#include "cppdefs.h"
MODULE u3dbc_mod
#ifdef SOLVE3D
!
!git $Id$
!svn $Id: u3dbc_ex.F 1151 2023-02-09 03:08:53Z arango $
!=======================================================================
! Copyright (c) 2002-2023 The ROMS/TOMS Group !
! Licensed under a MIT/X style license !
! See License_ROMS.md Hernan G. Arango !
!========================================== Alexander F. Shchepetkin ===
! !
! This subroutine sets lateral boundary conditions for total 3D !
! U-velocity. !
! !
!=======================================================================
!
implicit none
!
PRIVATE
PUBLIC :: u3dbc_tile
!
CONTAINS
!
!***********************************************************************
SUBROUTINE u3dbc (ng, tile, nout)
!***********************************************************************
!
USE mod_param
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile, nout
!
! Local variable declarations.
!
# include "tile.h"
!
CALL u3dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, N(ng), &
& IminS, ImaxS, JminS, JmaxS, &
& nstp(ng), nout, &
& OCEAN(ng) % u)
RETURN
END SUBROUTINE u3dbc
!
!***********************************************************************
SUBROUTINE u3dbc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, UBk, &
& IminS, ImaxS, JminS, JmaxS, &
& nstp, nout, &
& u)
!***********************************************************************
!
USE mod_param
USE mod_boundary
USE mod_clima
USE mod_grid
USE mod_ncparam
USE mod_scalars
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj, UBk
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: nstp, nout
!
# ifdef ASSUMED_SHAPE
real(r8), intent(inout) :: u(LBi:,LBj:,:,:)
# else
real(r8), intent(inout) :: u(LBi:UBi,LBj:UBj,UBk,2)
# endif
!
! Local variable declarations.
!
integer :: Imin, Imax
integer :: i, j, k
real(r8), parameter :: eps = 1.0E-20_r8
real(r8) :: Ce, Cx, cff, dUde, dUdt, dUdx
real(r8) :: obc_in, obc_out, 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,isUvel,ng)%radiation) THEN
DO k=1,N(ng)
DO j=Jstr,Jend+1
grad(Istr ,j)=u(Istr ,j ,k,nstp)- &
& u(Istr ,j-1,k,nstp)
grad(Istr+1,j)=u(Istr+1,j ,k,nstp)- &
& u(Istr+1,j-1,k,nstp)
END DO
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
dUdt=u(Istr+1,j,k,nstp)-u(Istr+1,j,k,nout)
dUdx=u(Istr+1,j,k,nstp)-u(Istr+2,j,k,nstp)
IF (LBC(iwest,isUvel,ng)%nudging) THEN
IF (LnudgeM3CLM(ng)) THEN
obc_out=0.5_r8* &
& (CLIMA(ng)%M3nudgcof(Istr-1,j,k)+ &
& CLIMA(ng)%M3nudgcof(Istr ,j,k))
obc_in =obcfac(ng)*obc_out
ELSE
obc_out=M3obc_out(ng,iwest)
obc_in =M3obc_in (ng,iwest)
END IF
IF ((dUdt*dUdx).lt.0.0_r8) THEN
tau=obc_in
ELSE
tau=obc_out
END IF
tau=tau*dt(ng)
END IF
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(cff*dUde,-1.0_r8))
# else
Ce=0.0_r8
# endif
# if defined CELERITY_WRITE && defined FORWARD_WRITE
BOUNDARY(ng)%u_west_Cx(j,k)=Cx
BOUNDARY(ng)%u_west_Ce(j,k)=Ce
BOUNDARY(ng)%u_west_C2(j,k)=cff
# endif
u(Istr,j,k,nout)=(1.0_r8-Cx)*u(Istr,j,k,nstp)+ &
& Cx*u(Istr+1,j,k,nstp)- &
& MAX(Ce,0.0_r8)*grad(Istr,j )- &
& MIN(Ce,0.0_r8)*grad(Istr,j+1)
IF (LBC(iwest,isUvel,ng)%nudging) THEN
u(Istr,j,k,nout)=u(Istr,j,k,nout)+ &
& tau*(BOUNDARY(ng)%u_west(j,k)- &
& u(Istr,j,k,nstp))
END IF
# ifdef MASKING
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
END DO
!
