#include "cppdefs.h" MODULE u2dbc_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 U-velocity. ! ! ! !======================================================================= ! implicit none PRIVATE PUBLIC :: u2dbc_tile CONTAINS ! !*********************************************************************** SUBROUTINE u2dbc (ng, tile, kout) !*********************************************************************** ! USE mod_param USE mod_ocean USE mod_stepping ! integer, intent(in) :: ng, tile, kout #include "tile.h" ! CALL u2dbc_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 u2dbc ! !*********************************************************************** SUBROUTINE u2dbc_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_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) :: vbar(LBi:,LBj:,:) real(r8), intent(in) :: zeta(LBi:,LBj:,:) real(r8), intent(inout) :: ubar(LBi:,LBj:,:) #else real(r8), intent(in) :: vbar(LBi:UBi,LBj:UBj,3) real(r8), intent(in) :: zeta(LBi:UBi,LBj:UBj,3) real(r8), intent(inout) :: ubar(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, dUde, dUdt, dUdx, 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 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=Jstr,Jend+1 grad(1,j)=ubar(Istr ,j ,know)- & & ubar(Istr ,j-1,know) grad(2,j)=ubar(Istr+1,j ,know)- & & ubar(Istr+1,j-1,know) END DO DO j=Jstr,Jend dUdt=ubar(Istr+1,j,know)-ubar(Istr+1,j,kout) dUdx=ubar(Istr+1,j,know)-ubar(Istr+2,j,know) # ifdef WEST_M2NUDGING tau=M2obc_out(ng,iwest) IF ((dUdt*dUdx).lt.0.0_r8) tau=M2obc_in(ng,iwest) tau=tau*dt2d # endif IF ((dUdt*dUdx).lt.0.0_r8) dUdt=0.0_r8 IF ((dUdt*(grad(Istr+1,j)+grad(Istr+1,j+1))).gt.0.0_r8) THEN dUde=grad(Istr+1,j ) ELSE dUde=grad(Istr+1,j+1) END IF cff=dUdt/MAX(dUdx*dUdx+dUde*dUde,eps) Cx=MIN(1.0_r8,cff*dUdx) # ifdef RADIATION_2D Ce=MIN(1.0_r8,MAX(-1.0_r8,cff*dUde)) # else Ce=0.0_r8 # endif ubar(Istr,j,kout)=(1.0_r8-Cx)*ubar(Istr,j,know)+ & & Cx*ubar(Istr+1,j,know)- & & MAX(Ce,0.0_r8)*grad(Istr,j )- & & MIN(Ce,0.0_r8)*grad(Istr,j+1) # ifdef WEST_M2NUDGING ubar(Istr,j,kout)=ubar(Istr,j,kout)+ & & tau*(BOUNDARY(ng)%ubar_west(j)- & & ubar(Istr,j,know)) # endif # ifdef MASKING ubar(Istr,j,kout)=ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) # endif END DO # elif defined WEST_M2FLATHER ! ! Western edge, Flather boundary condition. ! DO j=Jstr,Jend ubar(Istr,j,kout)=BOUNDARY(ng)%ubar_west(j)- & & SQRT(g/(0.5_r8*(GRID(ng)%h(Istr-1,j)+ & & GRID(ng)%h(Istr ,j))))* & & (0.5_r8*(zeta(Istr-1,j,know)+ & & zeta(Istr ,j,know))- & & BOUNDARY(ng)%zeta_west(j)) # ifdef MASKING ubar(Istr,j,kout)=ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) # endif END DO # elif defined