwhere where (abs(s%tauby)>100*par%g*par%rho*s%hv) s%tauby = sign(1.d0,s%tauby)*100*par%g*par%rho*s%hv endwhere ! ! Explicit Euler step momentum u-direction ! do j=jmin_uu,jmax_uu do i=imin_uu,imax_uu if(s%wetu(i,j)==1) then s%uu(i,j)=s%uu(i,j)-par%dt*(s%ududx(i,j)+s%vdudy(i,j)-s%viscu(i,j) & !Ap,Robert,Jaap + par%g*s%dzsdx(i,j) & + s%taubx(i,j)/(par%rho*s%hu(i,j)) & ! Dano: changed s%hum to s%hu NOT s%cf volume approach + s%Fvegu(i,j)/(par%rho*s%hu(i,j)) & - par%lwave*s%Fx(i,j)/(par%rho*max(s%hum(i,j),par%hmin)) & - fc*s%vu(i,j) & - par%rhoa*par%Cd*s%windsu(i,j)*sqrt(s%windsu(i,j)**2+s%windnv(i,j)**2)/(par%rho*s%hum(i,j))) ! Kees: wind correction else s%uu(i,j)=0.0d0 end if end do end do ! Lateral boundary conditions for uu if (s%ny>0) then if (manage_lowy) then !Dano/Robert only on outer boundary s%uu(1:s%nx+1,1)=s%uu(1:s%nx+1,2) ! RJ: can also be done after continuity but more appropriate here endif ! Lateral boundary at y=ny*dy if (manage_highy) then !Dano/Robert only at outer boundary s%uu(1:s%nx+1,s%ny+1)=s%uu(1:s%nx+1,s%ny) ! RJ: can also be done after continuity but more appropriate here endif endif ! ! Explicit Euler step momentum v-direction ! do j=jmin_vv,jmax_vv do i=imin_vv,imax_vv if(s%wetv(i,j)==1) then ! Robert: ensure taubx always has the same sign as uu (always decelerates) ! Dano: I don't agree s%vv(i,j)=s%vv(i,j)-par%dt*(s%udvdx(i,j)+s%vdvdy(i,j)-s%viscv(i,j)& !Ap,Robert,Jaap + par%g*s%dzsdy(i,j)& + s%tauby(i,j)/(par%rho*s%hv(i,j)) & ! Dano: s%hv instead of s%hvm, NOT cf volume approach + s%Fvegv(i,j)/(par%rho*s%hv(i,j)) & - par%lwave*s%Fy(i,j)/(par%rho*max(s%hvm(i,j),par%hmin)) & + fc*s%uv(i,j) & - par%rhoa*par%Cd*s%windnv(i,j)*sqrt(s%windsu(i,j)**2+s%windnv(i,j)**2)/(par%rho*s%hvm(i,j))) ! Kees: wind correction else s%vv(i,j)=0.0d0 end if end do end do ! Robert: Boundary conditions along the global boundaries ! Function flow_lat_bc located in boundaryconditions.F90 ! function call takes care of 1D vs 2D models and boundary condition types if (s%ny>0) then if (manage_lowy) then s%vv(:,1)=flow_lat_bc(s,par,par%right,1,2,s%udvdx(:,1),s%vdvdy(:,1),s%viscv(:,1)) endif if (manage_highy) then s%vv(:,s%ny)=flow_lat_bc(s,par,par%left,s%ny,s%ny-1,s%udvdx(:,s%ny),s%vdvdy(:,s%ny),s%viscv(:,s%ny)) endif endif #ifdef USEMPI call xmpi_shift_ee(s%uu) call xmpi_shift_ee(s%vv) #endif if (par%wavemodel==WAVEMODEL_NONH) then !Do explicit predictor step with pressure call nonh_cor(s,par,0,uu_old,vv_old) #ifdef USEMPI call xmpi_shift_ee(s%uu) call xmpi_shift_ee(s%vv) #endif end if if (par%secorder==1) then !Call second order correction to the advection call flow_secondorder_advUV(s,par,uu_old,vv_old) #ifdef USEMPI call xmpi_shift_ee(s%uu) call xmpi_shift_ee(s%vv) #endif end if if (par%wavemodel==WAVEMODEL_NONH) then ! do non-hydrostatic pressure compensation to solve short waves call nonh_cor(s,par,1,uu_old,vv_old) ! note: MPI shift in subroutine nonh_cor end if ! update hu en hv for continuity do j=1,s%ny+1 do i=1,s%nx+1 ! Water depth in u-points do continuity equation: upwind if (s%uu(i,j)>par%umin) then if (par%oldhu == 1) then s%hu(i,j)=s%hh(i,j) else s%hu(i,j)=s%zs(i,j)-max(s%zb(i,j),s%zb(min(s%nx,i)+1,j)) endif elseif (s%uu(i,j)<-par%umin) then if (par%oldhu == 1) then s%hu(i,j)=s%hh(min(s%nx,i)+1,j) else s%hu(i,j)=s%zs(min(s%nx,i)+1,j)-max(s%zb(i,j),s%zb(min(s%nx,i)+1,j)) endif else s%hu(i,j)=max(max(s%zs(i,j),s%zs(min(s%nx,i)+1,j))-max(s%zb(i,j),s%zb(min(s%nx,i)+1,j)),par%eps) end if end do end do s%hu = max(s%hu,0.d0) do j=1,s%ny+1 do i=1,s%nx+1 ! Water depth in v-points do continuity equation: upwind if (s%vv(i,j)>par%umin) then if (par%oldhu == 1) then s%hv(i,j)=s%hh(i,j) else s%hv(i,j)=s%zs(i,j)-max(s%zb(i,j),s%zb(i,min(s%ny,j)+1)) endif elseif (s%vv(i,j)<-par%umin) then if (par%oldhu == 1) then s%hv(i,j)=s%hh(i,min(s%ny,j)+1) else s%hv(i,j)=s%zs(i,min(s%ny,j)+1)-max(s%zb(i,j),s%zb(i,min(s%ny,j)+1)) endif else s%hv(i,j)=max(max(s%zs(i,j),s%zs(i,min(s%ny,j)+1))-max(s%zb(i,j),s%zb(i,min(s%ny,j)+1)),par%eps) end if end do end do s%hv = max(s%hv,0.d0) if (par%secorder == 1) then ! ! Correct the waterdepths in U/V points using second-order limited expressions ! call flow_secondorder_huhv(s,par) ! end if ! Flux in u-point s%qx=s%uu*s%hu ! Flux in v-points ! first column of qy is used later, and it is defined in the loop above ! no communication necessary at this point s%qy=s%vv*s%hv ! ! Add horizontal discharges ! call discharge_boundary_h(s,par) ! ! Update water level using continuity eq. ! if (s%ny>0) then do j=jmin_zs,jmax_zs do i=imin_zs,imax_zs s%dzsdt(i,j) = (-1.d0)*( s%qx(i,j)*s%dnu(i,j)-s%qx(i-1,j)*s%dnu(i-1,j) & + s%qy(i,j)*s%dsv(i,j)-s%qy(i,j-1)*s%dsv(i,j-1) )*s%dsdnzi(i,j) & - s%infil(i,j) end do end do s%zs(imin_zs:imax_zs,jmin_zs:jmax_zs) = s%zs(imin_zs:imax_zs,jmin_zs:jmax_zs)+s%dzsdt(imin_zs:imax_zs,jmin_zs:jmax_zs)*par%dt else j=1 do i=imin_zs,imax_zs s%dzsdt(i,j) = (-1.d0)*( s%qx(i,j)*s%dnu(i,j)-s%qx(i-1,j)*s%dnu(i-1,j) )*s%dsdnzi(i,j) & - s%infil(i,j) end do s%zs(imin_zs:imax_zs,1) = s%zs(imin_zs:imax_zs,1)+s%dzsdt(imin_zs:imax_zs,1)*par%dt endif !s%ny>0 if (par%secorder == 1) then ! ! P.B. Smit: The second order McCormack correction to the cont. eq. introduced ! minor damping. For this reason I removed it (Nov. 2014). ! call flow_secondorder_con(s,par,zs_old) endif ! wwvv zs, uu, vv have to be communicated now, because they are used later on #ifdef USEMPI call xmpi_shift_ee(s%zs) #endif if (par%secorder == 1 .or. par%wavemodel==WAVEMODEL_NONH) then