| 1 | SUBROUTINE timestep |
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| 2 | |
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| 3 | !------------------------------------------------------------------------------! |
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| 4 | ! Current revisions: |
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| 5 | ! ----------------- |
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| 6 | ! Additional timestep criterion in case of simulations with plant canopy |
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| 7 | ! |
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| 8 | ! Output of messages replaced by message handling routine. |
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| 9 | ! |
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| 10 | ! |
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| 11 | ! Former revisions: |
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| 12 | ! ----------------- |
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| 13 | ! $Id: timestep.f90 343 2009-06-24 12:59:09Z raasch $ |
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| 14 | ! |
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| 15 | ! 222 2009-01-12 16:04:16Z letzel |
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| 16 | ! Implementation of a MPI-1 Coupling: replaced myid with target_id |
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| 17 | ! Bugfix for nonparallel execution |
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| 18 | ! |
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| 19 | ! 108 2007-08-24 15:10:38Z letzel |
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| 20 | ! modifications to terminate coupled runs |
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| 21 | ! |
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| 22 | ! RCS Log replace by Id keyword, revision history cleaned up |
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| 23 | ! |
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| 24 | ! Revision 1.21 2006/02/23 12:59:44 raasch |
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| 25 | ! nt_anz renamed current_timestep_number |
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| 26 | ! |
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| 27 | ! Revision 1.1 1997/08/11 06:26:19 raasch |
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| 28 | ! Initial revision |
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| 29 | ! |
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| 30 | ! |
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| 31 | ! Description: |
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| 32 | ! ------------ |
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| 33 | ! Compute the time step under consideration of the FCL and diffusion criterion. |
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| 34 | !------------------------------------------------------------------------------! |
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| 35 | |
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| 36 | USE arrays_3d |
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| 37 | USE control_parameters |
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| 38 | USE cpulog |
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| 39 | USE grid_variables |
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| 40 | USE indices |
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| 41 | USE interfaces |
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| 42 | USE pegrid |
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| 43 | USE statistics |
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| 44 | |
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| 45 | IMPLICIT NONE |
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| 46 | |
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| 47 | INTEGER :: i, j, k |
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| 48 | |
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| 49 | REAL :: div, dt_diff, dt_diff_l, dt_plant_canopy, & |
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| 50 | dt_plant_canopy_l, & |
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| 51 | dt_plant_canopy_u, dt_plant_canopy_v, dt_plant_canopy_w, & |
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| 52 | dt_u, dt_v, dt_w, lad_max, percent_change, & |
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| 53 | u_gtrans_l, vabs_max, value, v_gtrans_l |
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| 54 | |
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| 55 | REAL, DIMENSION(2) :: uv_gtrans, uv_gtrans_l |
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| 56 | REAL, DIMENSION(nzb+1:nzt) :: dxyz2_min |
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| 57 | |
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| 58 | CALL cpu_log( log_point(12), 'calculate_timestep', 'start' ) |
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| 59 | |
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| 60 | ! |
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| 61 | !-- Determine the maxima of the velocity components. |
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| 62 | CALL global_min_max( nzb, nzt+1, nys-1, nyn+1, nxl-1, nxr+1, u, 'abs', & |
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| 63 | u_max, u_max_ijk ) |
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| 64 | CALL global_min_max( nzb, nzt+1, nys-1, nyn+1, nxl-1, nxr+1, v, 'abs', & |
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| 65 | v_max, v_max_ijk ) |
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| 66 | CALL global_min_max( nzb, nzt+1, nys-1, nyn+1, nxl-1, nxr+1, w, 'abs', & |
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| 67 | w_max, w_max_ijk ) |
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| 68 | |
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| 69 | ! |
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| 70 | !-- In case maxima of the horizontal velocity components have been found at the |
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| 71 | !-- bottom boundary (k=nzb), the corresponding maximum at level k=1 is chosen |
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| 72 | !-- if the Dirichlet-boundary condition ('mirror') has been set. This is |
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| 73 | !-- necessary, because otherwise in case of Galilei-transform a far too large |
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| 74 | !-- velocity (having the respective opposite sign) would be used for the time |
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| 75 | !-- step determination (almost double the mean flow velocity). |
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| 76 | IF ( ibc_uv_b == 0 ) THEN |
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| 77 | IF ( u_max_ijk(1) == nzb ) THEN |
