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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 1997-2014 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! ------------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: pres.f90 1683 2015-10-07 23:57:51Z gronemeier $
26	!
27	! 1682 2015-10-07 23:56:08Z knoop
28	! Code annotations made doxygen readable
29	!
30	! 1575 2015-03-27 09:56:27Z raasch
31	! poismg_fast + respective module added, adjustments for psolver-queries
32	!
33	! 1342 2014-03-26 17:04:47Z kanani
34	! REAL constants defined as wp-kind
35	!
36	! 1320 2014-03-20 08:40:49Z raasch
37	! ONLY-attribute added to USE-statements,
38	! kind-parameters added to all INTEGER and REAL declaration statements,
39	! kinds are defined in new module kinds,
40	! old module precision_kind is removed,
41	! revision history before 2012 removed,
42	! comment fields (!:) to be used for variable explanations added to
43	! all variable declaration statements
44	!
45	! 1318 2014-03-17 13:35:16Z raasch
46	! module interfaces removed
47	!
48	! 1306 2014-03-13 14:30:59Z raasch
49	! second argument removed from routine poisfft
50	!
51	! 1257 2013-11-08 15:18:40Z raasch
52	! openacc loop and loop vector clauses removed, independent clauses added,
53	! end parallel replaced by end parallel loop
54	!
55	! 1221 2013-09-10 08:59:13Z raasch
56	! openACC porting of reduction operations, loops for calculating d are
57	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
58	!
59	! 1212 2013-08-15 08:46:27Z raasch
60	! call of poisfft_hybrid removed
61	!
62	! 1117 2013-03-27 11:15:36Z suehring
63	! Bugfix in OpenMP parallelization.
64	!
65	! 1113 2013-03-10 02:48:14Z raasch
66	! GPU-porting of several loops, some loops rearranged
67	!
68	! 1111 2013-03-08 23:54:10Z
69	! openACC statements added,
70	! ibc_p_b = 2 removed
71	!
72	! 1092 2013-02-02 11:24:22Z raasch
73	! unused variables removed
74	!
75	! 1036 2012-10-22 13:43:42Z raasch
76	! code put under GPL (PALM 3.9)
77	!
78	! 1003 2012-09-14 14:35:53Z raasch
79	! adjustment of array tend for cases with unequal subdomain sizes removed
80	!
81	! Revision 1.1 1997/07/24 11:24:44 raasch
82	! Initial revision
83	!
84	!
85	! Description:
86	! ------------
87	!> Compute the divergence of the provisional velocity field. Solve the Poisson
88	!> equation for the perturbation pressure. Compute the final velocities using
89	!> this perturbation pressure. Compute the remaining divergence.
90	!------------------------------------------------------------------------------!
91	SUBROUTINE pres
92
93
94	USE arrays_3d, &
95	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, tend, u, v, w
96
97	USE control_parameters, &
98	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
99	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
100	mg_switch_to_pe0_level, on_device, outflow_l, outflow_n, &
101	outflow_r, outflow_s, psolver, simulated_time, subdomain_size, &
102	topography, volume_flow, volume_flow_area, volume_flow_initial
103
104	USE cpulog, &
105	ONLY: cpu_log, log_point, log_point_s
106
107	USE grid_variables, &
108	ONLY: ddx, ddy
109
110	USE indices, &
111	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
112	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
113	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzb_2d, nzt, nzt_mg, &
114	rflags_s_inner
115
116	USE kinds
117
118	USE pegrid
119
120	USE poisfft_mod, &
121	ONLY: poisfft
122
123	USE poismg_mod
124
125	USE statistics, &
126	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
127	weight_substep
128
129	IMPLICIT NONE
130
131	INTEGER(iwp) :: i !<
132	INTEGER(iwp) :: j !<
133	INTEGER(iwp) :: k !<
134
135	REAL(wp) :: ddt_3d !<
136	REAL(wp) :: localsum !<
137	REAL(wp) :: threadsum !<
138	REAL(wp) :: d_weight_pres !<
139
140	REAL(wp), DIMENSION(1:2) :: volume_flow_l !<
141	REAL(wp), DIMENSION(1:2) :: volume_flow_offset !<
142	REAL(wp), DIMENSION(1:nzt) :: w_l !<
143	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
144
145
146	CALL cpu_log( log_point(8), 'pres', 'start' )
147
148
149	ddt_3d = 1.0_wp / dt_3d
150	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
151
152	!
153	!-- Multigrid method expects array d to have one ghost layer.
154	!--
155	IF ( psolver(1:9) == 'multigrid' ) THEN
156
157	DEALLOCATE( d )
158	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
159
160	!
