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source: palm/trunk/SOURCE/pres.f90 @ 2022

Last change on this file since 2022 was 2001, checked in by knoop, 8 years ago
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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	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: pres.f90 2001 2016-08-20 18:41:22Z suehring $
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, tend, u, v, w
131
132	USE control_parameters, &
133	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
134	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
135	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
136	nest_domain, on_device, outflow_l, outflow_n, outflow_r, &
137	outflow_s, psolver, subdomain_size, topography, volume_flow, &
138	volume_flow_area, volume_flow_initial
139
140	USE cpulog, &
141	ONLY: cpu_log, log_point, log_point_s
142
143	USE grid_variables, &
144	ONLY: ddx, ddy
145
146	USE indices, &
147	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
148	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
149	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
150	rflags_s_inner
151
152	USE kinds
153
154	USE pegrid
155
156	USE pmc_interface, &
157	ONLY: nesting_mode
158
159	USE poisfft_mod, &
160	ONLY: poisfft
161
162	USE poismg_mod
163
164	USE statistics, &
165	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
166	weight_substep
167
168	IMPLICIT NONE
169
170	INTEGER(iwp) :: i !<
171	INTEGER(iwp) :: j !<
172	INTEGER(iwp) :: k !<
173
174	REAL(wp) :: ddt_3d !<
175	REAL(wp) :: d_weight_pres !<
176	REAL(wp) :: localsum !<
177	REAL(wp) :: threadsum !<
178	REAL(wp) :: weight_pres_l !<
179	REAL(wp) :: weight_substep_l !<
180
181	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
182	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
183	REAL(wp), DIMENSION(1:nzt) :: w_l !<
184	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
185
186	LOGICAL :: nest_domain_nvn !<
187
188
189	CALL cpu_log( log_point(8), 'pres', 'start' )
190
191
192	!
193	!-- Calculate quantities to be used locally
194	ddt_3d = 1.0_wp / dt_3d
195	IF ( intermediate_timestep_count == 0 ) THEN
196	!
197	!-- If pres is called before initial time step
198	weight_pres_l = 1.0_wp
199	d_weight_pres = 1.0_wp
200	weight_substep_l = 1.0_wp
201	ELSE
202	weight_pres_l = weight_pres(intermediate_timestep_count)
203	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
204	weight_substep_l = weight_substep(intermediate_timestep_count)
205	ENDIF
206
207	!
208	!-- Multigrid method expects array d to have one ghost layer.
209	!--
210	IF ( psolver(1:9) == 'multigrid' ) THEN
211
212	DEALLOCATE( d )
213	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
214
215	!
216	!-- Since p is later used to hold the weighted average of the substeps, it
217	!-- cannot be used in the iterative solver. Therefore, its initial value is
218	!-- stored on p_loc, which is then iteratively advanced in every substep.
219	IF ( intermediate_timestep_count <= 1 ) THEN
220	DO i = nxl-1, nxr+1
221	DO j = nys-1, nyn+1
222	DO k = nzb, nzt+1
223	p_loc(k,j,i) = p(k,j,i)
224	ENDDO
225	ENDDO
226	ENDDO
227	ENDIF
228
229	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
230
231	!
232	!-- Since p is later used to hold the weighted average of the substeps, it
233	!-- cannot be used in the iterative solver. Therefore, its initial value is
234	!-- stored on p_loc, which is then iteratively advanced in every substep.
235	p_loc = p
236
237	ENDIF
238
239	!
240	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
241	!-- boundary conditions
242	!-- WARNING: so far, this conservation does not work at the left/south
243	!-- boundary if the topography at the inflow differs from that at the
244	!-- outflow! For this case, volume_flow_area needs adjustment!
245	!
246	!-- Left/right
247	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
248
249	volume_flow(1) = 0.0_wp
250	volume_flow_l(1) = 0.0_wp
251
252	IF ( outflow_l ) THEN
253	i = 0
254	ELSEIF ( outflow_r ) THEN
255	i = nx+1
256	ENDIF
257
258	DO j = nys, nyn
259	!
260	!-- Sum up the volume flow through the south/north boundary
261	DO k = nzb_u_inner(j,i)+1, nzt
262	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
263	ENDDO
264	ENDDO
265
266	#if defined( __parallel )
267	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
268	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
269	MPI_SUM, comm1dy, ierr )
270	#else
271	volume_flow = volume_flow_l
272	#endif
273	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
274	/ volume_flow_area(1)
275
276	DO j = nysg, nyng
277	DO k = nzb_u_inner(j,i)+1, nzt
278	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
279	ENDDO
280	ENDDO
281
282	ENDIF
283
284	!
