source: palm/trunk/SOURCE/pres.f90 @ 1289

 SUBROUTINE pres

!--------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM is free software: you can redistribute it and/or modify it under the terms
! of the GNU General Public License as published by the Free Software Foundation,
! either version 3 of the License, or (at your option) any later version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2012  Leibniz University Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
!
!
! Former revisions:
! -----------------
! $Id: pres.f90 1258 2013-11-08 16:09:09Z raasch $
!
! 1257 2013-11-08 15:18:40Z raasch
! openacc loop and loop vector clauses removed, independent clauses added,
! end parallel replaced by end parallel loop
!
! 1221 2013-09-10 08:59:13Z raasch
! openACC porting of reduction operations, loops for calculating d are
! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
!
! 1212 2013-08-15 08:46:27Z raasch
! call of poisfft_hybrid removed
!
! 1117 2013-03-27 11:15:36Z suehring
! Bugfix in OpenMP parallelization.
!
! 1113 2013-03-10 02:48:14Z raasch
! GPU-porting of several loops, some loops rearranged
!
! 1111 2013-03-08 23:54:10Z
! openACC statements added,
! ibc_p_b = 2 removed
!
! 1092 2013-02-02 11:24:22Z raasch
! unused variables removed
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1003 2012-09-14 14:35:53Z raasch
! adjustment of array tend for cases with unequal subdomain sizes removed
!
! 778 2011-11-07 14:18:25Z fricke
! New allocation of tend when multigrid is used and the collected field on PE0
! has more grid points than the subdomain of an PE.
!
! 719 2011-04-06 13:05:23Z gryschka
! Bugfix in volume flow control for double cyclic boundary conditions
!
! 709 2011-03-30 09:31:40Z raasch
! formatting adjustments
!
! 707 2011-03-29 11:39:40Z raasch
! Calculation of weighted average of p is now handled in the same way
! regardless of the number of ghost layers (advection scheme),
! multigrid and sor method are using p_loc for iterative advancements of
! pressure, 
! localsum calculation modified for proper OpenMP reduction,
! bc_lr/ns replaced by bc_lr/ns_cyc
!
! 693 2011-03-08 09:..:..Z raasch
! bugfix: weighting coefficient added to ibm branch
!
! 680 2011-02-04 23:16:06Z gryschka
! bugfix: collective_wait
!
! 675 2011-01-19 10:56:55Z suehring
! Removed bugfix while copying tend.
!
! 673 2011-01-18 16:19:48Z suehring
! Weighting coefficients added for right computation of the pressure during
! Runge-Kutta substeps. 
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! New allocation of tend when ws-scheme and multigrid is used. This is due to 
! reasons of perforance of the data_exchange. The same is done with p after
! poismg is called.
! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no 
! multigrid is used. Calls of exchange_horiz are modified.
! bugfix: After pressure correction no volume flow correction in case of 
! non-cyclic boundary conditions 
! (has to be done only before pressure correction)
! Call of SOR routine is referenced with ddzu_pres.
!
! 622 2010-12-10 08:08:13Z raasch
! optional barriers included in order to speed up collective operations
!
! 151 2008-03-07 13:42:18Z raasch
! Bugfix in volume flow control for non-cyclic boundary conditions
!
! 106 2007-08-16 14:30:26Z raasch
! Volume flow conservation added for the remaining three outflow boundaries
!
! 85 2007-05-11 09:35:14Z raasch
! Division through dt_3d replaced by multiplication of the inverse.
! For performance optimisation, this is done in the loop calculating the
! divergence instead of using a seperate loop.
!
! 75 2007-03-22 09:54:05Z raasch
! Volume flow control for non-cyclic boundary conditions added (currently only
! for the north boundary!!), 2nd+3rd argument removed from exchange horiz,
! mean vertical velocity is removed in case of Neumann boundary conditions
! both at the bottom and the top
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.25  2006/04/26 13:26:12  raasch
! OpenMP optimization (+localsum, threadsum)
!
! Revision 1.1  1997/07/24 11:24:44  raasch
! Initial revision
!
!
! Description:
! ------------
! Compute the divergence of the provisional velocity field. Solve the Poisson
! equation for the perturbation pressure. Compute the final velocities using
! this perturbation pressure. Compute the remaining divergence.
!------------------------------------------------------------------------------!

