source: palm/trunk/SOURCE/timestep.f90 @ 4385

!> @file timestep.f90
!------------------------------------------------------------------------------!
! This file is part of the PALM model system.
!
! 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 1997-2020 Leibniz Universitaet Hannover
!------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
! 
! 
! Former revisions:
! -----------------
! $Id: timestep.f90 4360 2020-01-07 11:25:50Z hellstea $
! Added missing OpenMP directives
! 
! 4233 2019-09-20 09:55:54Z knoop
! OpenACC data update host removed
! 
! 4182 2019-08-22 15:20:23Z scharf
! Corrected "Former revisions" section
! 
! 4101 2019-07-17 15:14:26Z gronemeier
! - consider 2*Km within diffusion criterion as Km is considered twice within
!   the diffusion of e,
! - in RANS mode, instead of considering each wind component individually use
!   the wind speed of 3d wind vector in CFL criterion
! - do not limit the increase of dt based on its previous value in RANS mode
!
! 3658 2019-01-07 20:28:54Z knoop
! OpenACC port for SPEC
!
! Revision 1.1  1997/08/11 06:26:19  raasch
! Initial revision
!
!
! Description:
! ------------
!> Compute the time step under consideration of the FCL and diffusion criterion.
!------------------------------------------------------------------------------!
 SUBROUTINE timestep
 

    USE arrays_3d,                                                             &
        ONLY:  dzu, dzw, kh, km, u, u_stokes_zu, v, v_stokes_zu, w

    USE control_parameters,                                                    &
        ONLY:  cfl_factor, coupling_mode, dt_3d, dt_fixed, dt_max,             &
               galilei_transformation, message_string, rans_mode,              &
               stop_dt, terminate_coupled, terminate_coupled_remote,           &
               timestep_reason, u_gtrans, use_ug_for_galilei_tr, v_gtrans

    USE cpulog,                                                                &
        ONLY:  cpu_log, log_point

    USE grid_variables,                                                        &
        ONLY:  dx, dx2, dy, dy2

    USE indices,                                                               &
        ONLY:  nxl, nxlg, nxr, nxrg, nyn, nyng, nys, nysg, nzb, nzt

    USE interfaces

    USE kinds

    USE bulk_cloud_model_mod,                                                  &
        ONLY:  dt_precipitation

    USE pegrid

    USE pmc_interface,                                                         &
        ONLY:  nested_run

    USE statistics,                                                            &
        ONLY:  flow_statistics_called, hom, u_max, u_max_ijk, v_max, v_max_ijk,&
               w_max, w_max_ijk

    USE vertical_nesting_mod,                                                  &
        ONLY:  vnested, vnest_timestep_sync

    IMPLICIT NONE

    INTEGER(iwp) ::  i !< 
    INTEGER(iwp) ::  j !< 
    INTEGER(iwp) ::  k !< 
    INTEGER(iwp) ::  km_max_ijk(3) = -1  !< index values (i,j,k) of location where km_max occurs
    INTEGER(iwp) ::  kh_max_ijk(3) = -1  !< index values (i,j,k) of location where kh_max occurs

    LOGICAL ::  stop_dt_local !< local switch for controlling the time stepping

    REAL(wp) ::  div               !< 
    REAL(wp) ::  dt_diff           !< 
    REAL(wp) ::  dt_diff_l         !< 
    REAL(wp) ::  dt_u              !< 
    REAL(wp) ::  dt_u_l            !< 
    REAL(wp) ::  dt_v              !< 
    REAL(wp) ::  dt_v_l            !< 
    REAL(wp) ::  dt_w              !< 
    REAL(wp) ::  dt_w_l            !< 
    REAL(wp) ::  km_max            !< maximum of Km in entire domain
    REAL(wp) ::  kh_max            !< maximum of Kh in entire domain
    REAL(wp) ::  u_gtrans_l        !< 
    REAL(wp) ::  v_gtrans_l        !< 
 