! Western edge, clamped boundary condition.
!
ELSE IF (LBC(iwest,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
u(Istr,j,k,nout)=BOUNDARY(ng)%u_west(j,k)
# ifdef MASKING
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
END DO
!
! Western edge, gradient boundary condition.
!
ELSE IF (LBC(iwest,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
u(Istr,j,k,nout)=u(Istr+1,j,k,nout)
# ifdef MASKING
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask(Istr,j)
# endif
# ifdef WET_DRY
u(Istr,j,k,nout)=u(Istr,j,k,nout)* &
& GRID(ng)%umask_wet(Istr,j)
# endif
END IF
END DO
END DO
!
! Western edge, closed boundary condition.
!
ELSE IF (LBC(iwest,isUvel,ng)%closed) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%west(j)) THEN
u(Istr,j,k,nout)=0.0_r8
END IF
END DO
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,isUvel,ng)%radiation) THEN
DO k=1,N(ng)
DO j=Jstr,Jend+1
grad(Iend ,j)=u(Iend ,j ,k,nstp)- &
& u(Iend ,j-1,k,nstp)
grad(Iend+1,j)=u(Iend+1,j ,k,nstp)- &
& u(Iend+1,j-1,k,nstp)
END DO
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
dUdt=u(Iend,j,k,nstp)-u(Iend ,j,k,nout)
dUdx=u(Iend,j,k,nstp)-u(Iend-1,j,k,nstp)
IF (LBC(ieast,isUvel,ng)%nudging) THEN
IF (LnudgeM3CLM(ng)) THEN
obc_out=0.5_r8* &
& (CLIMA(ng)%M3nudgcof(Iend ,j,k)+ &
& CLIMA(ng)%M3nudgcof(Iend+1,j,k))
obc_in =obcfac(ng)*obc_out
ELSE
obc_out=M3obc_out(ng,ieast)
obc_in =M3obc_in (ng,ieast)
END IF
IF ((dUdt*dUdx).lt.0.0_r8) THEN
tau=obc_in
ELSE
tau=obc_out
END IF
tau=tau*dt(ng)
END IF
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(cff*dUde,-1.0_r8))
# else
Ce=0.0_r8
# endif
# if defined CELERITY_WRITE && defined FORWARD_WRITE
BOUNDARY(ng)%u_east_Cx(j,k)=Cx
BOUNDARY(ng)%u_east_Ce(j,k)=Ce
BOUNDARY(ng)%u_east_C2(j,k)=cff
# endif
u(Iend+1,j,k,nout)=(1.0_r8-Cx)*u(Iend+1,j,k,nstp)+ &
& Cx*u(Iend,j,k,nstp)- &
& MAX(Ce,0.0_r8)*grad(Iend+1,j )- &
& MIN(Ce,0.0_r8)*grad(Iend+1,j+1)
IF (LBC(ieast,isUvel,ng)%nudging) THEN
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)+ &
& tau*(BOUNDARY(ng)%u_east(j,k)- &
& u(Iend+1,j,k,nstp))
END IF
# ifdef MASKING
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
END DO
!
! Eastern edge, clamped boundary condition.
!
ELSE IF (LBC(ieast,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
u(Iend+1,j,k,nout)=BOUNDARY(ng)%u_east(j,k)
# ifdef MASKING
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
END DO
!
! Eastern edge, gradient boundary condition.
!
ELSE IF (LBC(ieast,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
u(Iend+1,j,k,nout)=u(Iend,j,k,nout)
# ifdef MASKING
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask(Iend+1,j)
# endif
# ifdef WET_DRY
u(Iend+1,j,k,nout)=u(Iend+1,j,k,nout)* &
& GRID(ng)%umask_wet(Iend+1,j)
# endif
END IF
END DO
END DO
!
! Eastern edge, closed boundary condition.
!
