#include "cppdefs.h"
MODULE us2dbc_mod
#ifdef WEC
!
!svn $Id: u2sdbc_im.F 779 2008-10-04 23:15:47Z jcwarner $
!=======================================================================
! Copyright (c) 2002-2017 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 Ustokes-velocity. !
! !
!=======================================================================
!
implicit none
PRIVATE
PUBLIC :: us2dbc, us2dbc_tile
CONTAINS
!
!***********************************************************************
SUBROUTINE us2dbc (ng, tile)
!***********************************************************************
!
USE mod_param
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
!
! Local variable declarations.
!
#include "tile.h"
!
CALL us2dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& OCEAN(ng) % ubar_stokes)
RETURN
END SUBROUTINE us2dbc
!
!***********************************************************************
SUBROUTINE us2dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& ubar_stokes)
!***********************************************************************
!
USE mod_param
USE mod_ncparam
USE mod_boundary
USE mod_grid
USE mod_scalars
# ifdef WET_DRY
USE mod_grid
# endif
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
# ifdef ASSUMED_SHAPE
real(r8), intent(inout) :: ubar_stokes(LBi:,LBj:)
# else
real(r8), intent(inout) :: ubar_stokes(LBi:UBi,LBj:UBj)
# endif
!
! Local variable declarations.
!
integer :: i, j, know
integer :: Imin, Imax
real(r8), parameter :: eps = 1.0E-20_r8
real(r8) :: Ce, Cx, cff5
real(r8) :: bry_pgr, bry_cor, bry_str, bry_val
real(r8) :: cff, cff1, cff2, dUde, dUdt, dUdx, tau
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad
#include "set_bounds.h"
!
!-----------------------------------------------------------------------
! Lateral boundary conditions at the western edge.
!-----------------------------------------------------------------------
!
IF (DOMAIN(ng)%Western_Edge(tile)) THEN
!
! Western edge, implicit upstream radiation condition.
!
IF (LBC(iwest,isU2Sd,ng)%radiation) THEN
DO j=Jstr,Jend+1
grad(Istr ,j)=ubar_stokes(Istr ,j )- &
& ubar_stokes(Istr ,j-1)
grad(Istr+1,j)=ubar_stokes(Istr+1,j )- &
& ubar_stokes(Istr+1,j-1)
END DO
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
dUdt=ubar_stokes(Istr+1,j)-ubar_stokes(Istr+1,j)
dUdx=ubar_stokes(Istr+1,j)-ubar_stokes(Istr+2,j)
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=MAX(dUdx*dUdx+dUde*dUde,eps)
Cx=dUdt*dUdx
# ifdef RADIATION_2D
Ce=MIN(cff,MAX(dUdt*dUde,-cff))
# else
Ce=0.0_r8
# endif
ubar_stokes(Istr,j)=(cff*ubar_stokes(Istr ,j)+ &
& Cx *ubar_stokes(Istr+1,j)- &
& MAX(Ce,0.0_r8)*grad(Istr,j )- &
& MIN(Ce,0.0_r8)*grad(Istr,j+1))/ &
& (cff+Cx)
# ifdef MASKING
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
!
! Western edge, clamped boundary condition.
!
ELSE IF (LBC(iwest,isU2Sd,ng)%clamped) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
ubar_stokes(Istr,j)=BOUNDARY(ng)%ubarstokes_west(j)
# ifdef MASKING
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
!
! Western edge, closed boundary condition.
!
ELSE IF (LBC(iwest,isU2Sd,ng)%closed) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
ubar_stokes(Istr,j)=0.0_r8
END IF
END DO
!
! Western edge, gradient boundary condition.
!
ELSE IF (LBC(iwest,isU2Sd,ng)%gradient) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
ubar_stokes(Istr,j)=ubar_stokes(Istr+1,j)
# ifdef MASKING
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
ubar_stokes(Istr,j)=ubar_stokes(Istr,j)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Lateral boundary conditions at the eastern edge.
!-----------------------------------------------------------------------
!
IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN
!
! Eastern edge, implicit upstream radiation condition.
!
