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1	SUBROUTINE pres
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later 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 1997-2012 Leibniz University Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: pres.f90 1222 2013-09-10 14:48:09Z raasch $
27	!
28	! 1221 2013-09-10 08:59:13Z raasch
29	! openACC porting of reduction operations, loops for calculating d are
30	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
31	!
32	! 1212 2013-08-15 08:46:27Z raasch
33	! call of poisfft_hybrid removed
34	!
35	! 1117 2013-03-27 11:15:36Z suehring
36	! Bugfix in OpenMP parallelization.
37	!
38	! 1113 2013-03-10 02:48:14Z raasch
39	! GPU-porting of several loops, some loops rearranged
40	!
41	! 1111 2013-03-08 23:54:10Z
42	! openACC statements added,
43	! ibc_p_b = 2 removed
44	!
45	! 1092 2013-02-02 11:24:22Z raasch
46	! unused variables removed
47	!
48	! 1036 2012-10-22 13:43:42Z raasch
49	! code put under GPL (PALM 3.9)
50	!
51	! 1003 2012-09-14 14:35:53Z raasch
52	! adjustment of array tend for cases with unequal subdomain sizes removed
53	!
54	! 778 2011-11-07 14:18:25Z fricke
55	! New allocation of tend when multigrid is used and the collected field on PE0
56	! has more grid points than the subdomain of an PE.
57	!
58	! 719 2011-04-06 13:05:23Z gryschka
59	! Bugfix in volume flow control for double cyclic boundary conditions
60	!
61	! 709 2011-03-30 09:31:40Z raasch
62	! formatting adjustments
63	!
64	! 707 2011-03-29 11:39:40Z raasch
65	! Calculation of weighted average of p is now handled in the same way
66	! regardless of the number of ghost layers (advection scheme),
67	! multigrid and sor method are using p_loc for iterative advancements of
68	! pressure,
69	! localsum calculation modified for proper OpenMP reduction,
70	! bc_lr/ns replaced by bc_lr/ns_cyc
71	!
72	! 693 2011-03-08 09:..:..Z raasch
73	! bugfix: weighting coefficient added to ibm branch
74	!
75	! 680 2011-02-04 23:16:06Z gryschka
76	! bugfix: collective_wait
77	!
78	! 675 2011-01-19 10:56:55Z suehring
79	! Removed bugfix while copying tend.
80	!
81	! 673 2011-01-18 16:19:48Z suehring
82	! Weighting coefficients added for right computation of the pressure during
83	! Runge-Kutta substeps.
84	!
85	! 667 2010-12-23 12:06:00Z suehring/gryschka
86	! New allocation of tend when ws-scheme and multigrid is used. This is due to
87	! reasons of perforance of the data_exchange. The same is done with p after
88	! poismg is called.
89	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no
90	! multigrid is used. Calls of exchange_horiz are modified.
91	! bugfix: After pressure correction no volume flow correction in case of
92	! non-cyclic boundary conditions
93	! (has to be done only before pressure correction)
94	! Call of SOR routine is referenced with ddzu_pres.
95	!
96	! 622 2010-12-10 08:08:13Z raasch
97	! optional barriers included in order to speed up collective operations
98	!
99	! 151 2008-03-07 13:42:18Z raasch
100	! Bugfix in volume flow control for non-cyclic boundary conditions
101	!
102	! 106 2007-08-16 14:30:26Z raasch
103	! Volume flow conservation added for the remaining three outflow boundaries
104	!
105	! 85 2007-05-11 09:35:14Z raasch
106	! Division through dt_3d replaced by multiplication of the inverse.
107	! For performance optimisation, this is done in the loop calculating the
108	! divergence instead of using a seperate loop.
109	!
110	! 75 2007-03-22 09:54:05Z raasch
111	! Volume flow control for non-cyclic boundary conditions added (currently only
112	! for the north boundary!!), 2nd+3rd argument removed from exchange horiz,
113	! mean vertical velocity is removed in case of Neumann boundary conditions
114	! both at the bottom and the top
115	!
116	! RCS Log replace by Id keyword, revision history cleaned up
117	!
