source: palm/trunk/SOURCE/boundary_conds.f90 @ 844

 SUBROUTINE boundary_conds( range )

!------------------------------------------------------------------------------!
! Current revisions:
! -----------------
! 
!  
! Former revisions:
! -----------------
! $Id: boundary_conds.f90 768 2011-10-14 06:57:15Z gryschka $
!
! 767 2011-10-14 06:39:12Z raasch
! ug,vg replaced by u_init,v_init as the Dirichlet top boundary condition
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
! Removed mirror boundary conditions for u and v at the bottom in case of 
! ibc_uv_b == 0. Instead, dirichelt boundary conditions (u=v=0) are set
! in init_3d_model 
!
! 107 2007-08-17 13:54:45Z raasch
! Boundary conditions for temperature adjusted for coupled runs,
! bugfixes for the radiation boundary conditions at the outflow: radiation
! conditions are used for every substep, phase speeds are calculated for the
! first Runge-Kutta substep only and then reused, several index values changed
!
! 95 2007-06-02 16:48:38Z raasch
! Boundary conditions for salinity added
!
! 75 2007-03-22 09:54:05Z raasch
! The "main" part sets conditions for time level t+dt instead of level t,
! outflow boundary conditions changed from Neumann to radiation condition,
! uxrp, vynp eliminated, moisture renamed humidity
!
! 19 2007-02-23 04:53:48Z raasch
! Boundary conditions for e(nzt), pt(nzt), and q(nzt) removed because these
! gridpoints are now calculated by the prognostic equation,
! Dirichlet and zero gradient condition for pt established at top boundary
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.15  2006/02/23 09:54:55  raasch
! Surface boundary conditions in case of topography: nzb replaced by
! 2d-k-index-arrays (nzb_w_inner, etc.). Conditions for u and v remain
! unchanged (still using nzb) because a non-flat topography must use a
! Prandtl-layer, which don't requires explicit setting of the surface values.
!
! Revision 1.1  1997/09/12 06:21:34  raasch
! Initial revision
!
!
! Description:
! ------------
! Boundary conditions for the prognostic quantities (range='main').
! In case of non-cyclic lateral boundaries the conditions for velocities at
! the outflow are set after the pressure solver has been called (range=
! 'outflow_uvw').
! One additional bottom boundary condition is applied for the TKE (=(u*)**2)
! in prandtl_fluxes. The cyclic lateral boundary conditions are implicitly
! handled in routine exchange_horiz. Pressure boundary conditions are
! explicitly set in routines pres, poisfft, poismg and sor.
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE control_parameters
    USE grid_variables
    USE indices
    USE pegrid

    IMPLICIT NONE

    CHARACTER (LEN=*) ::  range

    INTEGER ::  i, j, k

    REAL    ::  c_max, denom


    IF ( range == 'main')  THEN
!
!--    Bottom boundary 
       IF ( ibc_uv_b == 1 )  THEN
          u_p(nzb,:,:) = u_p(nzb+1,:,:)
          v_p(nzb,:,:) = v_p(nzb+1,:,:)
       ENDIF
       DO  i = nxlg, nxrg
          DO  j = nysg, nyng
             w_p(nzb_w_inner(j,i),j,i) = 0.0
          ENDDO
       ENDDO

!
!--    Top boundary
       IF ( ibc_uv_t == 0 )  THEN
           u_p(nzt+1,:,:) = u_init(nzt+1)
           v_p(nzt+1,:,:) = v_init(nzt+1)
       ELSE
           u_p(nzt+1,:,:) = u_p(nzt,:,:)
           v_p(nzt+1,:,:) = v_p(nzt,:,:)
       ENDIF
       w_p(nzt:nzt+1,:,:) = 0.0  ! nzt is not a prognostic level (but cf. pres)

!
!--    Temperature at bottom boundary.
!--    In case of coupled runs (ibc_pt_b = 2) the temperature is given by
!--    the sea surface temperature of the coupled ocean model.
       IF ( ibc_pt_b == 0 )  THEN
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                pt_p(nzb_s_inner(j,i),j,i) = pt(nzb_s_inner(j,i),j,i)
             ENDDO
          ENDDO
       ELSEIF ( ibc_pt_b == 1 )  THEN
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                pt_p(nzb_s_inner(j,i),j,i) = pt_p(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO
       ENDIF

