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source: palm/trunk/SOURCE/pres.f90 @ 2037

Last change on this file since 2037 was 2037, checked in by knoop, 7 years ago
Anelastic approximation implemented
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1	!> @file pres.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! 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 1997-2016 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	! Anelastic approximation implemented
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: pres.f90 2037 2016-10-26 11:15:40Z knoop $
27	!
28	! 2000 2016-08-20 18:09:15Z knoop
29	! Forced header and separation lines into 80 columns
30	!
31	! 1932 2016-06-10 12:09:21Z suehring
32	! Initial version of purely vertical nesting introduced.
33	!
34	! 1931 2016-06-10 12:06:59Z suehring
35	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
36	!
37	! 1929 2016-06-09 16:25:25Z suehring
38	! Bugfix: weight_substep for initial call, replace by local variable
39	!
40	! 1918 2016-05-27 14:35:57Z raasch
41	! sum of divergence is also calculated when pres is called before the initial
42	! first time step,
43	! stearing is modified by using intermediate_timestep_count = 0 in order to
44	! determine if pres is called before the first initial timestep,
45	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
46	! mean vertical velocity is also removed for the first time step
47	! bugfix for calculating divergences
48	!
49	! 1908 2016-05-25 17:22:32Z suehring
50	! New divergence for output into RUN_CONTROL file is calculated only at last
51	! Runge-Kutta step
52	!
53	! 1845 2016-04-08 08:29:13Z raasch
54	! nzb_2d replace by nzb_u\|v_inner
55	!
56	! 1799 2016-04-05 08:35:55Z gronemeier
57	! Bugfix: excluded third dimension from horizontal volume flow calculation
58	!
59	! 1762 2016-02-25 12:31:13Z hellstea
60	! Introduction of nested domain feature
61	!
62	! 1682 2015-10-07 23:56:08Z knoop
63	! Code annotations made doxygen readable
64	!
65	! 1575 2015-03-27 09:56:27Z raasch
66	! poismg_fast + respective module added, adjustments for psolver-queries
67	!
68	! 1342 2014-03-26 17:04:47Z kanani
69	! REAL constants defined as wp-kind
70	!
71	! 1320 2014-03-20 08:40:49Z raasch
72	! ONLY-attribute added to USE-statements,
73	! kind-parameters added to all INTEGER and REAL declaration statements,
74	! kinds are defined in new module kinds,
75	! old module precision_kind is removed,
76	! revision history before 2012 removed,
77	! comment fields (!:) to be used for variable explanations added to
78	! all variable declaration statements
79	!
80	! 1318 2014-03-17 13:35:16Z raasch
81	! module interfaces removed
82	!
83	! 1306 2014-03-13 14:30:59Z raasch
84	! second argument removed from routine poisfft
85	!
86	! 1257 2013-11-08 15:18:40Z raasch
87	! openacc loop and loop vector clauses removed, independent clauses added,
88	! end parallel replaced by end parallel loop
89	!
90	! 1221 2013-09-10 08:59:13Z raasch
91	! openACC porting of reduction operations, loops for calculating d are
92	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
93	!
94	! 1212 2013-08-15 08:46:27Z raasch
95	! call of poisfft_hybrid removed
96	!
97	! 1117 2013-03-27 11:15:36Z suehring
98	! Bugfix in OpenMP parallelization.
99	!
100	! 1113 2013-03-10 02:48:14Z raasch
101	! GPU-porting of several loops, some loops rearranged
102	!
103	! 1111 2013-03-08 23:54:10Z
104	! openACC statements added,
105	! ibc_p_b = 2 removed
106	!
107	! 1092 2013-02-02 11:24:22Z raasch
108	! unused variables removed
109	!
110	! 1036 2012-10-22 13:43:42Z raasch
111	! code put under GPL (PALM 3.9)
112	!
113	! 1003 2012-09-14 14:35:53Z raasch
114	! adjustment of array tend for cases with unequal subdomain sizes removed
115	!
116	! Revision 1.1 1997/07/24 11:24:44 raasch
117	! Initial revision
118	!
119	!
120	! Description:
121	! ------------
122	!> Compute the divergence of the provisional velocity field. Solve the Poisson
123	!> equation for the perturbation pressure. Compute the final velocities using
124	!> this perturbation pressure. Compute the remaining divergence.
125	!------------------------------------------------------------------------------!