118	! Revision 1.25 2006/04/26 13:26:12 raasch
119	! OpenMP optimization (+localsum, threadsum)
120	!
121	! Revision 1.1 1997/07/24 11:24:44 raasch
122	! Initial revision
123	!
124	!
125	! Description:
126	! ------------
127	! Compute the divergence of the provisional velocity field. Solve the Poisson
128	! equation for the perturbation pressure. Compute the final velocities using
129	! this perturbation pressure. Compute the remaining divergence.
130	!------------------------------------------------------------------------------!
131
132	USE arrays_3d
133	USE constants
134	USE control_parameters
135	USE cpulog
136	USE grid_variables
137	USE indices
138	USE interfaces
139	USE pegrid
140	USE poisfft_mod
141	USE statistics
142
143	IMPLICIT NONE
144
145	INTEGER :: i, j, k
146
147	REAL :: ddt_3d, localsum, threadsum, d_weight_pres
148
149	REAL, DIMENSION(1:2) :: volume_flow_l, volume_flow_offset
150	REAL, DIMENSION(1:nzt) :: w_l, w_l_l
151
152
153	CALL cpu_log( log_point(8), 'pres', 'start' )
154
155
156	ddt_3d = 1.0 / dt_3d
157	d_weight_pres = 1.0 / weight_pres(intermediate_timestep_count)
158
159	!
160	!-- Multigrid method expects array d to have one ghost layer.
161	!--
162	IF ( psolver == 'multigrid' ) THEN
163
164	DEALLOCATE( d )
165	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
166
167	!
168	!-- Since p is later used to hold the weighted average of the substeps, it
169	!-- cannot be used in the iterative solver. Therefore, its initial value is
170	!-- stored on p_loc, which is then iteratively advanced in every substep.
171	IF ( intermediate_timestep_count == 1 ) THEN
172	DO i = nxl-1, nxr+1
173	DO j = nys-1, nyn+1
174	DO k = nzb, nzt+1
175	p_loc(k,j,i) = p(k,j,i)
176	ENDDO
177	ENDDO
178	ENDDO
179	ENDIF
180
181	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
182
183	!
184	!-- Since p is later used to hold the weighted average of the substeps, it
185	!-- cannot be used in the iterative solver. Therefore, its initial value is
186	!-- stored on p_loc, which is then iteratively advanced in every substep.
187	p_loc = p
188
189	ENDIF
190
191	!
192	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
193	!-- boundary conditions
194	!-- WARNING: so far, this conservation does not work at the left/south
195	!-- boundary if the topography at the inflow differs from that at the
196	!-- outflow! For this case, volume_flow_area needs adjustment!
197	!
198	!-- Left/right
199	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
200
201	volume_flow(1) = 0.0
202	volume_flow_l(1) = 0.0
203
204	IF ( outflow_l ) THEN
205	i = 0
206	ELSEIF ( outflow_r ) THEN
207	i = nx+1
208	ENDIF
209
210	DO j = nys, nyn
211	!
212	!-- Sum up the volume flow through the south/north boundary
213	DO k = nzb_2d(j,i)+1, nzt
214	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
215	ENDDO
216	ENDDO
217
218	#if defined( __parallel )
219	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
220	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
221	MPI_SUM, comm1dy, ierr )
222	#else
223	volume_flow = volume_flow_l
224	#endif
225	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
226	/ volume_flow_area(1)
227
228	DO j = nysg, nyng
229	DO k = nzb_2d(j,i)+1, nzt
230	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
231	ENDDO
232	ENDDO
233
234	ENDIF
235
236	!
237	!-- South/north
238	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
239
240	volume_flow(2) = 0.0
241	volume_flow_l(2) = 0.0
242
243	IF ( outflow_s ) THEN
244	j = 0
245	ELSEIF ( outflow_n ) THEN
246	j = ny+1
247	ENDIF
248
249	DO i = nxl, nxr
250	!