!
!--    Temperature at top boundary
       IF ( ibc_pt_t == 0 )  THEN
           pt_p(nzt+1,:,:) = pt(nzt+1,:,:)
       ELSEIF ( ibc_pt_t == 1 )  THEN
           pt_p(nzt+1,:,:) = pt_p(nzt,:,:)
       ELSEIF ( ibc_pt_t == 2 )  THEN
           pt_p(nzt+1,:,:) = pt_p(nzt,:,:)   + bc_pt_t_val * dzu(nzt+1)
       ENDIF

!
!--    Boundary conditions for TKE
!--    Generally Neumann conditions with de/dz=0 are assumed
       IF ( .NOT. constant_diffusion )  THEN
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                e_p(nzb_s_inner(j,i),j,i) = e_p(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO
          e_p(nzt+1,:,:) = e_p(nzt,:,:)
       ENDIF

!
!--    Boundary conditions for salinity
       IF ( ocean )  THEN
!
!--       Bottom boundary: Neumann condition because salinity flux is always
!--       given
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                sa_p(nzb_s_inner(j,i),j,i) = sa_p(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO

!
!--       Top boundary: Dirichlet or Neumann
          IF ( ibc_sa_t == 0 )  THEN
              sa_p(nzt+1,:,:) = sa(nzt+1,:,:)
          ELSEIF ( ibc_sa_t == 1 )  THEN
              sa_p(nzt+1,:,:) = sa_p(nzt,:,:)
          ENDIF

       ENDIF

!
!--    Boundary conditions for total water content or scalar,
!--    bottom and top boundary (see also temperature)
       IF ( humidity  .OR.  passive_scalar )  THEN
!
!--       Surface conditions for constant_humidity_flux
          IF ( ibc_q_b == 0 ) THEN
             DO  i = nxlg, nxrg
                DO  j = nysg, nyng
                   q_p(nzb_s_inner(j,i),j,i) = q(nzb_s_inner(j,i),j,i)
                ENDDO
             ENDDO
          ELSE
             DO  i = nxlg, nxrg
                DO  j = nysg, nyng
                   q_p(nzb_s_inner(j,i),j,i) = q_p(nzb_s_inner(j,i)+1,j,i)
                ENDDO
             ENDDO
          ENDIF
!
!--       Top boundary
          q_p(nzt+1,:,:) = q_p(nzt,:,:)   + bc_q_t_val * dzu(nzt+1)


       ENDIF

!
!--    Lateral boundary conditions at the inflow. Quasi Neumann conditions
!--    are needed for the wall normal velocity in order to ensure zero
!--    divergence. Dirichlet conditions are used for all other quantities.
       IF ( inflow_s )  THEN
          v_p(:,nys,:) = v_p(:,nys-1,:)
       ELSEIF ( inflow_n ) THEN
          v_p(:,nyn,:) = v_p(:,nyn+1,:)
       ELSEIF ( inflow_l ) THEN
          u_p(:,:,nxl) = u_p(:,:,nxl-1)
       ELSEIF ( inflow_r ) THEN
          u_p(:,:,nxr) = u_p(:,:,nxr+1)
       ENDIF

!
!--    Lateral boundary conditions for scalar quantities at the outflow
       IF ( outflow_s )  THEN
          pt_p(:,nys-1,:)     = pt_p(:,nys,:)
          IF ( .NOT. constant_diffusion     )  e_p(:,nys-1,:) = e_p(:,nys,:)
          IF ( humidity .OR. passive_scalar )  q_p(:,nys-1,:) = q_p(:,nys,:)
       ELSEIF ( outflow_n )  THEN
          pt_p(:,nyn+1,:)     = pt_p(:,nyn,:)
          IF ( .NOT. constant_diffusion     )  e_p(:,nyn+1,:) = e_p(:,nyn,:)
          IF ( humidity .OR. passive_scalar )  q_p(:,nyn+1,:) = q_p(:,nyn,:)
       ELSEIF ( outflow_l )  THEN
          pt_p(:,:,nxl-1)     = pt_p(:,:,nxl)
          IF ( .NOT. constant_diffusion     )  e_p(:,:,nxl-1) = e_p(:,:,nxl)
          IF ( humidity .OR. passive_scalar )  q_p(:,:,nxl-1) = q_p(:,:,nxl)
       ELSEIF ( outflow_r )  THEN
          pt_p(:,:,nxr+1)     = pt_p(:,:,nxr)
          IF ( .NOT. constant_diffusion     )  e_p(:,:,nxr+1) = e_p(:,:,nxr)
          IF ( humidity .OR. passive_scalar )  q_p(:,:,nxr+1) = q_p(:,:,nxr)
       ENDIF

