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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 1763 2016-02-25 13:00:19Z raasch $
26	!
27	! 1762 2016-02-25 12:31:13Z hellstea
28	! Introduction of nested domain feature
29	!
30	! 1682 2015-10-07 23:56:08Z knoop
31	! Code annotations made doxygen readable
32	!
33	! 1575 2015-03-27 09:56:27Z raasch
34	! poismg_fast + respective module added, adjustments for psolver-queries
35	!
36	! 1342 2014-03-26 17:04:47Z kanani
37	! REAL constants defined as wp-kind
38	!
39	! 1320 2014-03-20 08:40:49Z raasch
40	! ONLY-attribute added to USE-statements,
41	! kind-parameters added to all INTEGER and REAL declaration statements,
42	! kinds are defined in new module kinds,
43	! old module precision_kind is removed,
44	! revision history before 2012 removed,
45	! comment fields (!:) to be used for variable explanations added to
46	! all variable declaration statements
47	!
48	! 1318 2014-03-17 13:35:16Z raasch
49	! module interfaces removed
50	!
51	! 1306 2014-03-13 14:30:59Z raasch
52	! second argument removed from routine poisfft
53	!
54	! 1257 2013-11-08 15:18:40Z raasch
55	! openacc loop and loop vector clauses removed, independent clauses added,
56	! end parallel replaced by end parallel loop
57	!
58	! 1221 2013-09-10 08:59:13Z raasch
59	! openACC porting of reduction operations, loops for calculating d are
60	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
61	!
62	! 1212 2013-08-15 08:46:27Z raasch
63	! call of poisfft_hybrid removed
64	!
65	! 1117 2013-03-27 11:15:36Z suehring
66	! Bugfix in OpenMP parallelization.
67	!
68	! 1113 2013-03-10 02:48:14Z raasch
69	! GPU-porting of several loops, some loops rearranged
70	!
71	! 1111 2013-03-08 23:54:10Z
72	! openACC statements added,
73	! ibc_p_b = 2 removed
74	!
75	! 1092 2013-02-02 11:24:22Z raasch
76	! unused variables removed
77	!
78	! 1036 2012-10-22 13:43:42Z raasch
79	! code put under GPL (PALM 3.9)
80	!
81	! 1003 2012-09-14 14:35:53Z raasch
82	! adjustment of array tend for cases with unequal subdomain sizes removed
83	!
84	! Revision 1.1 1997/07/24 11:24:44 raasch
85	! Initial revision
86	!
87	!
88	! Description:
89	! ------------
90	!> Compute the divergence of the provisional velocity field. Solve the Poisson
91	!> equation for the perturbation pressure. Compute the final velocities using
92	!> this perturbation pressure. Compute the remaining divergence.
93	!------------------------------------------------------------------------------!
94	SUBROUTINE pres
95
96
97	USE arrays_3d, &
98	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, tend, u, v, w
99
100	USE control_parameters, &
101	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
102	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
103	mg_switch_to_pe0_level, nest_domain, nest_bound_l, &
104	nest_bound_n, nest_bound_r, nest_bound_s, on_device, outflow_l, &
105	outflow_n, outflow_r, outflow_s, psolver, simulated_time, &
106	subdomain_size, topography, volume_flow, volume_flow_area, &
107	volume_flow_initial
108
109	USE cpulog, &
110	ONLY: cpu_log, log_point, log_point_s
111
112	USE grid_variables, &
113	ONLY: ddx, ddy
114
115	USE indices, &
116	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
117	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
118	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzb_2d, nzt, nzt_mg, &
119	rflags_s_inner
120
121	USE kinds
122
123	USE pegrid
124
125	USE poisfft_mod, &
126	ONLY: poisfft
127
128	USE poismg_mod
129
130	USE statistics, &
131	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
132	weight_substep
133
134	IMPLICIT NONE
135
136	INTEGER(iwp) :: i !<
137	INTEGER(iwp) :: j !<
138	INTEGER(iwp) :: k !<
139
140	REAL(wp) :: ddt_3d !<
141	REAL(wp) :: localsum !<
142	REAL(wp) :: threadsum !<
143	REAL(wp) :: d_weight_pres !<
144
145	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
146	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
147	REAL(wp), DIMENSION(1:nzt) :: w_l !<
148	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
149
150
151	CALL cpu_log( log_point(8), 'pres', 'start' )
152
153
154	ddt_3d = 1.0_wp / dt_3d
155	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
156
157	!
158	!-- Multigrid method expects array d to have one ghost layer.
159	!--
160	IF ( psolver(1:9) == 'multigrid' ) THEN
161
162	DEALLOCATE( d )
163	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
164
165	!