251	!-- Sum up the volume flow through the south/north boundary
252	DO k = nzb_2d(j,i)+1, nzt
253	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
254	ENDDO
255	ENDDO
256
257	#if defined( __parallel )
258	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
259	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
260	MPI_SUM, comm1dx, ierr )
261	#else
262	volume_flow = volume_flow_l
263	#endif
264	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
265	/ volume_flow_area(2)
266
267	DO i = nxlg, nxrg
268	DO k = nzb_v_inner(j,i)+1, nzt
269	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
270	ENDDO
271	ENDDO
272
273	ENDIF
274
275	!
276	!-- Remove mean vertical velocity
277	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN
278	IF ( simulated_time > 0.0 ) THEN ! otherwise nzb_w_inner not yet known
279	w_l = 0.0; w_l_l = 0.0
280	DO i = nxl, nxr
281	DO j = nys, nyn
282	DO k = nzb_w_inner(j,i)+1, nzt
283	w_l_l(k) = w_l_l(k) + w(k,j,i)
284	ENDDO
285	ENDDO
286	ENDDO
287	#if defined( __parallel )
288	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
289	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
290	comm2d, ierr )
291	#else
292	w_l = w_l_l
293	#endif
294	DO k = 1, nzt
295	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
296	ENDDO
297	DO i = nxlg, nxrg
298	DO j = nysg, nyng
299	DO k = nzb_w_inner(j,i)+1, nzt
300	w(k,j,i) = w(k,j,i) - w_l(k)
301	ENDDO
302	ENDDO
303	ENDDO
304	ENDIF
305	ENDIF
306
307	!
308	!-- Compute the divergence of the provisional velocity field.
309	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
310
311	IF ( psolver == 'multigrid' ) THEN
312	!$OMP PARALLEL DO SCHEDULE( STATIC )
313	DO i = nxl-1, nxr+1
314	DO j = nys-1, nyn+1
315	DO k = nzb, nzt+1
316	d(k,j,i) = 0.0
317	ENDDO
318	ENDDO
319	ENDDO
320	ELSE
321	!$OMP PARALLEL DO SCHEDULE( STATIC )
322	!$acc kernels present( d )
323	!$acc loop
324	DO i = nxl, nxr
325	DO j = nys, nyn
326	!$acc loop vector(32)
327	DO k = nzb+1, nzt
328	d(k,j,i) = 0.0
329	ENDDO
330	ENDDO
331	ENDDO
332	!$acc end kernels
333	ENDIF
334
335	localsum = 0.0
336	threadsum = 0.0
337
338	#if defined( __ibm )
339	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
340	!$OMP DO SCHEDULE( STATIC )
341	DO i = nxl, nxr
342	DO j = nys, nyn
343	DO k = nzb_s_inner(j,i)+1, nzt
344	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
345	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
346	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
347	* d_weight_pres
348	ENDDO
349	!
350	!-- Compute possible PE-sum of divergences for flow_statistics
351	DO k = nzb_s_inner(j,i)+1, nzt
352	threadsum = threadsum + ABS( d(k,j,i) )
353	ENDDO
354
355	ENDDO
356	ENDDO
357
358	localsum = localsum + threadsum * dt_3d * &
359	weight_pres(intermediate_timestep_count)
360
361	!$OMP END PARALLEL
362	#else
363
364	!$OMP PARALLEL PRIVATE (i,j,k)
365	!$OMP DO SCHEDULE( STATIC )
366	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
367	!$acc loop collapse( 3 )
368	DO i = nxl, nxr
369	DO j = nys, nyn
370	DO k = 1, nzt
371	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
372	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
373	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
374	* d_weight_pres * rflags_s_inner(k,j,i)
375	ENDDO
376	ENDDO
377	ENDDO
378	!$acc end kernels
379	!$OMP END PARALLEL
380
381	!
382	!-- Compute possible PE-sum of divergences for flow_statistics
383	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
384	!$OMP DO SCHEDULE( STATIC )
385	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
386	DO i = nxl, nxr
387	DO j = nys, nyn
388	DO k = nzb+1, nzt
389	threadsum = threadsum + ABS( d(k,j,i) )
390	ENDDO
391	ENDDO
392	ENDDO
393	!$acc end parallel
394	localsum = localsum + threadsum * dt_3d * &
395	weight_pres(intermediate_timestep_count)
396	!$OMP END PARALLEL
397	#endif
398
399	!