161	!-- Since p is later used to hold the weighted average of the substeps, it
162	!-- cannot be used in the iterative solver. Therefore, its initial value is
163	!-- stored on p_loc, which is then iteratively advanced in every substep.
164	IF ( intermediate_timestep_count == 1 ) THEN
165	DO i = nxl-1, nxr+1
166	DO j = nys-1, nyn+1
167	DO k = nzb, nzt+1
168	p_loc(k,j,i) = p(k,j,i)
169	ENDDO
170	ENDDO
171	ENDDO
172	ENDIF
173
174	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
175
176	!
177	!-- Since p is later used to hold the weighted average of the substeps, it
178	!-- cannot be used in the iterative solver. Therefore, its initial value is
179	!-- stored on p_loc, which is then iteratively advanced in every substep.
180	p_loc = p
181
182	ENDIF
183
184	!
185	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
186	!-- boundary conditions
187	!-- WARNING: so far, this conservation does not work at the left/south
188	!-- boundary if the topography at the inflow differs from that at the
189	!-- outflow! For this case, volume_flow_area needs adjustment!
190	!
191	!-- Left/right
192	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
193
194	volume_flow(1) = 0.0_wp
195	volume_flow_l(1) = 0.0_wp
196
197	IF ( outflow_l ) THEN
198	i = 0
199	ELSEIF ( outflow_r ) THEN
200	i = nx+1
201	ENDIF
202
203	DO j = nys, nyn
204	!
205	!-- Sum up the volume flow through the south/north boundary
206	DO k = nzb_2d(j,i)+1, nzt
207	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
208	ENDDO
209	ENDDO
210
211	#if defined( __parallel )
212	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
213	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
214	MPI_SUM, comm1dy, ierr )
215	#else
216	volume_flow = volume_flow_l
217	#endif
218	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
219	/ volume_flow_area(1)
220
221	DO j = nysg, nyng
222	DO k = nzb_2d(j,i)+1, nzt
223	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
224	ENDDO
225	ENDDO
226
227	ENDIF
228
229	!
230	!-- South/north
231	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
232
233	volume_flow(2) = 0.0_wp
234	volume_flow_l(2) = 0.0_wp
235
236	IF ( outflow_s ) THEN
237	j = 0
238	ELSEIF ( outflow_n ) THEN
239	j = ny+1
240	ENDIF
241
242	DO i = nxl, nxr
243	!
244	!-- Sum up the volume flow through the south/north boundary
245	DO k = nzb_2d(j,i)+1, nzt
246	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
247	ENDDO
248	ENDDO
249
250	#if defined( __parallel )
251	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
252	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
253	MPI_SUM, comm1dx, ierr )
254	#else
255	volume_flow = volume_flow_l
256	#endif
257	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
258	/ volume_flow_area(2)
259
260	DO i = nxlg, nxrg
261	DO k = nzb_v_inner(j,i)+1, nzt
262	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
263	ENDDO
264	ENDDO
265
266	ENDIF
267
268	!
269	!-- Remove mean vertical velocity
270	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN
271	IF ( simulated_time > 0.0_wp ) THEN ! otherwise nzb_w_inner not yet known
272	w_l = 0.0_wp; w_l_l = 0.0_wp
273	DO i = nxl, nxr
274	DO j = nys, nyn
275	DO k = nzb_w_inner(j,i)+1, nzt
276	w_l_l(k) = w_l_l(k) + w(k,j,i)
277	ENDDO
278	ENDDO
279	ENDDO
280	#if defined( __parallel )
281	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
282	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
283	comm2d, ierr )
284	#else
285	w_l = w_l_l
286	#endif
287	DO k = 1, nzt
288	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
289	ENDDO
290	DO i = nxlg, nxrg
291	DO j = nysg, nyng
292	DO k = nzb_w_inner(j,i)+1, nzt
293	w(k,j,i) = w(k,j,i) - w_l(k)
294	ENDDO
295	ENDDO
296	ENDDO
297	ENDIF
298	ENDIF
299
300	!
301	!-- Compute the divergence of the provisional velocity field.