WEST_M2CLAMPED ! ! Western edge, clamped boundary condition. ! DO j=Jstr,Jend ubar(Istr,j,kout)=BOUNDARY(ng)%ubar_west(j) # ifdef MASKING ubar(Istr,j,kout)=ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) # endif END DO # elif defined WEST_M2GRADIENT ! ! Western edge, gradient boundary condition. ! DO j=Jstr,Jend ubar(Istr,j,kout)=ubar(Istr+1,j,kout) # ifdef MASKING ubar(Istr,j,kout)=ubar(Istr,j,kout)* & & GRID(ng)%umask(Istr,j) # endif END DO # else ! ! Western edge, closed boundary condition. ! DO j=Jstr,Jend ubar(Istr,j,kout)=0.0_r8 END DO # 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=Jstr,Jend+1 grad(Iend ,j)=ubar(Iend ,j ,know)- & & ubar(Iend ,j-1,know) grad(Iend+1,j)=ubar(Iend+1,j ,know)- & & ubar(Iend+1,j-1,know) END DO DO j=Jstr,Jend dUdt=ubar(Iend,j,know)-ubar(Iend ,j,kout) dUdx=ubar(Iend,j,know)-ubar(Iend-1,j,know) # ifdef EAST_M2NUDGING tau=M2obc_out(ng,ieast) IF ((dUdt*dUdx).lt.0.0_r8) tau=M2obc_in(ng,ieast) tau=tau*dt2d # endif IF ((dUdt*dUdx).lt.0.0_r8) dUdt=0.0_r8 IF ((dUdt*(grad(Iend,j)+grad(Iend,j+1))).gt.0.0_r8) THEN dUde=grad(Iend,j) ELSE dUde=grad(Iend,j+1) END IF cff=dUdt/MAX(dUdx*dUdx+dUde*dUde,eps) Cx=MIN(1.0_r8,cff*dUdx) # ifdef RADIATION_2D Ce=MIN(1.0_r8,MAX(-1.0_r8,cff*dUde)) # else Ce=0.0_r8 # endif ubar(Iend+1,j,kout)=(1.0_r8-Cx)*ubar(Iend+1,j,know)+ & & Cx*ubar(Iend,j,know)- & & MAX(Ce,0.0_r8)*grad(Iend+1,j )- & & MIN(Ce,0.0_r8)*grad(Iend+1,j+1) # ifdef EAST_M2NUDGING ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)+ & & tau*(BOUNDARY(ng)%ubar_east(j)- & & ubar(Iend+1,j,know)) # endif # ifdef MASKING ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) # endif END DO # elif defined EAST_M2FLATHER ! ! Eastern edge, Flather boundary condition. ! DO j=Jstr,Jend ubar(Iend+1,j,kout)=BOUNDARY(ng)%ubar_east(j)+ & & SQRT(g/(0.5_r8*(GRID(ng)%h(Iend ,j)+ & & GRID(ng)%h(Iend+1,j))))* & & (0.5_r8*(zeta(Iend ,j,know)+ & & zeta(Iend+1,j,know))- & & BOUNDARY(ng)%zeta_east(j)) # ifdef MASKING ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) # endif END DO # elif defined EAST_M2CLAMPED ! ! Eastern edge, clamped boundary condition. ! DO j=Jstr,Jend ubar(Iend+1,j,kout)=BOUNDARY(ng)%ubar_east(j) # ifdef MASKING ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) # endif END DO # elif defined EAST_M2GRADIENT ! ! Eastern edge, gradient boundary condition. ! DO j=Jstr,Jend ubar(Iend+1,j,kout)=ubar(Iend,j,kout) # ifdef MASKING ubar(Iend+1,j,kout)=ubar(Iend+1,j,kout)* & & GRID(ng)%umask(Iend+1,j) # endif END DO # else ! ! Eastern edge, closed boundary condition. ! DO j=Jstr,Jend ubar(Iend+1,j,kout)=0.0_r8 END DO # endif END IF #endif #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=IstrU-1,Iend