400	!-- For completeness, set the divergence sum of all statistic regions to those
401	!-- of the total domain
402	sums_divold_l(0:statistic_regions) = localsum
403
404	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
405
406	!
407	!-- Compute the pressure perturbation solving the Poisson equation
408	IF ( psolver(1:7) == 'poisfft' ) THEN
409
410	!
411	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
412	IF ( psolver == 'poisfft' ) THEN
413
414	CALL poisfft( d, tend )
415
416	ENDIF
417
418	!
419	!-- Store computed perturbation pressure and set boundary condition in
420	!-- z-direction
421	!$OMP PARALLEL DO
422	!$acc kernels present( d, tend )
423	!$acc loop
424	DO i = nxl, nxr
425	DO j = nys, nyn
426	!$acc loop vector( 32 )
427	DO k = nzb+1, nzt
428	tend(k,j,i) = d(k,j,i)
429	ENDDO
430	ENDDO
431	ENDDO
432	!$acc end kernels
433
434	!
435	!-- Bottom boundary:
436	!-- This condition is only required for internal output. The pressure
437	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
438	IF ( ibc_p_b == 1 ) THEN
439	!
440	!-- Neumann (dp/dz = 0)
441	!$OMP PARALLEL DO
442	!$acc kernels present( nzb_s_inner, tend )
443	DO i = nxlg, nxrg
444	DO j = nysg, nyng
445	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
446	ENDDO
447	ENDDO
448	!$acc end kernels
449
450	ELSE
451	!
452	!-- Dirichlet
453	!$OMP PARALLEL DO
454	!$acc kernels present( tend )
455	DO i = nxlg, nxrg
456	DO j = nysg, nyng
457	tend(nzb_s_inner(j,i),j,i) = 0.0
458	ENDDO
459	ENDDO
460	!$acc end kernels
461
462	ENDIF
463
464	!
465	!-- Top boundary
466	IF ( ibc_p_t == 1 ) THEN
467	!
468	!-- Neumann
469	!$OMP PARALLEL DO
470	!$acc kernels present( tend )
471	DO i = nxlg, nxrg
472	DO j = nysg, nyng
473	tend(nzt+1,j,i) = tend(nzt,j,i)
474	ENDDO
475	ENDDO
476	!$acc end kernels
477
478	ELSE
479	!
480	!-- Dirichlet
481	!$OMP PARALLEL DO
482	!$acc kernels present( tend )
483	DO i = nxlg, nxrg
484	DO j = nysg, nyng
485	tend(nzt+1,j,i) = 0.0
486	ENDDO
487	ENDDO
488	!$acc end kernels
489
490	ENDIF
491
492	!
493	!-- Exchange boundaries for p
494	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
495	on_device = .TRUE. ! to be removed after complete porting
496	ELSE ! of ghost point exchange
497	!$acc update host( tend )
498	ENDIF
499	CALL exchange_horiz( tend, nbgp )
500	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
501	on_device = .FALSE. ! to be removed after complete porting
502	ELSE ! of ghost point exchange
503	!$acc update device( tend )
504	ENDIF
505
506	ELSEIF ( psolver == 'sor' ) THEN
507
508	!
509	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
510	!-- scheme
511	CALL sor( d, ddzu_pres, ddzw, p_loc )
512	tend = p_loc
513
514	ELSEIF ( psolver == 'multigrid' ) THEN
515
516	!
517	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
518	!-- array tend is used to store the residuals, logical exchange_mg is used
519	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
520	!-- ( nbgp ghost points ).
521
522	!-- If the number of grid points of the gathered grid, which is collected
523	!-- on PE0, is larger than the number of grid points of an PE, than array
524	!-- tend will be enlarged.