126	SUBROUTINE pres
127
128
129	USE arrays_3d, &
130	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
131	tend, u, v, w
132
133	USE control_parameters, &
134	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
135	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
136	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
137	nest_domain, on_device, outflow_l, outflow_n, outflow_r, &
138	outflow_s, psolver, subdomain_size, topography, volume_flow, &
139	volume_flow_area, volume_flow_initial
140
141	USE cpulog, &
142	ONLY: cpu_log, log_point, log_point_s
143
144	USE grid_variables, &
145	ONLY: ddx, ddy
146
147	USE indices, &
148	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
149	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
150	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
151	rflags_s_inner
152
153	USE kinds
154
155	USE pegrid
156
157	USE pmc_interface, &
158	ONLY: nesting_mode
159
160	USE poisfft_mod, &
161	ONLY: poisfft
162
163	USE poismg_mod
164
165	USE statistics, &
166	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
167	weight_substep
168
169	IMPLICIT NONE
170
171	INTEGER(iwp) :: i !<
172	INTEGER(iwp) :: j !<
173	INTEGER(iwp) :: k !<
174
175	REAL(wp) :: ddt_3d !<
176	REAL(wp) :: d_weight_pres !<
177	REAL(wp) :: localsum !<
178	REAL(wp) :: threadsum !<
179	REAL(wp) :: weight_pres_l !<
180	REAL(wp) :: weight_substep_l !<
181
182	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
183	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
184	REAL(wp), DIMENSION(1:nzt) :: w_l !<
185	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
186
187	LOGICAL :: nest_domain_nvn !<
188
189
190	CALL cpu_log( log_point(8), 'pres', 'start' )
191
192
193	!
194	!-- Calculate quantities to be used locally
195	ddt_3d = 1.0_wp / dt_3d
196	IF ( intermediate_timestep_count == 0 ) THEN
197	!
198	!-- If pres is called before initial time step
199	weight_pres_l = 1.0_wp
200	d_weight_pres = 1.0_wp
201	weight_substep_l = 1.0_wp
202	ELSE
203	weight_pres_l = weight_pres(intermediate_timestep_count)
204	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
205	weight_substep_l = weight_substep(intermediate_timestep_count)
206	ENDIF
207
208	!
209	!-- Multigrid method expects array d to have one ghost layer.
210	!--
211	IF ( psolver(1:9) == 'multigrid' ) THEN
212
213	DEALLOCATE( d )
214	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
215
216	!
217	!-- Since p is later used to hold the weighted average of the substeps, it
218	!-- cannot be used in the iterative solver. Therefore, its initial value is
219	!-- stored on p_loc, which is then iteratively advanced in every substep.
220	IF ( intermediate_timestep_count <= 1 ) THEN
221	DO i = nxl-1, nxr+1
222	DO j = nys-1, nyn+1
223	DO k = nzb, nzt+1
224	p_loc(k,j,i) = p(k,j,i)
225	ENDDO
226	ENDDO
227	ENDDO
228	ENDIF
229
230	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
231
232	!
233	!-- Since p is later used to hold the weighted average of the substeps, it
234	!-- cannot be used in the iterative solver. Therefore, its initial value is
235	!-- stored on p_loc, which is then iteratively advanced in every substep.
236	p_loc = p
237
238	ENDIF
239
240	!
241	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
242	!-- boundary conditions
243	!-- WARNING: so far, this conservation does not work at the left/south
244	!-- boundary if the topography at the inflow differs from that at the
245	!-- outflow! For this case, volume_flow_area needs adjustment!
246	!
247	!-- Left/right
248	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
249
250	volume_flow(1) = 0.0_wp
251	volume_flow_l(1) = 0.0_wp
252
253	IF ( outflow_l ) THEN
254	i = 0
255	ELSEIF ( outflow_r ) THEN
256	i = nx+1
257	ENDIF
258
259	DO j = nys, nyn
260	!
261	!-- Sum up the volume flow through the south/north boundary
262	DO k = nzb_u_inner(j,i)+1, nzt
263	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
264	ENDDO
265	ENDDO
266
267	#if defined( __parallel )
268	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
269	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
270	MPI_SUM, comm1dy, ierr )
271	#else
272	volume_flow = volume_flow_l
273	#endif
274	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
275	/ volume_flow_area(1)
276
277	DO j = nysg, nyng
278	DO k = nzb_u_inner(j,i)+1, nzt
279	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
280	ENDDO
281	ENDDO
282
283	ENDIF
284
285	!