302	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
303
304	IF ( psolver(1:9) == 'multigrid' ) THEN
305	!$OMP PARALLEL DO SCHEDULE( STATIC )
306	DO i = nxl-1, nxr+1
307	DO j = nys-1, nyn+1
308	DO k = nzb, nzt+1
309	d(k,j,i) = 0.0_wp
310	ENDDO
311	ENDDO
312	ENDDO
313	ELSE
314	!$OMP PARALLEL DO SCHEDULE( STATIC )
315	!$acc kernels present( d )
316	DO i = nxl, nxr
317	DO j = nys, nyn
318	DO k = nzb+1, nzt
319	d(k,j,i) = 0.0_wp
320	ENDDO
321	ENDDO
322	ENDDO
323	!$acc end kernels
324	ENDIF
325
326	localsum = 0.0_wp
327	threadsum = 0.0_wp
328
329	#if defined( __ibm )
330	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
331	!$OMP DO SCHEDULE( STATIC )
332	DO i = nxl, nxr
333	DO j = nys, nyn
334	DO k = nzb_s_inner(j,i)+1, nzt
335	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
336	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
337	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
338	* d_weight_pres
339	ENDDO
340	!
341	!-- Compute possible PE-sum of divergences for flow_statistics
342	DO k = nzb_s_inner(j,i)+1, nzt
343	threadsum = threadsum + ABS( d(k,j,i) )
344	ENDDO
345
346	ENDDO
347	ENDDO
348
349	localsum = localsum + threadsum * dt_3d * &
350	weight_pres(intermediate_timestep_count)
351
352	!$OMP END PARALLEL
353	#else
354
355	!$OMP PARALLEL PRIVATE (i,j,k)
356	!$OMP DO SCHEDULE( STATIC )
357	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
358	!$acc loop collapse( 3 )
359	DO i = nxl, nxr
360	DO j = nys, nyn
361	DO k = 1, nzt
362	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
363	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
364	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
365	* d_weight_pres * rflags_s_inner(k,j,i)
366	ENDDO
367	ENDDO
368	ENDDO
369	!$acc end kernels
370	!$OMP END PARALLEL
371
372	!
373	!-- Compute possible PE-sum of divergences for flow_statistics
374	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
375	!$OMP DO SCHEDULE( STATIC )
376	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
377	DO i = nxl, nxr
378	DO j = nys, nyn
379	DO k = nzb+1, nzt
380	threadsum = threadsum + ABS( d(k,j,i) )
381	ENDDO
382	ENDDO
383	ENDDO
384	!$acc end parallel loop
385	localsum = localsum + threadsum * dt_3d * &
386	weight_pres(intermediate_timestep_count)
387	!$OMP END PARALLEL
388	#endif
389
390	!
391	!-- For completeness, set the divergence sum of all statistic regions to those
392	!-- of the total domain
393	sums_divold_l(0:statistic_regions) = localsum
394
395	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
396
397	!
398	!-- Compute the pressure perturbation solving the Poisson equation
399	IF ( psolver == 'poisfft' ) THEN
400
401	!
402	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
403	CALL poisfft( d )
404
405	!
406	!-- Store computed perturbation pressure and set boundary condition in
407	!-- z-direction
408	!$OMP PARALLEL DO
409	!$acc kernels present( d, tend )
410	DO i = nxl, nxr
411	DO j = nys, nyn
412	DO k = nzb+1, nzt
413	tend(k,j,i) = d(k,j,i)
414	ENDDO
415	ENDDO
416	ENDDO
417	!$acc end kernels
418
419	!
420	!-- Bottom boundary:
421	!-- This condition is only required for internal output. The pressure
422	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
423	IF ( ibc_p_b == 1 ) THEN
424	!
425	!-- Neumann (dp/dz = 0)
426	!$OMP PARALLEL DO
427	!$acc kernels present( nzb_s_inner, tend )
428	DO i = nxlg, nxrg
429	DO j = nysg, nyng
430	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
431	ENDDO
432	ENDDO
433	!$acc end kernels
434
435	ELSE
436	!
437	!-- Dirichlet
438	!$OMP PARALLEL DO
439	!$acc kernels present( tend )
440	DO i = nxlg, nxrg
441	DO j = nysg, nyng
442	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
443	ENDDO
444	ENDDO
445	!$acc end kernels
446
447	ENDIF
448
449	!
450	!-- Top boundary
451	IF ( ibc_p_t == 1 ) THEN
452	!
453	!-- Neumann
454	!$OMP PARALLEL DO
455	!$acc kernels present( tend )
456	DO i = nxlg, nxrg
457	DO j = nysg, nyng
458	tend(nzt+1,j,i) = tend(nzt,j,i)
459	ENDDO
460	ENDDO
461	!$acc end kernels
462
463	ELSE
464	!
465	!-- Dirichlet
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) = 0.0_wp
471	ENDDO
472	ENDDO
473	!$acc end kernels
474
475	ENDIF
476
477	!