285	!-- South/north
286	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
287
288	volume_flow(2) = 0.0_wp
289	volume_flow_l(2) = 0.0_wp
290
291	IF ( outflow_s ) THEN
292	j = 0
293	ELSEIF ( outflow_n ) THEN
294	j = ny+1
295	ENDIF
296
297	DO i = nxl, nxr
298	!
299	!-- Sum up the volume flow through the south/north boundary
300	DO k = nzb_v_inner(j,i)+1, nzt
301	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
302	ENDDO
303	ENDDO
304
305	#if defined( __parallel )
306	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
307	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
308	MPI_SUM, comm1dx, ierr )
309	#else
310	volume_flow = volume_flow_l
311	#endif
312	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
313	/ volume_flow_area(2)
314
315	DO i = nxlg, nxrg
316	DO k = nzb_v_inner(j,i)+1, nzt
317	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
318	ENDDO
319	ENDDO
320
321	ENDIF
322
323	!
324	!-- Remove mean vertical velocity in case that Neumann conditions are
325	!-- used both at bottom and top boundary, and if not a nested domain in a
326	!-- normal nesting run. In case of vertical nesting, this must be done.
327	!-- Therefore an auxiliary logical variable nest_domain_nvn is used here, and
328	!-- nvn stands for non-vertical nesting.
329	!-- This cannot be done before the first initial time step because ngp_2dh_outer
330	!-- is not yet known then.
331	nest_domain_nvn = nest_domain
332	IF ( nest_domain .AND. nesting_mode == 'vertical' ) THEN
333	nest_domain_nvn = .FALSE.
334	ENDIF
335
336	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. &
337	.NOT. nest_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
338	THEN
339	w_l = 0.0_wp; w_l_l = 0.0_wp
340	DO i = nxl, nxr
341	DO j = nys, nyn
342	DO k = nzb_w_inner(j,i)+1, nzt
343	w_l_l(k) = w_l_l(k) + w(k,j,i)
344	ENDDO
345	ENDDO
346	ENDDO
347	#if defined( __parallel )
348	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
349	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
350	comm2d, ierr )
351	#else
352	w_l = w_l_l
353	#endif
354	DO k = 1, nzt
355	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
356	ENDDO
357	DO i = nxlg, nxrg
358	DO j = nysg, nyng
359	DO k = nzb_w_inner(j,i)+1, nzt
360	w(k,j,i) = w(k,j,i) - w_l(k)
361	ENDDO
362	ENDDO
363	ENDDO
364	ENDIF
365
366	!
367	!-- Compute the divergence of the provisional velocity field.
368	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
369
370	IF ( psolver(1:9) == 'multigrid' ) THEN
371	!$OMP PARALLEL DO SCHEDULE( STATIC )
372	DO i = nxl-1, nxr+1
373	DO j = nys-1, nyn+1
374	DO k = nzb, nzt+1
375	d(k,j,i) = 0.0_wp
376	ENDDO
377	ENDDO
378	ENDDO
379	ELSE
380	!$OMP PARALLEL DO SCHEDULE( STATIC )
381	!$acc kernels present( d )
382	DO i = nxl, nxr
383	DO j = nys, nyn
384	DO k = nzb+1, nzt
385	d(k,j,i) = 0.0_wp
386	ENDDO
387	ENDDO
388	ENDDO
389	!$acc end kernels
390	ENDIF
391
392	localsum = 0.0_wp
393	threadsum = 0.0_wp
394
395	#if defined( __ibm )
396	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
397	!$OMP DO SCHEDULE( STATIC )
398	DO i = nxl, nxr
399	DO j = nys, nyn
400	DO k = nzb_s_inner(j,i)+1, nzt
401	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
402	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
403	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
404	* d_weight_pres
405	ENDDO
406	!
