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source: palm/trunk/SOURCE/pres.f90 @ 4845

Last change on this file since 4845 was 4828, checked in by Giersch, 4 years ago
Copyright updated to year 2021, interface pmc_sort removed to accelarate the nesting code
Property svn:keywords set to `Id`
File size: 32.0 KB

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1	!> @file pres.f90
2	!--------------------------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms of the GNU General
6	! Public License as published by the Free Software Foundation, either version 3 of the License, or
7	! (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the
10	! implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
11	! Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with PALM. If not, see
14	! <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2021 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------------------------!
18	!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: pres.f90 4828 2021-01-05 11:21:41Z raasch $
27	! Bugfix in OpenMP directives - intel compiler do not allow reduction operations on array elements
28	!
29	! 4719 2020-10-01 11:28:33Z pavelkrc
30	! Bugfix of previous commit (div_old discrepancy)
31	!
32	! 4717 2020-09-30 22:27:40Z pavelkrc
33	! Fixes and optimizations of OpenMP parallelization, formatting of OpenMP
34	! directives (J. Resler)
35	!
36	! 4651 2020-08-27 07:17:45Z raasch
37	! preprocessor branch for ibm removed
38	!
39	! 4649 2020-08-25 12:11:17Z raasch
40	! File re-formatted to follow the PALM coding standard
41	!
42	! 4457 2020-03-11 14:20:43Z raasch
43	! use statement for exchange horiz added
44	!
45	! 4360 2020-01-07 11:25:50Z suehring
46	! Introduction of wall_flags_total_0, which currently sets bits based on static
47	! topography information used in wall_flags_static_0
48	!
49	! 4329 2019-12-10 15:46:36Z motisi
50	! Renamed wall_flags_0 to wall_flags_static_0
51	!
52	! 4182 2019-08-22 15:20:23Z scharf
53	! Corrected "Former revisions" section
54	!
55	! 4015 2019-06-05 13:25:35Z raasch
56	! variable child_domain_nvn eliminated
57	!
58	! 3849 2019-04-01 16:35:16Z knoop
59	! OpenACC port for SPEC
60	!
61	! Revision 1.1 1997/07/24 11:24:44 raasch
62	! Initial revision
63	!
64	!
65	!--------------------------------------------------------------------------------------------------!
66	! Description:
67	! ------------
68	!> Compute the divergence of the provisional velocity field. Solve the Poisson equation for the
69	!> perturbation pressure. Compute the final velocities using this perturbation pressure. Compute the
70	!> remaining divergence.
71	!--------------------------------------------------------------------------------------------------!
72	SUBROUTINE pres
73
74
75	USE arrays_3d, &
76	ONLY: d, &
77	ddzu, &
78	ddzu_pres, &
79	ddzw, &
80	dzw, &
81	p, &
82	p_loc, &
83	rho_air, &
84	rho_air_zw, &
85	tend, &
86	u, &
87	v, &
88	w
89
90	USE control_parameters, &
91	ONLY: bc_lr_cyc, &
92	bc_ns_cyc, &
93	bc_radiation_l, &
94	bc_radiation_n, &
95	bc_radiation_r, &
96	bc_radiation_s, &
97	child_domain, &
98	conserve_volume_flow, &
99	coupling_mode, &
100	dt_3d, &
101	gathered_size, &
102	ibc_p_b, &
103	ibc_p_t, &
104	intermediate_timestep_count, &
105	intermediate_timestep_count_max, &
106	mg_switch_to_pe0_level, &
107	nesting_offline, &
108	psolver, &
109	subdomain_size, &
110	topography, &
111	volume_flow, &
112	volume_flow_area, &
113	volume_flow_initial
114
115	USE cpulog, &
116	ONLY: cpu_log, &
117	log_point, &
118	log_point_s
119
120	USE exchange_horiz_mod, &
121	ONLY: exchange_horiz
122
123	USE grid_variables, &
124	ONLY: ddx, &
125	ddy
126
127	USE indices, &
128	ONLY: nbgp, &
129	ngp_2dh_outer, &
130	nx, &
131	nxl, &
132	nxlg, &
133	nxl_mg, &
134	nxr, &
135	nxrg, &
136	nxr_mg, &
137	ny, &
138	nys, &
139	nysg, &
140	nys_mg, &
141	nyn, &
142	nyng, &
143	nyn_mg, &
144	nzb, &
145	nzt, &
146	nzt_mg, &
147	wall_flags_total_0
148
149	USE kinds
150
151	USE pegrid
152
153	USE pmc_interface, &
154	ONLY: nesting_mode
155
156	USE poisfft_mod, &
157	ONLY: poisfft
158
159	USE poismg_mod
160
161	USE poismg_noopt_mod
162
163	USE statistics, &
164	ONLY: statistic_regions, &
165	sums_divnew_l, &
166	sums_divold_l, &
167	weight_pres, &
168	weight_substep
169
170	USE surface_mod, &
171	ONLY : bc_h
172
173	IMPLICIT NONE
174
175	INTEGER(iwp) :: i !<
176	INTEGER(iwp) :: j !<
177	INTEGER(iwp) :: k !<
178	INTEGER(iwp) :: m !<
179
180	REAL(wp) :: ddt_3d !<
181	REAL(wp) :: d_weight_pres !<
182	REAL(wp) :: localsum !<
183	REAL(wp) :: threadsum !<
184	REAL(wp) :: weight_pres_l !<
185	REAL(wp) :: weight_substep_l !<
186
187	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
188	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
189	REAL(wp), DIMENSION(1:nzt) :: w_l !<
190	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
191
192
193	CALL cpu_log( log_point(8), 'pres', 'start' )
194
195	!