478	!-- Exchange boundaries for p
479	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
480	on_device = .TRUE. ! to be removed after complete porting
481	ELSE ! of ghost point exchange
482	!$acc update host( tend )
483	ENDIF
484	CALL exchange_horiz( tend, nbgp )
485	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
486	on_device = .FALSE. ! to be removed after complete porting
487	ELSE ! of ghost point exchange
488	!$acc update device( tend )
489	ENDIF
490
491	ELSEIF ( psolver == 'sor' ) THEN
492
493	!
494	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
495	!-- scheme
496	CALL sor( d, ddzu_pres, ddzw, p_loc )
497	tend = p_loc
498
499	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
500
501	!
502	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
503	!-- array tend is used to store the residuals, logical exchange_mg is used
504	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
505	!-- ( nbgp ghost points ).
506
507	!-- If the number of grid points of the gathered grid, which is collected
508	!-- on PE0, is larger than the number of grid points of an PE, than array
509	!-- tend will be enlarged.
510	IF ( gathered_size > subdomain_size ) THEN
511	DEALLOCATE( tend )
512	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
513	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
514	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
515	mg_switch_to_pe0_level)+1) )
516	ENDIF
517
518	IF ( psolver == 'multigrid' ) THEN
519	CALL poismg( tend )
520	ELSE
521	CALL poismg_fast( tend )
522	ENDIF
523
524	IF ( gathered_size > subdomain_size ) THEN
525	DEALLOCATE( tend )
526	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
527	ENDIF
528
529	!
530	!-- Restore perturbation pressure on tend because this array is used
531	!-- further below to correct the velocity fields
532	DO i = nxl-1, nxr+1
533	DO j = nys-1, nyn+1
534	DO k = nzb, nzt+1
535	tend(k,j,i) = p_loc(k,j,i)
536	ENDDO
537	ENDDO
538	ENDDO
539
540	ENDIF
541
542	!
543	!-- Store perturbation pressure on array p, used for pressure data output.
544	!-- Ghost layers are added in the output routines (except sor-method: see below)
545	IF ( intermediate_timestep_count == 1 ) THEN
546	!$OMP PARALLEL PRIVATE (i,j,k)
547	!$OMP DO
548	!$acc kernels present( p, tend, weight_substep )
549	!$acc loop independent
550	DO i = nxl-1, nxr+1
551	!$acc loop independent
552	DO j = nys-1, nyn+1
553	!$acc loop independent
554	DO k = nzb, nzt+1
555	p(k,j,i) = tend(k,j,i) * &
556	weight_substep(intermediate_timestep_count)
557	ENDDO
558	ENDDO
559	ENDDO
560	!$acc end kernels
561	!$OMP END PARALLEL
562
563	ELSE
564	!$OMP PARALLEL PRIVATE (i,j,k)
565	!$OMP DO
566	!$acc kernels present( p, tend, weight_substep )
567	!$acc loop independent
568	DO i = nxl-1, nxr+1
569	!$acc loop independent
570	DO j = nys-1, nyn+1
571	!$acc loop independent
572	DO k = nzb, nzt+1
573	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
574	weight_substep(intermediate_timestep_count)
575	ENDDO
576	ENDDO
577	ENDDO
578	!$acc end kernels
579	!$OMP END PARALLEL
580
581	ENDIF
582
583	!
584	!-- SOR-method needs ghost layers for the next timestep
585	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
586
587	!
588	!-- Correction of the provisional velocities with the current perturbation
589	!-- pressure just computed
590	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
591	volume_flow_l(1) = 0.0_wp
592	volume_flow_l(2) = 0.0_wp
593	ENDIF
594
595	!$OMP PARALLEL PRIVATE (i,j,k)
596	!$OMP DO
597	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
598	!$acc loop independent
599	DO i = nxl, nxr
600	!$acc loop independent
601	DO j = nys, nyn
602	!$acc loop independent
603	DO k = 1, nzt
604	IF ( k > nzb_w_inner(j,i) ) THEN
605	w(k,j,i) = w(k,j,i) - dt_3d * &
606	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
607	weight_pres(intermediate_timestep_count)
608	ENDIF
609	ENDDO
610	!$acc loop independent
611	DO k = 1, nzt
612	IF ( k > nzb_u_inner(j,i) ) THEN
613	u(k,j,i) = u(k,j,i) - dt_3d * &
614	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
615	weight_pres(intermediate_timestep_count)
616	ENDIF
617	ENDDO
618	!$acc loop independent
619	DO k = 1, nzt
620	IF ( k > nzb_v_inner(j,i) ) THEN
621	v(k,j,i) = v(k,j,i) - dt_3d * &
622	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
623	weight_pres(intermediate_timestep_count)
624	ENDIF
625	ENDDO
626
627	ENDDO
628	ENDDO
629	!$acc end kernels
630	!$OMP END PARALLEL
631
632	!