    REAL(wp), DIMENSION(2)         ::  uv_gtrans   !< 
    REAL(wp), DIMENSION(2)         ::  uv_gtrans_l !< 
    REAL(wp), DIMENSION(3)         ::  reduce      !< 
    REAL(wp), DIMENSION(3)         ::  reduce_l    !< 
    REAL(wp), DIMENSION(nzb+1:nzt) ::  dxyz2_min   !<  
    !$ACC DECLARE CREATE(dxyz2_min)


    CALL cpu_log( log_point(12), 'calculate_timestep', 'start' )

!
!-- In case of Galilei-transform not using the geostrophic wind as translation
!-- velocity, compute the volume-averaged horizontal velocity components, which
!-- will then be subtracted from the horizontal wind for the time step and
!-- horizontal advection routines.
    IF ( galilei_transformation  .AND. .NOT.  use_ug_for_galilei_tr )  THEN
       IF ( flow_statistics_called )  THEN
!
!--       Horizontal averages already existent, just need to average them 
!--       vertically.
          u_gtrans = 0.0_wp
          v_gtrans = 0.0_wp
          DO  k = nzb+1, nzt
             u_gtrans = u_gtrans + hom(k,1,1,0)
             v_gtrans = v_gtrans + hom(k,1,2,0)
          ENDDO
          u_gtrans = u_gtrans / REAL( nzt - nzb, KIND=wp )
          v_gtrans = v_gtrans / REAL( nzt - nzb, KIND=wp )
       ELSE
!
!--       Averaging over the entire model domain.
          u_gtrans_l = 0.0_wp
          v_gtrans_l = 0.0_wp
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb+1, nzt
                   u_gtrans_l = u_gtrans_l + u(k,j,i)
                   v_gtrans_l = v_gtrans_l + v(k,j,i)
                ENDDO
             ENDDO
          ENDDO
          uv_gtrans_l(1) = u_gtrans_l /                                        &
                           REAL( (nxr-nxl+1)*(nyn-nys+1)*(nzt-nzb), KIND=wp )
          uv_gtrans_l(2) = v_gtrans_l /                                        &
                           REAL( (nxr-nxl+1)*(nyn-nys+1)*(nzt-nzb), KIND=wp )
#if defined( __parallel )
          IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
          CALL MPI_ALLREDUCE( uv_gtrans_l, uv_gtrans, 2, MPI_REAL, MPI_SUM,    &
                              comm2d, ierr )
          u_gtrans = uv_gtrans(1) / REAL( numprocs, KIND=wp )
          v_gtrans = uv_gtrans(2) / REAL( numprocs, KIND=wp )
#else
          u_gtrans = uv_gtrans_l(1)
          v_gtrans = uv_gtrans_l(2)
#endif
       ENDIF
    ENDIF

!
!-- Determine the maxima of the velocity components, including their
!-- grid index positions.
    CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, u, 'abs', 0.0_wp, &
                         u_max, u_max_ijk )
    CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, v, 'abs', 0.0_wp, &
                         v_max, v_max_ijk )
    CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, w, 'abs', 0.0_wp, &
                         w_max, w_max_ijk )

    IF ( .NOT. dt_fixed )  THEN
!
!--    Variable time step:
!--    Calculate the maximum time step according to the CFL-criterion
       dt_u_l = 999999.9_wp
       dt_v_l = 999999.9_wp
       dt_w_l = 999999.9_wp

       IF ( .NOT. rans_mode )  THEN
!
!--       Consider each velocity component individually

          !$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
          !$ACC COPY(dt_u_l, dt_v_l, dt_w_l, u_stokes_zu, v_stokes_zu) &
          !$ACC REDUCTION(MIN: dt_u_l, dt_v_l, dt_w_l) &
          !$ACC PRESENT(u, v, w, dzu)
          !$OMP PARALLEL DO PRIVATE(i,j,k) &
          !$OMP REDUCTION(MIN: dt_u_l, dt_v_l, dt_w_l)
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb+1, nzt
                   dt_u_l = MIN( dt_u_l, ( dx     /                               &
                                    ( ABS( u(k,j,i) - u_gtrans + u_stokes_zu(k) ) &
                                      + 1.0E-10_wp ) ) )
                   dt_v_l = MIN( dt_v_l, ( dy     /                               &
                                    ( ABS( v(k,j,i) - v_gtrans + v_stokes_zu(k) ) &
                                      + 1.0E-10_wp ) ) )
                   dt_w_l = MIN( dt_w_l, ( dzu(k) /                               &
                                    ( ABS( w(k,j,i) )            + 1.0E-10_wp ) ) )
                ENDDO
             ENDDO
          ENDDO

