source: palm/trunk/SOURCE/time_integration.f90 @ 1046

Last change on this file since 1046 was 1037, checked in by raasch, 12 years ago

last commit documented

  • Property svn:keywords set to Id
File size: 22.0 KB
Line 
1 SUBROUTINE time_integration
2
3!--------------------------------------------------------------------------------!
4! This file is part of PALM.
5!
6! PALM is free software: you can redistribute it and/or modify it under the terms
7! of the GNU General Public License as published by the Free Software Foundation,
8! either version 3 of the License, or (at your option) any later version.
9!
10! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
11! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
12! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
13!
14! You should have received a copy of the GNU General Public License along with
15! PALM. If not, see <http://www.gnu.org/licenses/>.
16!
17! Copyright 1997-2012  Leibniz University Hannover
18!--------------------------------------------------------------------------------!
19!
20! Current revisions:
21! -----------------
22!
23!
24! Former revisions:
25! -----------------
26! $Id: time_integration.f90 1037 2012-10-22 14:10:22Z maronga $
27!
28! 1036 2012-10-22 13:43:42Z raasch
29! code put under GPL (PALM 3.9)
30!
31! 1019 2012-09-28 06:46:45Z raasch
32! non-optimized version of prognostic_equations removed
33!
34! 1015 2012-09-27 09:23:24Z raasch
35! +call of prognostic_equations_acc
36!
37! 1001 2012-09-13 14:08:46Z raasch
38! all actions concerning leapfrog- and upstream-spline-scheme removed
39!
40! 849 2012-03-15 10:35:09Z raasch
41! advec_particles renamed lpm, first_call_advec_particles renamed first_call_lpm
42!
43! 825 2012-02-19 03:03:44Z raasch
44! wang_collision_kernel renamed wang_kernel
45!
46! 790 2011-11-29 03:11:20Z raasch
47! exchange of ghostpoints for array diss
48!
49! 707 2011-03-29 11:39:40Z raasch
50! bc_lr/ns replaced by bc_lr/ns_cyc, calls of exchange_horiz are modified,
51! adaption to sloping surface
52!
53! 667  2010-12-23 12:06:00Z suehring/gryschka
54! Calls of exchange_horiz are modified.
55! Adaption to slooping surface.
56!
57! 449 2010-02-02 11:23:59Z raasch
58! Bugfix: exchange of ghost points for prho included
59!
60! 410 2009-12-04 17:05:40Z letzel
61! masked data output
62!
63! 388 2009-09-23 09:40:33Z raasch
64! Using prho instead of rho in diffusvities.
65! Coupling with independent precursor runs.
66! Bugfix: output of particle time series only if particle advection is switched
67!         on
68!
69! 151 2008-03-07 13:42:18Z raasch
70! inflow turbulence is imposed by calling new routine inflow_turbulence
71!
72! 108 2007-08-24 15:10:38Z letzel
73! Call of new routine surface_coupler,
74! presure solver is called after the first Runge-Kutta substep instead of the
75! last in case that call_psolver_at_all_substeps = .F.; for this case, the
76! random perturbation has to be added to the velocity fields also after the
77! first substep
78!
79! 97 2007-06-21 08:23:15Z raasch
80! diffusivities is called with argument rho in case of ocean runs,
81! new argument pt_/prho_reference in calls of diffusivities,
82! ghostpoint exchange for salinity and density
83!
84! 87 2007-05-22 15:46:47Z raasch
85! var_hom renamed pr_palm
86!
87! 75 2007-03-22 09:54:05Z raasch
88! Move call of user_actions( 'after_integration' ) below increment of times
89! and counters,
90! calls of prognostic_equations_.. changed to .._noopt, .._cache, and
91! .._vector, these calls are now controlled by switch loop_optimization,
92! uxrp, vynp eliminated, 2nd+3rd argument removed from exchange horiz,
93! moisture renamed humidity
94!
95! RCS Log replace by Id keyword, revision history cleaned up
96!
97! Revision 1.8  2006/08/22 14:16:05  raasch
98! Disturbances are imposed only for the last Runge-Kutta-substep
99!
100! Revision 1.2  2004/04/30 13:03:40  raasch
101! decalpha-specific warning removed, routine name changed to time_integration,
102! particle advection is carried out only once during the intermediate steps,
103! impulse_advec renamed momentum_advec
104!
