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source: palm/trunk/SOURCE/pres.f90 @ 1878

Last change on this file since 1878 was 1846, checked in by raasch, 9 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 terms
6	! of the GNU General Public License as published by the Free Software Foundation,
7	! either version 3 of the License, or (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with
14	! PALM. If not, see <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2016 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! ------------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: pres.f90 1846 2016-04-08 08:30:46Z hellstea $
26	!
27	! 1845 2016-04-08 08:29:13Z raasch
28	! nzb_2d replace by nzb_u\|v_inner
29	!
30	! 1799 2016-04-05 08:35:55Z gronemeier
31	! Bugfix: excluded third dimension from horizontal volume flow calculation
32	!
33	! 1762 2016-02-25 12:31:13Z hellstea
34	! Introduction of nested domain feature
35	!
36	! 1682 2015-10-07 23:56:08Z knoop
37	! Code annotations made doxygen readable
38	!
39	! 1575 2015-03-27 09:56:27Z raasch
40	! poismg_fast + respective module added, adjustments for psolver-queries
41	!
42	! 1342 2014-03-26 17:04:47Z kanani
43	! REAL constants defined as wp-kind
44	!
45	! 1320 2014-03-20 08:40:49Z raasch
46	! ONLY-attribute added to USE-statements,
47	! kind-parameters added to all INTEGER and REAL declaration statements,
48	! kinds are defined in new module kinds,
49	! old module precision_kind is removed,
50	! revision history before 2012 removed,
51	! comment fields (!:) to be used for variable explanations added to
52	! all variable declaration statements
53	!
54	! 1318 2014-03-17 13:35:16Z raasch
55	! module interfaces removed
56	!
57	! 1306 2014-03-13 14:30:59Z raasch
58	! second argument removed from routine poisfft
59	!
60	! 1257 2013-11-08 15:18:40Z raasch
61	! openacc loop and loop vector clauses removed, independent clauses added,
62	! end parallel replaced by end parallel loop
63	!
64	! 1221 2013-09-10 08:59:13Z raasch
65	! openACC porting of reduction operations, loops for calculating d are
66	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
67	!
68	! 1212 2013-08-15 08:46:27Z raasch
69	! call of poisfft_hybrid removed
70	!
71	! 1117 2013-03-27 11:15:36Z suehring
72	! Bugfix in OpenMP parallelization.
73	!
74	! 1113 2013-03-10 02:48:14Z raasch
75	! GPU-porting of several loops, some loops rearranged
76	!
77	! 1111 2013-03-08 23:54:10Z
78	! openACC statements added,
79	! ibc_p_b = 2 removed
80	!
81	! 1092 2013-02-02 11:24:22Z raasch
82	! unused variables removed
83	!
84	! 1036 2012-10-22 13:43:42Z raasch
85	! code put under GPL (PALM 3.9)
86	!
87	! 1003 2012-09-14 14:35:53Z raasch
88	! adjustment of array tend for cases with unequal subdomain sizes removed
89	!
90	! Revision 1.1 1997/07/24 11:24:44 raasch
91	! Initial revision
92	!
93	!
94	! Description:
95	! ------------
96	!> Compute the divergence of the provisional velocity field. Solve the Poisson
97	!> equation for the perturbation pressure. Compute the final velocities using
98	!> this perturbation pressure. Compute the remaining divergence.
99	!------------------------------------------------------------------------------!
