source: palm/trunk/SOURCE/timestep.f90 @ 974

 SUBROUTINE timestep

!------------------------------------------------------------------------------!
! Current revisions:
! ------------------
! 
!
! Former revisions:
! -----------------
! $Id: timestep.f90 867 2012-03-28 06:54:50Z maronga $
!
! 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
!
! 707 2011-03-29 11:39:40Z raasch
! bc_lr/ns replaced by bc_lr/ns_cyc
!
! 667 2010-12-23 12:06:00Z suehring/gryschka
! Exchange of terminate_coupled between ocean and atmosphere via PE0
! Minimum grid spacing dxyz2_min(k) is now calculated using dzw instead of dzu
!
! 622 2010-12-10 08:08:13Z raasch
! optional barriers included in order to speed up collective operations
!
! 343 2009-06-24 12:59:09Z maronga
! Additional timestep criterion in case of simulations with plant canopy
! Output of messages replaced by message handling routine.
!
! 222 2009-01-12 16:04:16Z letzel
! Implementation of a MPI-1 Coupling: replaced myid with target_id
! Bugfix for nonparallel execution
!
! 108 2007-08-24 15:10:38Z letzel
! modifications to terminate coupled runs
!
! RCS Log replace by Id keyword, revision history cleaned up
!
! Revision 1.21  2006/02/23 12:59:44  raasch
! nt_anz renamed current_timestep_number
!
! 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.
!------------------------------------------------------------------------------!

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

    IMPLICIT NONE

    INTEGER ::  i, j, k, u_max_cfl_ijk(3), v_max_cfl_ijk(3)

    REAL ::  div, dt_diff, dt_diff_l, dt_plant_canopy,                 &
             dt_plant_canopy_l,                                        &
             dt_plant_canopy_u, dt_plant_canopy_v, dt_plant_canopy_w,  & 
             dt_u, dt_v, dt_w, lad_max, percent_change,                &
             u_gtrans_l, u_max_cfl, vabs_max, value, v_gtrans_l, v_max_cfl

    REAL, DIMENSION(2)         ::  uv_gtrans, uv_gtrans_l
    REAL, 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
          v_gtrans = 0.0
          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 )
          v_gtrans = v_gtrans / REAL( nzt - nzb )
       ELSE
!
!--       Averaging over the entire model domain.
          uv_gtrans_l = 0.0
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO  k = nzb+1, nzt
                   uv_gtrans_l(1) = uv_gtrans_l(1) + u(k,j,i)
                   uv_gtrans_l(2) = uv_gtrans_l(2) + v(k,j,i)
                ENDDO
             ENDDO
          ENDDO
          uv_gtrans_l = uv_gtrans_l / REAL( (nxr-nxl+1)*(nyn-nys+1)*(nzt-nzb) )
#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 )
          v_gtrans = uv_gtrans(2) / REAL( numprocs )
#else
          u_gtrans = uv_gtrans_l(1)
          v_gtrans = uv_gtrans_l(2)
#endif
       ENDIF
    ENDIF

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

!
!-- In case of Galilei transformation, the horizontal velocity maxima have
!-- to be calculated from the transformed horizontal velocities
    IF ( galilei_transformation )  THEN
       CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, u, 'absoff', &
                            u_gtrans, u_max_cfl, u_max_cfl_ijk )
       CALL global_min_max( nzb, nzt+1, nysg, nyng, nxlg, nxrg, v, 'absoff', &
                            v_gtrans, v_max_cfl, v_max_cfl_ijk )
    ELSE
       u_max_cfl = u_max
       v_max_cfl = v_max
       u_max_cfl_ijk = u_max_ijk
       v_max_cfl_ijk = v_max_ijk
    ENDIF


    IF ( .NOT. dt_fixed )  THEN
!
!--    Variable time step:
!
!--    For each component, compute the maximum time step according to the 
!--    CFL-criterion.
       dt_u = dx / ( ABS( u_max_cfl ) + 1.0E-10 )
       dt_v = dy / ( ABS( v_max_cfl ) + 1.0E-10 )
       dt_w = dzu(MAX( 1, w_max_ijk(1) )) / ( ABS( w_max ) + 1.0E-10 )