196	!-- Calculate quantities to be used locally
197	ddt_3d = 1.0_wp / dt_3d
198	IF ( intermediate_timestep_count == 0 ) THEN
199	!
200	!-- If pres is called before initial time step
201	weight_pres_l = 1.0_wp
202	d_weight_pres = 1.0_wp
203	weight_substep_l = 1.0_wp
204	ELSE
205	weight_pres_l = weight_pres(intermediate_timestep_count)
206	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
207	weight_substep_l = weight_substep(intermediate_timestep_count)
208	ENDIF
209
210	!
211	!-- Multigrid method expects array d to have one ghost layer.
212	!--
213	IF ( psolver(1:9) == 'multigrid' ) THEN
214
215	DEALLOCATE( d )
216	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
217
218	!
219	!-- Since p is later used to hold the weighted average of the substeps, it cannot be used in the
220	!-- iterative solver. Therefore, its initial value is stored on p_loc, which is then iteratively
221	!-- advanced in every substep.
222	IF ( intermediate_timestep_count <= 1 ) THEN
223	DO i = nxl-1, nxr+1
224	DO j = nys-1, nyn+1
225	DO k = nzb, nzt+1
226	p_loc(k,j,i) = p(k,j,i)
227	ENDDO
228	ENDDO
229	ENDDO
230	ENDIF
231
232	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
233
234	!
235	!-- Since p is later used to hold the weighted average of the substeps, it cannot be used in the
236	!-- iterative solver. Therefore, its initial value is stored on p_loc, which is then iteratively
237	!-- advanced in every substep.
238	p_loc = p
239
240	ENDIF
241
242	!
243	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral boundary conditions
244	!-- WARNING: so far, this conservation does not work at the left/south boundary if the topography at
245	!-- the inflow differs from that at the outflow! For this case, volume_flow_area needs
246	!-- adjustment!
247	!
248	!-- Left/right
249	IF ( conserve_volume_flow .AND. ( bc_radiation_l .OR. bc_radiation_r ) ) THEN
250
251	volume_flow(1) = 0.0_wp
252	volume_flow_l(1) = 0.0_wp
253
254	IF ( bc_radiation_l ) THEN
255	i = 0
256	ELSEIF ( bc_radiation_r ) THEN
257	i = nx+1
258	ENDIF
259
260	DO j = nys, nyn
261	!
262	!-- Sum up the volume flow through the south/north boundary
263	DO k = nzb+1, nzt
264	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k) &
265	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
266	ENDDO
267	ENDDO
268
269	#if defined( __parallel )
270	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
271	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, MPI_SUM, comm1dy, ierr )
272	#else
273	volume_flow = volume_flow_l
274	#endif
275	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) / volume_flow_area(1)
276
277	DO j = nysg, nyng
278	DO k = nzb+1, nzt
279	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
280	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
281	ENDDO
282	ENDDO
283
284	ENDIF
285
286	!