286	!-- South/north
287	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
288
289	volume_flow(2) = 0.0_wp
290	volume_flow_l(2) = 0.0_wp
291
292	IF ( outflow_s ) THEN
293	j = 0
294	ELSEIF ( outflow_n ) THEN
295	j = ny+1
296	ENDIF
297
298	DO i = nxl, nxr
299	!
300	!-- Sum up the volume flow through the south/north boundary
301	DO k = nzb_v_inner(j,i)+1, nzt
302	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
303	ENDDO
304	ENDDO
305
306	#if defined( __parallel )
307	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
308	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
309	MPI_SUM, comm1dx, ierr )
310	#else
311	volume_flow = volume_flow_l
312	#endif
313	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
314	/ volume_flow_area(2)
315
316	DO i = nxlg, nxrg
317	DO k = nzb_v_inner(j,i)+1, nzt
318	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
319	ENDDO
320	ENDDO
321
322	ENDIF
323
324	!
325	!-- Remove mean vertical velocity in case that Neumann conditions are
326	!-- used both at bottom and top boundary, and if not a nested domain in a
327	!-- normal nesting run. In case of vertical nesting, this must be done.
328	!-- Therefore an auxiliary logical variable nest_domain_nvn is used here, and
329	!-- nvn stands for non-vertical nesting.
330	!-- This cannot be done before the first initial time step because ngp_2dh_outer
331	!-- is not yet known then.
332	nest_domain_nvn = nest_domain
333	IF ( nest_domain .AND. nesting_mode == 'vertical' ) THEN
334	nest_domain_nvn = .FALSE.
335	ENDIF
336
337	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. &
338	.NOT. nest_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
339	THEN
340	w_l = 0.0_wp; w_l_l = 0.0_wp
341	DO i = nxl, nxr
342	DO j = nys, nyn
343	DO k = nzb_w_inner(j,i)+1, nzt
344	w_l_l(k) = w_l_l(k) + w(k,j,i)
345	ENDDO
346	ENDDO
347	ENDDO
348	#if defined( __parallel )
349	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
350	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
351	comm2d, ierr )
352	#else
353	w_l = w_l_l
354	#endif
355	DO k = 1, nzt
356	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
357	ENDDO
358	DO i = nxlg, nxrg
359	DO j = nysg, nyng
360	DO k = nzb_w_inner(j,i)+1, nzt
361	w(k,j,i) = w(k,j,i) - w_l(k)
362	ENDDO
363	ENDDO
364	ENDDO
365	ENDIF
366
367	!
368	!-- Compute the divergence of the provisional velocity field.
369	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
370
371	IF ( psolver(1:9) == 'multigrid' ) THEN
372	!$OMP PARALLEL DO SCHEDULE( STATIC )
373	DO i = nxl-1, nxr+1
374	DO j = nys-1, nyn+1
375	DO k = nzb, nzt+1
376	d(k,j,i) = 0.0_wp
377	ENDDO
378	ENDDO
379	ENDDO
380	ELSE
381	!$OMP PARALLEL DO SCHEDULE( STATIC )
382	!$acc kernels present( d )
383	DO i = nxl, nxr
384	DO j = nys, nyn
385	DO k = nzb+1, nzt
386	d(k,j,i) = 0.0_wp
387	ENDDO
388	ENDDO
389	ENDDO
390	!$acc end kernels
391	ENDIF
392
393	localsum = 0.0_wp
394	threadsum = 0.0_wp
395
396	#if defined( __ibm )
397	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
398	!$OMP DO SCHEDULE( STATIC )
399	DO i = nxl, nxr
400	DO j = nys, nyn
401	DO k = nzb_s_inner(j,i)+1, nzt
402	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
403	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
404	( w(k,j,i) * rho_air_zw(k) - &
405	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
406	) * ddt_3d * d_weight_pres
407	ENDDO
408	!