       ELSE
!
!--       Consider the wind speed at the scalar-grid point
!--       !> @note considering the wind speed instead of each individual wind
!--       !>       component is only a workaround so far. This might has to be
!--       !>       changed in the future.

          !$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
          !$ACC COPY(dt_u_l, u_stokes_zu, v_stokes_zu) &
          !$ACC REDUCTION(MIN: dt_u_l) &
          !$ACC PRESENT(u, v, w, dzu)
          !$OMP PARALLEL DO PRIVATE(i,j,k) &
          !$OMP REDUCTION(MIN: dt_u_l)
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb+1, nzt
                   dt_u_l = MIN( dt_u_l, ( MIN( dx, dy, dzu(k) ) / ( &
                      SQRT(  ( 0.5 * ( u(k,j,i) + u(k,j,i+1) ) - u_gtrans + u_stokes_zu(k) )**2   &
                           + ( 0.5 * ( v(k,j,i) + v(k,j+1,i) ) - v_gtrans + v_stokes_zu(k) )**2   &
                           + ( 0.5 * ( w(k,j,i) + w(k-1,j,i) )                             )**2 ) &
                      + 1.0E-10_wp ) ) )
                ENDDO
             ENDDO
          ENDDO
          
          dt_v_l = dt_u_l
          dt_w_l = dt_u_l

       ENDIF

#if defined( __parallel )
       reduce_l(1) = dt_u_l
       reduce_l(2) = dt_v_l
       reduce_l(3) = dt_w_l
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( reduce_l, reduce, 3, MPI_REAL, MPI_MIN, comm2d, ierr )
       dt_u = reduce(1)
       dt_v = reduce(2)
       dt_w = reduce(3)
#else
       dt_u = dt_u_l
       dt_v = dt_v_l
       dt_w = dt_w_l
#endif

!
!--    Compute time step according to the diffusion criterion.
!--    First calculate minimum grid spacing which only depends on index k.
!--    When using the dynamic subgrid model, negative km are possible.
       dt_diff_l = 999999.0_wp

       !$ACC PARALLEL LOOP PRESENT(dxyz2_min, dzw)
       DO  k = nzb+1, nzt
           dxyz2_min(k) = MIN( dx2, dy2, dzw(k)*dzw(k) ) * 0.125_wp
       ENDDO

       !$OMP PARALLEL private(i,j,k) reduction(MIN: dt_diff_l)
       !$OMP DO
       !$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
       !$ACC COPY(dt_diff_l) REDUCTION(MIN: dt_diff_l) &
       !$ACC PRESENT(dxyz2_min, kh, km)
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                dt_diff_l = MIN( dt_diff_l,                                       &
                                 dxyz2_min(k) /                                   &
                                    ( MAX( kh(k,j,i), 2.0_wp * ABS( km(k,j,i) ) ) &
                                      + 1E-20_wp ) )
             ENDDO
          ENDDO
       ENDDO
       !$OMP END PARALLEL
#if defined( __parallel )
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( dt_diff_l, dt_diff, 1, MPI_REAL, MPI_MIN, comm2d,   &
                           ierr )
#else
       dt_diff = dt_diff_l
#endif

!
!--    The time step is the minimum of the 3-4 components and the diffusion time
!--    step minus a reduction (cfl_factor) to be on the safe side.
!--    The time step must not exceed the maximum allowed value.
       dt_3d = cfl_factor * MIN( dt_diff, dt_u, dt_v, dt_w, dt_precipitation )
       dt_3d = MIN( dt_3d, dt_max )

!
!--    Remember the restricting time step criterion for later output.
       IF ( MIN( dt_u, dt_v, dt_w ) < dt_diff )  THEN
          timestep_reason = 'A'
       ELSE
          timestep_reason = 'D'
       ENDIF

!
!--    Set flag if the time step becomes too small.
       IF ( dt_3d < ( 0.00001_wp * dt_max ) )  THEN
          stop_dt = .TRUE.

