#include "cppdefs.h" MODULE v2dbc_mod ! !svn $Id$ !======================================================================= ! Copyright (c) 2002-2009 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt Hernan G. Arango ! !========================================== Alexander F. Shchepetkin === ! ! ! This subroutine sets lateral boundary conditions for vertically ! ! integrated V-velocity. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: v2dbc_tile CONTAINS ! !*********************************************************************** SUBROUTINE v2dbc (ng, tile, kout) !*********************************************************************** ! USE mod_param USE mod_ocean USE mod_stepping ! integer, intent(in) :: ng, tile, kout #include "tile.h" ! CALL v2dbc_tile (ng, Istr, Iend, Jstr, Jend, & & LBi, UBi, LBj, UBj, & & krhs(ng), kstp(ng), kout, & & OCEAN(ng) % ubar, & & OCEAN(ng) % vbar, & & OCEAN(ng) % zeta) RETURN END SUBROUTINE v2dbc ! !*********************************************************************** SUBROUTINE v2dbc_tile (ng, Istr, Iend, Jstr, Jend, & & LBi, UBi, LBj, UBj, & & krhs, kstp, kout, & & ubar, vbar, zeta) !*********************************************************************** ! USE mod_param USE mod_boundary USE mod_grid USE mod mask USE mod_scalars ! ! Imported variable declarations. ! integer, intent(in) :: ng, Iend, Istr, Jend, Jstr integer, intent(in) :: LBi, UBi, LBj, UBj integer, intent(in) :: krhs, kstp, kout #ifdef ASSUMED_SHAPE real(r8), intent(in) :: ubar(LBi:,LBj:,:) real(r8), intent(in) :: zeta(LBi:,LBj:,:) real(r8), intent(inout) :: vbar(LBi:,LBj:,:) #else real(r8), intent(in) :: ubar(LBi:UBi,LBj:UBj,3) real(r8), intent(in) :: zeta(LBi:UBi,LBj:UBj,3) real(r8), intent(inout) :: vbar(LBi:UBi,LBj:UBj,3) #endif ! ! Local variable declarations. ! integer :: IstrR, IendR, JstrR, JendR, IstrU, JstrV integer :: i, j, know real(r8), parameter :: eps = 1.0E-20_r8 real(r8) :: Ce, Cx, cff, dt2d, dVde, dVdt, dVdx, tau real(r8), dimension(PRIVATE_2D_SCRATCH_ARRAY) :: grad #include "set_bounds.h" ! !----------------------------------------------------------------------- ! Set time-indices !----------------------------------------------------------------------- ! IF (FIRST_2D_STEP) THEN know=krhs dt2d=dtfast(ng) ELSE IF (PREDICTOR_2D_STEP(ng)) THEN know=krhs dt2d=2.0_r8*dtfast(ng) ELSE know=kstp dt2d=dtfast(ng) END IF #ifndef NS_PERIODIC ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the southern edge. !----------------------------------------------------------------------- ! IF (SOUTHERN_EDGE) THEN # if defined SOUTH_M2RADIATION ! ! Southern edge, implicit upstream radiation condition. ! DO i=Istr,Iend+1 grad(i,Jstr )=vbar(i ,Jstr ,know)- & & vbar(i-1,Jstr ,know) grad(i,Jstr+1)=vbar(i ,Jstr+1,know)- & & vbar(i-1,Jstr+1,know) END DO DO i=Istr,Iend dVdt=vbar(i,Jstr+1,know)-vbar(i,Jstr+1,kout) dVde=vbar(i,Jstr+1,know)-vbar(i,Jstr+2,know) # ifdef SOUTH_M2NUDGING tau=M2obc_out(ng,isouth) IF ((dVdt*dVde).lt.0.0_r8) tau=M2obc_in(ng,isouth) tau=tau*dt2d # endif IF ((dVdt*dVde).