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| 78 | u_max = -u_max |
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| 79 | u_max_ijk(1) = nzb + 1 |
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| 80 | ENDIF |
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| 81 | IF ( v_max_ijk(1) == nzb ) THEN |
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| 82 | v_max = -v_max |
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| 83 | v_max_ijk(1) = nzb + 1 |
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| 84 | ENDIF |
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| 85 | ENDIF |
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| 86 | |
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| 87 | ! |
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| 88 | !-- In case of Galilei-transform not using the geostrophic wind as translation |
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| 89 | !-- velocity, compute the volume-averaged horizontal velocity components, which |
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| 90 | !-- will then be subtracted from the horizontal wind for the time step and |
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| 91 | !-- horizontal advection routines. |
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| 92 | IF ( galilei_transformation .AND. .NOT. use_ug_for_galilei_tr ) THEN |
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| 93 | IF ( flow_statistics_called ) THEN |
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| 94 | ! |
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| 95 | !-- Horizontal averages already existent, just need to average them |
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| 96 | !-- vertically. |
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| 97 | u_gtrans = 0.0 |
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| 98 | v_gtrans = 0.0 |
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| 99 | DO k = nzb+1, nzt |
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| 100 | u_gtrans = u_gtrans + hom(k,1,1,0) |
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| 101 | v_gtrans = v_gtrans + hom(k,1,2,0) |
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| 102 | ENDDO |
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| 103 | u_gtrans = u_gtrans / REAL( nzt - nzb ) |
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| 104 | v_gtrans = v_gtrans / REAL( nzt - nzb ) |
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| 105 | ELSE |
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| 106 | ! |
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| 107 | !-- Averaging over the entire model domain. |
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| 108 | uv_gtrans_l = 0.0 |
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| 109 | DO i = nxl, nxr |
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| 110 | DO j = nys, nyn |
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| 111 | DO k = nzb+1, nzt |
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| 112 | uv_gtrans_l(1) = uv_gtrans_l(1) + u(k,j,i) |
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| 113 | uv_gtrans_l(2) = uv_gtrans_l(2) + v(k,j,i) |
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| 114 | ENDDO |
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| 115 | ENDDO |
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| 116 | ENDDO |
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| 117 | uv_gtrans_l = uv_gtrans_l / REAL( (nxr-nxl+1)*(nyn-nys+1)*(nzt-nzb) ) |
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| 118 | #if defined( __parallel ) |
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| 119 | CALL MPI_ALLREDUCE( uv_gtrans_l, uv_gtrans, 2, MPI_REAL, MPI_SUM, & |
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| 120 | comm2d, ierr ) |
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| 121 | u_gtrans = uv_gtrans(1) / REAL( numprocs ) |
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| 122 | v_gtrans = uv_gtrans(2) / REAL( numprocs ) |
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| 123 | #else |
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| 124 | u_gtrans = uv_gtrans_l(1) |
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| 125 | v_gtrans = uv_gtrans_l(2) |
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| 126 | #endif |
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| 127 | ENDIF |
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| 128 | ENDIF |
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| 129 | |
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| 130 | IF ( .NOT. dt_fixed ) THEN |
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| 131 | ! |
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| 132 | !-- Variable time step: |
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| 133 | ! |
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| 134 | !-- For each component, compute the maximum time step according to the |
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| 135 | !-- FCL-criterion. |
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| 136 | dt_u = dx / ( ABS( u_max - u_gtrans ) + 1.0E-10 ) |
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| 137 | dt_v = dy / ( ABS( v_max - v_gtrans ) + 1.0E-10 ) |
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| 138 | dt_w = dzu(MAX( 1, w_max_ijk(1) )) / ( ABS( w_max ) + 1.0E-10 ) |
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| 139 | |
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| 140 | ! |
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| 141 | !-- Compute time step according to the diffusion criterion. |
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| 142 | !-- First calculate minimum grid spacing which only depends on index k |
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| 143 | !-- Note: also at k=nzb+1 a full grid length is being assumed, although |
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| 144 | !-- in the Prandtl-layer friction term only dz/2 is used. |
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| 145 | !-- Experience from the old model seems to justify this. |
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| 146 | dt_diff_l = 999999.0 |
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| 147 | |
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| 148 | DO k = nzb+1, nzt |
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| 149 | dxyz2_min(k) = MIN( dx2, dy2, dzu(k)*dzu(k) ) * 0.125 |
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| 150 | ENDDO |
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| 151 | |
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| 152 | !$OMP PARALLEL private(i,j,k,value) reduction(MIN: dt_diff_l) |
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| 153 | !$OMP DO |
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| 154 | DO i = nxl, nxr |