166	!-- Since p is later used to hold the weighted average of the substeps, it
167	!-- cannot be used in the iterative solver. Therefore, its initial value is
168	!-- stored on p_loc, which is then iteratively advanced in every substep.
169	IF ( intermediate_timestep_count <= 1 ) THEN
170	DO i = nxl-1, nxr+1
171	DO j = nys-1, nyn+1
172	DO k = nzb, nzt+1
173	p_loc(k,j,i) = p(k,j,i)
174	ENDDO
175	ENDDO
176	ENDDO
177	ENDIF
178
179	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
180
181	!
182	!-- Since p is later used to hold the weighted average of the substeps, it
183	!-- cannot be used in the iterative solver. Therefore, its initial value is
184	!-- stored on p_loc, which is then iteratively advanced in every substep.
185	p_loc = p
186
187	ENDIF
188
189	!
190	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
191	!-- boundary conditions
192	!-- WARNING: so far, this conservation does not work at the left/south
193	!-- boundary if the topography at the inflow differs from that at the
194	!-- outflow! For this case, volume_flow_area needs adjustment!
195	!
196	!-- Left/right
197	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
198
199	volume_flow(1) = 0.0_wp
200	volume_flow_l(1) = 0.0_wp
201
202	IF ( outflow_l ) THEN
203	i = 0
204	ELSEIF ( outflow_r ) THEN
205	i = nx+1
206	ENDIF
207
208	DO j = nys, nyn
209	!
210	!-- Sum up the volume flow through the south/north boundary
211	DO k = nzb_2d(j,i)+1, nzt
212	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
213	ENDDO
214	ENDDO
215
216	#if defined( __parallel )
217	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
218	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
219	MPI_SUM, comm1dy, ierr )
220	#else
221	volume_flow = volume_flow_l
222	#endif
223	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
224	/ volume_flow_area(1)
225
226	DO j = nysg, nyng
227	DO k = nzb_2d(j,i)+1, nzt
228	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
229	ENDDO
230	ENDDO
231
232	ENDIF
233
234	!
235	!-- South/north
236	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
237
238	volume_flow(2) = 0.0_wp
239	volume_flow_l(2) = 0.0_wp
240
241	IF ( outflow_s ) THEN
242	j = 0
243	ELSEIF ( outflow_n ) THEN
244	j = ny+1
245	ENDIF
246
247	DO i = nxl, nxr
248	!
249	!-- Sum up the volume flow through the south/north boundary
250	DO k = nzb_2d(j,i)+1, nzt
251	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
252	ENDDO
253	ENDDO
254
255	#if defined( __parallel )
256	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
257	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
258	MPI_SUM, comm1dx, ierr )
259	#else
260	volume_flow = volume_flow_l
261	#endif
262	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
263	/ volume_flow_area(2)
264
265	DO i = nxlg, nxrg
266	DO k = nzb_v_inner(j,i)+1, nzt
267	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
268	ENDDO
269	ENDDO
270
271	ENDIF
272
273	!
274	!-- Remove mean vertical velocity in case that Neumann conditions are
275	!-- used both at bottom and top boundary, and if not a nested domain
276	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nest_domain) THEN
277	IF ( simulated_time > 0.0_wp ) THEN ! otherwise nzb_w_inner not yet known
278	w_l = 0.0_wp; w_l_l = 0.0_wp
279	DO i = nxl, nxr
280	DO j = nys, nyn
281	DO k = nzb_w_inner(j,i)+1, nzt
282	w_l_l(k) = w_l_l(k) + w(k,j,i)
283	ENDDO
284	ENDDO
285	ENDDO
286	#if defined( __parallel )
287	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
288	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
289	comm2d, ierr )
290	#else
291	w_l = w_l_l
292	#endif
293	DO k = 1, nzt
294	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
295	ENDDO
296	DO i = nxlg, nxrg
297	DO j = nysg, nyng
298	DO k = nzb_w_inner(j,i)+1, nzt
299	w(k,j,i) = w(k,j,i) - w_l(k)
300	ENDDO
301	ENDDO
302	ENDDO
303	ENDIF
304	ENDIF
305
306	!
307	!-- Compute the divergence of the provisional velocity field.
