source: palm/trunk/SOURCE/timestep.f90 @ 1727

!> @file timestep.f90
!--------------------------------------------------------------------------------!
! 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 1997-2014 Leibniz Universitaet Hannover
!--------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
! 
! 
! Former revisions:
! -----------------
! $Id: timestep.f90 1683 2015-10-07 23:57:51Z knoop $
!
! 1682 2015-10-07 23:56:08Z knoop
! Code annotations made doxygen readable 
! 
! 1484 2014-10-21 10:53:05Z kanani
! Changes due to new module structure of the plant canopy model:
!   calculations and parameters related to the plant canopy model removed
!   (the limitation of the canopy drag, i.e. that the canopy drag itself should
!   not change the sign of the velocity components, is now assured for in the
!   calculation of the canopy tendency terms in subroutine plant_canopy_model) 
! 
! 1342 2014-03-26 17:04:47Z kanani
! REAL constants defined as wp-kind
!
! 1322 2014-03-20 16:38:49Z raasch
! REAL functions provided with KIND-attribute
!
! 1320 2014-03-20 08:40:49Z raasch
! ONLY-attribute added to USE-statements,
! kind-parameters added to all INTEGER and REAL declaration statements,
! kinds are defined in new module kinds,
! old module precision_kind is removed,
! revision history before 2012 removed,
! comment fields (!:) to be used for variable explanations added to
! all variable declaration statements 
! 
! 1257 2013-11-08 15:18:40Z raasch
! openacc porting
! bugfix for calculation of advective timestep in case of vertically stretched
! grids
!
! 1092 2013-02-02 11:24:22Z raasch
! unused variables removed
!
! 1053 2012-11-13 17:11:03Z hoffmann
! timestep is reduced in two-moment cloud scheme according to the maximum 
! terminal velocity of rain drops
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 1001 2012-09-13 14:08:46Z raasch
! all actions concerning leapfrog scheme removed
!
! 978 2012-08-09 08:28:32Z fricke
! restriction of the outflow damping layer in the diffusion criterion removed
!
! 866 2012-03-28 06:44:41Z raasch
! bugfix for timestep calculation in case of Galilei transformation,
! special treatment in case of mirror velocity boundary condition removed
!
! 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, v, w

    USE cloud_parameters,                                                      &
        ONLY:  dt_precipitation

    USE control_parameters,                                                    &
        ONLY:  cfl_factor, coupling_mode, dt_3d, dt_fixed, dt_max,             &
               galilei_transformation, old_dt, message_string,                 &
               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 pegrid

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

    IMPLICIT NONE

    INTEGER(iwp) ::  i !< 
    INTEGER(iwp) ::  j !< 
    INTEGER(iwp) ::  k !< 

    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) ::  u_gtrans_l        !< 
    REAL(wp) ::  u_max_l           !< 
    REAL(wp) ::  u_min_l           !< 
    REAL(wp) ::  value             !< 
    REAL(wp) ::  v_gtrans_l        !< 
    REAL(wp) ::  v_max_l           !< 
    REAL(wp) ::  v_min_l           !< 
    REAL(wp) ::  w_max_l           !< 
    REAL(wp) ::  w_min_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   !<  



    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
          !$acc parallel present( u, v )
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb+1, nzt
                   u_gtrans_l = u_gtrans_l + u(k,j,i)
                   v_gtrans_l = v_gtrans_l + v(k,j,i)
                ENDDO
             ENDDO
          ENDDO
          !$acc end parallel
          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.
#if defined( __openacc )
    IF ( dt_fixed )  THEN  ! otherwise do it further below for better cache usage
       u_max_l = -999999.9_wp
       u_min_l =  999999.9_wp
       v_max_l = -999999.9_wp
       v_min_l =  999999.9_wp
       w_max_l = -999999.9_wp
       w_min_l =  999999.9_wp
       !$acc parallel present( u, v, w )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                u_max_l = MAX( u_max_l, u(k,j,i) )
                u_min_l = MIN( u_min_l, u(k,j,i) )
                v_max_l = MAX( v_max_l, v(k,j,i) )
                v_min_l = MIN( v_min_l, v(k,j,i) )
                w_max_l = MAX( w_max_l, w(k,j,i) )
                w_min_l = MIN( w_min_l, w(k,j,i) )
             ENDDO
          ENDDO
       ENDDO
       !$acc end parallel
#if defined( __parallel )
       reduce_l(1) = u_max_l
       reduce_l(2) = v_max_l
       reduce_l(3) = w_max_l
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( reduce_l, reduce, 3, MPI_REAL, MPI_MAX, comm2d, ierr )
       u_max = reduce(1)
       v_max = reduce(2)
       w_max = reduce(3)
       reduce_l(1) = u_min_l
       reduce_l(2) = v_min_l
       reduce_l(3) = w_min_l
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( reduce_l, reduce, 3, MPI_REAL, MPI_MIN, comm2d, ierr )
       IF ( ABS( reduce(1) ) > u_max )  u_max = reduce(1)
       IF ( ABS( reduce(2) ) > v_max )  v_max = reduce(2)
       IF ( ABS( reduce(3) ) > w_max )  w_max = reduce(3)
#else
       IF ( ABS( u_min_l ) > u_max_l )  THEN
          u_max = u_min_l
       ELSE
          u_max = u_max_l
       ENDIF
       IF ( ABS( v_min_l ) > v_max_l )  THEN
          v_max = v_min_l
       ELSE
          v_max = v_max_l
       ENDIF
       IF ( ABS( w_min_l ) > w_max_l )  THEN
          w_max = w_min_l
       ELSE
          w_max = w_max_l
       ENDIF
#endif
    ENDIF
#else
    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 )
#endif