407	!-- Compute possible PE-sum of divergences for flow_statistics
408	DO k = nzb_s_inner(j,i)+1, nzt
409	threadsum = threadsum + ABS( d(k,j,i) )
410	ENDDO
411
412	ENDDO
413	ENDDO
414
415	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
416	intermediate_timestep_count == 0 ) THEN
417	localsum = localsum + threadsum * dt_3d * weight_pres_l
418	ENDIF
419	!$OMP END PARALLEL
420	#else
421
422	!$OMP PARALLEL PRIVATE (i,j,k)
423	!$OMP DO SCHEDULE( STATIC )
424	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
425	!$acc loop collapse( 3 )
426	DO i = nxl, nxr
427	DO j = nys, nyn
428	DO k = 1, nzt
429	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
430	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
431	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
432	* d_weight_pres * rflags_s_inner(k,j,i)
433	ENDDO
434	ENDDO
435	ENDDO
436	!$acc end kernels
437	!$OMP END PARALLEL
438
439	!
440	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
441	!-- computation only at last Runge-Kutta substep.
442	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
443	intermediate_timestep_count == 0 ) THEN
444	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
445	!$OMP DO SCHEDULE( STATIC )
446	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
447	DO i = nxl, nxr
448	DO j = nys, nyn
449	DO k = nzb+1, nzt
450	threadsum = threadsum + ABS( d(k,j,i) )
451	ENDDO
452	ENDDO
453	ENDDO
454	!$acc end parallel loop
455	localsum = localsum + threadsum * dt_3d * weight_pres_l
456	!$OMP END PARALLEL
457	ENDIF
458	#endif
459
460	!
461	!-- For completeness, set the divergence sum of all statistic regions to those
462	!-- of the total domain
463	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
464	intermediate_timestep_count == 0 ) THEN
465	sums_divold_l(0:statistic_regions) = localsum
466	ENDIF
467
468	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
469
470	!
471	!-- Compute the pressure perturbation solving the Poisson equation
472	IF ( psolver == 'poisfft' ) THEN
473
474	!
475	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
476	CALL poisfft( d )
477
478	!
479	!-- Store computed perturbation pressure and set boundary condition in
480	!-- z-direction
481	!$OMP PARALLEL DO
482	!$acc kernels present( d, tend )
483	DO i = nxl, nxr
484	DO j = nys, nyn
485	DO k = nzb+1, nzt
486	tend(k,j,i) = d(k,j,i)
487	ENDDO
488	ENDDO
489	ENDDO
490	!$acc end kernels
491
492	!
493	!-- Bottom boundary:
494	!-- This condition is only required for internal output. The pressure
495	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
496	IF ( ibc_p_b == 1 ) THEN
497	!
498	!-- Neumann (dp/dz = 0)
499	!$OMP PARALLEL DO
500	!$acc kernels present( nzb_s_inner, tend )
501	DO i = nxlg, nxrg
502	DO j = nysg, nyng
503	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
504	ENDDO
505	ENDDO
506	!$acc end kernels
507
508	ELSE
509	!
510	!-- Dirichlet
511	!$OMP PARALLEL DO
512	!$acc kernels present( tend )
513	DO i = nxlg, nxrg
514	DO j = nysg, nyng
515	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
516	ENDDO
517	ENDDO
518	!$acc end kernels
519
520	ENDIF
521
522	!
523	!-- Top boundary
524	IF ( ibc_p_t == 1 ) THEN
525	!
526	!-- Neumann
527	!$OMP PARALLEL DO
528	!$acc kernels present( tend )
529	DO i = nxlg, nxrg
530	DO j = nysg, nyng
531	tend(nzt+1,j,i) = tend(nzt,j,i)
532	ENDDO
533	ENDDO
534	!$acc end kernels
535
536	ELSE
537	!
538	!-- Dirichlet
539	!$OMP PARALLEL DO
540	!$acc kernels present( tend )
541	DO i = nxlg, nxrg
542	DO j = nysg, nyng
543	tend(nzt+1,j,i) = 0.0_wp
544	ENDDO
545	ENDDO
546	!$acc end kernels
547
548	ENDIF
549
550	!
551	!-- Exchange boundaries for p
552	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
553	on_device = .TRUE. ! to be removed after complete porting
554	ELSE ! of ghost point exchange
555	!$acc update host( tend )
556	ENDIF
557	CALL exchange_horiz( tend, nbgp )
558	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
559	on_device = .FALSE. ! to be removed after complete porting
560	ELSE ! of ghost point exchange
561	!$acc update device( tend )
562	ENDIF
563
564	ELSEIF ( psolver == 'sor' ) THEN
565
566	!