287	!-- South/north
288	IF ( conserve_volume_flow .AND. ( bc_radiation_n .OR. bc_radiation_s ) ) THEN
289
290	volume_flow(2) = 0.0_wp
291	volume_flow_l(2) = 0.0_wp
292
293	IF ( bc_radiation_s ) THEN
294	j = 0
295	ELSEIF ( bc_radiation_n ) THEN
296	j = ny+1
297	ENDIF
298
299	DO i = nxl, nxr
300	!
301	!-- Sum up the volume flow through the south/north boundary
302	DO k = nzb+1, nzt
303	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k) &
304	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
305	ENDDO
306	ENDDO
307
308	#if defined( __parallel )
309	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
310	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, MPI_SUM, comm1dx, ierr )
311	#else
312	volume_flow = volume_flow_l
313	#endif
314	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) / volume_flow_area(2)
315
316	DO i = nxlg, nxrg
317	DO k = nzb+1, nzt
318	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
319	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
320	ENDDO
321	ENDDO
322
323	ENDIF
324
325	!
326	!-- Remove mean vertical velocity in case that Neumann conditions are used both at bottom and top
327	!-- boundary. With Neumann conditions at both vertical boundaries, the solver cannot remove mean
328	!-- vertical velocities. They should be removed, because incompressibility requires that the
329	!-- vertical gradient of vertical velocity is zero. Since w=0 at the solid surface, it must be zero
330	!-- everywhere.
331	!-- This must not be done in case of a 3d-nesting child domain, because a mean vertical velocity
332	!-- can physically exist in such a domain.
333	!-- Also in case of offline nesting, mean vertical velocities may exist (and must not be removed),
334	!-- caused by horizontal divergence/convergence of the large scale flow that is prescribed at the
335	!-- side boundaries.
336	!-- The removal cannot be done before the first initial time step because ngp_2dh_outer is not yet
337	!-- known then.
338	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nesting_offline &
339	.AND. .NOT. ( child_domain .AND. nesting_mode /= 'vertical' ) &
340	.AND. intermediate_timestep_count /= 0 ) THEN
341	w_l = 0.0_wp; w_l_l = 0.0_wp
342	DO i = nxl, nxr
343	DO j = nys, nyn
344	DO k = nzb+1, nzt
345	w_l_l(k) = w_l_l(k) + w(k,j,i) &
346	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
347	ENDDO
348	ENDDO
349	ENDDO
350	#if defined( __parallel )
351	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
352	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, comm2d, ierr )
353	#else
354	w_l = w_l_l
355	#endif
356	DO k = 1, nzt
357	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
358	ENDDO
359	DO i = nxlg, nxrg
360	DO j = nysg, nyng
361	DO k = nzb+1, nzt
362	w(k,j,i) = w(k,j,i) - w_l(k) &
363	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
364	ENDDO
365	ENDDO
366	ENDDO
367	ENDIF
368
369	!
370	!-- Compute the divergence of the provisional velocity field.
371	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
372
373	IF ( psolver(1:9) == 'multigrid' ) THEN
374	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
375	DO i = nxl-1, nxr+1
376	DO j = nys-1, nyn+1
377	DO k = nzb, nzt+1
378	d(k,j,i) = 0.0_wp
379	ENDDO
380	ENDDO
381	ENDDO
382	ELSE
383	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
384	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
385	!$ACC PRESENT(d)
386	DO i = nxl, nxr
387	DO j = nys, nyn
388	DO k = nzb+1, nzt
389	d(k,j,i) = 0.0_wp
390	ENDDO
391	ENDDO
392	ENDDO
393	ENDIF
394
395	localsum = 0.0_wp
396	threadsum = 0.0_wp
397
398	!$OMP PARALLEL PRIVATE (i,j,k)
399	!$OMP DO SCHEDULE( STATIC )
400	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
401	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_total_0) &
402	!$ACC PRESENT(d)
403	DO i = nxl, nxr
404	DO j = nys, nyn
405	DO k = 1, nzt
406	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
407	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
408	( w(k,j,i) * rho_air_zw(k) - w(k-1,j,i) * rho_air_zw(k-1) ) &
409	* ddzw(k) ) * ddt_3d * d_weight_pres &
410	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 0 ) )
411	ENDDO
412	ENDDO
413	ENDDO
414	!$OMP END PARALLEL
415
416	!
417	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out computation only at last
418	!-- Runge-Kutta substep.