409	!-- Compute possible PE-sum of divergences for flow_statistics
410	DO k = nzb_s_inner(j,i)+1, nzt
411	threadsum = threadsum + ABS( d(k,j,i) )
412	ENDDO
413
414	ENDDO
415	ENDDO
416
417	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
418	intermediate_timestep_count == 0 ) THEN
419	localsum = localsum + threadsum * dt_3d * weight_pres_l
420	ENDIF
421	!$OMP END PARALLEL
422	#else
423
424	!$OMP PARALLEL PRIVATE (i,j,k)
425	!$OMP DO SCHEDULE( STATIC )
426	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
427	!$acc loop collapse( 3 )
428	DO i = nxl, nxr
429	DO j = nys, nyn
430	DO k = 1, nzt
431	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
432	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
433	( w(k,j,i) * rho_air_zw(k) - &
434	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
435	) * ddt_3d * d_weight_pres * rflags_s_inner(k,j,i)
436	ENDDO
437	ENDDO
438	ENDDO
439	!$acc end kernels
440	!$OMP END PARALLEL
441
442	!
443	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
444	!-- computation only at last Runge-Kutta substep.
445	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
446	intermediate_timestep_count == 0 ) THEN
447	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
448	!$OMP DO SCHEDULE( STATIC )
449	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
450	DO i = nxl, nxr
451	DO j = nys, nyn
452	DO k = nzb+1, nzt
453	threadsum = threadsum + ABS( d(k,j,i) )
454	ENDDO
455	ENDDO
456	ENDDO
457	!$acc end parallel loop
458	localsum = localsum + threadsum * dt_3d * weight_pres_l
459	!$OMP END PARALLEL
460	ENDIF
461	#endif
462
463	!
464	!-- For completeness, set the divergence sum of all statistic regions to those
465	!-- of the total domain
466	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
467	intermediate_timestep_count == 0 ) THEN
468	sums_divold_l(0:statistic_regions) = localsum
469	ENDIF
470
471	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
472
473	!
474	!-- Compute the pressure perturbation solving the Poisson equation
475	IF ( psolver == 'poisfft' ) THEN
476
477	!
478	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
479	CALL poisfft( d )
480
481	!
482	!-- Store computed perturbation pressure and set boundary condition in
483	!-- z-direction
484	!$OMP PARALLEL DO
485	!$acc kernels present( d, tend )
486	DO i = nxl, nxr
487	DO j = nys, nyn
488	DO k = nzb+1, nzt
489	tend(k,j,i) = d(k,j,i)
490	ENDDO
491	ENDDO
492	ENDDO
493	!$acc end kernels
494
495	!
496	!-- Bottom boundary:
497	!-- This condition is only required for internal output. The pressure
498	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
499	IF ( ibc_p_b == 1 ) THEN
500	!
501	!-- Neumann (dp/dz = 0)
502	!$OMP PARALLEL DO
503	!$acc kernels present( nzb_s_inner, tend )
504	DO i = nxlg, nxrg
505	DO j = nysg, nyng
506	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
507	ENDDO
508	ENDDO
509	!$acc end kernels
510
511	ELSE
512	!
513	!-- Dirichlet
514	!$OMP PARALLEL DO
515	!$acc kernels present( tend )
516	DO i = nxlg, nxrg
517	DO j = nysg, nyng
518	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
519	ENDDO
520	ENDDO
521	!$acc end kernels
522
523	ENDIF
524
525	!
526	!-- Top boundary
527	IF ( ibc_p_t == 1 ) THEN
528	!
529	!-- Neumann
530	!$OMP PARALLEL DO
531	!$acc kernels present( tend )
532	DO i = nxlg, nxrg
533	DO j = nysg, nyng
534	tend(nzt+1,j,i) = tend(nzt,j,i)
535	ENDDO
536	ENDDO
537	!$acc end kernels
538
539	ELSE
540	!
541	!-- Dirichlet
542	!$OMP PARALLEL DO
543	!$acc kernels present( tend )
544	DO i = nxlg, nxrg
545	DO j = nysg, nyng
546	tend(nzt+1,j,i) = 0.0_wp
547	ENDDO
548	ENDDO
549	!$acc end kernels
550
551	ENDIF
552
553	!
554	!-- Exchange boundaries for p
555	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
556	on_device = .TRUE. ! to be removed after complete porting
557	ELSE ! of ghost point exchange
558	!$acc update host( tend )
559	ENDIF
560	CALL exchange_horiz( tend, nbgp )
561	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
562	on_device = .FALSE. ! to be removed after complete porting
563	ELSE ! of ghost point exchange
564	!$acc update device( tend )
565	ENDIF
566
567	ELSEIF ( psolver == 'sor' ) THEN
568
569	!