105! Revision 1.1  1997/08/11 06:19:04  raasch
106! Initial revision
107!
108!
109! Description:
110! ------------
111! Integration in time of the model equations, statistical analysis and graphic
112! output
113!------------------------------------------------------------------------------!
114
115    USE arrays_3d
116    USE averaging
117    USE control_parameters
118    USE cpulog
119#if defined( __dvrp_graphics )
120    USE DVRP
121#endif
122    USE grid_variables
123    USE indices
124    USE interaction_droplets_ptq_mod
125    USE interfaces
126    USE particle_attributes
127    USE pegrid
128    USE prognostic_equations_mod
129    USE statistics
130    USE user_actions_mod
131
132    IMPLICIT NONE
133
134    CHARACTER (LEN=9) ::  time_to_string
135    INTEGER ::  i, j, k
136
137!
138!-- At the beginning of a simulation determine the time step as well as
139!-- determine and print out the run control parameters
140    IF ( simulated_time == 0.0 )  CALL timestep
141
142    CALL run_control
143
144
145!
146!-- Data exchange between coupled models in case that a call has been omitted
147!-- at the end of the previous run of a job chain.
148    IF ( coupling_mode /= 'uncoupled'  .AND.  run_coupled )  THEN
149!
150!--    In case of model termination initiated by the local model the coupler
151!--    must not be called because this would again cause an MPI hang.
152       DO WHILE ( time_coupling >= dt_coupling .AND. terminate_coupled == 0 )
153          CALL surface_coupler
154          time_coupling = time_coupling - dt_coupling
155       ENDDO
156       IF (time_coupling == 0.0 .AND. time_since_reference_point < dt_coupling)&
157       THEN
158          time_coupling = time_since_reference_point
159       ENDIF
160    ENDIF
161
162
163#if defined( __dvrp_graphics )
164!
165!-- Time measurement with dvrp software 
166    CALL DVRP_LOG_EVENT( 2, current_timestep_number )
167#endif
168
169!
170!-- Start of the time loop
171    DO  WHILE ( simulated_time < end_time  .AND.  .NOT. stop_dt  .AND. &
172                .NOT. terminate_run )
173
174       CALL cpu_log( log_point_s(10), 'timesteps', 'start' )
175!
176!--    Determine size of next time step
177       IF ( simulated_time /= 0.0 )  CALL timestep
178!
179!--    Execute the user-defined actions
180       CALL user_actions( 'before_timestep' )
181
182!
183!--    Start of intermediate step loop
184       intermediate_timestep_count = 0
185       DO  WHILE ( intermediate_timestep_count < &
186                   intermediate_timestep_count_max )
187
188          intermediate_timestep_count = intermediate_timestep_count + 1
189
190!
191!--       Set the steering factors for the prognostic equations which depend
192!--       on the timestep scheme
193          CALL timestep_scheme_steering
194
195!
196!--       Solve the prognostic equations. A fast cache optimized version with
197!--       only one single loop is used in case of Piascek-Williams advection
198!--       scheme. NEC vector machines use a different version, because
199!--       in the other versions a good vectorization is prohibited due to
200!--       inlining problems.
201          IF ( loop_optimization == 'cache' )  THEN
202             CALL prognostic_equations_cache
203          ELSEIF ( loop_optimization == 'vector' )  THEN
204             CALL prognostic_equations_vector
205          ELSEIF ( loop_optimization == 'acc' )  THEN
206             CALL prognostic_equations_acc
207          ENDIF
208
209!
210!--       Particle transport/physics with the Lagrangian particle model
211!--       (only once during intermediate steps, because it uses an Euler-step)
212          IF ( particle_advection  .AND.                         &
213               simulated_time >= particle_advection_start  .AND. &
214               intermediate_timestep_count == 1 )  THEN
215             CALL lpm
216             first_call_lpm = .FALSE.
217          ENDIF
218
219!
220!--       Interaction of droplets with temperature and specific humidity.
221!--       Droplet condensation and evaporation is calculated within
222!--       advec_particles.
223          IF ( cloud_droplets  .AND.  &
224               intermediate_timestep_count == intermediate_timestep_count_max )&
225          THEN
226             CALL interaction_droplets_ptq
227          ENDIF
228
229!