    ENDIF

!
!-- Radiation boundary condition for the velocities at the respective outflow
    IF ( outflow_s )  THEN

       c_max = dy / dt_3d

       DO i = nxlg, nxrg
          DO k = nzb+1, nzt+1

!
!--          Calculate the phase speeds for u,v, and w. In case of using a
!--          Runge-Kutta scheme, do this for the first substep only and then
!--          reuse this values for the further substeps.
             IF ( intermediate_timestep_count == 1 )  THEN

                denom = u_m_s(k,0,i) - u_m_s(k,1,i)

                IF ( denom /= 0.0 )  THEN
                   c_u(k,i) = -c_max * ( u(k,0,i) - u_m_s(k,0,i) ) / denom
                   IF ( c_u(k,i) < 0.0 )  THEN
                      c_u(k,i) = 0.0
                   ELSEIF ( c_u(k,i) > c_max )  THEN
                      c_u(k,i) = c_max
                   ENDIF
                ELSE
                   c_u(k,i) = c_max
                ENDIF

                denom = v_m_s(k,1,i) - v_m_s(k,2,i)

                IF ( denom /= 0.0 )  THEN
                   c_v(k,i) = -c_max * ( v(k,1,i) - v_m_s(k,1,i) ) / denom
                   IF ( c_v(k,i) < 0.0 )  THEN
                      c_v(k,i) = 0.0
                   ELSEIF ( c_v(k,i) > c_max )  THEN
                      c_v(k,i) = c_max
                   ENDIF
                ELSE
                   c_v(k,i) = c_max
                ENDIF

                denom = w_m_s(k,0,i) - w_m_s(k,1,i)

                IF ( denom /= 0.0 )  THEN
                   c_w(k,i) = -c_max * ( w(k,0,i) - w_m_s(k,0,i) ) / denom
                   IF ( c_w(k,i) < 0.0 )  THEN
                      c_w(k,i) = 0.0
                   ELSEIF ( c_w(k,i) > c_max )  THEN
                      c_w(k,i) = c_max
                   ENDIF
                ELSE
                   c_w(k,i) = c_max
                ENDIF

!
!--             Save old timelevels for the next timestep
                u_m_s(k,:,i) = u(k,0:1,i)
                v_m_s(k,:,i) = v(k,1:2,i)
                w_m_s(k,:,i) = w(k,0:1,i)

             ENDIF

!
!--          Calculate the new velocities
             u_p(k,-1,i) = u(k,-1,i) - dt_3d * tsc(2) * c_u(k,i) * &
                                       ( u(k,-1,i) - u(k,0,i) ) * ddy

             v_p(k,0,i)  = v(k,0,i)  - dt_3d * tsc(2) * c_v(k,i) * &
                                       ( v(k,0,i) - v(k,1,i) ) * ddy

             w_p(k,-1,i) = w(k,-1,i) - dt_3d * tsc(2) * c_w(k,i) * &
                                       ( w(k,-1,i) - w(k,0,i) ) * ddy

          ENDDO
       ENDDO

!
!--    Bottom boundary at the outflow
       IF ( ibc_uv_b == 0 )  THEN
          u_p(nzb,-1,:) = 0.0 
          v_p(nzb,0,:)  = 0.0  
       ELSE                    
          u_p(nzb,-1,:) =  u_p(nzb+1,-1,:)
          v_p(nzb,0,:)  =  v_p(nzb+1,0,:)
       ENDIF
       w_p(nzb,-1,:) = 0.0