419	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
420	intermediate_timestep_count == 0 ) THEN
421	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
422	!$OMP DO SCHEDULE( STATIC )
423	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
424	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
425	!$ACC PRESENT(d)
426	DO i = nxl, nxr
427	DO j = nys, nyn
428	DO k = nzb+1, nzt
429	threadsum = threadsum + ABS( d(k,j,i) )
430	ENDDO
431	ENDDO
432	ENDDO
433	localsum = localsum + threadsum * dt_3d * weight_pres_l
434	!$OMP END PARALLEL
435	ENDIF
436
437	!
438	!-- For completeness, set the divergence sum of all statistic regions to those of the total domain
439	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
440	intermediate_timestep_count == 0 ) THEN
441	sums_divold_l(0:statistic_regions) = localsum
442	ENDIF
443
444	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
445
446	!
447	!-- Compute the pressure perturbation solving the Poisson equation
448	IF ( psolver == 'poisfft' ) THEN
449
450	!
451	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
452	CALL poisfft( d )
453
454	!
455	!-- Store computed perturbation pressure and set boundary condition in z-direction
456	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
457	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
458	!$ACC PRESENT(d, tend)
459	DO i = nxl, nxr
460	DO j = nys, nyn
461	DO k = nzb+1, nzt
462	tend(k,j,i) = d(k,j,i)
463	ENDDO
464	ENDDO
465	ENDDO
466
467	!
468	!-- Bottom boundary:
469	!-- This condition is only required for internal output. The pressure gradient
470	!-- (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
471	IF ( ibc_p_b == 1 ) THEN
472	!
473	!-- Neumann (dp/dz = 0). Using surface data type, first for non-natural surfaces, then for
474	!-- natural and urban surfaces
475	!-- Upward facing
476	!$OMP PARALLEL DO PRIVATE( m, i, j, k ) SCHEDULE( STATIC )
477	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
478	!$ACC PRESENT(bc_h, tend)
479	DO m = 1, bc_h(0)%ns
480	i = bc_h(0)%i(m)
481	j = bc_h(0)%j(m)
482	k = bc_h(0)%k(m)
483	tend(k-1,j,i) = tend(k,j,i)
484	ENDDO
485	!
486	!-- Downward facing
487	!$OMP PARALLEL DO PRIVATE( m, i, j, k ) SCHEDULE( STATIC )
488	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
489	!$ACC PRESENT(bc_h, tend)
490	DO m = 1, bc_h(1)%ns
491	i = bc_h(1)%i(m)
492	j = bc_h(1)%j(m)
493	k = bc_h(1)%k(m)
494	tend(k+1,j,i) = tend(k,j,i)
495	ENDDO
496
497	ELSE
498	!
499	!-- Dirichlet. Using surface data type, first for non-natural surfaces, then for natural and
500	!-- urban surfaces
501	!-- Upward facing
502	!$OMP PARALLEL DO PRIVATE( m, i, j, k ) SCHEDULE( STATIC )
503	DO m = 1, bc_h(0)%ns
504	i = bc_h(0)%i(m)
505	j = bc_h(0)%j(m)
506	k = bc_h(0)%k(m)
507	tend(k-1,j,i) = 0.0_wp
508	ENDDO
509	!
510	!-- Downward facing
511	!$OMP PARALLEL DO PRIVATE( m, i, j, k ) SCHEDULE( STATIC )
512	DO m = 1, bc_h(1)%ns
513	i = bc_h(1)%i(m)
514	j = bc_h(1)%j(m)
515	k = bc_h(1)%k(m)
516	tend(k+1,j,i) = 0.0_wp
517	ENDDO
518
519	ENDIF
520
521	!
522	!-- Top boundary
523	IF ( ibc_p_t == 1 ) THEN
524	!
525	!-- Neumann
526	!$OMP PARALLEL DO PRIVATE (i,j) SCHEDULE( STATIC )
527	DO i = nxlg, nxrg
528	DO j = nysg, nyng
529	tend(nzt+1,j,i) = tend(nzt,j,i)
530	ENDDO
531	ENDDO
532
533	ELSE
534	!
535	!-- Dirichlet
536	!$OMP PARALLEL DO PRIVATE (i,j) SCHEDULE( STATIC )
537	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j) &
538	!$ACC PRESENT(tend)
539	DO i = nxlg, nxrg
540	DO j = nysg, nyng
541	tend(nzt+1,j,i) = 0.0_wp
542	ENDDO
543	ENDDO
544
545	ENDIF
546
547	!