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(i,Jstr+1)+grad(i+1,Jstr+1))).gt.0.0_r8) THEN dVdx=grad(i ,Jstr+1) ELSE dVdx=grad(i+1,Jstr+1) END IF cff=dVdt/MAX(dVdx*dVdx+dVde*dVde,eps) # ifdef RADIATION_2D Cx=MIN(1.0_r8,MAX(-1.0_r8,cff*dVdx)) # else Cx=0.0_r8 # endif Ce=MIN(1.0_r8,cff*dVde) vbar(i,Jstr,kout)=(1.0_r8-Ce)*vbar(i,Jstr,know)+ & & Ce*vbar(i,Jstr+1,know)- & & MAX(Cx,0.0_r8)*grad(i ,Jstr)- & & MIN(Cx,0.0_r8)*grad(i+1,Jstr) # ifdef SOUTH_M2NUDGING vbar(i,Jstr,kout)=vbar(i,Jstr,kout)+ & & tau*(BOUNDARY(ng)%vbar_south(i)- & & vbar(i,Jstr,know)) # endif # ifdef MASKING vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif END DO # elif defined SOUTH_M2FLATHER ! ! Southern edge, Flather boundary condition. ! DO i=Istr,Iend vbar(i,Jstr,kout)=BOUNDARY(ng)%vbar_south(i)- & & SQRT(g/(0.5_r8*(GRID(ng)%h(i,Jstr-1)+ & & GRID(ng)%h(i,Jstr ))))* & & (0.5_r8*(zeta(i,0,know)+zeta(i,Jstr,know))- & & BOUNDARY(ng)%zeta_south(i)) # ifdef MASKING vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif END DO # elif defined SOUTH_M2CLAMPED ! ! Southern edge, clamped boundary condition. ! DO i=Istr,Iend vbar(i,Jstr,kout)=BOUNDARY(ng)%vbar_south(i) # ifdef MASKING vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif END DO # elif defined SOUTH_M2GRADIENT ! ! Southern edge, gradient boundary condition. ! DO i=Istr,Iend vbar(i,Jstr,kout)=vbar(i,Jstr+1,kout) # ifdef MASKING vbar(i,Jstr,kout)=vbar(i,Jstr,kout)* & & GRID(ng)%vmask(i,Jstr) # endif END DO # else ! ! Southern edge, closed boundary condition. ! DO i=Istr,Iend vbar(i,Jstr,kout)=0.0_r8 END DO # endif END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the northern edge. !----------------------------------------------------------------------- ! IF (NORTHERN_EDGE) THEN # if defined NORTH_M2RADIATION ! ! Northern edge, implicit upstream radiation condition. ! DO i=Istr,Iend+1 grad(i,Jend )=vbar(i ,Jend ,know)- & & vbar(i-1,Jend ,know) grad(i,Jend+1)=vbar(i ,Jend+1,know)- & & vbar(i-1,Jend+1,know) END DO DO i=Istr,Iend dVdt=vbar(i,Jend,know)-vbar(i,Jend ,kout) dVde=vbar(i,Jend,know)-vbar(i,Jend-1,know) # ifdef NORTH_M2NUDGING tau=M2obc_out(ng,inorth) IF ((dVdt*dVde).lt.0.0_r8) tau=M2obc_in(ng,inorth) tau=tau*dt2d # endif IF ((dVdt*dVde).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(i,Jend)+grad(i+1,Jend))).gt.0.0_r8) THEN dVdx=grad(i ,Jend) ELSE dVdx=grad(i+1,Jend) END IF cff=dVdt/MAX(dVdx*dVdx+dVde*dVde,eps) # ifdef RADIATION_2D Cx=MIN(1.0_r8,MAX(-1.0_r8,cff*dVdx)) # else Cx=0.0_r8 # endif Ce=MIN(1.0_r8,cff*dVde) vbar(i,Jend+1,kout)=(1.0_r8-Ce)*vbar(i,Jend+1,know)+ & & Ce*vbar(i,Jend,know)- & & MAX(Cx,0.0_r8)*grad(i ,Jend+1)- & & MIN(Cx,0.0_r8)*grad(i+1,Jend+1) # ifdef NORTH_M2NUDGING vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)+ & & tau*(BOUNDARY(ng)%vbar_north(i)- & & vbar(i,Jend+1,know)) # endif # ifdef MASKING vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif END DO # elif defined NORTH_M2FLATHER ! ! Northern edge, Flather boundary condition. ! DO i=Istr,Iend vbar(i,Jend+1,kout)=BOUNDARY(ng)%vbar_north(i)+ & & SQRT(g/(0.5_r8*(GRID(ng)%h(i,Jend )+ & & GRID(ng)%h(i,Jend+1))))* & & (0.5_r8*(zeta(i,Jend ,know)+ & & zeta(i,Jend+1,know))- & & BOUNDARY(ng)%zeta_north(i)) # ifdef MASKING vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif END DO # elif defined NORTH_M2CLAMPED ! ! Northern edge, clamped boundary condition. ! DO i=Istr,Iend vbar(i,Jend+1,kout)=BOUNDARY(ng)%vbar_north(i) # ifdef MASKING vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif END DO # elif defined NORTH_M2GRADIENT ! ! Northern edge, gradient boundary condition. ! DO i=Istr,Iend vbar(i,Jend+1,kout)=vbar(i,Jend,kout) # ifdef MASKING vbar(i,Jend+1,kout)=vbar(i,Jend+1,kout)* & & GRID(ng)%vmask(i,Jend+1) # endif END DO # else ! ! Northern edge, closed boundary condition. ! DO i=Istr,Iend vbar(i,Jend+1,kout)=0.0_r8 END DO # endif END IF #endif #ifndef EW_PERIODIC ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the western edge. !----------------------------------------------------------------------- ! IF (WESTERN_EDGE) THEN # if defined WEST_M2RADIATION ! ! Western edge, implicit upstream radiation condition. ! DO j=JstrV-1,Jend grad(Istr-1,j)=vbar(Istr-1,j+1,know)- & & vbar(Istr-1,j ,know) grad(Istr ,j)=vbar(Istr ,j+1,know)- & & vbar(Istr ,j ,know) END DO DO j=JstrV,Jend dVdt=vbar(Istr,j,know)-vbar(Istr ,j,kout) dVdx=vbar(Istr,j,know)-vbar(Istr+1,j,know) # ifdef WEST_M2NUDGING tau=M2obc_out(ng,iwest) IF ((dVdt*dVdx).lt.0.0_r8) tau=M2obc_in(ng,iwest) tau=tau*dt2d # endif IF ((dVdt*dVdx).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(Istr,j-1)+grad(Istr,j))).gt.0.0_r8) THEN dVde=grad(Istr,j-1) ELSE dVde=grad(Istr,j ) END IF cff=dVdt/MAX(dVdx*dVdx+dVde*dVde,eps) Cx=MIN(1.0_r8,cff*dVdx) # ifdef RADIATION_2D Ce=MIN(1.0_r8,MAX(-1.0_r8,cff*dVde)) # else Ce=0.0_r8 # endif vbar(Istr-1,j,kout)=(1.0_r8-Cx)*vbar(Istr-1,j,know)+ & & Cx*vbar(Istr,j,know)- & & MAX(Ce,0.0_r8)*grad(Istr-1,j-1)- & & MIN(Ce,0.0_r8)*grad(Istr-1,j ) # ifdef WEST_M2NUDGING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)+ & & tau*(BOUNDARY(ng)%vbar_west(j)- & & vbar(Istr-1,j,know)) # endif # ifdef MASKING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif END DO # elif defined WEST_M2FLATHER ! ! Western edge, Chapman boundary condition. ! DO j=JstrV,Jend Cx=dt2d*0.5_r8*(GRID(ng)%pm(Istr,j-1)+ & & GRID(ng)%pm(Istr,j ))* & & SQRT(g*0.5_r8*(GRID(ng)%h(Istr,j-1)+ & & GRID(ng)%h(Istr,j ))) vbar(Istr-1,j,kout)=(vbar(Istr-1,j,know)+ & & Cx*vbar(Istr,j,kout))/ & & (1.0_r8+Cx) # ifdef MASKING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif END DO # elif defined WEST_M2CLAMPED ! ! Western edge, clamped boundary condition. ! DO j=JstrV,Jend vbar(Istr-1,j,kout)=BOUNDARY(ng)%vbar_west(j) # ifdef MASKING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif END DO # elif defined WEST_M2GRADIENT ! ! Western edge, gradient boundary condition. ! DO j=JstrV,Jend vbar(Istr-1,j,kout)=vbar(Istr,j,kout) # ifdef MASKING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif END DO # else ! ! Western edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef NS_PERIODIC # define J_RANGE JstrV,Jend # else # define J_RANGE Jstr,JendR # endif DO j=J_RANGE vbar(Istr-1,j,kout)=gamma2(ng)*vbar(Istr,j,kout) # ifdef MASKING vbar(Istr-1,j,kout)=vbar(Istr-1,j,kout)* & & GRID(ng)%vmask(Istr-1,j) # endif END DO # undef J_RANGE # endif END IF ! !----------------------------------------------------------------------- ! Lateral boundary conditions at the eastern edge. !