    USE arrays_3d
    USE constants
    USE control_parameters
    USE cpulog
    USE grid_variables
    USE indices
    USE interfaces
    USE pegrid
    USE poisfft_mod
    USE statistics

    IMPLICIT NONE

    INTEGER ::  i, j, k

    REAL    ::  ddt_3d, localsum, threadsum, d_weight_pres

    REAL, DIMENSION(1:2) ::  volume_flow_l, volume_flow_offset
    REAL, DIMENSION(1:nzt) ::  w_l, w_l_l


    CALL cpu_log( log_point(8), 'pres', 'start' )


    ddt_3d = 1.0 / dt_3d
    d_weight_pres = 1.0 / weight_pres(intermediate_timestep_count)

!
!-- Multigrid method expects array d to have one ghost layer.
!-- 
    IF ( psolver == 'multigrid' )  THEN
     
       DEALLOCATE( d )
       ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) ) 

!
!--    Since p is later used to hold the weighted average of the substeps, it
!--    cannot be used in the iterative solver. Therefore, its initial value is
!--    stored on p_loc, which is then iteratively advanced in every substep.
       IF ( intermediate_timestep_count == 1 )  THEN
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                DO  k = nzb, nzt+1
                   p_loc(k,j,i) = p(k,j,i)
                ENDDO
             ENDDO
          ENDDO
       ENDIF
       
    ELSEIF ( psolver == 'sor'  .AND.  intermediate_timestep_count == 1 )  THEN

!
!--    Since p is later used to hold the weighted average of the substeps, it
!--    cannot be used in the iterative solver. Therefore, its initial value is
!--    stored on p_loc, which is then iteratively advanced in every substep.
       p_loc = p

    ENDIF

!
!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
!-- boundary conditions
!-- WARNING: so far, this conservation does not work at the left/south
!--          boundary if the topography at the inflow differs from that at the
!--          outflow! For this case, volume_flow_area needs adjustment!
!
!-- Left/right
    IF ( conserve_volume_flow  .AND.  ( outflow_l .OR. outflow_r ) )  THEN

       volume_flow(1)   = 0.0
       volume_flow_l(1) = 0.0

       IF ( outflow_l )  THEN
          i = 0
       ELSEIF ( outflow_r )  THEN
          i = nx+1
       ENDIF

       DO  j = nys, nyn
!
!--       Sum up the volume flow through the south/north boundary
          DO  k = nzb_2d(j,i)+1, nzt
             volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
          ENDDO
       ENDDO

#if defined( __parallel )   
       IF ( collective_wait )  CALL MPI_BARRIER( comm1dy, ierr )
       CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
                           MPI_SUM, comm1dy, ierr )   
#else
       volume_flow = volume_flow_l  
#endif
       volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
                               / volume_flow_area(1)

       DO  j = nysg, nyng
          DO  k = nzb_2d(j,i)+1, nzt
             u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
          ENDDO
       ENDDO

    ENDIF

!
!-- South/north
    IF ( conserve_volume_flow  .AND.  ( outflow_n .OR. outflow_s ) )  THEN

       volume_flow(2)   = 0.0
       volume_flow_l(2) = 0.0

       IF ( outflow_s )  THEN
          j = 0
       ELSEIF ( outflow_n )  THEN
          j = ny+1
       ENDIF

       DO  i = nxl, nxr
!
!--       Sum up the volume flow through the south/north boundary
          DO  k = nzb_2d(j,i)+1, nzt
             volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
          ENDDO
       ENDDO

#if defined( __parallel )   
       IF ( collective_wait )  CALL MPI_BARRIER( comm1dx, ierr )
       CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
                           MPI_SUM, comm1dx, ierr )   
#else
       volume_flow = volume_flow_l  
#endif
       volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) )    &
                               / volume_flow_area(2)

       DO  i = nxlg, nxrg
          DO  k = nzb_v_inner(j,i)+1, nzt
             v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
          ENDDO
       ENDDO

    ENDIF

!
!-- Remove mean vertical velocity
    IF ( ibc_p_b == 1  .AND.  ibc_p_t == 1 )  THEN
       IF ( simulated_time > 0.0 )  THEN ! otherwise nzb_w_inner not yet known
          w_l = 0.0;  w_l_l = 0.0
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb_w_inner(j,i)+1, nzt
                   w_l_l(k) = w_l_l(k) + w(k,j,i)
                ENDDO
             ENDDO
          ENDDO
#if defined( __parallel )   
          IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
          CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
                              comm2d, ierr )
#else
          w_l = w_l_l  
#endif
          DO  k = 1, nzt
             w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
          ENDDO
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                DO  k = nzb_w_inner(j,i)+1, nzt
                   w(k,j,i) = w(k,j,i) - w_l(k)
                ENDDO
             ENDDO
          ENDDO
       ENDIF
    ENDIF