grad(i,Jstr-1)=ubar(i+1,Jstr-1,know)- & & ubar(i ,Jstr-1,know) grad(i,Jstr )=ubar(i+1,Jstr ,know)- & & ubar(i ,Jstr ,know) END DO DO i=IstrU,Iend dUdt=ubar(i,Jstr,know)-ubar(i,Jstr ,kout) dUde=ubar(i,Jstr,know)-ubar(i,Jstr+1,know) # ifdef SOUTH_M2NUDGING tau=M2obc_out(ng,isouth) IF ((dUdt*dUde).lt.0.0_r8) tau=M2obc_in(ng,isouth) tau=tau*dt2d # endif IF ((dUdt*dUde).lt.0.0_r8) dUdt=0.0_r8 IF ((dUdt*(grad(i-1,Jstr)+grad(i,Jstr))).gt.0.0_r8) THEN dUdx=grad(i-1,Jstr) ELSE dUdx=grad(i ,Jstr) END IF cff=dUdt/MAX(dUdx*dUdx+dUde*dUde,eps) # ifdef RADIATION_2D Cx=MIN(1.0_r8,MAX(-1.0_r8,cff*dUdx)) # else Cx=0.0_r8 # endif Ce=MIN(1.0_r8,cff*dUde) ubar(i,Jstr-1,kout)=(1.0_r8-Ce)*ubar(i,Jstr-1,know)+ & & Ce*ubar(i,Jstr,know)- & & MAX(Cx,0.0_r8)*grad(i-1,Jstr-1)- & & MIN(Cx,0.0_r8)*grad(i ,Jstr-1) # ifdef SOUTH_M2NUDGING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)+ & & tau*(BOUNDARY(ng)%ubar_south(i)- & & ubar(i,Jstr-1,know)) # endif # ifdef MASKING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO # elif defined SOUTH_M2FLATHER ! ! Southern edge, Chapman boundary condition. ! DO i=IstrU,Iend Ce=dt2d*0.5_r8*(GRID(ng)%pn(i-1,Jstr)+ & & GRID(ng)%pn(i ,Jstr))* & & SQRT(g*0.5_r8*(GRID(ng)%h(i-1,Jstr)+ & & GRID(ng)%h(i ,Jstr))) ubar(i,Jstr-1,kout)=(ubar(i,Jstr-1,know)+ & & Ce*ubar(i,Jstr,kout))/ & & (1.0_r8+Ce) # ifdef MASKING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO # elif defined SOUTH_M2CLAMPED ! ! Southern edge, clamped boundary condition. ! DO i=IstrU,Iend ubar(i,Jstr-1,kout)=BOUNDARY(ng)%ubar_south(i) # ifdef MASKING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO # elif defined SOUTH_M2GRADIENT ! ! Southern edge, gradient boundary condition. ! DO i=IstrU,Iend ubar(i,Jstr-1,kout)=ubar(i,Jstr,kout) # ifdef MASKING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO # else ! ! Southern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef EW_PERIODIC # define I_RANGE IstrU,Iend # else # define I_RANGE Istr,IendR # endif DO i=I_RANGE ubar(i,Jstr-1,kout)=gamma2(ng)*ubar(i,Jstr,kout) # ifdef MASKING ubar(i,Jstr-1,kout)=ubar(i,Jstr-1,kout)* & & GRID(ng)%umask(i,Jstr-1) # endif END DO # undef I_RANGE # 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=IstrU-1,Iend grad(i,Jend )=ubar(i+1,Jend ,know)- & & ubar(i ,Jend ,know) grad(i,Jend+1)=ubar(i+1,Jend+1,know)- & & ubar(i ,Jend+1,know) END DO DO i=IstrU,Iend dUdt=ubar(i,Jend,know)-ubar(i,Jend ,kout) dUde=ubar(i,Jend,know)-ubar(i,Jend-1,know) # ifdef NORTH_M2NUDGING tau=M2obc_out(ng,inorth) IF ((dUdt*dUde).lt.0.0_r8) tau=M2obc_in(ng,inorth) tau=tau*dt2d # endif IF ((dUdt*dUde).lt.0.0_r8) dUdt=0.0_r8 IF ((dUdt*(grad(i-1,Jend)+grad(i,Jend))).gt.0.0_r8) THEN