308	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
309
310	IF ( psolver(1:9) == 'multigrid' ) THEN
311	!$OMP PARALLEL DO SCHEDULE( STATIC )
312	DO i = nxl-1, nxr+1
313	DO j = nys-1, nyn+1
314	DO k = nzb, nzt+1
315	d(k,j,i) = 0.0_wp
316	ENDDO
317	ENDDO
318	ENDDO
319	ELSE
320	!$OMP PARALLEL DO SCHEDULE( STATIC )
321	!$acc kernels present( d )
322	DO i = nxl, nxr
323	DO j = nys, nyn
324	DO k = nzb+1, nzt
325	d(k,j,i) = 0.0_wp
326	ENDDO
327	ENDDO
328	ENDDO
329	!$acc end kernels
330	ENDIF
331
332	localsum = 0.0_wp
333	threadsum = 0.0_wp
334
335	#if defined( __ibm )
336	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
337	!$OMP DO SCHEDULE( STATIC )
338	DO i = nxl, nxr
339	DO j = nys, nyn
340	DO k = nzb_s_inner(j,i)+1, nzt
341	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
342	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
343	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
344	* d_weight_pres
345	ENDDO
346	!
347	!-- Compute possible PE-sum of divergences for flow_statistics
348	DO k = nzb_s_inner(j,i)+1, nzt
349	threadsum = threadsum + ABS( d(k,j,i) )
350	ENDDO
351
352	ENDDO
353	ENDDO
354
355	localsum = localsum + threadsum * dt_3d * &
356	weight_pres(intermediate_timestep_count)
357
358	!$OMP END PARALLEL
359	#else
360
361	!$OMP PARALLEL PRIVATE (i,j,k)
362	!$OMP DO SCHEDULE( STATIC )
363	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
364	!$acc loop collapse( 3 )
365	DO i = nxl, nxr
366	DO j = nys, nyn
367	DO k = 1, nzt
368	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
369	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
370	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
371	* d_weight_pres * rflags_s_inner(k,j,i)
372	ENDDO
373	ENDDO
374	ENDDO
375	!$acc end kernels
376	!$OMP END PARALLEL
377
378	!
379	!-- Compute possible PE-sum of divergences for flow_statistics
380	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
381	!$OMP DO SCHEDULE( STATIC )
382	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
383	DO i = nxl, nxr
384	DO j = nys, nyn
385	DO k = nzb+1, nzt
386	threadsum = threadsum + ABS( d(k,j,i) )
387	ENDDO
388	ENDDO
389	ENDDO
390	!$acc end parallel loop
391	localsum = localsum + threadsum * dt_3d * &
392	weight_pres(intermediate_timestep_count)
393	!$OMP END PARALLEL
394	#endif
395
396	!
397	!-- For completeness, set the divergence sum of all statistic regions to those
398	!-- of the total domain
399	sums_divold_l(0:statistic_regions) = localsum
400
401	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
402
403	!
404	!-- Compute the pressure perturbation solving the Poisson equation
405	IF ( psolver == 'poisfft' ) THEN
406
407	!
408	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
409	CALL poisfft( d )
410
411	!
412	!-- Store computed perturbation pressure and set boundary condition in
413	!-- z-direction
414	!$OMP PARALLEL DO
415	!$acc kernels present( d, tend )
416	DO i = nxl, nxr
417	DO j = nys, nyn
418	DO k = nzb+1, nzt
419	tend(k,j,i) = d(k,j,i)
420	ENDDO
421	ENDDO
422	ENDDO
423	!$acc end kernels
424
425	!
426	!-- Bottom boundary:
427	!-- This condition is only required for internal output. The pressure
428	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
429	IF ( ibc_p_b == 1 ) THEN
430	!
431	!-- Neumann (dp/dz = 0)
432	!$OMP PARALLEL DO
433	!$acc kernels present( nzb_s_inner, tend )
434	DO i = nxlg, nxrg
435	DO j = nysg, nyng
436	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
437	ENDDO
438	ENDDO
439	!$acc end kernels
440
441	ELSE
442	!
443	!-- Dirichlet
444	!$OMP PARALLEL DO
445	!$acc kernels present( tend )
446	DO i = nxlg, nxrg
447	DO j = nysg, nyng
448	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
449	ENDDO
450	ENDDO
451	!$acc end kernels
452
453	ENDIF
454
455	!
456	!-- Top boundary
457	IF ( ibc_p_t == 1 ) THEN
458	!
459	!-- Neumann
460	!$OMP PARALLEL DO
461	!$acc kernels present( tend )
462	DO i = nxlg, nxrg
463	DO j = nysg, nyng
464	tend(nzt+1,j,i) = tend(nzt,j,i)
465	ENDDO
466	ENDDO
467	!$acc end kernels
468
469	ELSE
470	!
471	!-- Dirichlet
472	!$OMP PARALLEL DO
473	!$acc kernels present( tend )
474	DO i = nxlg, nxrg
475	DO j = nysg, nyng
476	tend(nzt+1,j,i) = 0.0_wp
477	ENDDO
478	ENDDO
479	!$acc end kernels
480
481	ENDIF
482
483	!