!
!-- Compute the divergence of the provisional velocity field.
    CALL cpu_log( log_point_s(1), 'divergence', 'start' )

    IF ( psolver == 'multigrid' )  THEN
       !$OMP PARALLEL DO SCHEDULE( STATIC )
       DO  i = nxl-1, nxr+1
          DO  j = nys-1, nyn+1
             DO  k = nzb, nzt+1
                d(k,j,i) = 0.0
             ENDDO
          ENDDO
       ENDDO
    ELSE
       !$OMP PARALLEL DO SCHEDULE( STATIC )
       !$acc kernels present( d )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                d(k,j,i) = 0.0
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels
    ENDIF

    localsum  = 0.0
    threadsum = 0.0

#if defined( __ibm )
    !$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
    !$OMP DO SCHEDULE( STATIC )
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb_s_inner(j,i)+1, nzt
             d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
                          ( v(k,j+1,i) - v(k,j,i) ) * ddy + &
                          ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d      &
                                                                * d_weight_pres 
          ENDDO
!
!--       Compute possible PE-sum of divergences for flow_statistics
          DO  k = nzb_s_inner(j,i)+1, nzt
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO

       ENDDO
    ENDDO

    localsum = localsum + threadsum * dt_3d * &
                          weight_pres(intermediate_timestep_count)

    !$OMP END PARALLEL
#else

    !$OMP PARALLEL PRIVATE (i,j,k)
    !$OMP DO SCHEDULE( STATIC )
    !$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
    !$acc loop collapse( 3 )
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = 1, nzt
             d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx +             &
                        ( v(k,j+1,i) - v(k,j,i) ) * ddy +               &
                        ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d  &
                        * d_weight_pres * rflags_s_inner(k,j,i)
          ENDDO
       ENDDO
    ENDDO
    !$acc end kernels
    !$OMP END PARALLEL

!
!-- Compute possible PE-sum of divergences for flow_statistics
    !$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
    !$OMP DO SCHEDULE( STATIC )
    !$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO
       ENDDO
    ENDDO
    !$acc end parallel loop
    localsum = localsum + threadsum * dt_3d * &
                          weight_pres(intermediate_timestep_count)
    !$OMP END PARALLEL
#endif

!
!-- For completeness, set the divergence sum of all statistic regions to those
!-- of the total domain
    sums_divold_l(0:statistic_regions) = localsum

    CALL cpu_log( log_point_s(1), 'divergence', 'stop' )

!
!-- Compute the pressure perturbation solving the Poisson equation
    IF ( psolver(1:7) == 'poisfft' )  THEN

!
!--    Solve Poisson equation via FFT and solution of tridiagonal matrices
       IF ( psolver == 'poisfft' )  THEN

          CALL poisfft( d, tend )

       ENDIF

!
!--    Store computed perturbation pressure and set boundary condition in
!--    z-direction
       !$OMP PARALLEL DO
       !$acc kernels present( d, tend )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                tend(k,j,i) = d(k,j,i)
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels

!
!--    Bottom boundary:
!--    This condition is only required for internal output. The pressure
!--    gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
       IF ( ibc_p_b == 1 )  THEN
!
!--       Neumann (dp/dz = 0)
          !$OMP PARALLEL DO
          !$acc kernels present( nzb_s_inner, tend )
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO
          !$acc end kernels

       ELSE
!
!--       Dirichlet
          !$OMP PARALLEL DO
          !$acc kernels present( tend )
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                tend(nzb_s_inner(j,i),j,i) = 0.0
             ENDDO
          ENDDO
          !$acc end kernels

       ENDIF

!
!--    Top boundary
       IF ( ibc_p_t == 1 )  THEN
!
!--       Neumann
          !$OMP PARALLEL DO
          !$acc kernels present( tend )
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                tend(nzt+1,j,i) = tend(nzt,j,i)
             ENDDO
          ENDDO
          !$acc end kernels

       ELSE
!
!--       Dirichlet
          !$OMP PARALLEL DO
          !$acc kernels present( tend )
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                tend(nzt+1,j,i) = 0.0
             ENDDO
          ENDDO
          !$acc end kernels