IF (LBC(ieast,isU2Sd,ng)%radiation) THEN
DO j=Jstr,Jend+1
grad(Iend ,j)=ubar_stokes(Iend ,j )- &
& ubar_stokes(Iend ,j-1)
grad(Iend+1,j)=ubar_stokes(Iend+1,j )- &
& ubar_stokes(Iend+1,j-1)
END DO
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
dUdt=ubar_stokes(Iend,j)-ubar_stokes(Iend ,j)
dUdx=ubar_stokes(Iend,j)-ubar_stokes(Iend-1,j)
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=MAX(dUdx*dUdx+dUde*dUde,eps)
Cx=dUdt*dUdx
# ifdef RADIATION_2D
Ce=MIN(cff,MAX(dUdt*dUde,-cff))
# else
Ce=0.0_r8
# endif
ubar_stokes(Iend+1,j)=(cff*ubar_stokes(Iend+1,j)+ &
& Cx *ubar_stokes(Iend ,j)- &
& MAX(Ce,0.0_r8)*grad(Iend+1,j )- &
& MIN(Ce,0.0_r8)*grad(Iend+1,j+1))/ &
& (cff+Cx)
# ifdef MASKING
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
!
! Eastern edge, clamped boundary condition.
!
ELSE IF (LBC(ieast,isU2Sd,ng)%clamped) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
ubar_stokes(Iend+1,j)=BOUNDARY(ng)%ubarstokes_east(j)
# ifdef MASKING
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
!
! Eastern edge, closed boundary condition.
!
ELSE IF (LBC(ieast,isU2Sd,ng)%closed) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
ubar_stokes(Iend+1,j)=0.0_r8
END IF
END DO
!
! Eastern edge, gradient boundary condition.
!
ELSE IF (LBC(ieast,isU2Sd,ng)%gradient) THEN
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
ubar_stokes(Iend+1,j)=ubar_stokes(Iend,j)
# ifdef MASKING
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
ubar_stokes(Iend+1,j)=ubar_stokes(Iend+1,j)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Lateral boundary conditions at the southern edge.
!-----------------------------------------------------------------------
!
IF (DOMAIN(ng)%Southern_Edge(tile)) THEN
!
! Southern edge, implicit upstream radiation condition.
!
IF (LBC(isouth,isU2Sd,ng)%radiation) THEN
DO i=IstrU-1,Iend
grad(i,Jstr-1)=ubar_stokes(i+1,Jstr-1)- &
& ubar_stokes(i ,Jstr-1)
grad(i,Jstr )=ubar_stokes(i+1,Jstr )- &
& ubar_stokes(i ,Jstr )
END DO
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
dUdt=ubar_stokes(i,Jstr)-ubar_stokes(i,Jstr )
dUde=ubar_stokes(i,Jstr)-ubar_stokes(i,Jstr+1)
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=MAX(dUdx*dUdx+dUde*dUde,eps)
# ifdef RADIATION_2D
Cx=MIN(cff,MAX(dUdt*dUdx,-cff))
# else
Cx=0.0_r8
# endif
Ce=dUdt*dUde
ubar_stokes(i,Jstr-1)=(cff*ubar_stokes(i,Jstr-1)+ &
& Ce*ubar_stokes(i,Jstr )- &
& MAX(Cx,0.0_r8)*grad(i-1,Jstr-1)- &
& MIN(Cx,0.0_r8)*grad(i ,Jstr-1))/ &
& (cff+Ce)
# ifdef MASKING
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
!
! Southern edge, clamped boundary condition.
!
ELSE IF (LBC(isouth,isU2Sd,ng)%clamped) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
ubar_stokes(i,Jstr-1)=BOUNDARY(ng)%ubarstokes_south(i)
# ifdef MASKING
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
!
! Southern edge, gradient boundary condition.
!
ELSE IF (LBC(isouth,isU2Sd,ng)%gradient) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr)
# ifdef MASKING
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
END IF
END DO
!
! Southern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (LBC(isouth,isU2Sd,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO i=Imin,Imax
IF (LBC_apply(ng)%south(i)) THEN
ubar_stokes(i,Jstr-1)=gamma2(ng)*ubar_stokes(i,Jstr)
# ifdef MASKING
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jstr-1)=ubar_stokes(i,Jstr-1)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Lateral boundary conditions at the northern edge.
!-----------------------------------------------------------------------
!