230!--       Exchange of ghost points (lateral boundary conditions)
231          CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'start' )
232          CALL exchange_horiz( u_p, nbgp )
233          CALL exchange_horiz( v_p, nbgp )
234          CALL exchange_horiz( w_p, nbgp )
235          CALL exchange_horiz( pt_p, nbgp )
236          IF ( .NOT. constant_diffusion )  CALL exchange_horiz( e_p, nbgp )
237          IF ( ocean )  THEN
238             CALL exchange_horiz( sa_p, nbgp )
239             CALL exchange_horiz( rho, nbgp )
240             CALL exchange_horiz( prho, nbgp )
241          ENDIF
242          IF (humidity  .OR.  passive_scalar)  CALL exchange_horiz( q_p, nbgp )
243          IF ( cloud_droplets )  THEN
244             CALL exchange_horiz( ql, nbgp )
245             CALL exchange_horiz( ql_c, nbgp )
246             CALL exchange_horiz( ql_v, nbgp )
247             CALL exchange_horiz( ql_vp, nbgp )
248          ENDIF
249          IF ( wang_kernel )  CALL exchange_horiz( diss, nbgp )
250
251          CALL cpu_log( log_point(26), 'exchange-horiz-progn', 'stop' )
252
253!
254!--       Boundary conditions for the prognostic quantities (except of the
255!--       velocities at the outflow in case of a non-cyclic lateral wall)
256          CALL boundary_conds( 'main' )
257
258!
259!--       Swap the time levels in preparation for the next time step.
260          CALL swap_timelevel
261
262!
263!--       Temperature offset must be imposed at cyclic boundaries in x-direction
264!--       when a sloping surface is used
265          IF ( sloping_surface )  THEN
266             IF ( nxl ==  0 )  pt(:,:,nxlg:nxl-1) = pt(:,:,nxlg:nxl-1) - &
267                                                    pt_slope_offset
268             IF ( nxr == nx )  pt(:,:,nxr+1:nxrg) = pt(:,:,nxr+1:nxrg) + &
269                                                    pt_slope_offset
270          ENDIF
271
272!
273!--       Impose a turbulent inflow using the recycling method
274          IF ( turbulent_inflow )  CALL  inflow_turbulence
275
276!
277!--       Impose a random perturbation on the horizontal velocity field
278          IF ( create_disturbances  .AND.                                      &
279               ( call_psolver_at_all_substeps  .AND.                           &
280               intermediate_timestep_count == intermediate_timestep_count_max )&
281          .OR. ( .NOT. call_psolver_at_all_substeps  .AND.                     &
282               intermediate_timestep_count == 1 ) )                            &
283          THEN
284             time_disturb = time_disturb + dt_3d
285             IF ( time_disturb >= dt_disturb )  THEN
286                IF ( hom(nzb+5,1,pr_palm,0) < disturbance_energy_limit )  THEN
287                   CALL disturb_field( nzb_u_inner, tend, u )
288                   CALL disturb_field( nzb_v_inner, tend, v )
289                ELSEIF ( .NOT. bc_lr_cyc  .OR.  .NOT. bc_ns_cyc )  THEN
290!
291!--                Runs with a non-cyclic lateral wall need perturbations
292!--                near the inflow throughout the whole simulation
293                   dist_range = 1
294                   CALL disturb_field( nzb_u_inner, tend, u )
295                   CALL disturb_field( nzb_v_inner, tend, v )
296                   dist_range = 0
297                ENDIF
298                time_disturb = time_disturb - dt_disturb
299             ENDIF
300          ENDIF
301
302!
303!--       Reduce the velocity divergence via the equation for perturbation
304!--       pressure.
305          IF ( intermediate_timestep_count == 1  .OR. &
306                call_psolver_at_all_substeps )  THEN
307             CALL pres
308          ENDIF
309!
310!--       Update device memory for calculating diffusion quantities and for next
311!--       timestep
312          !$acc update device( e, pt, u, v, w )
313          !$acc update device( q )  if ( allocated( q ) )
314
315!
316!--       If required, compute virtuell potential temperature
317          IF ( humidity )  THEN
318             CALL compute_vpt
319             !$acc update device( vpt )
320          ENDIF
321
322!