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| 155 | DO j = nys, nyn |
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| 156 | DO k = nzb+1, nzt |
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| 157 | value = dxyz2_min(k) / ( MAX( kh(k,j,i), km(k,j,i) ) + 1E-20 ) |
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| 158 | |
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| 159 | dt_diff_l = MIN( value, dt_diff_l ) |
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| 160 | ENDDO |
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| 161 | ENDDO |
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| 162 | ENDDO |
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| 163 | !$OMP END PARALLEL |
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| 164 | #if defined( __parallel ) |
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| 165 | CALL MPI_ALLREDUCE( dt_diff_l, dt_diff, 1, MPI_REAL, MPI_MIN, comm2d, & |
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| 166 | ierr ) |
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| 167 | #else |
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| 168 | dt_diff = dt_diff_l |
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| 169 | #endif |
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| 170 | |
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| 171 | ! |
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| 172 | !-- In case of non-cyclic lateral boundaries, the diffusion time step |
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| 173 | !-- may be further restricted by the lateral damping layer (damping only |
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| 174 | !-- along x and y) |
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| 175 | IF ( bc_lr /= 'cyclic' ) THEN |
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| 176 | dt_diff = MIN( dt_diff, 0.125 * dx2 / ( km_damp_max + 1E-20 ) ) |
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| 177 | ELSEIF ( bc_ns /= 'cyclic' ) THEN |
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| 178 | dt_diff = MIN( dt_diff, 0.125 * dy2 / ( km_damp_max + 1E-20 ) ) |
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| 179 | ENDIF |
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| 180 | |
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| 181 | ! |
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| 182 | !-- Additional timestep criterion with plant canopies: |
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| 183 | !-- it is not allowed to extract more than the available momentum |
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| 184 | IF ( plant_canopy ) THEN |
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| 185 | |
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| 186 | dt_plant_canopy_l = 0.0 |
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| 187 | DO i = nxl, nxr |
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| 188 | DO j = nys, nyn |
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| 189 | DO k = nzb+1, nzt |
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| 190 | dt_plant_canopy_u = cdc(k,j,i) * lad_u(k,j,i) * & |
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| 191 | SQRT( u(k,j,i)**2 + & |
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| 192 | ( ( v(k,j,i-1) + & |
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| 193 | v(k,j,i) + & |
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| 194 | v(k,j+1,i) + & |
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| 195 | v(k,j+1,i-1) ) & |
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| 196 | / 4.0 )**2 + & |
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| 197 | ( ( w(k-1,j,i-1) + & |
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| 198 | w(k-1,j,i) + & |
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| 199 | w(k,j,i-1) + & |
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| 200 | w(k,j,i) ) & |
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| 201 | / 4.0 )**2 ) |
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| 202 | IF ( dt_plant_canopy_u > dt_plant_canopy_l ) THEN |
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| 203 | dt_plant_canopy_l = dt_plant_canopy_u |
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| 204 | ENDIF |
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| 205 | dt_plant_canopy_v = cdc(k,j,i) * lad_v(k,j,i) * & |
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| 206 | SQRT( ( ( u(k,j-1,i) + & |
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| 207 | u(k,j-1,i+1) + & |
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| 208 | u(k,j,i) + & |
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| 209 | u(k,j,i+1) ) & |
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| 210 | / 4.0 )**2 + & |
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| 211 | v(k,j,i)**2 + & |
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| 212 | ( ( w(k-1,j-1,i) + & |
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| 213 | w(k-1,j,i) + & |
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| 214 | w(k,j-1,i) + & |
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| 215 | w(k,j,i) ) & |
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| 216 | / 4.0 )**2 ) |
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| 217 | IF ( dt_plant_canopy_v > dt_plant_canopy_l ) THEN |
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| 218 | dt_plant_canopy_l = dt_plant_canopy_v |
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| 219 | ENDIF |
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| 220 | dt_plant_canopy_w = cdc(k,j,i) * lad_w(k,j,i) * & |
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| 221 | SQRT( ( ( u(k,j,i) + & |
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| 222 | u(k,j,i+1) + & |
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| 223 | u(k+1,j,i) + & |
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| 224 | u(k+1,j,i+1) ) & |
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| 225 | / 4.0 )**2 + & |
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| 226 | ( ( v(k,j,i) + & |
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| 227 | v(k,j+1,i) + & |
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| 228 | v(k+1,j,i) + & |
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| 229 | v(k+1,j+1,i) ) & |
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| 230 | / 4.0 )**2 + & |
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| 231 | w(k,j,i)**2 ) |
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| 232 | IF ( dt_plant_canopy_w > dt_plant_canopy_l ) THEN |
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| 233 | dt_plant_canopy_l = dt_plant_canopy_w |
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| 234 | ENDIF |
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| 235 | ENDDO |
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| 236 | ENDDO |
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| 237 | ENDDO |