!
!--    Top boundary at the outflow
       IF ( ibc_uv_t == 0 )  THEN
          u_p(nzt+1,-1,:) = u_init(nzt+1)
          v_p(nzt+1,0,:)  = v_init(nzt+1)
       ELSE
          u_p(nzt+1,-1,:) = u(nzt,-1,:)
          v_p(nzt+1,0,:)  = v(nzt,0,:)
       ENDIF
       w_p(nzt:nzt+1,-1,:) = 0.0

    ENDIF

    IF ( outflow_n )  THEN

       c_max = dy / dt_3d

       DO i = nxlg, nxrg
          DO k = nzb+1, nzt+1

!
!--          Calculate the phase speeds for u,v, and w. In case of using a
!--          Runge-Kutta scheme, do this for the first substep only and then
!--          reuse this values for the further substeps.
             IF ( intermediate_timestep_count == 1 )  THEN

                denom = u_m_n(k,ny,i) - u_m_n(k,ny-1,i)

                IF ( denom /= 0.0 )  THEN
                   c_u(k,i) = -c_max * ( u(k,ny,i) - u_m_n(k,ny,i) ) / denom
                   IF ( c_u(k,i) < 0.0 )  THEN
                      c_u(k,i) = 0.0
                   ELSEIF ( c_u(k,i) > c_max )  THEN
                      c_u(k,i) = c_max
                   ENDIF
                ELSE
                   c_u(k,i) = c_max
                ENDIF

                denom = v_m_n(k,ny,i) - v_m_n(k,ny-1,i)

                IF ( denom /= 0.0 )  THEN
                   c_v(k,i) = -c_max * ( v(k,ny,i) - v_m_n(k,ny,i) ) / denom
                   IF ( c_v(k,i) < 0.0 )  THEN
                      c_v(k,i) = 0.0
                   ELSEIF ( c_v(k,i) > c_max )  THEN
                      c_v(k,i) = c_max
                   ENDIF
                ELSE
                   c_v(k,i) = c_max
                ENDIF

                denom = w_m_n(k,ny,i) - w_m_n(k,ny-1,i)

                IF ( denom /= 0.0 )  THEN
                   c_w(k,i) = -c_max * ( w(k,ny,i) - w_m_n(k,ny,i) ) / denom
                   IF ( c_w(k,i) < 0.0 )  THEN
                      c_w(k,i) = 0.0
                   ELSEIF ( c_w(k,i) > c_max )  THEN
                      c_w(k,i) = c_max
                   ENDIF
                ELSE
                   c_w(k,i) = c_max
                ENDIF

!
!--             Swap timelevels for the next timestep
                u_m_n(k,:,i) = u(k,ny-1:ny,i)
                v_m_n(k,:,i) = v(k,ny-1:ny,i)
                w_m_n(k,:,i) = w(k,ny-1:ny,i)

             ENDIF

!
!--          Calculate the new velocities
             u_p(k,ny+1,i) = u(k,ny+1,i) - dt_3d * tsc(2) * c_u(k,i) * &
                                           ( u(k,ny+1,i) - u(k,ny,i) ) * ddy

             v_p(k,ny+1,i) = v(k,ny+1,i) - dt_3d * tsc(2) * c_v(k,i) * &
                                           ( v(k,ny+1,i) - v(k,ny,i) ) * ddy

             w_p(k,ny+1,i) = w(k,ny+1,i) - dt_3d * tsc(2) * c_w(k,i) * &
                                           ( w(k,ny+1,i) - w(k,ny,i) ) * ddy

          ENDDO
       ENDDO

!
!--    Bottom boundary at the outflow
       IF ( ibc_uv_b == 0 )  THEN
          u_p(nzb,ny+1,:) = 0.0 
          v_p(nzb,ny+1,:) = 0.0   
       ELSE                    
          u_p(nzb,ny+1,:) =  u_p(nzb+1,ny+1,:)
          v_p(nzb,ny+1,:) =  v_p(nzb+1,ny+1,:)
       ENDIF
       w_p(nzb,ny+1,:) = 0.0