----------------------------------------------------------------------- ! IF (EASTERN_EDGE) THEN # if defined EAST_M2RADIATION ! ! Eastern edge, implicit upstream radiation condition. ! DO j=JstrV-1,Jend grad(Iend ,j)=vbar(Iend ,j+1,know)- & & vbar(Iend ,j ,know) grad(Iend+1,j)=vbar(Iend+1,j+1,know)- & & vbar(Iend+1,j ,know) END DO DO j=JstrV,Jend dVdt=vbar(Iend,j,know)-vbar(Iend ,j,kout) dVdx=vbar(Iend,j,know)-vbar(Iend-1,j,know) # ifdef EAST_M2NUDGING tau=M2obc_out(ng,ieast) IF ((dVdt*dVdx).lt.0.0_r8) tau=M2obc_in(ng,ieast) tau=tau*dt2d # endif IF ((dVdt*dVdx).lt.0.0_r8) dVdt=0.0_r8 IF ((dVdt*(grad(Iend,j-1)+grad(Iend,j))).gt.0.0_r8) THEN dVde=grad(Iend,j-1) ELSE dVde=grad(Iend,j ) END IF cff=dVdt/MAX(dVdx*dVdx+dVde*dVde,eps) Cx=MIN(1.0_r8,cff*dVdx) # ifdef RADIATION_2D Ce=MIN(1.0_r8,MAX(-1.0_r8,cff*dVde)) # else Ce=0.0_r8 # endif vbar(Iend+1,j,kout)=(1.0_r8-Cx)*vbar(Iend+1,j,know)+ & & Cx*vbar(Iend,j,know)- & & MAX(Ce,0.0_r8)*grad(Iend+1,j-1)- & & MIN(Ce,0.0_r8)*grad(Iend+1,j ) # ifdef EAST_M2NUDGING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)+ & & tau*(BOUNDARY(ng)%vbar_east(j)- & & vbar(Iend+1,j,know)) # endif # ifdef MASKING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO # elif defined EAST_M2FLATHER ! ! Eastern edge, Chapman boundary condition. ! DO j=JstrV,Jend Cx=dt2d*0.5_r8*(GRID(ng)%pm(Iend,j-1)+ & & GRID(ng)%pm(Iend,j ))* & & SQRT(g*0.5_r8*(GRID(ng)%h(Iend,j-1)+ & & GRID(ng)%h(Iend,j ))) vbar(Iend+1,j,kout)=(vbar(Iend+1,j,know)+ & & Cx*vbar(Iend,j,kout))/ & & (1.0_r8+Cx) # ifdef MASKING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO # elif defined EAST_M2CLAMPED ! ! Eastern edge, clamped boundary condition. ! DO j=JstrV,Jend vbar(Iend+1,j,kout)=BOUNDARY(ng)%vbar_east(j) # ifdef MASKING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO # elif defined EAST_M2GRADIENT ! ! Eastern edge, gradient boundary condition. ! DO j=JstrV,Jend vbar(Iend+1,j,kout)=vbar(Iend,j,kout) # ifdef MASKING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO # else ! ! Eastern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef NS_PERIODIC # define J_RANGE JstrV,Jend # else # define J_RANGE Jstr,JendR # endif DO j=J_RANGE vbar(Iend+1,j,kout)=gamma2(ng)*vbar(Iend,j,kout) # ifdef MASKING vbar(Iend+1,j,kout)=vbar(Iend+1,j,kout)* & & GRID(ng)%vmask(Iend+1,j) # endif END DO # undef J_RANGE # endif END IF #endif #if !defined EW_PERIODIC && !defined NS_PERIODIC ! !----------------------------------------------------------------------- ! Boundary corners. !----------------------------------------------------------------------- ! IF ((SOUTHERN_EDGE).and.(WESTERN_EDGE)) THEN vbar(Istr-1,Jstr,kout)=0.5_r8*(vbar(Istr-1,Jstr+1,kout)+ & & vbar(Istr ,Jstr ,kout)) END IF IF ((SOUTHERN_EDGE).and.(EASTERN_EDGE)) THEN vbar(Iend+1,Jstr,kout)=0.5_r8*(vbar(Iend ,Jstr ,kout)+ & & vbar(Iend+1,Jstr+1,kout)) END IF IF ((NORTHERN_EDGE).and.(WESTERN_EDGE)) THEN vbar(Istr-1,Jend+1,kout)=0.5_r8*(vbar(Istr-1,Jend ,kout)+ & & vbar(Istr ,Jend+1,kout)) END IF IF ((NORTHERN_EDGE).and.(EASTERN_EDGE)) THEN vbar(Iend+1,Jend+1,kout)=0.5_r8*(vbar(Iend+1,Jend ,kout)+ & & vbar(Iend ,Jend+1,kout)) END IF #endif RETURN END SUBROUTINE v2dbc_tile END MODULE v2dbc_mod