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| 238 | |
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| 239 | IF ( dt_plant_canopy_l > 0.0 ) THEN |
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| 240 | ! |
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| 241 | !-- Invert dt_plant_canopy_l and apply a security timestep factor 0.1 |
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| 242 | dt_plant_canopy_l = 0.1 / dt_plant_canopy_l |
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| 243 | ELSE |
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| 244 | ! |
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| 245 | !-- In case of inhomogeneous plant canopy, some processors may have no |
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| 246 | !-- canopy at all. Then use dt_max as dummy instead. |
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| 247 | dt_plant_canopy_l = dt_max |
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| 248 | ENDIF |
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| 249 | |
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| 250 | ! |
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| 251 | !-- Determine the global minumum |
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| 252 | #if defined( __parallel ) |
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| 253 | CALL MPI_ALLREDUCE( dt_plant_canopy_l, dt_plant_canopy, 1, MPI_REAL, & |
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| 254 | MPI_MIN, comm2d, ierr ) |
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| 255 | #else |
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| 256 | dt_plant_canopy = dt_plant_canopy_l |
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| 257 | #endif |
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| 258 | |
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| 259 | ELSE |
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| 260 | ! |
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| 261 | !-- Use dt_diff as dummy value to avoid extra IF branches further below |
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| 262 | dt_plant_canopy = dt_diff |
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| 263 | |
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| 264 | ENDIF |
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| 265 | |
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| 266 | ! |
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| 267 | !-- The time step is the minimum of the 3-4 components and the diffusion time |
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| 268 | !-- step minus a reduction to be on the safe side. Factor 0.5 is necessary |
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| 269 | !-- since the leap-frog scheme always progresses by 2 * delta t. |
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| 270 | !-- The user has to set the cfl_factor small enough to ensure that the |
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| 271 | !-- divergences do not become too large. |
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| 272 | !-- The time step must not exceed the maximum allowed value. |
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| 273 | IF ( timestep_scheme(1:5) == 'runge' ) THEN |
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| 274 | dt_3d = cfl_factor * MIN( dt_diff, dt_plant_canopy, dt_u, dt_v, dt_w ) |
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| 275 | ELSE |
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| 276 | dt_3d = cfl_factor * 0.5 * & |
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| 277 | MIN( dt_diff, dt_plant_canopy, dt_u, dt_v, dt_w ) |
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| 278 | ENDIF |
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| 279 | dt_3d = MIN( dt_3d, dt_max ) |
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| 280 | |
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| 281 | ! |
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| 282 | !-- Remember the restricting time step criterion for later output. |
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| 283 | IF ( MIN( dt_u, dt_v, dt_w ) < MIN( dt_diff, dt_plant_canopy ) ) THEN |
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| 284 | timestep_reason = 'A' |
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| 285 | ELSEIF ( dt_plant_canopy < dt_diff ) THEN |
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| 286 | timestep_reason = 'C' |
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| 287 | ELSE |
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| 288 | timestep_reason = 'D' |
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| 289 | ENDIF |
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| 290 | |
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| 291 | ! |
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| 292 | !-- Set flag if the time step becomes too small. |
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| 293 | IF ( dt_3d < ( 0.00001 * dt_max ) ) THEN |
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| 294 | stop_dt = .TRUE. |
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| 295 | |
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| 296 | WRITE( message_string, * ) 'Time step has reached minimum limit.', & |
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| 297 | '&dt = ', dt_3d, ' s Simulation is terminated.', & |
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| 298 | '&old_dt = ', old_dt, ' s', & |
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| 299 | '&dt_u = ', dt_u, ' s', & |
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| 300 | '&dt_v = ', dt_v, ' s', & |
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| 301 | '&dt_w = ', dt_w, ' s', & |
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| 302 | '&dt_diff = ', dt_diff, ' s', & |
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| 303 | '&dt_plant_canopy = ', dt_plant_canopy, ' s', & |
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| 304 | '&u_max = ', u_max, ' m/s k=', u_max_ijk(1), & |
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| 305 | ' j=', u_max_ijk(2), ' i=', u_max_ijk(3), & |
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| 306 | '&v_max = ', v_max, ' m/s k=', v_max_ijk(1), & |
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| 307 | ' j=', v_max_ijk(2), ' i=', v_max_ijk(3), & |
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| 308 | '&w_max = ', w_max, ' m/s k=', w_max_ijk(1), & |
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| 309 | ' j=', w_max_ijk(2), ' i=', w_max_ijk(3) |
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| 310 | CALL message( 'timestep', 'PA0312', 0, 1, 0, 6, 0 ) |
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| 311 | ! |
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| 312 | !-- In case of coupled runs inform the remote model of the termination |