IF (DOMAIN(ng)%Northern_Edge(tile)) THEN
!
! Northern edge, implicit upstream radiation condition.
!
IF (LBC(inorth,isU2Sd,ng)%radiation) THEN
DO i=IstrU-1,Iend
grad(i,Jend )=ubar_stokes(i+1,Jend )- &
& ubar_stokes(i ,Jend )
grad(i,Jend+1)=ubar_stokes(i+1,Jend+1)- &
& ubar_stokes(i ,Jend+1)
END DO
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
dUdt=ubar_stokes(i,Jend)-ubar_stokes(i,Jend )
dUde=ubar_stokes(i,Jend)-ubar_stokes(i,Jend-1)
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=MAX(dUdx*dUdx+dUde*dUde,eps)
# ifdef RADIATION_2D
Cx=MIN(cff,MAX(dUdt*dUdx,-cff))
# else
Cx=0.0_r8
# endif
Ce=dUdt*dUde
ubar_stokes(i,Jend+1)=(cff*ubar_stokes(i,Jend+1)+ &
& Ce *ubar_stokes(i,Jend )- &
& MAX(Cx,0.0_r8)*grad(i-1,Jend+1)- &
& MIN(Cx,0.0_r8)*grad(i ,Jend+1))/ &
& (cff+Ce)
# ifdef MASKING
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
!
! Northern edge, clamped boundary condition.
!
ELSE IF (LBC(inorth,isU2Sd,ng)%clamped) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
ubar_stokes(i,Jend+1)=BOUNDARY(ng)%ubarstokes_north(i)
# ifdef MASKING
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
!
! Northern edge, gradient boundary condition.
!
ELSE IF (LBC(inorth,isU2Sd,ng)%gradient) THEN
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend)
# ifdef MASKING
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask(i,Jend+1)
# endif
END IF
END DO
!
! Northern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (LBC(inorth,isU2Sd,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO i=Imin,Imax
IF (LBC_apply(ng)%north(i)) THEN
ubar_stokes(i,Jend+1)=gamma2(ng)*ubar_stokes(i,Jend)
# ifdef MASKING
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
ubar_stokes(i,Jend+1)=ubar_stokes(i,Jend+1)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
END IF
END IF
!
!-----------------------------------------------------------------------
! Boundary corners.
!-----------------------------------------------------------------------
!
IF (.not.(EWperiodic(ng).or.NSperiodic(ng))) THEN
IF (DOMAIN(ng)%SouthWest_Corner(tile)) THEN
IF (LBC_apply(ng)%south(Istr ).and. &
& LBC_apply(ng)%west (Jstr-1)) THEN
ubar_stokes(Istr,Jstr-1)=0.5_r8* &
& (ubar_stokes(Istr+1,Jstr-1)+ &
& ubar_stokes(Istr ,Jstr ))
END IF
END IF
IF (DOMAIN(ng)%SouthEast_Corner(tile)) THEN
IF (LBC_apply(ng)%south(Iend+1).and. &
& LBC_apply(ng)%east (Jstr-1)) THEN
ubar_stokes(Iend+1,Jstr-1)=0.5_r8* &
& (ubar_stokes(Iend ,Jstr-1)+ &
& ubar_stokes(Iend+1,Jstr ))
END IF
END IF
IF (DOMAIN(ng)%NorthWest_Corner(tile)) THEN
IF (LBC_apply(ng)%north(Istr ).and. &
& LBC_apply(ng)%west (Jend+1)) THEN
ubar_stokes(Istr,Jend+1)=0.5_r8* &
& (ubar_stokes(Istr ,Jend )+ &
& ubar_stokes(Istr+1,Jend+1))
END IF
END IF
IF (DOMAIN(ng)%NorthEast_Corner(tile)) THEN
IF (LBC_apply(ng)%north(Iend+1).and. &
& LBC_apply(ng)%east (Jend+1)) THEN
ubar_stokes(Iend+1,Jend+1)=0.5_r8* &
& (ubar_stokes(Iend+1,Jend )+ &
& ubar_stokes(Iend ,Jend+1))
END IF
END IF
END IF
RETURN
END SUBROUTINE us2dbc_tile
#endif
END MODULE us2dbc_mod