100	SUBROUTINE pres
101
102
103	USE arrays_3d, &
104	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, tend, u, v, w
105
106	USE control_parameters, &
107	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
108	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
109	mg_switch_to_pe0_level, nest_domain, nest_bound_l, &
110	nest_bound_n, nest_bound_r, nest_bound_s, on_device, outflow_l, &
111	outflow_n, outflow_r, outflow_s, psolver, simulated_time, &
112	subdomain_size, topography, volume_flow, volume_flow_area, &
113	volume_flow_initial
114
115	USE cpulog, &
116	ONLY: cpu_log, log_point, log_point_s
117
118	USE grid_variables, &
119	ONLY: ddx, ddy
120
121	USE indices, &
122	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
123	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
124	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
125	rflags_s_inner
126
127	USE kinds
128
129	USE pegrid
130
131	USE poisfft_mod, &
132	ONLY: poisfft
133
134	USE poismg_mod
135
136	USE statistics, &
137	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
138	weight_substep
139
140	IMPLICIT NONE
141
142	INTEGER(iwp) :: i !<
143	INTEGER(iwp) :: j !<
144	INTEGER(iwp) :: k !<
145
146	REAL(wp) :: ddt_3d !<
147	REAL(wp) :: localsum !<
148	REAL(wp) :: threadsum !<
149	REAL(wp) :: d_weight_pres !<
150
151	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
152	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
153	REAL(wp), DIMENSION(1:nzt) :: w_l !<
154	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
155
156
157	CALL cpu_log( log_point(8), 'pres', 'start' )
158
159
160	ddt_3d = 1.0_wp / dt_3d
161	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
162
163	!
164	!-- Multigrid method expects array d to have one ghost layer.
165	!--
166	IF ( psolver(1:9) == 'multigrid' ) THEN
167
168	DEALLOCATE( d )
169	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
170
171	!
172	!-- Since p is later used to hold the weighted average of the substeps, it
173	!-- cannot be used in the iterative solver. Therefore, its initial value is
174	!-- stored on p_loc, which is then iteratively advanced in every substep.
175	IF ( intermediate_timestep_count <= 1 ) THEN
176	DO i = nxl-1, nxr+1
177	DO j = nys-1, nyn+1
178	DO k = nzb, nzt+1
179	p_loc(k,j,i) = p(k,j,i)
180	ENDDO
181	ENDDO
182	ENDDO
183	ENDIF
184
185	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
186
187	!
188	!-- Since p is later used to hold the weighted average of the substeps, it
189	!-- cannot be used in the iterative solver. Therefore, its initial value is
190	!-- stored on p_loc, which is then iteratively advanced in every substep.
191	p_loc = p
192
193	ENDIF
194
195	!
196	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
197	!-- boundary conditions
198	!-- WARNING: so far, this conservation does not work at the left/south
199	!-- boundary if the topography at the inflow differs from that at the
200	!-- outflow! For this case, volume_flow_area needs adjustment!
201	!
202	!-- Left/right
203	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
204
205	volume_flow(1) = 0.0_wp
206	volume_flow_l(1) = 0.0_wp
207
208	IF ( outflow_l ) THEN
209	i = 0
210	ELSEIF ( outflow_r ) THEN
211	i = nx+1
212	ENDIF
213
214	DO j = nys, nyn
215	!
216	!-- Sum up the volume flow through the south/north boundary
217	DO k = nzb_u_inner(j,i)+1, nzt
218	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
219	ENDDO
220	ENDDO
221
222	#if defined( __parallel )
223	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
224	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
225	MPI_SUM, comm1dy, ierr )
226	#else
227	volume_flow = volume_flow_l
228	#endif
229	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
230	/ volume_flow_area(1)
231
232	DO j = nysg, nyng
233	DO k = nzb_u_inner(j,i)+1, nzt
234	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
235	ENDDO
236	ENDDO
237
238	ENDIF
239
240	!
241	!-- South/north
242	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
243
244	volume_flow(2) = 0.0_wp
245	volume_flow_l(2) = 0.0_wp
246
247	IF ( outflow_s ) THEN
248	j = 0
249	ELSEIF ( outflow_n ) THEN
250	j = ny+1
251	ENDIF
252
253	DO i = nxl, nxr
254	!