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| 313 | !-- and its reason, provided the remote model has not already been |
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| 314 | !-- informed of another termination reason (terminate_coupled > 0) before. |
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| 315 | #if defined( __parallel ) |
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| 316 | IF ( coupling_mode /= 'uncoupled' .AND. terminate_coupled == 0 ) THEN |
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| 317 | terminate_coupled = 2 |
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| 318 | CALL MPI_SENDRECV( & |
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| 319 | terminate_coupled, 1, MPI_INTEGER, target_id, 0, & |
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| 320 | terminate_coupled_remote, 1, MPI_INTEGER, target_id, 0, & |
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| 321 | comm_inter, status, ierr ) |
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| 322 | ENDIF |
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| 323 | #endif |
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| 324 | ENDIF |
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| 325 | |
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| 326 | ! |
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| 327 | !-- Ensure a smooth value (two significant digits) of the timestep. For |
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| 328 | !-- other schemes than Runge-Kutta, the following restrictions appear: |
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| 329 | !-- The current timestep is only then changed, if the change relative to |
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| 330 | !-- its previous value exceeds +5 % or -2 %. In case of a timestep |
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| 331 | !-- reduction, at least 30 iterations have to be performed before a timestep |
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| 332 | !-- enlargement is permitted again. |
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| 333 | percent_change = dt_3d / old_dt - 1.0 |
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| 334 | IF ( percent_change > 0.05 .OR. percent_change < -0.02 .OR. & |
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| 335 | timestep_scheme(1:5) == 'runge' ) THEN |
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| 336 | |
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| 337 | ! |
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| 338 | !-- Time step enlargement by no more than 2 %. |
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| 339 | IF ( percent_change > 0.0 .AND. simulated_time /= 0.0 .AND. & |
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| 340 | timestep_scheme(1:5) /= 'runge' ) THEN |
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| 341 | dt_3d = 1.02 * old_dt |
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| 342 | ENDIF |
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| 343 | |
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| 344 | ! |
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| 345 | !-- A relatively smooth value of the time step is ensured by taking |
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| 346 | !-- only the first two significant digits. |
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| 347 | div = 1000.0 |
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| 348 | DO WHILE ( dt_3d < div ) |
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| 349 | div = div / 10.0 |
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| 350 | ENDDO |
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| 351 | dt_3d = NINT( dt_3d * 100.0 / div ) * div / 100.0 |
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| 352 | |
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| 353 | ! |
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| 354 | !-- Now the time step can be adjusted. |
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| 355 | IF ( percent_change < 0.0 .OR. timestep_scheme(1:5) == 'runge' ) & |
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| 356 | THEN |
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| 357 | ! |
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| 358 | !-- Time step reduction. |
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| 359 | old_dt = dt_3d |
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| 360 | dt_changed = .TRUE. |
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| 361 | ELSE |
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| 362 | ! |
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| 363 | !-- For other timestep schemes , the time step is only enlarged |
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| 364 | !-- after at least 30 iterations since the previous time step |
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| 365 | !-- change or, of course, after model initialization. |
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| 366 | IF ( current_timestep_number >= last_dt_change + 30 .OR. & |
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| 367 | simulated_time == 0.0 ) THEN |
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| 368 | old_dt = dt_3d |
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| 369 | dt_changed = .TRUE. |
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| 370 | ELSE |
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| 371 | dt_3d = old_dt |
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| 372 | dt_changed = .FALSE. |
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| 373 | ENDIF |
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| 374 | |
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| 375 | ENDIF |
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| 376 | ELSE |
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| 377 | ! |
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| 378 | !-- No time step change since the difference is too small. |
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| 379 | dt_3d = old_dt |
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| 380 | dt_changed = .FALSE. |
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| 381 | ENDIF |
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| 382 | |
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| 383 | IF ( dt_changed ) last_dt_change = current_timestep_number |
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| 384 | |
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| 385 | ENDIF |
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| 386 | CALL cpu_log( log_point(12), 'calculate_timestep', 'stop' ) |
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| 387 | |
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| 388 | END SUBROUTINE timestep |
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