323!--       If required, compute liquid water content
324          IF ( cloud_physics )  THEN
325             CALL calc_liquid_water_content
326             !$acc update device( ql )
327          ENDIF
328
329!
330!--       Compute the diffusion quantities
331          IF ( .NOT. constant_diffusion )  THEN
332
333!
334!--          First the vertical fluxes in the Prandtl layer are being computed
335             IF ( prandtl_layer )  THEN
336                CALL cpu_log( log_point(19), 'prandtl_fluxes', 'start' )
337                CALL prandtl_fluxes
338                CALL cpu_log( log_point(19), 'prandtl_fluxes', 'stop' )
339!
340!++             Statistics still require updates on host
341                !$acc update host( qs, qsws, rif, shf, ts )
342             ENDIF
343
344!
345!--          Compute the diffusion coefficients
346             CALL cpu_log( log_point(17), 'diffusivities', 'start' )
347             IF ( .NOT. humidity ) THEN
348                IF ( ocean )  THEN
349                   CALL diffusivities( prho, prho_reference )
350                ELSE
351                   CALL diffusivities( pt, pt_reference )
352                ENDIF
353             ELSE
354                CALL diffusivities( vpt, pt_reference )
355             ENDIF
356             CALL cpu_log( log_point(17), 'diffusivities', 'stop' )
357!
358!++          Statistics still require update of diffusivities on host
359             !$acc update host( kh, km )
360
361          ENDIF
362
363       ENDDO   ! Intermediate step loop
364
365!
366!--    Increase simulation time and output times
367       current_timestep_number    = current_timestep_number + 1
368       simulated_time             = simulated_time   + dt_3d
369       simulated_time_chr         = time_to_string( simulated_time )
370       time_since_reference_point = simulated_time - coupling_start_time
371
372       IF ( simulated_time >= skip_time_data_output_av )  THEN
373          time_do_av         = time_do_av       + dt_3d
374       ENDIF
375       IF ( simulated_time >= skip_time_do2d_xy )  THEN
376          time_do2d_xy       = time_do2d_xy     + dt_3d
377       ENDIF
378       IF ( simulated_time >= skip_time_do2d_xz )  THEN
379          time_do2d_xz       = time_do2d_xz     + dt_3d
380       ENDIF
381       IF ( simulated_time >= skip_time_do2d_yz )  THEN
382          time_do2d_yz       = time_do2d_yz     + dt_3d
383       ENDIF
384       IF ( simulated_time >= skip_time_do3d    )  THEN
385          time_do3d          = time_do3d        + dt_3d
386       ENDIF
387       DO  mid = 1, masks
388          IF ( simulated_time >= skip_time_domask(mid) )  THEN
389             time_domask(mid)= time_domask(mid) + dt_3d
390          ENDIF
391       ENDDO
392       time_dvrp          = time_dvrp        + dt_3d
393       IF ( simulated_time >= skip_time_dosp )  THEN
394          time_dosp       = time_dosp        + dt_3d
395       ENDIF
396       time_dots          = time_dots        + dt_3d
397       IF ( .NOT. first_call_lpm )  THEN
398          time_dopts      = time_dopts       + dt_3d
399       ENDIF
400       IF ( simulated_time >= skip_time_dopr )  THEN
401          time_dopr       = time_dopr        + dt_3d
402       ENDIF
403       time_dopr_listing          = time_dopr_listing        + dt_3d
404       time_run_control   = time_run_control + dt_3d
405
406!
407!--    Data exchange between coupled models
408       IF ( coupling_mode /= 'uncoupled'  .AND.  run_coupled )  THEN
409          time_coupling = time_coupling + dt_3d
410
411!
412!--       In case of model termination initiated by the local model
413!--       (terminate_coupled > 0), the coupler must be skipped because it would
414!--       cause an MPI intercomminucation hang.
415!--       If necessary, the coupler will be called at the beginning of the
416!--       next restart run.
417          DO WHILE ( time_coupling >= dt_coupling .AND. terminate_coupled == 0 )
418             CALL surface_coupler
419             time_coupling = time_coupling - dt_coupling
420          ENDDO
421       ENDIF
422
423!
424!--    Execute user-defined actions
425       CALL user_actions( 'after_integration' )
426
427!