255	!-- Sum up the volume flow through the south/north boundary
256	DO k = nzb_v_inner(j,i)+1, nzt
257	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
258	ENDDO
259	ENDDO
260
261	#if defined( __parallel )
262	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
263	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
264	MPI_SUM, comm1dx, ierr )
265	#else
266	volume_flow = volume_flow_l
267	#endif
268	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
269	/ volume_flow_area(2)
270
271	DO i = nxlg, nxrg
272	DO k = nzb_v_inner(j,i)+1, nzt
273	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
274	ENDDO
275	ENDDO
276
277	ENDIF
278
279	!
280	!-- Remove mean vertical velocity in case that Neumann conditions are
281	!-- used both at bottom and top boundary, and if not a nested domain
282	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nest_domain) THEN
283	IF ( simulated_time > 0.0_wp ) THEN ! otherwise nzb_w_inner not yet known
284	w_l = 0.0_wp; w_l_l = 0.0_wp
285	DO i = nxl, nxr
286	DO j = nys, nyn
287	DO k = nzb_w_inner(j,i)+1, nzt
288	w_l_l(k) = w_l_l(k) + w(k,j,i)
289	ENDDO
290	ENDDO
291	ENDDO
292	#if defined( __parallel )
293	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
294	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
295	comm2d, ierr )
296	#else
297	w_l = w_l_l
298	#endif
299	DO k = 1, nzt
300	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
301	ENDDO
302	DO i = nxlg, nxrg
303	DO j = nysg, nyng
304	DO k = nzb_w_inner(j,i)+1, nzt
305	w(k,j,i) = w(k,j,i) - w_l(k)
306	ENDDO
307	ENDDO
308	ENDDO
309	ENDIF
310	ENDIF
311
312	!
313	!-- Compute the divergence of the provisional velocity field.
314	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
315
316	IF ( psolver(1:9) == 'multigrid' ) THEN
317	!$OMP PARALLEL DO SCHEDULE( STATIC )
318	DO i = nxl-1, nxr+1
319	DO j = nys-1, nyn+1
320	DO k = nzb, nzt+1
321	d(k,j,i) = 0.0_wp
322	ENDDO
323	ENDDO
324	ENDDO
325	ELSE
326	!$OMP PARALLEL DO SCHEDULE( STATIC )
327	!$acc kernels present( d )
328	DO i = nxl, nxr
329	DO j = nys, nyn
330	DO k = nzb+1, nzt
331	d(k,j,i) = 0.0_wp
332	ENDDO
333	ENDDO
334	ENDDO
335	!$acc end kernels
336	ENDIF
337
338	localsum = 0.0_wp
339	threadsum = 0.0_wp
340
341	#if defined( __ibm )
342	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
343	!$OMP DO SCHEDULE( STATIC )
344	DO i = nxl, nxr
345	DO j = nys, nyn
346	DO k = nzb_s_inner(j,i)+1, nzt
347	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
348	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
349	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
350	* d_weight_pres
351	ENDDO
352	!
353	!-- Compute possible PE-sum of divergences for flow_statistics
354	DO k = nzb_s_inner(j,i)+1, nzt
355	threadsum = threadsum + ABS( d(k,j,i) )
356	ENDDO
357
358	ENDDO
359	ENDDO
360
361	localsum = localsum + threadsum * dt_3d * &
362	weight_pres(intermediate_timestep_count)
363
364	!$OMP END PARALLEL
365	#else
366
367	!$OMP PARALLEL PRIVATE (i,j,k)
368	!$OMP DO SCHEDULE( STATIC )
369	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
370	!$acc loop collapse( 3 )
371	DO i = nxl, nxr
372	DO j = nys, nyn
373	DO k = 1, nzt
374	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
375	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
376	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
377	* d_weight_pres * rflags_s_inner(k,j,i)
378	ENDDO
379	ENDDO
380	ENDDO
381	!$acc end kernels
382	!$OMP END PARALLEL
383
384	!
385	!-- Compute possible PE-sum of divergences for flow_statistics
386	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
387	!$OMP DO SCHEDULE( STATIC )
388	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
389	DO i = nxl, nxr
390	DO j = nys, nyn
391	DO k = nzb+1, nzt
392	threadsum = threadsum + ABS( d(k,j,i) )
393	ENDDO
394	ENDDO
395	ENDDO
396	!$acc end parallel loop
397	localsum = localsum + threadsum * dt_3d * &
398	weight_pres(intermediate_timestep_count)
399	!$OMP END PARALLEL
400	#endif
401
402	!