vv_old = s%vv uu_old = s%uu zs_old = s%zs endif ! ! U and V in cell centre; do output and sediment stirring ! s%u(2:s%nx,:)=0.5d0*(s%uu(1:s%nx-1,:)+s%uu(2:s%nx,:)) ! offshore boundary if(manage_lowx) then s%u(1,:)=s%uu(1,:) endif if(manage_highx) then s%u(s%nx+1,:)=s%u(s%nx,:) endif if (s%ny>0) then s%v(:,2:s%ny)=0.5d0*(s%vv(:,1:s%ny-1)+s%vv(:,2:s%ny)) if(manage_lowy) then s%v(:,1)=s%vv(:,1) endif if(manage_highy) then s%v(:,s%ny+1)=s%v(:,s%ny) ! bas: need this for calculation of s%ee in wci routine endif !Ap s%v(s%nx+1,:)=s%v(s%nx,:) else ! Dano s%v=s%vv endif !s%ny>0 ! Robert + Jaap: compute derivatives of u and v ! sinthm = sin(s%thetamean-s%alfaz) costhm = cos(s%thetamean-s%alfaz) ! V-velocities at u-points if (s%ny>0) then s%vu(1:s%nx,2:s%ny)= 0.25d0*(s%vv(1:s%nx,1:s%ny-1)+s%vv(1:s%nx,2:s%ny)+ & s%vv(2:s%nx+1,1:s%ny-1)+s%vv(2:s%nx+1,2:s%ny)) ! how about boundaries? if(manage_lowy) then s%vu(:,1) = s%vu(:,2) endif if(manage_highy) then s%vu(:,s%ny+1) = s%vu(:,s%ny) endif else s%vu(1:s%nx,1)= 0.5d0*(s%vv(1:s%nx,1)+s%vv(2:s%nx+1,1)) endif !s%ny>0 ! wwvv fill in vu(:1) and vu(:ny+1) for non-lowy and non-highy processes ! and vu(nx+1,:) s%vu=s%vu*s%wetu ! V-stokes velocities at U point if (s%ny>0) then vsu(1:s%nx,2:s%ny)=0.5d0*(s%ust(1:s%nx,2:s%ny)*sinthm(1:s%nx,2:s%ny)+ & s%ust(2:s%nx+1,2:s%ny)*sinthm(2:s%nx+1,2:s%ny)) if(manage_lowy) then vsu(:,1)=vsu(:,2) endif if(manage_highy) then vsu(:,s%ny+1) = vsu(:,s%ny) endif else vsu(1:s%nx,1)=0.5d0*(s%ust(1:s%nx,1)*sinthm(1:s%nx,1)+ & s%ust(2:s%nx+1,1)*sinthm(2:s%nx+1,1)) endif !s%ny>0 ! wwvv same for vsu vsu = vsu*s%wetu ! U-stokes velocities at U point if (s%ny>0) then usu(1:s%nx,2:s%ny)=0.5d0*(s%ust(1:s%nx ,2:s%ny)*costhm(1:s%nx ,2:s%ny)+ & s%ust(2:s%nx+1,2:s%ny)*costhm(2:s%nx+1,2:s%ny)) if(manage_lowy) then usu(:,1)=usu(:,2) endif if(manage_highy) then usu(:,s%ny+1)=usu(:,s%ny) endif else usu(1:s%nx,1)=0.5d0*(s%ust(1:s%nx,1)*costhm(1:s%nx,1)+ & s%ust(2:s%nx+1,1)*costhm(2:s%nx+1,1)) endif !s%ny>0 ! wwvv same for usu usu=usu*s%wetu ! V-euler velocities at u-point veu = s%vu - vsu ! U-euler velocties at u-point s%ueu = s%uu - usu ! Velocity magnitude at u-points if (par%sedtrans == 0) then s%vmagu=sqrt(s%uu**2+s%vu**2) endif ! Eulerian velocity magnitude at u-points s%vmageu=sqrt(s%ueu**2+veu**2) ! Ue and Ve in cell centre; do output and sediment stirring s%ue(2:s%nx,:)=0.5d0*(s%ueu(1:s%nx-1,:)+s%ueu(2:s%nx,:)) s%ue(1,:)=s%ueu(1,:) ! wwvv ue(nx+1,:) ? if (s%ny>0) then s%ve(:,2:s%ny)=0.5d0*(s%vev(:,1:s%ny-1)+s%vev(:,2:s%ny)) !Jaap s%ny+1 s%ve(:,1)=s%vev(:,1) else s%ve(:,1) = s%vev(:,1) endif !s%ny>0 ! U-velocities at v-points if (s%ny>0) then s%uv(2:s%nx,1:s%ny)= .25d0*(s%uu(1:s%nx-1,1:s%ny)+s%uu(2:s%nx,1:s%ny)+ & s%uu(1:s%nx-1,2:s%ny+1)+s%uu(2:s%nx,2:s%ny+1)) ! boundaries? ! wwvv and what about uv(:,1) ? if(manage_highy) then s%uv(:,s%ny+1) = s%uv(:,s%ny) endif else s%uv(2:s%nx,1)= .5d0*(s%uu(1:s%nx-1,1)+s%uu(2:s%nx,1)) endif !s%ny>0 ! wwvv fix uv(:,ny+1) for non-right processes ! uv(1,:) and uv(nx+1,:) need to be filled in for ! non-bot or top processes s%uv=s%uv*s%wetv ! V-stokes velocities at V point if (s%ny>0) then vsv(2:s%nx,1:s%ny)=0.5d0*(s%ust(2:s%nx,1:s%ny)*sinthm(2:s%nx,1:s%ny)+& s%ust(2:s%nx,2:s%ny+1)*sinthm(2:s%nx,2:s%ny+1)) if(manage_lowy) then vsv(:,1) = vsv(:,2) endif if(manage_highy) then vsv(:,s%ny+1) = vsv(:,s%ny) endif else vsv(2:s%nx,1)= s%ust(2:s%nx,1)*sinthm(2:s%nx,1) endif !s%ny>0 ! wwvv fix vsv(:,1) and vsv(:,ny+1) and vsv(1,:) and vsv(nx+1,:) vsv=vsv*s%wetv ! U-stokes velocities at V point if (s%ny>0) then usv(2:s%nx,1:s%ny)=0.5d0*(s%ust(2:s%nx,1:s%ny)*costhm(2:s%nx,1:s%ny)+& s%ust(2:s%nx,2:s%ny+1)*costhm(2:s%nx,2:s%ny+1)) if(manage_lowy) then usv(:,1) = usv(:,2) endif if(manage_highy) then usv(:,s%ny+1) = usv(:,s%ny) endif else usv(2:s%nx,1)=s%ust(2:s%nx,1)*costhm(2:s%nx,1) endif !s%ny>0 ! wwvv fix usv(:,1) and usv(:,ny+1) and usv(1,:) and usv(nx+1,:) usv=usv*s%wetv ! V-euler velocities at V-point s%vev = s%vv - vsv ! U-euler velocties at V-point uev = s%uv - usv ! Velocity magnitude at v-points if (par%sedtrans==0) then s%vmagv=sqrt(s%uv**2+s%vv**2) endif ! Eulerian velocity magnitude at v-points s%vmagev=sqrt(uev**2+s%vev**2) ! wwvv vev(nx+1,:) ? ! s%hold =s%hh ! wwvv ? s%hold is never else used ! s%hh = max(s%zs-s%zb,par%eps) ! water depth s%zs1 = s%zs-s%zs0 ! water level minus tide s%maxzs=max(s%zs,s%maxzs) s%minzs=min(s%zs,s%minzs) ! XBeach uses same input for Van Rijn, 1993 (quasi 3d), but doesn't use this module if (par%nz>1 .and. par%form /= FORM_VANRIJN1993) then do j=1,s%ny+1 do i=1,s%nx+1 if (s%wetz(i,j) .eq. 1) then ks=12.d0*s%hh(i,j)/10.d0**(sqrt(par%g/s%cfu(i,j))/18.d0) tauw=par%rhoa*par%Cd*sqrt(s%windsu(i,j)**2+s%windnv(i,j)**2) tauwx=s%windsu(i,j)*tauw tauwy=s%windnv(i,j)*tauw call vsm_u_XB ( s%ue(i,j) ,s%ve(i,j) ,s%hh(i,j) ,ks , & par%rho ,tauwx ,tauwy ,s%thetamean(i,j)-s%alfaz(i,j), & s%urms(i,j) ,s%sigm(i,j) ,s%k(i,j) ,s%Dr(i,j) , & s%E(i,j) ,s%R(i,j) ,fcvisc,facdel ,par%ws , & s%fw(i,j) ,facdf ,swglm ,par%nz ,s%sigz , & s%uz(i,j,:) ,s%vz(i,j,:) ,s%ustz(i,j,:) ,s%nutz(i,j,:), & s%ue_sed(i,j),s%ve_sed(i,j) ) else s%uz(i,j,:)=0.d0 s%vz(i,j,:)=0.d0 s%ustz(i,j,:)=0.d0 s%nutz(i,j,:)=0.d0 s%ue_sed(i,j)=0.d0 s%ve_sed(i,j)=0.d0 endif enddo enddo else s%ue_sed=s%ue s%ve_sed=s%ve endif end subroutine flow subroutine visc_smagorinsky(s,par) use params, only: parameters use spaceparamsdef, only: manage_lowx, manage_highx, manage_lowy, manage_highy, spacepars IMPLICIT NONE ! DATE AUTHOR CHANGES ! ! December 2010 Pieter Bart Smit New Subroutine ! March 2010 Pieter Bart Smit Changed formulation to standard smag. model !