484	!-- Exchange boundaries for p
485	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
486	on_device = .TRUE. ! to be removed after complete porting
487	ELSE ! of ghost point exchange
488	!$acc update host( tend )
489	ENDIF
490	CALL exchange_horiz( tend, nbgp )
491	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
492	on_device = .FALSE. ! to be removed after complete porting
493	ELSE ! of ghost point exchange
494	!$acc update device( tend )
495	ENDIF
496
497	ELSEIF ( psolver == 'sor' ) THEN
498
499	!
500	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
501	!-- scheme
502	CALL sor( d, ddzu_pres, ddzw, p_loc )
503	tend = p_loc
504
505	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
506
507	!
508	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
509	!-- array tend is used to store the residuals, logical exchange_mg is used
510	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
511	!-- ( nbgp ghost points ).
512
513	!-- If the number of grid points of the gathered grid, which is collected
514	!-- on PE0, is larger than the number of grid points of an PE, than array
515	!-- tend will be enlarged.
516	IF ( gathered_size > subdomain_size ) THEN
517	DEALLOCATE( tend )
518	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
519	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
520	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
521	mg_switch_to_pe0_level)+1) )
522	ENDIF
523
524	IF ( psolver == 'multigrid' ) THEN
525	CALL poismg( tend )
526	ELSE
527	CALL poismg_fast( tend )
528	ENDIF
529
530	IF ( gathered_size > subdomain_size ) THEN
531	DEALLOCATE( tend )
532	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
533	ENDIF
534
535	!
536	!-- Restore perturbation pressure on tend because this array is used
537	!-- further below to correct the velocity fields
538	DO i = nxl-1, nxr+1
539	DO j = nys-1, nyn+1
540	DO k = nzb, nzt+1
541	tend(k,j,i) = p_loc(k,j,i)
542	ENDDO
543	ENDDO
544	ENDDO
545
546	ENDIF
547
548	!
549	!-- Store perturbation pressure on array p, used for pressure data output.
550	!-- Ghost layers are added in the output routines (except sor-method: see below)
551	IF ( intermediate_timestep_count == 1 ) THEN
552	!$OMP PARALLEL PRIVATE (i,j,k)
553	!$OMP DO
554	!$acc kernels present( p, tend, weight_substep )
555	!$acc loop independent
556	DO i = nxl-1, nxr+1
557	!$acc loop independent
558	DO j = nys-1, nyn+1
559	!$acc loop independent
560	DO k = nzb, nzt+1
561	p(k,j,i) = tend(k,j,i) * &
562	weight_substep(intermediate_timestep_count)
563	ENDDO
564	ENDDO
565	ENDDO
566	!$acc end kernels
567	!$OMP END PARALLEL
568
569	ELSEIF ( intermediate_timestep_count > 1 ) THEN
570	!$OMP PARALLEL PRIVATE (i,j,k)
571	!$OMP DO
572	!$acc kernels present( p, tend, weight_substep )
573	!$acc loop independent
574	DO i = nxl-1, nxr+1
575	!$acc loop independent
576	DO j = nys-1, nyn+1
577	!$acc loop independent
578	DO k = nzb, nzt+1
579	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
580	weight_substep(intermediate_timestep_count)
581	ENDDO
582	ENDDO
583	ENDDO
584	!$acc end kernels
585	!$OMP END PARALLEL
586
587	ENDIF
588
589	!
590	!-- SOR-method needs ghost layers for the next timestep
591	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
592
593	!
594	!-- Correction of the provisional velocities with the current perturbation
595	!-- pressure just computed
596	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
597	volume_flow_l(1) = 0.0_wp
598	volume_flow_l(2) = 0.0_wp
599	ENDIF
600
601	!$OMP PARALLEL PRIVATE (i,j,k)
602	!$OMP DO
603	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
604	!$acc loop independent
605	DO i = nxl, nxr
606	!$acc loop independent
607	DO j = nys, nyn
608	!$acc loop independent
609	DO k = 1, nzt
610	IF ( k > nzb_w_inner(j,i) ) THEN
611	w(k,j,i) = w(k,j,i) - dt_3d * &
612	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
613	weight_pres(intermediate_timestep_count)
614	ENDIF
615	ENDDO
616	!$acc loop independent
617	DO k = 1, nzt
618	IF ( k > nzb_u_inner(j,i) ) THEN
619	u(k,j,i) = u(k,j,i) - dt_3d * &
620	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
621	weight_pres(intermediate_timestep_count)
622	ENDIF
623	ENDDO
624	!$acc loop independent
625	DO k = 1, nzt
626	IF ( k > nzb_v_inner(j,i) ) THEN
627	v(k,j,i) = v(k,j,i) - dt_3d * &
628	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
629	weight_pres(intermediate_timestep_count)
630	ENDIF
631	ENDDO
632
633	ENDDO
634	ENDDO
635	!$acc end kernels
636	!$OMP END PARALLEL
637
638	!