       ENDIF

!
!--    Exchange boundaries for p
       IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
          on_device = .TRUE.         ! to be removed after complete porting
       ELSE                          ! of ghost point exchange
          !$acc update host( tend )
       ENDIF
       CALL exchange_horiz( tend, nbgp )
       IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
          on_device = .FALSE.        ! to be removed after complete porting
       ELSE                          ! of ghost point exchange
          !$acc update device( tend )
       ENDIF
      
    ELSEIF ( psolver == 'sor' )  THEN

!
!--    Solve Poisson equation for perturbation pressure using SOR-Red/Black
!--    scheme
       CALL sor( d, ddzu_pres, ddzw, p_loc )
       tend = p_loc

    ELSEIF ( psolver == 'multigrid' )  THEN

!
!--    Solve Poisson equation for perturbation pressure using Multigrid scheme,
!--    array tend is used to store the residuals, logical exchange_mg is used
!--    to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
!--    ( nbgp ghost points ).

!--    If the number of grid points of the gathered grid, which is collected
!--    on PE0, is larger than the number of grid points of an PE, than array
!--    tend will be enlarged. 
       IF ( gathered_size > subdomain_size )  THEN
          DEALLOCATE( tend )
          ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg(          &
                    mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
                    nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg(                   &
                    mg_switch_to_pe0_level)+1) )
       ENDIF

       CALL poismg( tend )

       IF ( gathered_size > subdomain_size )  THEN
          DEALLOCATE( tend )
          ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
       ENDIF

!
!--    Restore perturbation pressure on tend because this array is used
!--    further below to correct the velocity fields
       DO  i = nxl-1, nxr+1
          DO  j = nys-1, nyn+1
             DO  k = nzb, nzt+1
                tend(k,j,i) = p_loc(k,j,i)
             ENDDO
          ENDDO
       ENDDO

    ENDIF

!
!-- Store perturbation pressure on array p, used for pressure data output.
!-- Ghost layers are added in the output routines (except sor-method: see below)
    IF ( intermediate_timestep_count == 1 )  THEN
       !$OMP PARALLEL PRIVATE (i,j,k)
       !$OMP DO
       !$acc kernels present( p, tend, weight_substep )
       !$acc loop independent
       DO  i = nxl-1, nxr+1
          !$acc loop independent
          DO  j = nys-1, nyn+1
             !$acc loop independent
             DO  k = nzb, nzt+1
                p(k,j,i) = tend(k,j,i) * &
                           weight_substep(intermediate_timestep_count)
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels
       !$OMP END PARALLEL

    ELSE 
       !$OMP PARALLEL PRIVATE (i,j,k)
       !$OMP DO
       !$acc kernels present( p, tend, weight_substep )
       !$acc loop independent
       DO  i = nxl-1, nxr+1
          !$acc loop independent
          DO  j = nys-1, nyn+1
             !$acc loop independent
             DO  k = nzb, nzt+1
                p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
                           weight_substep(intermediate_timestep_count)
             ENDDO
          ENDDO
       ENDDO
       !$acc end kernels
       !$OMP END PARALLEL

    ENDIF
       
!
!-- SOR-method needs ghost layers for the next timestep
    IF ( psolver == 'sor' )  CALL exchange_horiz( p, nbgp )

!
!-- Correction of the provisional velocities with the current perturbation 
!-- pressure just computed
    IF ( conserve_volume_flow  .AND.  ( bc_lr_cyc .OR. bc_ns_cyc ) )  THEN
       volume_flow_l(1) = 0.0
       volume_flow_l(2) = 0.0
    ENDIF

    !$OMP PARALLEL PRIVATE (i,j,k)
    !$OMP DO
    !$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
    !$acc loop independent
    DO  i = nxl, nxr   
       !$acc loop independent
       DO  j = nys, nyn
          !$acc loop independent
          DO  k = 1, nzt
             IF ( k > nzb_w_inner(j,i) )  THEN
                w(k,j,i) = w(k,j,i) - dt_3d *                                 &
                           ( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) *      &
                           weight_pres(intermediate_timestep_count)
             ENDIF
          ENDDO
          !$acc loop independent
          DO  k = 1, nzt
             IF ( k > nzb_u_inner(j,i) )  THEN
                u(k,j,i) = u(k,j,i) - dt_3d *                                 &
                           ( tend(k,j,i) - tend(k,j,i-1) ) * ddx *            &
                           weight_pres(intermediate_timestep_count)
             ENDIF
          ENDDO
          !$acc loop independent
          DO  k = 1, nzt
             IF ( k > nzb_v_inner(j,i) )  THEN
                v(k,j,i) = v(k,j,i) - dt_3d *                                 &
                           ( tend(k,j,i) - tend(k,j-1,i) ) * ddy *            &
                           weight_pres(intermediate_timestep_count)
             ENDIF
          ENDDO                                                         