548	!-- Exchange boundaries for p
549	CALL exchange_horiz( tend, nbgp )
550
551	ELSEIF ( psolver == 'sor' ) THEN
552
553	!
554	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black scheme
555	CALL sor( d, ddzu_pres, ddzw, p_loc )
556	tend = p_loc
557
558	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
559
560	!
561	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme, array tend is used
562	!-- to store the residuals.
563
564	!-- If the number of grid points of the gathered grid, which is collected on PE0, is larger than
565	!-- the number of grid points of an PE, than array tend will be enlarged.
566	IF ( gathered_size > subdomain_size ) THEN
567	DEALLOCATE( tend )
568	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
569	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1, &
570	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg(mg_switch_to_pe0_level)+1) )
571	ENDIF
572
573	IF ( psolver == 'multigrid' ) THEN
574	CALL poismg( tend )
575	ELSE
576	CALL poismg_noopt( tend )
577	ENDIF
578
579	IF ( gathered_size > subdomain_size ) THEN
580	DEALLOCATE( tend )
581	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
582	ENDIF
583
584	!
585	!-- Restore perturbation pressure on tend because this array is used further below to correct the
586	!-- velocity fields
587	DO i = nxl-1, nxr+1
588	DO j = nys-1, nyn+1
589	DO k = nzb, nzt+1
590	tend(k,j,i) = p_loc(k,j,i)
591	ENDDO
592	ENDDO
593	ENDDO
594
595	ENDIF
596
597	!
598	!-- Store perturbation pressure on array p, used for pressure data output.
599	!-- Ghost layers are added in the output routines (except sor-method: see below)
600	IF ( intermediate_timestep_count <= 1 ) THEN
601	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
602	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
603	!$ACC PRESENT(p, tend)
604	DO i = nxl-1, nxr+1
605	DO j = nys-1, nyn+1
606	DO k = nzb, nzt+1
607	p(k,j,i) = tend(k,j,i) * weight_substep_l
608	ENDDO
609	ENDDO
610	ENDDO
611
612	ELSEIF ( intermediate_timestep_count > 1 ) THEN
613	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
614	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
615	!$ACC PRESENT(p, tend)
616	DO i = nxl-1, nxr+1
617	DO j = nys-1, nyn+1
618	DO k = nzb, nzt+1
619	p(k,j,i) = p(k,j,i) + tend(k,j,i) * weight_substep_l
620	ENDDO
621	ENDDO
622	ENDDO
623
624	ENDIF
625
626	!
627	!-- SOR-method needs ghost layers for the next timestep
628	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
629
630	!
631	!-- Correction of the provisional velocities with the current perturbation pressure just computed
632	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
633	volume_flow_l(1) = 0.0_wp
634	volume_flow_l(2) = 0.0_wp
635	ENDIF
636	!
637	!-- Add pressure gradients to the velocity components. Note, the loops are running over the entire
638	!-- model domain, even though, in case of non-cyclic boundaries u- and v-component are not
639	!-- prognostic at i=0 and j=0, respectiveley. However, in case of Dirichlet boundary conditions for
640	!-- the velocities, zero-gradient conditions for the pressure are set, so that no modification is
641	!-- imposed at the boundaries.
642	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
643	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k) &
644	!$ACC PRESENT(u, v, w, tend, ddzu, wall_flags_total_0)
645	DO i = nxl, nxr
646	DO j = nys, nyn
647
648	DO k = nzb+1, nzt
649	w(k,j,i) = w(k,j,i) - dt_3d * ( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) &
650	* weight_pres_l &
651	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
652	ENDDO
653
654	DO k = nzb+1, nzt
655	u(k,j,i) = u(k,j,i) - dt_3d * ( tend(k,j,i) - tend(k,j,i-1) ) * ddx * weight_pres_l &
656	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
657	ENDDO
658
659	DO k = nzb+1, nzt
660	v(k,j,i) = v(k,j,i) - dt_3d * ( tend(k,j,i) - tend(k,j-1,i) ) * ddy * weight_pres_l &
661	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
662	ENDDO
663
664	ENDDO
665	ENDDO
666
667	!
668	!-- The vertical velocity is not set to zero at nzt + 1 for nested domains. Instead it is set to the
669	!-- values of nzt (see routine vnest_boundary_conds or pmci_interp_tril_t) BEFORE calling the
670	!-- pressure solver. To avoid jumps while plotting profiles, w at the top has to be set to the
671	!-- values in height nzt after above modifications. Hint: w level nzt+1 does not impact results.