403	!-- For completeness, set the divergence sum of all statistic regions to those
404	!-- of the total domain
405	sums_divold_l(0:statistic_regions) = localsum
406
407	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
408
409	!
410	!-- Compute the pressure perturbation solving the Poisson equation
411	IF ( psolver == 'poisfft' ) THEN
412
413	!
414	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
415	CALL poisfft( d )
416
417	!
418	!-- Store computed perturbation pressure and set boundary condition in
419	!-- z-direction
420	!$OMP PARALLEL DO
421	!$acc kernels present( d, tend )
422	DO i = nxl, nxr
423	DO j = nys, nyn
424	DO k = nzb+1, nzt
425	tend(k,j,i) = d(k,j,i)
426	ENDDO
427	ENDDO
428	ENDDO
429	!$acc end kernels
430
431	!
432	!-- Bottom boundary:
433	!-- This condition is only required for internal output. The pressure
434	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
435	IF ( ibc_p_b == 1 ) THEN
436	!
437	!-- Neumann (dp/dz = 0)
438	!$OMP PARALLEL DO
439	!$acc kernels present( nzb_s_inner, tend )
440	DO i = nxlg, nxrg
441	DO j = nysg, nyng
442	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
443	ENDDO
444	ENDDO
445	!$acc end kernels
446
447	ELSE
448	!
449	!-- Dirichlet
450	!$OMP PARALLEL DO
451	!$acc kernels present( tend )
452	DO i = nxlg, nxrg
453	DO j = nysg, nyng
454	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
455	ENDDO
456	ENDDO
457	!$acc end kernels
458
459	ENDIF
460
461	!
462	!-- Top boundary
463	IF ( ibc_p_t == 1 ) THEN
464	!
465	!-- Neumann
466	!$OMP PARALLEL DO
467	!$acc kernels present( tend )
468	DO i = nxlg, nxrg
469	DO j = nysg, nyng
470	tend(nzt+1,j,i) = tend(nzt,j,i)
471	ENDDO
472	ENDDO
473	!$acc end kernels
474
475	ELSE
476	!
477	!-- Dirichlet
478	!$OMP PARALLEL DO
479	!$acc kernels present( tend )
480	DO i = nxlg, nxrg
481	DO j = nysg, nyng
482	tend(nzt+1,j,i) = 0.0_wp
483	ENDDO
484	ENDDO
485	!$acc end kernels
486
487	ENDIF
488
489	!
490	!-- Exchange boundaries for p
491	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
492	on_device = .TRUE. ! to be removed after complete porting
493	ELSE ! of ghost point exchange
494	!$acc update host( tend )
495	ENDIF
496	CALL exchange_horiz( tend, nbgp )
497	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
498	on_device = .FALSE. ! to be removed after complete porting
499	ELSE ! of ghost point exchange
500	!$acc update device( tend )
501	ENDIF
502
503	ELSEIF ( psolver == 'sor' ) THEN
504
505	!
506	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
507	!-- scheme
508	CALL sor( d, ddzu_pres, ddzw, p_loc )
509	tend = p_loc
510
511	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
512
513	!
514	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
515	!-- array tend is used to store the residuals, logical exchange_mg is used
516	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
517	!-- ( nbgp ghost points ).
518
519	!-- If the number of grid points of the gathered grid, which is collected
520	!-- on PE0, is larger than the number of grid points of an PE, than array
521	!-- tend will be enlarged.
522	IF ( gathered_size > subdomain_size ) THEN
523	DEALLOCATE( tend )
524	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
525	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
526	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
527	mg_switch_to_pe0_level)+1) )
528	ENDIF
529
530	IF ( psolver == 'multigrid' ) THEN
531	CALL poismg( tend )
532	ELSE
533	CALL poismg_fast( tend )
534	ENDIF
535
536	IF ( gathered_size > subdomain_size ) THEN
537	DEALLOCATE( tend )
538	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
539	ENDIF
540
541	!