428!--    If Galilei transformation is used, determine the distance that the
429!--    model has moved so far
430       IF ( galilei_transformation )  THEN
431          advected_distance_x = advected_distance_x + u_gtrans * dt_3d
432          advected_distance_y = advected_distance_y + v_gtrans * dt_3d
433       ENDIF
434
435!
436!--    Check, if restart is necessary (because cpu-time is expiring or
437!--    because it is forced by user) and set stop flag
438!--    This call is skipped if the remote model has already initiated a restart.
439       IF ( .NOT. terminate_run )  CALL check_for_restart
440
441!
442!--    Carry out statistical analysis and output at the requested output times.
443!--    The MOD function is used for calculating the output time counters (like
444!--    time_dopr) in order to regard a possible decrease of the output time
445!--    interval in case of restart runs
446
447!
448!--    Set a flag indicating that so far no statistics have been created
449!--    for this time step
450       flow_statistics_called = .FALSE.
451
452!
453!--    If required, call flow_statistics for averaging in time
454       IF ( averaging_interval_pr /= 0.0  .AND.  &
455            ( dt_dopr - time_dopr ) <= averaging_interval_pr  .AND.  &
456            simulated_time >= skip_time_dopr )  THEN
457          time_dopr_av = time_dopr_av + dt_3d
458          IF ( time_dopr_av >= dt_averaging_input_pr )  THEN
459             do_sum = .TRUE.
460             time_dopr_av = MOD( time_dopr_av, &
461                                    MAX( dt_averaging_input_pr, dt_3d ) )
462          ENDIF
463       ENDIF
464       IF ( do_sum )  CALL flow_statistics
465
466!
467!--    Sum-up 3d-arrays for later output of time-averaged 2d/3d/masked data
468       IF ( averaging_interval /= 0.0  .AND.                                &
469            ( dt_data_output_av - time_do_av ) <= averaging_interval  .AND. &
470            simulated_time >= skip_time_data_output_av )                    &
471       THEN
472          time_do_sla = time_do_sla + dt_3d
473          IF ( time_do_sla >= dt_averaging_input )  THEN
474             CALL sum_up_3d_data
475             average_count_3d = average_count_3d + 1
476             time_do_sla = MOD( time_do_sla, MAX( dt_averaging_input, dt_3d ) )
477          ENDIF
478       ENDIF
479
480!
481!--    Calculate spectra for time averaging
482       IF ( averaging_interval_sp /= 0.0  .AND.  &
483            ( dt_dosp - time_dosp ) <= averaging_interval_sp  .AND.  &
484            simulated_time >= skip_time_dosp )  THEN
485          time_dosp_av = time_dosp_av + dt_3d
486          IF ( time_dosp_av >= dt_averaging_input_pr )  THEN
487             CALL calc_spectra
488             time_dosp_av = MOD( time_dosp_av, &
489                                 MAX( dt_averaging_input_pr, dt_3d ) )
490          ENDIF
491       ENDIF
492
493!
494!--    Computation and output of run control parameters.
495!--    This is also done whenever perturbations have been imposed
496       IF ( time_run_control >= dt_run_control  .OR.                     &
497            timestep_scheme(1:5) /= 'runge'  .OR.  disturbance_created ) &
498       THEN
499          CALL run_control
500          IF ( time_run_control >= dt_run_control )  THEN
501             time_run_control = MOD( time_run_control, &
502                                     MAX( dt_run_control, dt_3d ) )
503          ENDIF
504       ENDIF
505
506!
507!--    Profile output (ASCII) on file
508       IF ( time_dopr_listing >= dt_dopr_listing )  THEN
509          CALL print_1d
510          time_dopr_listing = MOD( time_dopr_listing, MAX( dt_dopr_listing, &
511                                                           dt_3d ) )
512       ENDIF
513
514!
515!--    Graphic output for PROFIL
516       IF ( time_dopr >= dt_dopr )  THEN
517          IF ( dopr_n /= 0 )  CALL data_output_profiles
518          time_dopr = MOD( time_dopr, MAX( dt_dopr, dt_3d ) )
519          time_dopr_av = 0.0    ! due to averaging (see above)
520       ENDIF
521
522!
523!--    Graphic output for time series
524       IF ( time_dots >= dt_dots )  THEN
525          CALL data_output_tseries
526          time_dots = MOD( time_dots, MAX( dt_dots, dt_3d ) )
527       ENDIF
528
529!