639	!-- Sum up the volume flow through the right and north boundary
640	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
641	nxr == nx ) THEN
642
643	!$OMP PARALLEL PRIVATE (j,k)
644	!$OMP DO
645	DO j = nys, nyn
646	!$OMP CRITICAL
647	DO k = nzb_2d(j,nx) + 1, nzt
648	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
649	ENDDO
650	!$OMP END CRITICAL
651	ENDDO
652	!$OMP END PARALLEL
653
654	ENDIF
655
656	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
657	nyn == ny ) THEN
658
659	!$OMP PARALLEL PRIVATE (i,k)
660	!$OMP DO
661	DO i = nxl, nxr
662	!$OMP CRITICAL
663	DO k = nzb_2d(ny,i) + 1, nzt
664	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
665	ENDDO
666	!$OMP END CRITICAL
667	ENDDO
668	!$OMP END PARALLEL
669
670	ENDIF
671
672	!
673	!-- Conserve the volume flow
674	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
675
676	#if defined( __parallel )
677	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
678	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
679	MPI_SUM, comm2d, ierr )
680	#else
681	volume_flow = volume_flow_l
682	#endif
683
684	volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
685	volume_flow_area
686
687	!$OMP PARALLEL PRIVATE (i,j,k)
688	!$OMP DO
689	DO i = nxl, nxr
690	DO j = nys, nyn
691	DO k = nzb_u_inner(j,i) + 1, nzt
692	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
693	ENDDO
694	DO k = nzb_v_inner(j,i) + 1, nzt
695	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
696	ENDDO
697	ENDDO
698	ENDDO
699
700	!$OMP END PARALLEL
701
702	ENDIF
703
704	!
705	!-- Exchange of boundaries for the velocities
706	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
707	on_device = .TRUE. ! to be removed after complete porting
708	ELSE ! of ghost point exchange
709	!$acc update host( u, v, w )
710	ENDIF
711	CALL exchange_horiz( u, nbgp )
712	CALL exchange_horiz( v, nbgp )
713	CALL exchange_horiz( w, nbgp )
714	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
715	on_device = .FALSE. ! to be removed after complete porting
716	ELSE ! of ghost point exchange
717	!$acc update device( u, v, w )
718	ENDIF
719
720	!
721	!-- Compute the divergence of the corrected velocity field,
722	!-- a possible PE-sum is computed in flow_statistics
723	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
724	sums_divnew_l = 0.0_wp
725
726	!
727	!-- d must be reset to zero because it can contain nonzero values below the
728	!-- topography
729	IF ( topography /= 'flat' ) d = 0.0_wp
730
731	localsum = 0.0_wp
732	threadsum = 0.0_wp
733
734	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
735	!$OMP DO SCHEDULE( STATIC )
736	#if defined( __ibm )
737	DO i = nxl, nxr
738	DO j = nys, nyn
739	DO k = nzb_s_inner(j,i)+1, nzt
740	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
741	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
742	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
743	ENDDO
744	DO k = nzb+1, nzt
745	threadsum = threadsum + ABS( d(k,j,i) )
746	ENDDO
747	ENDDO
748	ENDDO
749	#else
750	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
751	!$acc loop collapse( 3 )
752	DO i = nxl, nxr
753	DO j = nys, nyn
754	DO k = 1, nzt
755	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
756	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
757	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
758	) * rflags_s_inner(k,j,i)
759	ENDDO
760	ENDDO
761	ENDDO
762	!$acc end kernels
763	!
764	!-- Compute possible PE-sum of divergences for flow_statistics
765	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
766	DO i = nxl, nxr
767	DO j = nys, nyn
768	DO k = nzb+1, nzt
769	threadsum = threadsum + ABS( d(k,j,i) )
770	ENDDO
771	ENDDO
772	ENDDO
773	!$acc end parallel loop
774	#endif
775
776	localsum = localsum + threadsum
777	!$OMP END PARALLEL
778
779	!
780	!-- For completeness, set the divergence sum of all statistic regions to those
781	!-- of the total domain
782	sums_divnew_l(0:statistic_regions) = localsum
783
784	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
785
786	CALL cpu_log( log_point(8), 'pres', 'stop' )
787
788
789	END SUBROUTINE pres

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