570	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
571	!-- scheme
572	CALL sor( d, ddzu_pres, ddzw, p_loc )
573	tend = p_loc
574
575	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
576
577	!
578	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
579	!-- array tend is used to store the residuals, logical exchange_mg is used
580	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
581	!-- ( nbgp ghost points ).
582
583	!-- If the number of grid points of the gathered grid, which is collected
584	!-- on PE0, is larger than the number of grid points of an PE, than array
585	!-- tend will be enlarged.
586	IF ( gathered_size > subdomain_size ) THEN
587	DEALLOCATE( tend )
588	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
589	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
590	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
591	mg_switch_to_pe0_level)+1) )
592	ENDIF
593
594	IF ( psolver == 'multigrid' ) THEN
595	CALL poismg( tend )
596	ELSE
597	CALL poismg_noopt( tend )
598	ENDIF
599
600	IF ( gathered_size > subdomain_size ) THEN
601	DEALLOCATE( tend )
602	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
603	ENDIF
604
605	!
606	!-- Restore perturbation pressure on tend because this array is used
607	!-- further below to correct the velocity fields
608	DO i = nxl-1, nxr+1
609	DO j = nys-1, nyn+1
610	DO k = nzb, nzt+1
611	tend(k,j,i) = p_loc(k,j,i)
612	ENDDO
613	ENDDO
614	ENDDO
615
616	ENDIF
617
618	!
619	!-- Store perturbation pressure on array p, used for pressure data output.
620	!-- Ghost layers are added in the output routines (except sor-method: see below)
621	IF ( intermediate_timestep_count <= 1 ) THEN
622	!$OMP PARALLEL PRIVATE (i,j,k)
623	!$OMP DO
624	!$acc kernels present( p, tend, weight_substep_l )
625	!$acc loop independent
626	DO i = nxl-1, nxr+1
627	!$acc loop independent
628	DO j = nys-1, nyn+1
629	!$acc loop independent
630	DO k = nzb, nzt+1
631	p(k,j,i) = tend(k,j,i) * &
632	weight_substep_l
633	ENDDO
634	ENDDO
635	ENDDO
636	!$acc end kernels
637	!$OMP END PARALLEL
638
639	ELSEIF ( intermediate_timestep_count > 1 ) THEN
640	!$OMP PARALLEL PRIVATE (i,j,k)
641	!$OMP DO
642	!$acc kernels present( p, tend, weight_substep_l )
643	!$acc loop independent
644	DO i = nxl-1, nxr+1
645	!$acc loop independent
646	DO j = nys-1, nyn+1
647	!$acc loop independent
648	DO k = nzb, nzt+1
649	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
650	weight_substep_l
651	ENDDO
652	ENDDO
653	ENDDO
654	!$acc end kernels
655	!$OMP END PARALLEL
656
657	ENDIF
658
659	!
660	!-- SOR-method needs ghost layers for the next timestep
661	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
662
663	!
664	!-- Correction of the provisional velocities with the current perturbation
665	!-- pressure just computed
666	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
667	volume_flow_l(1) = 0.0_wp
668	volume_flow_l(2) = 0.0_wp
669	ENDIF
670
671	!$OMP PARALLEL PRIVATE (i,j,k)
672	!$OMP DO
673	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w )
674	!$acc loop independent
675	DO i = nxl, nxr
676	!$acc loop independent
677	DO j = nys, nyn
678	!$acc loop independent
679	DO k = 1, nzt
680	IF ( k > nzb_w_inner(j,i) ) THEN
681	w(k,j,i) = w(k,j,i) - dt_3d * &
682	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
683	weight_pres_l
684	ENDIF
685	ENDDO
686	!$acc loop independent
687	DO k = 1, nzt
688	IF ( k > nzb_u_inner(j,i) ) THEN
689	u(k,j,i) = u(k,j,i) - dt_3d * &
690	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
691	weight_pres_l
692	ENDIF
693	ENDDO
694	!$acc loop independent
695	DO k = 1, nzt
696	IF ( k > nzb_v_inner(j,i) ) THEN
697	v(k,j,i) = v(k,j,i) - dt_3d * &
698	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
699	weight_pres_l
700	ENDIF
701	ENDDO
702
703	ENDDO
704	ENDDO
705	!$acc end kernels
706	!$OMP END PARALLEL
707
708	!