!
!--    Top boundary at the outflow
       IF ( ibc_uv_t == 0 )  THEN
          u_p(nzt+1,ny+1,:) = u_init(nzt+1)
          v_p(nzt+1,ny+1,:) = v_init(nzt+1)
       ELSE
          u_p(nzt+1,ny+1,:) = u_p(nzt,nyn+1,:)
          v_p(nzt+1,ny+1,:) = v_p(nzt,nyn+1,:)
       ENDIF
       w_p(nzt:nzt+1,ny+1,:) = 0.0

    ENDIF

    IF ( outflow_l )  THEN

       c_max = dx / dt_3d

       DO j = nysg, nyng
          DO k = nzb+1, nzt+1

!
!--          Calculate the phase speeds for u,v, and w. In case of using a
!--          Runge-Kutta scheme, do this for the first substep only and then
!--          reuse this values for the further substeps.
             IF ( intermediate_timestep_count == 1 )  THEN

                denom = u_m_l(k,j,1) - u_m_l(k,j,2)

                IF ( denom /= 0.0 )  THEN
                   c_u(k,j) = -c_max * ( u(k,j,1) - u_m_l(k,j,1) ) / denom
                   IF ( c_u(k,j) < 0.0 )  THEN
                      c_u(k,j) = 0.0
                   ELSEIF ( c_u(k,j) > c_max )  THEN
                      c_u(k,j) = c_max
                   ENDIF
                ELSE
                   c_u(k,j) = c_max
                ENDIF

                denom = v_m_l(k,j,0) - v_m_l(k,j,1)

                IF ( denom /= 0.0 )  THEN
                   c_v(k,j) = -c_max * ( v(k,j,0) - v_m_l(k,j,0) ) / denom
                   IF ( c_v(k,j) < 0.0 )  THEN
                      c_v(k,j) = 0.0
                   ELSEIF ( c_v(k,j) > c_max )  THEN
                      c_v(k,j) = c_max
                   ENDIF
                ELSE
                   c_v(k,j) = c_max
                ENDIF

                denom = w_m_l(k,j,0) - w_m_l(k,j,1)

                IF ( denom /= 0.0 )  THEN
                   c_w(k,j) = -c_max * ( w(k,j,0) - w_m_l(k,j,0) ) / denom
                   IF ( c_w(k,j) < 0.0 )  THEN
                      c_w(k,j) = 0.0
                   ELSEIF ( c_w(k,j) > c_max )  THEN
                      c_w(k,j) = c_max
                   ENDIF
                ELSE
                   c_w(k,j) = c_max
                ENDIF

!
!--             Swap timelevels for the next timestep
                u_m_l(k,j,:) = u(k,j,1:2)
                v_m_l(k,j,:) = v(k,j,0:1)
                w_m_l(k,j,:) = w(k,j,0:1)

             ENDIF

!
!--          Calculate the new velocities
             u_p(k,j,0)  = u(k,j,0)  - dt_3d * tsc(2) * c_u(k,j) * &
                                       ( u(k,j,0) - u(k,j,1) ) * ddx

             v_p(k,j,-1) = v(k,j,-1) - dt_3d * tsc(2) * c_v(k,j) * &
                                       ( v(k,j,-1) - v(k,j,0) ) * ddx

             w_p(k,j,-1) = w(k,j,-1) - dt_3d * tsc(2) * c_w(k,j) * &
                                       ( w(k,j,-1) - w(k,j,0) ) * ddx

          ENDDO
       ENDDO

!
!--    Bottom boundary at the outflow
       IF ( ibc_uv_b == 0 )  THEN
          u_p(nzb,:,0)  = 0.0 
          v_p(nzb,:,-1) = 0.0
       ELSE                    
          u_p(nzb,:,0)  =  u_p(nzb+1,:,0)
          v_p(nzb,:,-1) =  v_p(nzb+1,:,-1)
       ENDIF
       w_p(nzb,:,-1) = 0.0

!
!--    Top boundary at the outflow
       IF ( ibc_uv_t == 0 )  THEN
          u_p(nzt+1,:,-1) = u_init(nzt+1)
          v_p(nzt+1,:,-1) = v_init(nzt+1)
       ELSE
          u_p(nzt+1,:,-1) = u_p(nzt,:,-1)
          v_p(nzt+1,:,-1) = v_p(nzt,:,-1)
       ENDIF
       w_p(nzt:nzt+1,:,-1) = 0.0