525	IF ( gathered_size > subdomain_size ) THEN
526	DEALLOCATE( tend )
527	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
528	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
529	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
530	mg_switch_to_pe0_level)+1) )
531	ENDIF
532
533	CALL poismg( tend )
534
535	IF ( gathered_size > subdomain_size ) THEN
536	DEALLOCATE( tend )
537	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
538	ENDIF
539
540	!
541	!-- Restore perturbation pressure on tend because this array is used
542	!-- further below to correct the velocity fields
543	DO i = nxl-1, nxr+1
544	DO j = nys-1, nyn+1
545	DO k = nzb, nzt+1
546	tend(k,j,i) = p_loc(k,j,i)
547	ENDDO
548	ENDDO
549	ENDDO
550
551	ENDIF
552
553	!
554	!-- Store perturbation pressure on array p, used for pressure data output.
555	!-- Ghost layers are added in the output routines (except sor-method: see below)
556	IF ( intermediate_timestep_count == 1 ) THEN
557	!$OMP PARALLEL PRIVATE (i,j,k)
558	!$OMP DO
559	!$acc kernels present( p, tend, weight_substep )
560	!$acc loop
561	DO i = nxl-1, nxr+1
562	DO j = nys-1, nyn+1
563	!$acc loop vector( 32 )
564	DO k = nzb, nzt+1
565	p(k,j,i) = tend(k,j,i) * &
566	weight_substep(intermediate_timestep_count)
567	ENDDO
568	ENDDO
569	ENDDO
570	!$acc end kernels
571	!$OMP END PARALLEL
572
573	ELSE
574	!$OMP PARALLEL PRIVATE (i,j,k)
575	!$OMP DO
576	!$acc kernels present( p, tend, weight_substep )
577	!$acc loop
578	DO i = nxl-1, nxr+1
579	DO j = nys-1, nyn+1
580	!$acc loop vector( 32 )
581	DO k = nzb, nzt+1
582	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
583	weight_substep(intermediate_timestep_count)
584	ENDDO
585	ENDDO
586	ENDDO
587	!$acc end kernels
588	!$OMP END PARALLEL
589
590	ENDIF
591
592	!
593	!-- SOR-method needs ghost layers for the next timestep
594	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
595
596	!
597	!-- Correction of the provisional velocities with the current perturbation
598	!-- pressure just computed
599	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
600	volume_flow_l(1) = 0.0
601	volume_flow_l(2) = 0.0
602	ENDIF
603
604	!$OMP PARALLEL PRIVATE (i,j,k)
605	!$OMP DO
606	!$acc kernels present( ddzu, nzb_u_inner, nzb_v_inner, nzb_w_inner, tend, u, v, w, weight_pres )
607	!$acc loop
608	DO i = nxl, nxr
609	DO j = nys, nyn
610	!$acc loop vector( 32 )
611	DO k = 1, nzt
612	IF ( k > nzb_w_inner(j,i) ) THEN
613	w(k,j,i) = w(k,j,i) - dt_3d * &
614	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
615	weight_pres(intermediate_timestep_count)
616	ENDIF
617	ENDDO
618	!$acc loop vector( 32 )
619	DO k = 1, nzt
620	IF ( k > nzb_u_inner(j,i) ) THEN
621	u(k,j,i) = u(k,j,i) - dt_3d * &
622	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
623	weight_pres(intermediate_timestep_count)
624	ENDIF
625	ENDDO
626	!$acc loop vector( 32 )
627	DO k = 1, nzt
628	IF ( k > nzb_v_inner(j,i) ) THEN
629	v(k,j,i) = v(k,j,i) - dt_3d * &
630	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
631	weight_pres(intermediate_timestep_count)
632	ENDIF
633	ENDDO
634
635	ENDDO
636	ENDDO
637	!$acc end kernels
638	!$OMP END PARALLEL
639
640	!
