SUBROUTINE pres

!------------------------------------------------------------------------------!
! Actual revisions:
! -----------------
! Volume flow conservation added for the remaining three outflow boundaries
!
! Former revisions:
! -----------------
! $Id: pres.f90 106 2007-08-16 14:30:26Z letzel $
!
! 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 poisfft_hybrid_mod
    USE statistics

    IMPLICIT NONE

    INTEGER ::  i, j, k, sr

    REAL    ::  ddt_3d, localsum, threadsum

    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

!
!-- Multigrid method needs additional grid points for the divergence array
    IF ( psolver == 'multigrid' )  THEN
       DEALLOCATE( d )
       ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
    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) * dzu(k)
          ENDDO
       ENDDO

#if defined( __parallel )   
       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 = nys, nyn
          DO  k = nzb_v_inner(j,i) + 1, nzt
             u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
          ENDDO
       ENDDO

       CALL exchange_horiz( u )

    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) * dzu(k)
          ENDDO
       ENDDO

#if defined( __parallel )   
       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 = nxl, nxr
          DO  k = nzb_v_inner(j,i) + 1, nzt
             v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
          ENDDO
       ENDDO

       CALL exchange_horiz( v )

    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 is 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 )   
          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 = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                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 )
       DO  i = nxl, nxra
          DO  j = nys, nyna
             DO  k = nzb+1, nzta
                d(k,j,i) = 0.0
             ENDDO
          ENDDO
       ENDDO
    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
          ENDDO
!
!--       Additional pressure boundary condition at the bottom boundary for 
!--       inhomogeneous Prandtl layer heat fluxes and temperatures, respectively
!--       dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0.
!--       This condition must not be applied at the start of a run, because then
!--       flow_statistics has not yet been called and thus sums = 0.
          IF ( ibc_p_b == 2  .AND.  sums(nzb+1,4) /= 0.0 )  THEN
             k = nzb_s_inner(j,i)
             d(k+1,j,i) = d(k+1,j,i) + (                                     &
                                         ( usws(j,i+1) - usws(j,i) ) * ddx   &
                                       + ( vsws(j+1,i) - vsws(j,i) ) * ddy   &
                                       - g * ( pt(k+1,j,i) - sums(k+1,4) ) / &
                                         sums(k+1,4)                         &
                                       ) * ddzw(k+1) * ddt_3d
          ENDIF

!
!--       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
    !$OMP END PARALLEL
#else
    IF ( ibc_p_b == 2 .AND. sums(nzb+1,4) /= 0.0 )  THEN
       !$OMP PARALLEL PRIVATE (i,j,k)
       !$OMP DO SCHEDULE( STATIC )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb_s_inner(j,i)+1, nzt
                d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
                             ( v(k,j+1,i) - v(k,j,i) ) * ddy + &
                             ( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d
             ENDDO
          ENDDO
!
!--       Additional pressure boundary condition at the bottom boundary for
!--       inhomogeneous Prandtl layer heat fluxes and temperatures, respectively
!--       dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0.
!--       This condition must not be applied at the start of a run, because then
!--       flow_statistics has not yet been called and thus sums = 0.
          DO  j = nys, nyn
              k = nzb_s_inner(j,i)
              d(k+1,j,i) = d(k+1,j,i) + (                        &
                             ( usws(j,i+1) - usws(j,i) ) * ddx   &
                           + ( vsws(j+1,i) - vsws(j,i) ) * ddy   &
                           - g * ( pt(k+1,j,i) - sums(k+1,4) ) / &
                             sums(k+1,4)                         &
                                        ) * ddzw(k+1) * ddt_3d
          ENDDO
       ENDDO
       !$OMP END PARALLEL

    ELSE

       !$OMP PARALLEL PRIVATE (i,j,k)
       !$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
             ENDDO
          ENDDO
       ENDDO
       !$OMP END PARALLEL

    ENDIF

!
!-- Compute possible PE-sum of divergences for flow_statistics
    !$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
    !$OMP DO SCHEDULE( STATIC )
    DO  i = nxl, nxr
       DO  j = nys, nyn
          DO  k = nzb+1, nzt
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO
       ENDDO
    ENDDO
    localsum = ( localsum + threadsum ) * dt_3d
    !$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

!
!-- Determine absolute minimum/maximum (only for test cases, therefore as
!-- comment line)
!    CALL global_min_max( nzb+1, nzt, nys, nyn, nxl, nxr, d, 'abs', divmax, &
!                         divmax_ijk )

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

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

!
!--    Enlarge the size of tend, used as a working array for the transpositions
       IF ( nxra > nxr  .OR.  nyna > nyn  .OR.  nza > nz )  THEN
          DEALLOCATE( tend )
          ALLOCATE( tend(1:nza,nys:nyna,nxl:nxra) )
       ENDIF

!
!--    Solve Poisson equation via FFT and solution of tridiagonal matrices
       IF ( psolver == 'poisfft' )  THEN
!
!--       Solver for 2d-decomposition
          CALL poisfft( d, tend )
       ELSEIF ( psolver == 'poisfft_hybrid' )  THEN 
!
!--       Solver for 1d-decomposition (using MPI and OpenMP).
!--       The old hybrid-solver is still included here, as long as there
!--       are some optimization problems in poisfft
          CALL poisfft_hybrid( d )
       ENDIF