672	IF ( child_domain .OR. coupling_mode == 'vnested_fine' ) THEN
673	w(nzt+1,:,:) = w(nzt,:,:)
674	ENDIF
675
676	!
677	!-- Sum up the volume flow through the right and north boundary
678	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. nxr == nx ) THEN
679	threadsum = 0.0_wp
680	!
681	!-- Summation of the volume flow is done on threadsum rather than on volumen_flow itself.
682	!-- This is because intel compiler, when compiled with openmp, do not allow reduction
683	!-- operation on array elements.
684	!$OMP PARALLEL DO PRIVATE (j,k) REDUCTION (+:threadsum)
685	DO j = nys, nyn
686	DO k = nzb+1, nzt
687	threadsum = threadsum + u(k,j,nxr) * dzw(k) &
688	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,nxr), 1 ) )
689	ENDDO
690	ENDDO
691	volume_flow_l(1) = threadsum
692
693	ENDIF
694
695	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. nyn == ny ) THEN
696	threadsum = 0.0_wp
697	!$OMP PARALLEL DO PRIVATE (j,k) REDUCTION (+:threadsum)
698	DO i = nxl, nxr
699	DO k = nzb+1, nzt
700	threadsum = threadsum + v(k,nyn,i) * dzw(k) &
701	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,nyn,i), 2 ) )
702	ENDDO
703	ENDDO
704	volume_flow_l(2) = threadsum
705
706	ENDIF
707
708	!
709	!-- Conserve the volume flow
710	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
711
712	#if defined( __parallel )
713	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
714	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, MPI_SUM, comm2d, ierr )
715	#else
716	volume_flow = volume_flow_l
717	#endif
718
719	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) &
720	/ volume_flow_area(1:2)
721
722	!$OMP PARALLEL DO PRIVATE (i,j,k) SCHEDULE( STATIC )
723	DO i = nxl, nxr
724	DO j = nys, nyn
725	DO k = nzb+1, nzt
726	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
727	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 1 ) )
728	ENDDO
729	DO k = nzb+1, nzt
730	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
731	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 2 ) )
732	ENDDO
733	ENDDO
734	ENDDO
735
736	ENDIF
737
738	!
739	!-- Exchange of boundaries for the velocities
740	CALL exchange_horiz( u, nbgp )
741	CALL exchange_horiz( v, nbgp )
742	CALL exchange_horiz( w, nbgp )
743
744	!
745	!-- Compute the divergence of the corrected velocity field.
746	!-- A possible PE-sum is computed in flow_statistics. Carry out computation only at last
747	!-- Runge-Kutta step.
748	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
749	intermediate_timestep_count == 0 ) THEN
750	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
751	sums_divnew_l = 0.0_wp
752
753	!
754	!-- d must be reset to zero because it can contain nonzero values below the topography
755	IF ( topography /= 'flat' ) d = 0.0_wp
756
757	localsum = 0.0_wp
758	threadsum = 0.0_wp
759
760	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
761	!$OMP DO SCHEDULE( STATIC )
762	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
763	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_total_0) &
764	!$ACC PRESENT(d)
765	DO i = nxl, nxr
766	DO j = nys, nyn
767	DO k = nzb+1, nzt
768	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
769	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
770	( w(k,j,i) * rho_air_zw(k) - w(k-1,j,i) * rho_air_zw(k-1) ) &
771	* ddzw(k) ) &
772	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 0 ) )
773	ENDDO
774	ENDDO
775	ENDDO
776	!
777	!-- Compute possible PE-sum of divergences for flow_statistics
778	!$OMP DO SCHEDULE( STATIC )
779	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
780	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
781	!$ACC PRESENT(d)
782	DO i = nxl, nxr
783	DO j = nys, nyn
784	DO k = nzb+1, nzt
785	threadsum = threadsum + ABS( d(k,j,i) )
786	ENDDO
787	ENDDO
788	ENDDO
789
790	localsum = localsum + threadsum
791	!$OMP END PARALLEL
792
793	!
794	!-- For completeness, set the divergence sum of all statistic regions to those of the total
795	!-- domain
796	sums_divnew_l(0:statistic_regions) = localsum
797
798	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
799
800	ENDIF
801
802	CALL cpu_log( log_point(8), 'pres', 'stop' )
803
804	END SUBROUTINE pres

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