!
!--    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

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

!$OMP PARALLEL private(i,j,k,value) reduction(MIN: dt_diff_l)
!$OMP DO
       DO  i = nxl, nxr
          DO  j = nys, nyn
             DO  k = nzb+1, nzt
                value = dxyz2_min(k) / ( MAX( kh(k,j,i), km(k,j,i) ) + 1E-20 )

                dt_diff_l = MIN( value, dt_diff_l )
             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

!
!--    In case of non-cyclic lateral boundaries, the diffusion time step
!--    may be further restricted by the lateral damping layer (damping only
!--    along x and y)
       IF ( .NOT. bc_lr_cyc )  THEN
          dt_diff = MIN( dt_diff, 0.125 * dx2 / ( km_damp_max + 1E-20 ) )
       ELSEIF ( .NOT. bc_ns_cyc )  THEN
          dt_diff = MIN( dt_diff, 0.125 * dy2 / ( km_damp_max + 1E-20 ) )
       ENDIF

!
!--    Additional timestep criterion with plant canopies: 
!--    it is not allowed to extract more than the available momentum
       IF ( plant_canopy ) THEN

          dt_plant_canopy_l = 0.0
          DO  i = nxl, nxr
             DO  j = nys, nyn
                DO k = nzb+1, nzt
                   dt_plant_canopy_u = cdc(k,j,i) * lad_u(k,j,i) *  &
                                       SQRT(     u(k,j,i)**2     +  &
                                             ( ( v(k,j,i-1)      +  &
                                                 v(k,j,i)        +  &
                                                 v(k,j+1,i)      +  &
                                                 v(k,j+1,i-1) )     &
                                               / 4.0 )**2        +  &
                                             ( ( w(k-1,j,i-1)    +  &
                                                 w(k-1,j,i)      +  &
                                                 w(k,j,i-1)      +  &
                                                 w(k,j,i) )         &
                                                 / 4.0 )**2 ) 
                   IF ( dt_plant_canopy_u > dt_plant_canopy_l ) THEN
                      dt_plant_canopy_l = dt_plant_canopy_u  
                   ENDIF
                   dt_plant_canopy_v = cdc(k,j,i) * lad_v(k,j,i) *  &
                                       SQRT( ( ( u(k,j-1,i)      +  &
                                                 u(k,j-1,i+1)    +  &
                                                 u(k,j,i)        +  &
                                                 u(k,j,i+1) )       &
                                               / 4.0 )**2        +  &
                                                 v(k,j,i)**2     +  &
                                             ( ( w(k-1,j-1,i)    +  &
                                                 w(k-1,j,i)      +  &
                                                 w(k,j-1,i)      +  &
                                                 w(k,j,i) )         &
                                                 / 4.0 )**2 ) 
                   IF ( dt_plant_canopy_v > dt_plant_canopy_l ) THEN
                      dt_plant_canopy_l = dt_plant_canopy_v
                   ENDIF                   
                   dt_plant_canopy_w = cdc(k,j,i) * lad_w(k,j,i) *  &
                                       SQRT( ( ( u(k,j,i)        +  &
                                                 u(k,j,i+1)      +  &
                                                 u(k+1,j,i)      +  &
                                                 u(k+1,j,i+1) )     &
                                               / 4.0 )**2        +  &
                                             ( ( v(k,j,i)        +  &
                                                 v(k,j+1,i)      +  &
                                                 v(k+1,j,i)      +  &
                                                 v(k+1,j+1,i) )     &
                                               / 4.0 )**2        +  &
                                                 w(k,j,i)**2 )     
                   IF ( dt_plant_canopy_w > dt_plant_canopy_l ) THEN
                      dt_plant_canopy_l = dt_plant_canopy_w
                   ENDIF
                ENDDO
             ENDDO
          ENDDO 

          IF ( dt_plant_canopy_l > 0.0 ) THEN
!
!--          Invert dt_plant_canopy_l and apply a security timestep factor 0.1
             dt_plant_canopy_l = 0.1 / dt_plant_canopy_l
          ELSE
!
!--          In case of inhomogeneous plant canopy, some processors may have no
!--          canopy at all. Then use dt_max as dummy instead.
             dt_plant_canopy_l = dt_max
          ENDIF