------------------------------------------------------------------------------- ! DECLARATIONS !------------------------------------------------------------------------------- !-------------------------- PURPOSE ---------------------------- ! ! Calculates the turbulent viscocity coefficient nuh according to the smagorinsky ! subgrid model. ! !-------------------------- METHOD ---------------------------- ! ! The turbulent viscocity is given as: ! ! nuh = C^2*dx*dy*Tau ! ! Tau =2^(1/2) * [ (du/dx)^2 + (dv/dy)^2 + 1/2 * (du/dy + dv/dx)^2 ] ^ (1/2) ! ! Where ! ! dx,dy : grid size ! C : Constant ~0.15 (set by par%nuh) ! Tau : Measure for the magnitude of the turbulent stresses ! !-------------------------- ARGUMENTS ---------------------------- type(spacepars),target ,intent(inout) :: s type(parameters) ,intent(in) :: par !-------------------------- LOCAL VARIABLES ---------------------------- real*8 :: dudx !U Velocity gradient in x-dir real*8 :: dudy !U Velocity gradient in y-dir real*8 :: dvdx !V Velocity gradient in x-dir real*8 :: dvdy !V Velocity gradient in y-dir real*8 :: Tau !Measure for magnitude viscous stresses real*8 :: l !Local gridcell area integer :: i !Index variable integer :: j !Index variable !------------------------------------------------------------------------------- ! IMPLEMENTATION !------------------------------------------------------------------------------- !MPI WARNING -> Check loop indices if (s%ny>2) then do j=2,s%ny do i=2,s%nx dudx = (s%uu(i,j)-s%uu(i-1,j))/s%dsz(i,j) dudy = .5d0*(s%uu(i,j+1) - s%uu(i,j-1) + s%uu(i-1,j+1) - s%uu(i-1,j-1))/(s%dnv(i,j)+s%dnv(i,j-1)) dvdx = .5d0*(s%vv(i+1,j) - s%vv(i-1,j) + s%vv(i+1,j-1) - s%vv(i-1,j-1))/(s%dsu(i,j)+s%dsu(i-1,j)) dvdy = (s%vv(i,j)-s%vv(i,j-1))/s%dnz(i,j) Tau = sqrt(2.0d0 * dudx**2+2.0d0 * dvdy**2 + (dvdx+dudy)**2) l = 1.d0/s%dsdnzi(i,j) s%nuh(i,j) = par%nuh**2 * l * Tau * real(s%wetu(i,j)*s%wetu(i-1,j)*s%wetv(i,j)*s%wetv(i,j-1),kind=8) enddo enddo else j = max(s%ny,1) do i=2,s%nx dudx = (s%uu(i,j)-s%uu(i-1,j))/s%dsz(i,j) dvdx = (s%vv(i+1,j) - s%vv(i-1,j) )/(s%dsu(i,j)+s%dsu(i-1,j)) Tau = sqrt(2.0d0 * dudx**2 + dvdx**2) if (par%dy > -1.d0) then l = s%dsz(i,j)*par%dy else l = s%dsz(i,j)**2 endif s%nuh(i,j) = par%nuh**2 * l * Tau * real(s%wetu(i,j)*s%wetu(i-1,j),kind=8) enddo endif !s%ny>2 if (s%ny>0) then if (manage_lowy) s%nuh(:,1) = s%nuh(:,2) if (manage_highy) s%nuh(:,s%ny+1) = s%nuh(:,s%ny) endif if (manage_lowx) s%nuh(1,:) = s%nuh(2,:) if (manage_highx) s%nuh(s%nx+1,:) = s%nuh(s%nx,:) end subroutine visc_smagorinsky end module flow_timestep_module