567	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
568	!-- scheme
569	CALL sor( d, ddzu_pres, ddzw, p_loc )
570	tend = p_loc
571
572	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
573
574	!
575	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
576	!-- array tend is used to store the residuals, logical exchange_mg is used
577	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
578	!-- ( nbgp ghost points ).
579
580	!-- If the number of grid points of the gathered grid, which is collected
581	!-- on PE0, is larger than the number of grid points of an PE, than array
582	!-- tend will be enlarged.
583	IF ( gathered_size > subdomain_size ) THEN
584	DEALLOCATE( tend )
585	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
586	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
587	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
588	mg_switch_to_pe0_level)+1) )
589	ENDIF
590
591	IF ( psolver == 'multigrid' ) THEN
592	CALL poismg( tend )
593	ELSE
594	CALL poismg_noopt( tend )
595	ENDIF
596
597	IF ( gathered_size > subdomain_size ) THEN
598	DEALLOCATE( tend )
599	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
600	ENDIF
601
602	!
603	!-- Restore perturbation pressure on tend because this array is used
604	!-- further below to correct the velocity fields
605	DO i = nxl-1, nxr+1
606	DO j = nys-1, nyn+1
607	DO k = nzb, nzt+1
608	tend(k,j,i) = p_loc(k,j,i)
609	ENDDO
610	ENDDO
611	ENDDO
612
613	ENDIF
614
615	!
616	!-- Store perturbation pressure on array p, used for pressure data output.
617	!-- Ghost layers are added in the output routines (except sor-method: see below)
618	IF ( intermediate_timestep_count <= 1 ) THEN
619	!$OMP PARALLEL PRIVATE (i,j,k)
620	!$OMP DO
621	!$acc kernels present( p, tend, weight_substep_l )
622	!$acc loop independent
623	DO i = nxl-1, nxr+1
624	!$acc loop independent
625	DO j = nys-1, nyn+1
626	!$acc loop independent
627	DO k = nzb, nzt+1
628	p(k,j,i) = tend(k,j,i) * &
629	weight_substep_l
630	ENDDO
631	ENDDO
632	ENDDO
633	!$acc end kernels
634	!$OMP END PARALLEL
635
636	ELSEIF ( intermediate_timestep_count > 1 ) THEN
637	!$OMP PARALLEL PRIVATE (i,j,k)
638	!$OMP DO
639	!$acc kernels present( p, tend, weight_substep_l )
640	!$acc loop independent
641	DO i = nxl-1, nxr+1
642	!$acc loop independent
643	DO j = nys-1, nyn+1
644	!$acc loop independent
645	DO k = nzb, nzt+1
646	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
647	weight_substep_l
648	ENDDO
649	ENDDO
650	ENDDO
651	!$acc end kernels
652	!$OMP END PARALLEL
653
654	ENDIF
655
656	!
657	!-- SOR-method needs ghost layers for the next timestep
658	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
659
660	!
661	!-- Correction of the provisional velocities with the current perturbation
662	!-- pressure just computed
663	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
664	volume_flow_l(1) = 0.0_wp
665	volume_flow_l(2) = 0.0_wp
666	ENDIF
667
668	!$OMP PARALLEL PRIVATE (i,j,k)
669	!$OMP DO
670	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w )
671	!$acc loop independent
672	DO i = nxl, nxr
673	!$acc loop independent
674	DO j = nys, nyn
675	!$acc loop independent
676	DO k = 1, nzt
677	IF ( k > nzb_w_inner(j,i) ) THEN
678	w(k,j,i) = w(k,j,i) - dt_3d * &
679	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
680	weight_pres_l
681	ENDIF
682	ENDDO
683	!$acc loop independent
684	DO k = 1, nzt
685	IF ( k > nzb_u_inner(j,i) ) THEN
686	u(k,j,i) = u(k,j,i) - dt_3d * &
687	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
688	weight_pres_l
689	ENDIF
690	ENDDO
691	!$acc loop independent
692	DO k = 1, nzt
693	IF ( k > nzb_v_inner(j,i) ) THEN
694	v(k,j,i) = v(k,j,i) - dt_3d * &
695	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
696	weight_pres_l
697	ENDIF
698	ENDDO
699
700	ENDDO
701	ENDDO
702	!$acc end kernels
703	!$OMP END PARALLEL
704
705	!