530!--    Output of spectra (formatted for use with PROFIL), in case of no
531!--    time averaging, spectra has to be calculated before
532       IF ( time_dosp >= dt_dosp )  THEN
533          IF ( average_count_sp == 0 )  CALL calc_spectra
534          CALL data_output_spectra
535          time_dosp = MOD( time_dosp, MAX( dt_dosp, dt_3d ) )
536       ENDIF
537
538!
539!--    2d-data output (cross-sections)
540       IF ( time_do2d_xy >= dt_do2d_xy )  THEN
541          CALL data_output_2d( 'xy', 0 )
542          time_do2d_xy = MOD( time_do2d_xy, MAX( dt_do2d_xy, dt_3d ) )
543       ENDIF
544       IF ( time_do2d_xz >= dt_do2d_xz )  THEN
545          CALL data_output_2d( 'xz', 0 )
546          time_do2d_xz = MOD( time_do2d_xz, MAX( dt_do2d_xz, dt_3d ) )
547       ENDIF
548       IF ( time_do2d_yz >= dt_do2d_yz )  THEN
549          CALL data_output_2d( 'yz', 0 )
550          time_do2d_yz = MOD( time_do2d_yz, MAX( dt_do2d_yz, dt_3d ) )
551       ENDIF
552
553!
554!--    3d-data output (volume data)
555       IF ( time_do3d >= dt_do3d )  THEN
556          CALL data_output_3d( 0 )
557          time_do3d = MOD( time_do3d, MAX( dt_do3d, dt_3d ) )
558       ENDIF
559
560!
561!--    masked data output
562       DO  mid = 1, masks
563          IF ( time_domask(mid) >= dt_domask(mid) )  THEN
564             CALL data_output_mask( 0 )
565             time_domask(mid) = MOD( time_domask(mid),  &
566                                     MAX( dt_domask(mid), dt_3d ) )
567          ENDIF
568       ENDDO
569
570!
571!--    Output of time-averaged 2d/3d/masked data
572       IF ( time_do_av >= dt_data_output_av )  THEN
573          CALL average_3d_data
574          CALL data_output_2d( 'xy', 1 )
575          CALL data_output_2d( 'xz', 1 )
576          CALL data_output_2d( 'yz', 1 )
577          CALL data_output_3d( 1 )
578          DO  mid = 1, masks
579             CALL data_output_mask( 1 )
580          ENDDO
581          time_do_av = MOD( time_do_av, MAX( dt_data_output_av, dt_3d ) )
582       ENDIF
583
584!
585!--    Output of particle time series
586       IF ( particle_advection )  THEN
587          IF ( time_dopts >= dt_dopts  .OR. &
588               ( simulated_time >= particle_advection_start  .AND. &
589                 first_call_lpm ) )  THEN
590             CALL data_output_ptseries
591             time_dopts = MOD( time_dopts, MAX( dt_dopts, dt_3d ) )
592          ENDIF
593       ENDIF
594
595!
596!--    Output of dvrp-graphics (isosurface, particles, slicer)
597#if defined( __dvrp_graphics )
598       CALL DVRP_LOG_EVENT( -2, current_timestep_number-1 )
599#endif
600       IF ( time_dvrp >= dt_dvrp )  THEN
601          CALL data_output_dvrp
602          time_dvrp = MOD( time_dvrp, MAX( dt_dvrp, dt_3d ) )
603       ENDIF
604#if defined( __dvrp_graphics )
605       CALL DVRP_LOG_EVENT( 2, current_timestep_number )
606#endif
607
608!
609!--    If required, set the heat flux for the next time step at a random value
610       IF ( constant_heatflux  .AND.  random_heatflux )  CALL disturb_heatflux
611
612!
613!--    Execute user-defined actions
614       CALL user_actions( 'after_timestep' )
615
616       CALL cpu_log( log_point_s(10), 'timesteps', 'stop' )
617
618
619    ENDDO   ! time loop
620
621#if defined( __dvrp_graphics )
622    CALL DVRP_LOG_EVENT( -2, current_timestep_number )
623#endif
624
625 END SUBROUTINE time_integration
Note: See TracBrowser for help on using the repository browser.