542	!-- Restore perturbation pressure on tend because this array is used
543	!-- further below to correct the velocity fields
544	DO i = nxl-1, nxr+1
545	DO j = nys-1, nyn+1
546	DO k = nzb, nzt+1
547	tend(k,j,i) = p_loc(k,j,i)
548	ENDDO
549	ENDDO
550	ENDDO
551
552	ENDIF
553
554	!
555	!-- Store perturbation pressure on array p, used for pressure data output.
556	!-- Ghost layers are added in the output routines (except sor-method: see below)
557	IF ( intermediate_timestep_count == 1 ) THEN
558	!$OMP PARALLEL PRIVATE (i,j,k)
559	!$OMP DO
560	!$acc kernels present( p, tend, weight_substep )
561	!$acc loop independent
562	DO i = nxl-1, nxr+1
563	!$acc loop independent
564	DO j = nys-1, nyn+1
565	!$acc loop independent
566	DO k = nzb, nzt+1
567	p(k,j,i) = tend(k,j,i) * &
568	weight_substep(intermediate_timestep_count)
569	ENDDO
570	ENDDO
571	ENDDO
572	!$acc end kernels
573	!$OMP END PARALLEL
574
575	ELSEIF ( intermediate_timestep_count > 1 ) THEN
576	!$OMP PARALLEL PRIVATE (i,j,k)
577	!$OMP DO
578	!$acc kernels present( p, tend, weight_substep )
579	!$acc loop independent
580	DO i = nxl-1, nxr+1
581	!$acc loop independent
582	DO j = nys-1, nyn+1
583	!$acc loop independent
584	DO k = nzb, nzt+1
585	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
586	weight_substep(intermediate_timestep_count)
587	ENDDO
588	ENDDO
589	ENDDO
590	!$acc end kernels
591	!$OMP END PARALLEL
592
593	ENDIF
594
595	!
596	!-- SOR-method needs ghost layers for the next timestep
597	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
598
599	!
600	!-- Correction of the provisional velocities with the current perturbation
601	!-- pressure just computed
602	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
603	volume_flow_l(1) = 0.0_wp
604	volume_flow_l(2) = 0.0_wp
605	ENDIF
606
607	!$OMP PARALLEL PRIVATE (i,j,k)
608	!$OMP DO
609	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
610	!$acc loop independent
611	DO i = nxl, nxr
612	!$acc loop independent
613	DO j = nys, nyn
614	!$acc loop independent
615	DO k = 1, nzt
616	IF ( k > nzb_w_inner(j,i) ) THEN
617	w(k,j,i) = w(k,j,i) - dt_3d * &
618	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
619	weight_pres(intermediate_timestep_count)
620	ENDIF
621	ENDDO
622	!$acc loop independent
623	DO k = 1, nzt
624	IF ( k > nzb_u_inner(j,i) ) THEN
625	u(k,j,i) = u(k,j,i) - dt_3d * &
626	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
627	weight_pres(intermediate_timestep_count)
628	ENDIF
629	ENDDO
630	!$acc loop independent
631	DO k = 1, nzt
632	IF ( k > nzb_v_inner(j,i) ) THEN
633	v(k,j,i) = v(k,j,i) - dt_3d * &
634	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
635	weight_pres(intermediate_timestep_count)
636	ENDIF
637	ENDDO
638
639	ENDDO
640	ENDDO
641	!$acc end kernels
642	!$OMP END PARALLEL
643
644	!