ELSE IF (LBC(ieast,isUvel,ng)%closed) THEN
DO k=1,N(ng)
DO j=Jstr,Jend
IF (LBC_apply(ng)%east(j)) THEN
u(Iend+1,j,k,nout)=0.0_r8
END IF
END DO
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,isUvel,ng)%radiation) THEN
DO k=1,N(ng)
DO i=IstrU-1,Iend
grad(i,Jstr-1)=u(i+1,Jstr-1,k,nstp)- &
& u(i ,Jstr-1,k,nstp)
grad(i,Jstr )=u(i+1,Jstr ,k,nstp)- &
& u(i ,Jstr ,k,nstp)
END DO
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
dUdt=u(i,Jstr,k,nstp)-u(i,Jstr ,k,nout)
dUde=u(i,Jstr,k,nstp)-u(i,Jstr+1,k,nstp)
IF (LBC(isouth,isUvel,ng)%nudging) THEN
IF (LnudgeM3CLM(ng)) THEN
obc_out=0.5_r8* &
& (CLIMA(ng)%M3nudgcof(i-1,Jstr-1,k)+ &
& CLIMA(ng)%M3nudgcof(i ,Jstr-1,k))
obc_in =obcfac(ng)*obc_out
ELSE
obc_out=M3obc_out(ng,isouth)
obc_in =M3obc_in (ng,isouth)
END IF
IF ((dUdt*dUde).lt.0.0_r8) THEN
tau=obc_in
ELSE
tau=obc_out
END IF
tau=tau*dt(ng)
END IF
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(cff*dUdx,-1.0_r8))
# else
Cx=0.0_r8
# endif
Ce=MIN(1.0_r8,cff*dUde)
# if defined CELERITY_WRITE && defined FORWARD_WRITE
BOUNDARY(ng)%u_south_Cx(i,k)=Cx
BOUNDARY(ng)%u_south_Ce(i,k)=Ce
BOUNDARY(ng)%u_south_C2(i,k)=cff
# endif
u(i,Jstr-1,k,nout)=(1.0_r8-Ce)*u(i,Jstr-1,k,nstp)+ &
& Ce*u(i,Jstr,k,nstp)- &
& MAX(Cx,0.0_r8)*grad(i-1,Jstr-1)- &
& MIN(Cx,0.0_r8)*grad(i ,Jstr-1)
IF (LBC(isouth,isUvel,ng)%nudging) THEN
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)+ &
& tau*(BOUNDARY(ng)%u_south(i,k)- &
& u(i,Jstr-1,k,nstp))
END IF
# ifdef MASKING
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
END DO
!
! Southern edge, clamped boundary condition.
!
ELSE IF (LBC(isouth,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
u(i,Jstr-1,k,nout)=BOUNDARY(ng)%u_south(i,k)
# ifdef MASKING
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
END DO
!
! Southern edge, gradient boundary condition.
!
ELSE IF (LBC(isouth,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%south(i)) THEN
u(i,Jstr-1,k,nout)=u(i,Jstr,k,nout)
# ifdef MASKING
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_MASK
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
END DO
!