    IF ( .NOT. dt_fixed )  THEN
#if defined( __openacc )
!
!--    Variable time step:
!--    Calculate the maximum time step according to the CFL-criterion,
!--    individually for each velocity component
       dt_u_l  =  999999.9_wp
       dt_v_l  =  999999.9_wp
       dt_w_l  =  999999.9_wp
       u_max_l = -999999.9_wp
       u_min_l =  999999.9_wp
       v_max_l = -999999.9_wp
       v_min_l =  999999.9_wp
       w_max_l = -999999.9_wp
       w_min_l =  999999.9_wp
       !$acc parallel loop collapse(3) present( u, v, w )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                dt_u_l  = MIN( dt_u_l, ( dx     / ( ABS( u(k,j,i) - u_gtrans ) + 1.0E-10_wp ) ) )
                dt_v_l  = MIN( dt_v_l, ( dy     / ( ABS( v(k,j,i) - v_gtrans ) + 1.0E-10_wp ) ) )
                dt_w_l  = MIN( dt_w_l, ( dzu(k) / ( ABS( w(k,j,i) )            + 1.0E-10_wp ) ) )
                u_max_l = MAX( u_max_l, u(k,j,i) )
                u_min_l = MIN( u_min_l, u(k,j,i) )
                v_max_l = MAX( v_max_l, v(k,j,i) )
                v_min_l = MIN( v_min_l, v(k,j,i) )
                w_max_l = MAX( w_max_l, w(k,j,i) )
                w_min_l = MIN( w_min_l, w(k,j,i) )
             ENDDO
          ENDDO
       ENDDO
       !$acc end parallel

#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)

       reduce_l(1) = u_max_l
       reduce_l(2) = v_max_l
       reduce_l(3) = w_max_l
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( reduce_l, reduce, 3, MPI_REAL, MPI_MAX, comm2d, ierr )
       u_max = reduce(1)
       v_max = reduce(2)
       w_max = reduce(3)
       reduce_l(1) = u_min_l
       reduce_l(2) = v_min_l
       reduce_l(3) = w_min_l
       IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
       CALL MPI_ALLREDUCE( reduce_l, reduce, 3, MPI_REAL, MPI_MIN, comm2d, ierr )
       IF ( ABS( reduce(1) ) > u_max )  u_max = reduce(1)
       IF ( ABS( reduce(2) ) > v_max )  v_max = reduce(2)
       IF ( ABS( reduce(3) ) > w_max )  w_max = reduce(3)
#else
       dt_u = dt_u_l
       dt_v = dt_v_l
       dt_w = dt_w_l

       IF ( ABS( u_min_l ) > u_max_l )  THEN
          u_max = u_min_l
       ELSE
          u_max = u_max_l
       ENDIF
       IF ( ABS( v_min_l ) > v_max_l )  THEN
          v_max = v_min_l
       ELSE
          v_max = v_max_l
       ENDIF
       IF ( ABS( w_min_l ) > w_max_l )  THEN
          w_max = w_min_l
       ELSE
          w_max = w_max_l
       ENDIF
#endif

#else
!
!--    Variable time step:
!--    Calculate the maximum time step according to the CFL-criterion,
!--    individually for each velocity component
       dt_u_l = 999999.9_wp
       dt_v_l = 999999.9_wp
       dt_w_l = 999999.9_wp
       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 ) + 1.0E-10_wp ) ) )
                dt_v_l = MIN( dt_v_l, ( dy     / ( ABS( v(k,j,i) - v_gtrans ) + 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

#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

#endif

!
!--    Compute time step according to the diffusion criterion.
!--    First calculate minimum grid spacing which only depends on index k
!--    Note: also at k=nzb+1 a full grid length is being assumed, although
!--          in the Prandtl-layer friction term only dz/2 is used.
!--          Experience from the old model seems to justify this.
       dt_diff_l = 999999.0_wp

       DO  k = nzb+1, nzt
           dxyz2_min(k) = MIN( dx2, dy2, dzw(k)*dzw(k) ) * 0.125_wp
       ENDDO

!$OMP PARALLEL private(i,j,k,value) reduction(MIN: dt_diff_l)
!$OMP DO
       !$acc parallel loop collapse(3) present( kh, km )
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                dt_diff_l = MIN( dt_diff_l, dxyz2_min(k) / &
                                       ( MAX( kh(k,j,i), km(k,j,i) ) + 1E-20_wp ) )
             ENDDO
          ENDDO
       ENDDO
       !$acc end parallel
!$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.

          WRITE( message_string, * ) 'Time step has reached minimum limit.',  &
               '&dt              = ', dt_3d, ' s  Simulation is terminated.', &
               '&old_dt          = ', old_dt, ' s',                           &
               '&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)
          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

!
!--    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

!
!--    Adjust the time step
       old_dt = dt_3d

    ENDIF

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

 END SUBROUTINE timestep