!
!--    Resize tend to its normal size
       IF ( nxra > nxr  .OR.  nyna > nyn  .OR.  nza > nz )  THEN
          DEALLOCATE( tend )
          ALLOCATE( tend(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
       ENDIF

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

!
!--    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
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO

       ELSEIF ( ibc_p_b == 2 )  THEN
!
!--       Neumann condition for inhomogeneous surfaces,
!--       here currently still in the form of a zero gradient. Actually 
!--       dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0 would have to be used for
!--       the computation (cf. above: computation of divergences).
          !$OMP PARALLEL DO
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
             ENDDO
          ENDDO

       ELSE
!
!--       Dirichlet
          !$OMP PARALLEL DO
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                tend(nzb_s_inner(j,i),j,i) = 0.0
             ENDDO
          ENDDO

       ENDIF

!
!--    Top boundary
       IF ( ibc_p_t == 1 )  THEN
!
!--       Neumann
          !$OMP PARALLEL DO
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                tend(nzt+1,j,i) = tend(nzt,j,i)
             ENDDO
          ENDDO

       ELSE
!
!--       Dirichlet
          !$OMP PARALLEL DO
          DO  i = nxl-1, nxr+1
             DO  j = nys-1, nyn+1
                tend(nzt+1,j,i) = 0.0
             ENDDO
          ENDDO

       ENDIF

!
!--    Exchange boundaries for p
       CALL exchange_horiz( tend )
      
    ELSEIF ( psolver == 'sor' )  THEN

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

    ELSEIF ( psolver == 'multigrid' )  THEN

!
!--    Solve Poisson equation for perturbation pressure using Multigrid scheme,
!--    array tend is used to store the residuals
       CALL poismg( tend )
 
!
!--    Restore perturbation pressure on tend because this array is used
!--    further below to correct the velocity fields
       tend = p

    ENDIF

!
!-- Store perturbation pressure on array p, used in the momentum equations
    IF ( psolver(1:7) == 'poisfft' )  THEN
!
!--    Here, only the values from the left and right boundaries are copied
!--    The remaining values are copied in the following loop due to speed
!--    optimization
       !$OMP PARALLEL DO
       DO  j = nys-1, nyn+1
          DO  k = nzb, nzt+1
             p(k,j,nxl-1) = tend(k,j,nxl-1)
             p(k,j,nxr+1) = tend(k,j,nxr+1)
          ENDDO
       ENDDO
    ENDIF

!
!-- Correction of the provisional velocities with the current perturbation 
!-- pressure just computed
    IF ( conserve_volume_flow  .AND. &
         ( bc_lr == 'cyclic'  .OR.  bc_ns == 'cyclic' ) )  THEN
       volume_flow_l(1) = 0.0
       volume_flow_l(2) = 0.0
    ENDIF
    !$OMP PARALLEL PRIVATE (i,j,k)
    !$OMP DO
    DO  i = nxl, nxr
       IF ( psolver(1:7) == 'poisfft' )  THEN
          DO  j = nys-1, nyn+1
             DO  k = nzb, nzt+1
                p(k,j,i) = tend(k,j,i)
             ENDDO
          ENDDO
       ENDIF
       DO  j = nys, nyn
          DO  k = nzb_w_inner(j,i)+1, nzt
             w(k,j,i) = w(k,j,i) - dt_3d * &
                                   ( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1)
          ENDDO
          DO  k = nzb_u_inner(j,i)+1, nzt
             u(k,j,i) = u(k,j,i) - dt_3d * ( tend(k,j,i) - tend(k,j,i-1) ) * ddx
          ENDDO
          DO  k = nzb_v_inner(j,i)+1, nzt
             v(k,j,i) = v(k,j,i) - dt_3d * ( tend(k,j,i) - tend(k,j-1,i) ) * ddy
          ENDDO

!
!--       Sum up the volume flow through the right and north boundary
          IF ( conserve_volume_flow  .AND.  bc_lr == 'cyclic'  .AND. &
               i == nx )  THEN
             !$OMP CRITICAL
             DO  k = nzb_2d(j,i) + 1, nzt
                volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzu(k)
             ENDDO
             !$OMP END CRITICAL
          ENDIF
          IF ( conserve_volume_flow  .AND.  bc_ns == 'cyclic'  .AND. &
               j == ny )  THEN
             !$OMP CRITICAL
             DO  k = nzb_2d(j,i) + 1, nzt
                volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzu(k)
             ENDDO
             !$OMP END CRITICAL
          ENDIF

       ENDDO
    ENDDO
    !$OMP END PARALLEL

!
!-- Conserve the volume flow
    IF ( conserve_volume_flow  .AND. &
         ( bc_lr == 'cyclic'  .OR.  bc_ns == 'cyclic' ) )  THEN

#if defined( __parallel )   
       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
             IF ( bc_lr == 'cyclic' )  THEN
                DO  k = nzb_u_inner(j,i) + 1, nzt
                   u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
                ENDDO
             ENDIF
             IF ( bc_ns == 'cyclic' )  THEN
                DO  k = nzb_v_inner(j,i) + 1, nzt
                   v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
                ENDDO
             ENDIF
          ENDDO
       ENDDO
       !$OMP END PARALLEL

    ENDIF

!
!-- Exchange of boundaries for the velocities
    CALL exchange_horiz( u )
    CALL exchange_horiz( v )
    CALL exchange_horiz( w )

!
!-- 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
    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)
             threadsum = threadsum + ABS( d(k,j,i) )
          ENDDO
       ENDDO
    ENDDO
#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