    ENDIF

    IF ( outflow_r )  THEN

       c_max = dx / dt_3d

       DO j = nysg, nyng
          DO k = nzb+1, nzt+1

!
!--          Calculate the phase speeds for u,v, and w. In case of using a
!--          Runge-Kutta scheme, do this for the first substep only and then
!--          reuse this values for the further substeps.
             IF ( intermediate_timestep_count == 1 )  THEN

                denom = u_m_r(k,j,nx) - u_m_r(k,j,nx-1)

                IF ( denom /= 0.0 )  THEN
                   c_u(k,j) = -c_max * ( u(k,j,nx) - u_m_r(k,j,nx) ) / denom
                   IF ( c_u(k,j) < 0.0 )  THEN
                      c_u(k,j) = 0.0
                   ELSEIF ( c_u(k,j) > c_max )  THEN
                      c_u(k,j) = c_max
                   ENDIF
                ELSE
                   c_u(k,j) = c_max
                ENDIF

                denom = v_m_r(k,j,nx) - v_m_r(k,j,nx-1)

                IF ( denom /= 0.0 )  THEN
                   c_v(k,j) = -c_max * ( v(k,j,nx) - v_m_r(k,j,nx) ) / denom
                   IF ( c_v(k,j) < 0.0 )  THEN
                      c_v(k,j) = 0.0
                   ELSEIF ( c_v(k,j) > c_max )  THEN
                      c_v(k,j) = c_max
                   ENDIF
                ELSE
                   c_v(k,j) = c_max
                ENDIF

                denom = w_m_r(k,j,nx) - w_m_r(k,j,nx-1)

                IF ( denom /= 0.0 )  THEN
                   c_w(k,j) = -c_max * ( w(k,j,nx) - w_m_r(k,j,nx) ) / denom
                   IF ( c_w(k,j) < 0.0 )  THEN
                      c_w(k,j) = 0.0
                   ELSEIF ( c_w(k,j) > c_max )  THEN
                      c_w(k,j) = c_max
                   ENDIF
                ELSE
                   c_w(k,j) = c_max
                ENDIF

!
!--             Swap timelevels for the next timestep
                u_m_r(k,j,:) = u(k,j,nx-1:nx)
                v_m_r(k,j,:) = v(k,j,nx-1:nx)
                w_m_r(k,j,:) = w(k,j,nx-1:nx)

             ENDIF

!
!--          Calculate the new velocities
             u_p(k,j,nx+1) = u(k,j,nx+1) - dt_3d * tsc(2) * c_u(k,j) * &
                                           ( u(k,j,nx+1) - u(k,j,nx) ) * ddx

             v_p(k,j,nx+1) = v(k,j,nx+1) - dt_3d * tsc(2) * c_v(k,j) * &
                                           ( v(k,j,nx+1) - v(k,j,nx) ) * ddx

             w_p(k,j,nx+1) = w(k,j,nx+1) - dt_3d * tsc(2) * c_w(k,j) * &
                                           ( w(k,j,nx+1) - w(k,j,nx) ) * ddx

          ENDDO
       ENDDO

!
!--    Bottom boundary at the outflow
       IF ( ibc_uv_b == 0 )  THEN
          u_p(nzb,:,nx+1) = 0.0
          v_p(nzb,:,nx+1) = 0.0 
       ELSE                    
          u_p(nzb,:,nx+1) =  u_p(nzb+1,:,nx+1)
          v_p(nzb,:,nx+1) =  v_p(nzb+1,:,nx+1)
       ENDIF
       w_p(nzb,:,nx+1) = 0.0

!
!--    Top boundary at the outflow
       IF ( ibc_uv_t == 0 )  THEN
          u_p(nzt+1,:,nx+1) = u_init(nzt+1)
          v_p(nzt+1,:,nx+1) = v_init(nzt+1)
       ELSE
          u_p(nzt+1,:,nx+1) = u_p(nzt,:,nx+1)
          v_p(nzt+1,:,nx+1) = v_p(nzt,:,nx+1)
       ENDIF
       w(nzt:nzt+1,:,nx+1) = 0.0

    ENDIF

 
 END SUBROUTINE boundary_conds