!
!--       Determine the maxima of the diffusion coefficients, including their
!--       grid index positions.
          CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, km, 'abs',  &
                               0.0_wp, km_max, km_max_ijk )
          CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, kh, 'abs',  &
                               0.0_wp, kh_max, kh_max_ijk )

          WRITE( message_string, * ) 'Time step has reached minimum limit.',   &
               '&dt              = ', dt_3d, ' s  Simulation is terminated.',  &
               '&dt_u            = ', dt_u, ' s',                              &
               '&dt_v            = ', dt_v, ' s',                              &
               '&dt_w            = ', dt_w, ' s',                              &
               '&dt_diff         = ', dt_diff, ' s',                           &
               '&u_max           = ', u_max, ' m/s    k=', u_max_ijk(1),       &
               '  j=', u_max_ijk(2), '  i=', u_max_ijk(3),                     &
               '&v_max           = ', v_max, ' m/s    k=', v_max_ijk(1),       &
               '  j=', v_max_ijk(2), '  i=', v_max_ijk(3),                     &
               '&w_max           = ', w_max, ' m/s    k=', w_max_ijk(1),       &
               '  j=', w_max_ijk(2), '  i=', w_max_ijk(3),                     &
               '&km_max          = ', km_max, ' m2/s2  k=', km_max_ijk(1),     &
               '  j=', km_max_ijk(2), '  i=', km_max_ijk(3),                   &
               '&kh_max          = ', kh_max, ' m2/s2  k=', kh_max_ijk(1),     &
                '  j=', kh_max_ijk(2), '  i=', kh_max_ijk(3)
          CALL message( 'timestep', 'PA0312', 0, 1, 0, 6, 0 )
!
!--       In case of coupled runs inform the remote model of the termination 
!--       and its reason, provided the remote model has not already been 
!--       informed of another termination reason (terminate_coupled > 0) before.
#if defined( __parallel )
          IF ( coupling_mode /= 'uncoupled' .AND. terminate_coupled == 0 )  THEN
             terminate_coupled = 2
             IF ( myid == 0 )  THEN
                CALL MPI_SENDRECV( &
                     terminate_coupled,        1, MPI_INTEGER, target_id,  0,  &
                     terminate_coupled_remote, 1, MPI_INTEGER, target_id,  0,  &
                     comm_inter, status, ierr )
             ENDIF
             CALL MPI_BCAST( terminate_coupled_remote, 1, MPI_INTEGER, 0,      &
                             comm2d, ierr)
          ENDIF
#endif
       ENDIF

!
!--    In case of nested runs all parent/child processes have to terminate if
!--    one process has set the stop flag, i.e. they need to set the stop flag
!--    too.
       IF ( nested_run )  THEN
          stop_dt_local = stop_dt
#if defined( __parallel )
          CALL MPI_ALLREDUCE( stop_dt_local, stop_dt, 1, MPI_LOGICAL, MPI_LOR, &
                              MPI_COMM_WORLD, ierr )
#endif
       ENDIF

!
!--    Ensure a smooth value (two significant digits) of the timestep.
       div = 1000.0_wp
       DO  WHILE ( dt_3d < div )
          div = div / 10.0_wp
       ENDDO
       dt_3d = NINT( dt_3d * 100.0_wp / div ) * div / 100.0_wp

    ENDIF

!
!-- Vertical nesting: coarse and fine grid timestep has to be identical    
    IF ( vnested )  CALL vnest_timestep_sync

    CALL cpu_log( log_point(12), 'calculate_timestep', 'stop' )

 END SUBROUTINE timestep