641	!-- Sum up the volume flow through the right and north boundary
642	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
643	nxr == nx ) THEN
644
645	!$OMP PARALLEL PRIVATE (j,k)
646	!$OMP DO
647	DO j = nys, nyn
648	!$OMP CRITICAL
649	DO k = nzb_2d(j,nx) + 1, nzt
650	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
651	ENDDO
652	!$OMP END CRITICAL
653	ENDDO
654	!$OMP END PARALLEL
655
656	ENDIF
657
658	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
659	nyn == ny ) THEN
660
661	!$OMP PARALLEL PRIVATE (i,k)
662	!$OMP DO
663	DO i = nxl, nxr
664	!$OMP CRITICAL
665	DO k = nzb_2d(ny,i) + 1, nzt
666	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
667	ENDDO
668	!$OMP END CRITICAL
669	ENDDO
670	!$OMP END PARALLEL
671
672	ENDIF
673
674	!
675	!-- Conserve the volume flow
676	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
677
678	#if defined( __parallel )
679	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
680	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
681	MPI_SUM, comm2d, ierr )
682	#else
683	volume_flow = volume_flow_l
684	#endif
685
686	volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
687	volume_flow_area
688
689	!$OMP PARALLEL PRIVATE (i,j,k)
690	!$OMP DO
691	DO i = nxl, nxr
692	DO j = nys, nyn
693	DO k = nzb_u_inner(j,i) + 1, nzt
694	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
695	ENDDO
696	DO k = nzb_v_inner(j,i) + 1, nzt
697	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
698	ENDDO
699	ENDDO
700	ENDDO
701
702	!$OMP END PARALLEL
703
704	ENDIF
705
706	!
707	!-- Exchange of boundaries for the velocities
708	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
709	on_device = .TRUE. ! to be removed after complete porting
710	ELSE ! of ghost point exchange
711	!$acc update host( u, v, w )
712	ENDIF
713	CALL exchange_horiz( u, nbgp )
714	CALL exchange_horiz( v, nbgp )
715	CALL exchange_horiz( w, nbgp )
716	IF ( numprocs == 1 ) THEN ! workaround for single-core GPU runs
717	on_device = .FALSE. ! to be removed after complete porting
718	ELSE ! of ghost point exchange
719	!$acc update device( u, v, w )
720	ENDIF
721
722	!
723	!-- Compute the divergence of the corrected velocity field,
724	!-- a possible PE-sum is computed in flow_statistics
725	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
726	sums_divnew_l = 0.0
727
728	!
729	!-- d must be reset to zero because it can contain nonzero values below the
730	!-- topography
731	IF ( topography /= 'flat' ) d = 0.0
732
733	localsum = 0.0
734	threadsum = 0.0
735
736	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
737	!$OMP DO SCHEDULE( STATIC )
738	#if defined( __ibm )
739	DO i = nxl, nxr
740	DO j = nys, nyn
741	DO k = nzb_s_inner(j,i)+1, nzt
742	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
743	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
744	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
745	ENDDO
746	DO k = nzb+1, nzt
747	threadsum = threadsum + ABS( d(k,j,i) )
748	ENDDO
749	ENDDO
750	ENDDO
751	#else
752	!$acc kernels present( d, ddzw, rflags_s_inner, u, v, w )
753	!$acc loop collapse( 3 )
754	DO i = nxl, nxr
755	DO j = nys, nyn
756	DO k = 1, nzt
757	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
758	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
759	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) &
760	) * rflags_s_inner(k,j,i)
761	ENDDO
762	ENDDO
763	ENDDO
764	!$acc end kernels
765	!
766	!-- Compute possible PE-sum of divergences for flow_statistics
767	!$acc parallel loop collapse(3) present( d ) reduction(+:threadsum)
768	DO i = nxl, nxr
769	DO j = nys, nyn
770	DO k = nzb+1, nzt
771	threadsum = threadsum + ABS( d(k,j,i) )
772	ENDDO
773	ENDDO
774	ENDDO
775	!$acc end parallel
776	#endif
777
778	localsum = localsum + threadsum
779	!$OMP END PARALLEL
780
781	!
782	!-- For completeness, set the divergence sum of all statistic regions to those
783	!-- of the total domain
784	sums_divnew_l(0:statistic_regions) = localsum
785
786	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
787
788	CALL cpu_log( log_point(8), 'pres', 'stop' )
789
790
791	END SUBROUTINE pres

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