       ENDDO
    ENDDO
    !$acc end kernels
    !$OMP END PARALLEL

!
!-- Sum up the volume flow through the right and north boundary
    IF ( conserve_volume_flow  .AND.  bc_lr_cyc  .AND.  bc_ns_cyc  .AND.  &
         nxr == nx )  THEN

       !$OMP PARALLEL PRIVATE (j,k)
       !$OMP DO
       DO  j = nys, nyn
          !$OMP CRITICAL
          DO  k = nzb_2d(j,nx) + 1, nzt
             volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
          ENDDO
          !$OMP END CRITICAL
       ENDDO
       !$OMP END PARALLEL

    ENDIF

    IF ( conserve_volume_flow  .AND.  bc_ns_cyc  .AND.  bc_lr_cyc  .AND.  &
         nyn == ny )  THEN

       !$OMP PARALLEL PRIVATE (i,k)
       !$OMP DO
       DO  i = nxl, nxr
          !$OMP CRITICAL
          DO  k = nzb_2d(ny,i) + 1, nzt
             volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
           ENDDO
          !$OMP END CRITICAL
       ENDDO
       !$OMP END PARALLEL

    ENDIF
    
!
!-- Conserve the volume flow
    IF ( conserve_volume_flow  .AND.  ( bc_lr_cyc  .AND.  bc_ns_cyc ) )  THEN

#if defined( __parallel )   
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
                           MPI_SUM, comm2d, ierr )  
#else
       volume_flow = volume_flow_l  
#endif   

       volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
                            volume_flow_area

       !$OMP PARALLEL PRIVATE (i,j,k)
       !$OMP DO
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_u_inner(j,i) + 1, nzt
                u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
             ENDDO
             DO k = nzb_v_inner(j,i) + 1, nzt
                v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
             ENDDO
          ENDDO
       ENDDO

       !$OMP END PARALLEL

    ENDIF

!
!-- Exchange of boundaries for the velocities
    IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
       on_device = .TRUE.         ! to be removed after complete porting
    ELSE                          ! of ghost point exchange
       !$acc update host( u, v, w )
    ENDIF
    CALL exchange_horiz( u, nbgp )
    CALL exchange_horiz( v, nbgp )
    CALL exchange_horiz( w, nbgp )
    IF ( numprocs == 1 )  THEN    ! workaround for single-core GPU runs
       on_device = .FALSE.        ! to be removed after complete porting
    ELSE                          ! of ghost point exchange
       !$acc update device( u, v, w )
    ENDIF

!
!-- Compute the divergence of the corrected velocity field,
!-- a possible PE-sum is computed in flow_statistics 
    CALL cpu_log( log_point_s(1), 'divergence', 'start' )
    sums_divnew_l = 0.0

!
!-- d must be reset to zero because it can contain nonzero values below the
!-- topography
    IF ( topography /= 'flat' )  d = 0.0

    localsum  = 0.0
    threadsum = 0.0

    !$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
    !$OMP DO SCHEDULE( STATIC )
#if defined( __ibm )
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb_s_inner(j,i)+1, nzt
             d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
                        ( v(k,j+1,i) - v(k,j,i) ) * ddy + &
                        ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
          ENDDO
          DO  k = nzb+1, nzt
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO
       ENDDO
    ENDDO
#else
    !$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
    !$acc loop collapse( 3 )
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = 1, nzt
                d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx +   &
                             ( v(k,j+1,i) - v(k,j,i) ) * ddy +   &
                             ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
                           ) * rflags_s_inner(k,j,i)
          ENDDO
       ENDDO
    ENDDO
    !$acc end kernels
!
!-- Compute possible PE-sum of divergences for flow_statistics
    !$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO
       ENDDO
    ENDDO
    !$acc end parallel loop
#endif

    localsum = localsum + threadsum
    !$OMP END PARALLEL

!
!-- For completeness, set the divergence sum of all statistic regions to those
!-- of the total domain
    sums_divnew_l(0:statistic_regions) = localsum

    CALL cpu_log( log_point_s(1), 'divergence', 'stop' )

    CALL cpu_log( log_point(8), 'pres', 'stop' )


 END SUBROUTINE pres