706	!-- Sum up the volume flow through the right and north boundary
707	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
708	nxr == nx ) THEN
709
710	!$OMP PARALLEL PRIVATE (j,k)
711	!$OMP DO
712	DO j = nys, nyn
713	!$OMP CRITICAL
714	DO k = nzb_u_inner(j,nx) + 1, nzt
715	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
716	ENDDO
717	!$OMP END CRITICAL
718	ENDDO
719	!$OMP END PARALLEL
720
721	ENDIF
722
723	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
724	nyn == ny ) THEN
725
726	!$OMP PARALLEL PRIVATE (i,k)
727	!$OMP DO
728	DO i = nxl, nxr
729	!$OMP CRITICAL
730	DO k = nzb_v_inner(ny,i) + 1, nzt
731	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
732	ENDDO
733	!$OMP END CRITICAL
734	ENDDO
735	!$OMP END PARALLEL
736
737	ENDIF
738
739	!
740	!-- Conserve the volume flow
741	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
742
743	#if defined( __parallel )
744	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
745	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
746	MPI_SUM, comm2d, ierr )
747	#else
748	volume_flow = volume_flow_l
749	#endif
750
751	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
752	volume_flow_area(1:2)
753
754	!$OMP PARALLEL PRIVATE (i,j,k)
755	!$OMP DO
756	DO i = nxl, nxr
757	DO j = nys, nyn
758	DO k = nzb_u_inner(j,i) + 1, nzt
759	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
760	ENDDO
761	DO k = nzb_v_inner(j,i) + 1, nzt
762	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
763	ENDDO
764	ENDDO
765	ENDDO
766
767	!$OMP END PARALLEL
768
769	ENDIF
770
771	!
772	!-- Exchange of boundaries for the velocities
773	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
774	on_device = .TRUE. ! to be removed after complete porting
775	ELSE ! of ghost point exchange
776	!$acc update host( u, v, w )
777	ENDIF
778	CALL exchange_horiz( u, nbgp )
779	CALL exchange_horiz( v, nbgp )
780	CALL exchange_horiz( w, nbgp )
781	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
782	on_device = .FALSE. ! to be removed after complete porting
783	ELSE ! of ghost point exchange
784	!$acc update device( u, v, w )
785	ENDIF
786
787	!
788	!-- Compute the divergence of the corrected velocity field,
789	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
790	!-- only at last Runge-Kutta step.
791	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
792	intermediate_timestep_count == 0 ) THEN
793	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
794	sums_divnew_l = 0.0_wp
795
796	!
797	!-- d must be reset to zero because it can contain nonzero values below the
798	!-- topography
799	IF ( topography /= 'flat' ) d = 0.0_wp
800
801	localsum = 0.0_wp
802	threadsum = 0.0_wp
803
804	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
805	!$OMP DO SCHEDULE( STATIC )
806	#if defined( __ibm )
807	DO i = nxl, nxr
808	DO j = nys, nyn
809	DO k = nzb_s_inner(j,i)+1, nzt
810	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
811	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
812	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
813	ENDDO
814	DO k = nzb+1, nzt
815	threadsum = threadsum + ABS( d(k,j,i) )
816	ENDDO
817	ENDDO
818	ENDDO
819	#else
820	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
821	!$acc loop collapse( 3 )
822	DO i = nxl, nxr
823	DO j = nys, nyn
824	DO k = 1, nzt
825	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
826	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
827	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
828	) * rflags_s_inner(k,j,i)
829	ENDDO
830	ENDDO
831	ENDDO
832	!$acc end kernels
833	!
834	!-- Compute possible PE-sum of divergences for flow_statistics
835	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
836	DO i = nxl, nxr
837	DO j = nys, nyn
838	DO k = nzb+1, nzt
839	threadsum = threadsum + ABS( d(k,j,i) )
840	ENDDO
841	ENDDO
842	ENDDO
843	!$acc end parallel loop
844	#endif
845
846	localsum = localsum + threadsum
847	!$OMP END PARALLEL
848
849	!
850	!-- For completeness, set the divergence sum of all statistic regions to those
851	!-- of the total domain
852	sums_divnew_l(0:statistic_regions) = localsum
853
854	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
855
856	ENDIF
857
858	CALL cpu_log( log_point(8), 'pres', 'stop' )
859
860
861	END SUBROUTINE pres

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