633	!-- Sum up the volume flow through the right and north boundary
634	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
635	nxr == nx ) THEN
636
637	!$OMP PARALLEL PRIVATE (j,k)
638	!$OMP DO
639	DO j = nys, nyn
640	!$OMP CRITICAL
641	DO k = nzb_2d(j,nx) + 1, nzt
642	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
643	ENDDO
644	!$OMP END CRITICAL
645	ENDDO
646	!$OMP END PARALLEL
647
648	ENDIF
649
650	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
651	nyn == ny ) THEN
652
653	!$OMP PARALLEL PRIVATE (i,k)
654	!$OMP DO
655	DO i = nxl, nxr
656	!$OMP CRITICAL
657	DO k = nzb_2d(ny,i) + 1, nzt
658	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
659	ENDDO
660	!$OMP END CRITICAL
661	ENDDO
662	!$OMP END PARALLEL
663
664	ENDIF
665
666	!
667	!-- Conserve the volume flow
668	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
669
670	#if defined( __parallel )
671	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
672	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
673	MPI_SUM, comm2d, ierr )
674	#else
675	volume_flow = volume_flow_l
676	#endif
677
678	volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
679	volume_flow_area
680
681	!$OMP PARALLEL PRIVATE (i,j,k)
682	!$OMP DO
683	DO i = nxl, nxr
684	DO j = nys, nyn
685	DO k = nzb_u_inner(j,i) + 1, nzt
686	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
687	ENDDO
688	DO k = nzb_v_inner(j,i) + 1, nzt
689	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
690	ENDDO
691	ENDDO
692	ENDDO
693
694	!$OMP END PARALLEL
695
696	ENDIF
697
698	!
699	!-- Exchange of boundaries for the velocities
700	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
701	on_device = .TRUE. ! to be removed after complete porting
702	ELSE ! of ghost point exchange
703	!$acc update host( u, v, w )
704	ENDIF
705	CALL exchange_horiz( u, nbgp )
706	CALL exchange_horiz( v, nbgp )
707	CALL exchange_horiz( w, nbgp )
708	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
709	on_device = .FALSE. ! to be removed after complete porting
710	ELSE ! of ghost point exchange
711	!$acc update device( u, v, w )
712	ENDIF
713
714	!
715	!-- Compute the divergence of the corrected velocity field,
716	!-- a possible PE-sum is computed in flow_statistics
717	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
718	sums_divnew_l = 0.0_wp
719
720	!
721	!-- d must be reset to zero because it can contain nonzero values below the
722	!-- topography
723	IF ( topography /= 'flat' ) d = 0.0_wp
724
725	localsum = 0.0_wp
726	threadsum = 0.0_wp
727
728	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
729	!$OMP DO SCHEDULE( STATIC )
730	#if defined( __ibm )
731	DO i = nxl, nxr
732	DO j = nys, nyn
733	DO k = nzb_s_inner(j,i)+1, nzt
734	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
735	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
736	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
737	ENDDO
738	DO k = nzb+1, nzt
739	threadsum = threadsum + ABS( d(k,j,i) )
740	ENDDO
741	ENDDO
742	ENDDO
743	#else
744	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
745	!$acc loop collapse( 3 )
746	DO i = nxl, nxr
747	DO j = nys, nyn
748	DO k = 1, nzt
749	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
750	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
751	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
752	) * rflags_s_inner(k,j,i)
753	ENDDO
754	ENDDO
755	ENDDO
756	!$acc end kernels
757	!
758	!-- Compute possible PE-sum of divergences for flow_statistics
759	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
760	DO i = nxl, nxr
761	DO j = nys, nyn
762	DO k = nzb+1, nzt
763	threadsum = threadsum + ABS( d(k,j,i) )
764	ENDDO
765	ENDDO
766	ENDDO
767	!$acc end parallel loop
768	#endif
769
770	localsum = localsum + threadsum
771	!$OMP END PARALLEL
772
773	!
774	!-- For completeness, set the divergence sum of all statistic regions to those
775	!-- of the total domain
776	sums_divnew_l(0:statistic_regions) = localsum
777
778	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
779
780	CALL cpu_log( log_point(8), 'pres', 'stop' )
781
782
783	END SUBROUTINE pres

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