709	!-- Sum up the volume flow through the right and north boundary
710	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
711	nxr == nx ) THEN
712
713	!$OMP PARALLEL PRIVATE (j,k)
714	!$OMP DO
715	DO j = nys, nyn
716	!$OMP CRITICAL
717	DO k = nzb_u_inner(j,nx) + 1, nzt
718	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
719	ENDDO
720	!$OMP END CRITICAL
721	ENDDO
722	!$OMP END PARALLEL
723
724	ENDIF
725
726	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
727	nyn == ny ) THEN
728
729	!$OMP PARALLEL PRIVATE (i,k)
730	!$OMP DO
731	DO i = nxl, nxr
732	!$OMP CRITICAL
733	DO k = nzb_v_inner(ny,i) + 1, nzt
734	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
735	ENDDO
736	!$OMP END CRITICAL
737	ENDDO
738	!$OMP END PARALLEL
739
740	ENDIF
741
742	!
743	!-- Conserve the volume flow
744	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
745
746	#if defined( __parallel )
747	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
748	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
749	MPI_SUM, comm2d, ierr )
750	#else
751	volume_flow = volume_flow_l
752	#endif
753
754	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
755	volume_flow_area(1:2)
756
757	!$OMP PARALLEL PRIVATE (i,j,k)
758	!$OMP DO
759	DO i = nxl, nxr
760	DO j = nys, nyn
761	DO k = nzb_u_inner(j,i) + 1, nzt
762	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
763	ENDDO
764	DO k = nzb_v_inner(j,i) + 1, nzt
765	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
766	ENDDO
767	ENDDO
768	ENDDO
769
770	!$OMP END PARALLEL
771
772	ENDIF
773
774	!
775	!-- Exchange of boundaries for the velocities
776	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
777	on_device = .TRUE. ! to be removed after complete porting
778	ELSE ! of ghost point exchange
779	!$acc update host( u, v, w )
780	ENDIF
781	CALL exchange_horiz( u, nbgp )
782	CALL exchange_horiz( v, nbgp )
783	CALL exchange_horiz( w, nbgp )
784	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
785	on_device = .FALSE. ! to be removed after complete porting
786	ELSE ! of ghost point exchange
787	!$acc update device( u, v, w )
788	ENDIF
789
790	!
791	!-- Compute the divergence of the corrected velocity field,
792	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
793	!-- only at last Runge-Kutta step.
794	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
795	intermediate_timestep_count == 0 ) THEN
796	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
797	sums_divnew_l = 0.0_wp
798
799	!
800	!-- d must be reset to zero because it can contain nonzero values below the
801	!-- topography
802	IF ( topography /= 'flat' ) d = 0.0_wp
803
804	localsum = 0.0_wp
805	threadsum = 0.0_wp
806
807	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
808	!$OMP DO SCHEDULE( STATIC )
809	#if defined( __ibm )
810	DO i = nxl, nxr
811	DO j = nys, nyn
812	DO k = nzb_s_inner(j,i)+1, nzt
813	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
814	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
815	( w(k,j,i) * rho_air_zw(k) - &
816	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k)
817	ENDDO
818	DO k = nzb+1, nzt
819	threadsum = threadsum + ABS( d(k,j,i) )
820	ENDDO
821	ENDDO
822	ENDDO
823	#else
824	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
825	!$acc loop collapse( 3 )
826	DO i = nxl, nxr
827	DO j = nys, nyn
828	DO k = 1, nzt
829	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
830	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
831	( w(k,j,i) * rho_air_zw(k) - &
832	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
833	) * rflags_s_inner(k,j,i)
834	ENDDO
835	ENDDO
836	ENDDO
837	!$acc end kernels
838	!
839	!-- Compute possible PE-sum of divergences for flow_statistics
840	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
841	DO i = nxl, nxr
842	DO j = nys, nyn
843	DO k = nzb+1, nzt
844	threadsum = threadsum + ABS( d(k,j,i) )
845	ENDDO
846	ENDDO
847	ENDDO
848	!$acc end parallel loop
849	#endif
850
851	localsum = localsum + threadsum
852	!$OMP END PARALLEL
853
854	!
855	!-- For completeness, set the divergence sum of all statistic regions to those
856	!-- of the total domain
857	sums_divnew_l(0:statistic_regions) = localsum
858
859	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
860
861	ENDIF
862
863	CALL cpu_log( log_point(8), 'pres', 'stop' )
864
865
866	END SUBROUTINE pres

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