! Southern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (LBC(isouth,isUvel,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO k=1,N(ng)
DO i=Imin,Imax
IF (LBC_apply(ng)%south(i)) THEN
u(i,Jstr-1,k,nout)=gamma2(ng)*u(i,Jstr,k,nout)
# ifdef MASKING
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask(i,Jstr-1)
# endif
# ifdef WET_DRY
u(i,Jstr-1,k,nout)=u(i,Jstr-1,k,nout)* &
& GRID(ng)%umask_wet(i,Jstr-1)
# endif
END IF
END DO
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,isUvel,ng)%radiation) THEN
DO k=1,N(ng)
DO i=IstrU-1,Iend
grad(i,Jend )=u(i+1,Jend ,k,nstp)- &
& u(i ,Jend ,k,nstp)
grad(i,Jend+1)=u(i+1,Jend+1,k,nstp)- &
& u(i ,Jend+1,k,nstp)
END DO
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
dUdt=u(i,Jend,k,nstp)-u(i,Jend ,k,nout)
dUde=u(i,Jend,k,nstp)-u(i,Jend-1,k,nstp)
IF (LBC(inorth,isUvel,ng)%nudging) THEN
IF (LnudgeM3CLM(ng)) THEN
obc_out=0.5_r8* &
& (CLIMA(ng)%M3nudgcof(i-1,Jend+1,k)+ &
& CLIMA(ng)%M3nudgcof(i ,Jend+1,k))
obc_in =obcfac(ng)*obc_out
ELSE
obc_out=M3obc_out(ng,inorth)
obc_in =M3obc_in (ng,inorth)
END IF
IF ((dUdt*dUde).lt.0.0_r8) THEN
tau=obc_in
ELSE
tau=obc_out
END IF
tau=tau*dt(ng)
END IF
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(cff*dUdx,-1.0_r8))
# else
Cx=0.0_r8
# endif
Ce=MIN(1.0_r8,cff*dUde)
# if defined CELERITY_WRITE && defined FORWARD_WRITE
BOUNDARY(ng)%u_north_Cx(i,k)=Cx
BOUNDARY(ng)%u_north_Ce(i,k)=Ce
BOUNDARY(ng)%u_north_C2(i,k)=cff
# endif
u(i,Jend+1,k,nout)=(1.0_r8-Ce)*u(i,Jend+1,k,nstp)+ &
& Ce*u(i,Jend,k,nstp)- &
& MAX(Cx,0.0_r8)*grad(i-1,Jend+1)- &
& MIN(Cx,0.0_r8)*grad(i ,Jend+1)
IF (LBC(inorth,isUvel,ng)%nudging) THEN
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)+ &
& tau*(BOUNDARY(ng)%u_north(i,k)- &
& u(i,Jend+1,k,nstp))
END IF
# ifdef MASKING
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
END DO
!
! Northern edge, clamped boundary condition.
!
ELSE IF (LBC(inorth,isUvel,ng)%clamped) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
u(i,Jend+1,k,nout)=BOUNDARY(ng)%u_north(i,k)
# ifdef MASKING
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
END DO
!
! Northern edge, gradient boundary condition.
!
ELSE IF (LBC(inorth,isUvel,ng)%gradient) THEN
DO k=1,N(ng)
DO i=IstrU,Iend
IF (LBC_apply(ng)%north(i)) THEN
u(i,Jend+1,k,nout)=u(i,Jend,k,nout)
# ifdef MASKING
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
END DO
!
! Northern edge, closed boundary condition: free slip (gamma2=1) or
! no slip (gamma2=-1).
!
ELSE IF (LBC(inorth,isUvel,ng)%closed) THEN
IF (EWperiodic(ng)) THEN
Imin=IstrU
Imax=Iend
ELSE
Imin=Istr
Imax=IendR
END IF
DO k=1,N(ng)
DO i=Imin,Imax
IF (LBC_apply(ng)%north(i)) THEN
u(i,Jend+1,k,nout)=gamma2(ng)*u(i,Jend,k,nout)
# ifdef MASKING
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask(i,Jend+1)
# endif
# ifdef WET_DRY
u(i,Jend+1,k,nout)=u(i,Jend+1,k,nout)* &
& GRID(ng)%umask_wet(i,Jend+1)
# endif
END IF
END DO
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
DO k=1,N(ng)
u(Istr,Jstr-1,k,nout)=0.5_r8*(u(Istr+1,Jstr-1,k,nout)+ &
& u(Istr ,Jstr ,k,nout))
END DO
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
DO k=1,N(ng)
u(Iend+1,Jstr-1,k,nout)=0.5_r8*(u(Iend ,Jstr-1,k,nout)+ &
& u(Iend+1,Jstr ,k,nout))
END DO
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
DO k=1,N(ng)
u(Istr,Jend+1,k,nout)=0.5_r8*(u(Istr ,Jend ,k,nout)+ &
& u(Istr+1,Jend+1,k,nout))
END DO
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
DO k=1,N(ng)
u(Iend+1,Jend+1,k,nout)=0.5_r8*(u(Iend+1,Jend ,k,nout)+ &
& u(Iend ,Jend+1,k,nout))
END DO
END IF
END IF
END IF
RETURN
END SUBROUTINE u3dbc_tile
#endif
END MODULE u3dbc_mod