dUdx=grad(i-1,Jend) ELSE dUdx=grad(i ,Jend) END IF cff=dUdt/MAX(dUdx*dUdx+dUde*dUde,eps) # ifdef RADIATION_2D Cx=MIN(1.0_r8,MAX(-1.0_r8,cff*dUdx)) # else Cx=0.0_r8 # endif Ce=MIN(1.0_r8,cff*dUde) ubar(i,Jend+1,kout)=(1.0_r8-Ce)*ubar(i,Jend+1,know)+ & & Ce*ubar(i,Jend,know)- & & MAX(Cx,0.0_r8)*grad(i-1,Jend+1)- & & MIN(Cx,0.0_r8)*grad(i ,Jend+1) # ifdef NORTH_M2NUDGING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)+ & & tau*(BOUNDARY(ng)%ubar_north(i)- & & ubar(i,Jend+1,know)) # endif # ifdef MASKING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) # endif END DO # elif defined NORTH_M2FLATHER ! ! Northern edge, Chapman boundary condition. ! DO i=IstrU,Iend Ce=dt2d*0.5_r8*(GRID(ng)%pn(i-1,Jend)+ & & GRID(ng)%pn(i ,Jend))* & & SQRT(g*0.5_r8*(GRID(ng)%h(i-1,Jend)+ & & GRID(ng)%h(i ,Jend))) ubar(i,Jend+1,kout)=(ubar(i,Jend+1,know)+ & & Ce*ubar(i,Jend,kout))/ & & (1.0_r8+Ce) # ifdef MASKING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) # endif END DO # elif defined NORTH_M2CLAMPED ! ! Northern edge, clamped boundary condition. ! DO i=IstrU,Iend ubar(i,Jend+1,kout)=BOUNDARY(ng)%ubar_north(i) # ifdef MASKING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) # endif END DO # elif defined NORTH_M2GRADIENT ! ! Northern edge, gradient boundary condition. ! DO i=IstrU,Iend ubar(i,Jend+1,kout)=ubar(i,Jend,kout) # ifdef MASKING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) # endif END DO # else ! ! Northern edge, closed boundary condition: free slip (gamma2=1) or ! no slip (gamma2=-1). ! # ifdef EW_PERIODIC # define I_RANGE IstrU,Iend # else # define I_RANGE Istr,IendR # endif DO i=I_RANGE ubar(i,Jend+1,kout)=gamma2(ng)*ubar(i,Jend,kout) # ifdef MASKING ubar(i,Jend+1,kout)=ubar(i,Jend+1,kout)* & & GRID(ng)%umask(i,Jend+1) # endif END DO # undef I_RANGE # endif END IF #endif #if !defined EW_PERIODIC && !defined NS_PERIODIC ! !----------------------------------------------------------------------- ! Boundary corners. !----------------------------------------------------------------------- ! IF ((SOUTHERN_EDGE).and.(WESTERN_EDGE)) THEN ubar(Istr,Jstr-1,kout)=0.5_r8*(ubar(Istr+1,Jstr-1,kout)+ & & ubar(Istr ,Jstr ,kout)) END IF IF ((SOUTHERN_EDGE).and.(EASTERN_EDGE)) THEN ubar(Iend+1,Jstr-1,kout)=0.5_r8*(ubar(Iend ,Jstr-1,kout)+ & & ubar(Iend+1,Jstr ,kout)) END IF IF ((NORTHERN_EDGE).and.(WESTERN_EDGE)) THEN ubar(Istr,Jend+1,kout)=0.5_r8*(ubar(Istr+1,Jend+1,kout)+ & & ubar(Istr ,Jend ,kout)) END IF IF ((NORTHERN_EDGE).and.(EASTERN_EDGE)) THEN ubar(Iend+1,Jend+1,kout)=0.5_r8*(ubar(Iend ,Jend+1,kout)+ & & ubar(Iend+1,Jend ,kout)) END IF #endif RETURN END SUBROUTINE u2dbc_tile END MODULE u2dbc_mod