!
!--       Determine the global minumum
#if defined( __parallel )
          IF ( collective_wait )  CALL MPI_BARRIER( comm2d, ierr )
          CALL MPI_ALLREDUCE( dt_plant_canopy_l, dt_plant_canopy, 1, MPI_REAL, &
                              MPI_MIN, comm2d, ierr )
#else
          dt_plant_canopy = dt_plant_canopy_l
#endif

       ELSE
!
!--       Use dt_diff as dummy value to avoid extra IF branches further below
          dt_plant_canopy = dt_diff

       ENDIF

!
!--    The time step is the minimum of the 3-4 components and the diffusion time
!--    step minus a reduction to be on the safe side. Factor 0.5 is necessary 
!--    since the leap-frog scheme always progresses by 2 * delta t.
!--    The user has to set the cfl_factor small enough to ensure that the 
!--    divergences do not become too large.
!--    The time step must not exceed the maximum allowed value.
       IF ( timestep_scheme(1:5) == 'runge' )  THEN
          dt_3d = cfl_factor * MIN( dt_diff, dt_plant_canopy, dt_u, dt_v, dt_w )
       ELSE
          dt_3d = cfl_factor * 0.5 *  &
                  MIN( dt_diff, dt_plant_canopy, dt_u, dt_v, dt_w )
       ENDIF
       dt_3d = MIN( dt_3d, dt_max )

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

!
!--    Set flag if the time step becomes too small.
       IF ( dt_3d < ( 0.00001 * 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',                          &
               '&dt_plant_canopy = ', dt_plant_canopy, ' s',                  &
               '&u_max_cfl   = ', u_max_cfl, ' m/s   k=', u_max_cfl_ijk(1),   &
               '  j=', u_max_ijk(2), '  i=', u_max_ijk(3),                    &
               '&v_max_cfl   = ', v_max_cfl, ' m/s   k=', v_max_cfl_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. For
!--    other schemes than Runge-Kutta, the following restrictions appear:
!--    The current timestep is only then changed, if the change relative to
!--    its previous value exceeds +5 % or -2 %. In case of a timestep
!--    reduction, at least 30 iterations have to be performed before a timestep
!--    enlargement is permitted again.
       percent_change = dt_3d / old_dt - 1.0
       IF ( percent_change > 0.05  .OR.  percent_change < -0.02  .OR. &
            timestep_scheme(1:5) == 'runge' )  THEN

!
!--       Time step enlargement by no more than 2 %.
          IF ( percent_change > 0.0  .AND.  simulated_time /= 0.0  .AND. &
               timestep_scheme(1:5) /= 'runge' )  THEN
             dt_3d = 1.02 * old_dt
          ENDIF

!
!--       A relatively smooth value of the time step is ensured by taking
!--       only the first two significant digits.
          div = 1000.0
          DO  WHILE ( dt_3d < div )
             div = div / 10.0
          ENDDO
          dt_3d = NINT( dt_3d * 100.0 / div ) * div / 100.0

!
!--       Now the time step can be adjusted.
          IF ( percent_change < 0.0  .OR.  timestep_scheme(1:5) == 'runge' ) &
          THEN
!
!--          Time step reduction.
             old_dt = dt_3d
             dt_changed = .TRUE.
          ELSE
!
!--          For other timestep schemes , the time step is only enlarged
!--          after at least 30 iterations since the previous time step
!--          change or, of course, after model initialization.
             IF ( current_timestep_number >= last_dt_change + 30  .OR. &
                  simulated_time == 0.0 )  THEN
                old_dt = dt_3d
                dt_changed = .TRUE.
             ELSE
                dt_3d = old_dt
                dt_changed = .FALSE.
             ENDIF

          ENDIF
       ELSE
!
!--       No time step change since the difference is too small.
          dt_3d = old_dt
          dt_changed = .FALSE.
       ENDIF

       IF ( dt_changed )  last_dt_change = current_timestep_number

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

 END SUBROUTINE timestep