645	!-- Sum up the volume flow through the right and north boundary
646	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
647	nxr == nx ) THEN
648
649	!$OMP PARALLEL PRIVATE (j,k)
650	!$OMP DO
651	DO j = nys, nyn
652	!$OMP CRITICAL
653	DO k = nzb_u_inner(j,nx) + 1, nzt
654	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
655	ENDDO
656	!$OMP END CRITICAL
657	ENDDO
658	!$OMP END PARALLEL
659
660	ENDIF
661
662	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
663	nyn == ny ) THEN
664
665	!$OMP PARALLEL PRIVATE (i,k)
666	!$OMP DO
667	DO i = nxl, nxr
668	!$OMP CRITICAL
669	DO k = nzb_v_inner(ny,i) + 1, nzt
670	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
671	ENDDO
672	!$OMP END CRITICAL
673	ENDDO
674	!$OMP END PARALLEL
675
676	ENDIF
677
678	!
679	!-- Conserve the volume flow
680	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
681
682	#if defined( __parallel )
683	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
684	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
685	MPI_SUM, comm2d, ierr )
686	#else
687	volume_flow = volume_flow_l
688	#endif
689
690	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
691	volume_flow_area(1:2)
692
693	!$OMP PARALLEL PRIVATE (i,j,k)
694	!$OMP DO
695	DO i = nxl, nxr
696	DO j = nys, nyn
697	DO k = nzb_u_inner(j,i) + 1, nzt
698	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
699	ENDDO
700	DO k = nzb_v_inner(j,i) + 1, nzt
701	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
702	ENDDO
703	ENDDO
704	ENDDO
705
706	!$OMP END PARALLEL
707
708	ENDIF
709
710	!
711	!-- Exchange of boundaries for the velocities
712	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
713	on_device = .TRUE. ! to be removed after complete porting
714	ELSE ! of ghost point exchange
715	!$acc update host( u, v, w )
716	ENDIF
717	CALL exchange_horiz( u, nbgp )
718	CALL exchange_horiz( v, nbgp )
719	CALL exchange_horiz( w, nbgp )
720	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
721	on_device = .FALSE. ! to be removed after complete porting
722	ELSE ! of ghost point exchange
723	!$acc update device( u, v, w )
724	ENDIF
725
726	!
727	!-- Compute the divergence of the corrected velocity field,
728	!-- a possible PE-sum is computed in flow_statistics
729	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
730	sums_divnew_l = 0.0_wp
731
732	!
733	!-- d must be reset to zero because it can contain nonzero values below the
734	!-- topography
735	IF ( topography /= 'flat' ) d = 0.0_wp
736
737	localsum = 0.0_wp
738	threadsum = 0.0_wp
739
740	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
741	!$OMP DO SCHEDULE( STATIC )
742	#if defined( __ibm )
743	DO i = nxl, nxr
744	DO j = nys, nyn
745	DO k = nzb_s_inner(j,i)+1, nzt
746	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
747	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
748	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
749	ENDDO
750	DO k = nzb+1, nzt
751	threadsum = threadsum + ABS( d(k,j,i) )
752	ENDDO
753	ENDDO
754	ENDDO
755	#else
756	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
757	!$acc loop collapse( 3 )
758	DO i = nxl, nxr
759	DO j = nys, nyn
760	DO k = 1, nzt
761	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
762	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
763	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
764	) * rflags_s_inner(k,j,i)
765	ENDDO
766	ENDDO
767	ENDDO
768	!$acc end kernels
769	!
770	!-- Compute possible PE-sum of divergences for flow_statistics
771	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
772	DO i = nxl, nxr
773	DO j = nys, nyn
774	DO k = nzb+1, nzt
775	threadsum = threadsum + ABS( d(k,j,i) )
776	ENDDO
777	ENDDO
778	ENDDO
779	!$acc end parallel loop
780	#endif
781
782	localsum = localsum + threadsum
783	!$OMP END PARALLEL
784
785	!
786	!-- For completeness, set the divergence sum of all statistic regions to those
787	!-- of the total domain
788	sums_divnew_l(0:statistic_regions) = localsum
789
790	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
791
792	CALL cpu_log( log_point(8), 'pres', 'stop' )
793
794
795	END SUBROUTINE pres

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