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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
6	! terms of the GNU General Public License as published by the Free Software
7	! Foundation, either version 3 of the License, or (at your option) any later
8	! 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 1997-2017 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: pres.f90 2119 2017-01-17 16:51:50Z raasch $
27	!
28	! 2118 2017-01-17 16:38:49Z raasch
29	! OpenACC directives and related code removed
30	!
31	! 2073 2016-11-30 14:34:05Z raasch
32	! openmp bugfix for calculation of new divergence
33	!
34	! 2037 2016-10-26 11:15:40Z knoop
35	! Anelastic approximation implemented
36	!
37	! 2000 2016-08-20 18:09:15Z knoop
38	! Forced header and separation lines into 80 columns
39	!
40	! 1932 2016-06-10 12:09:21Z suehring
41	! Initial version of purely vertical nesting introduced.
42	!
43	! 1931 2016-06-10 12:06:59Z suehring
44	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
45	!
46	! 1929 2016-06-09 16:25:25Z suehring
47	! Bugfix: weight_substep for initial call, replace by local variable
48	!
49	! 1918 2016-05-27 14:35:57Z raasch
50	! sum of divergence is also calculated when pres is called before the initial
51	! first time step,
52	! stearing is modified by using intermediate_timestep_count = 0 in order to
53	! determine if pres is called before the first initial timestep,
54	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
55	! mean vertical velocity is also removed for the first time step
56	! bugfix for calculating divergences
57	!
58	! 1908 2016-05-25 17:22:32Z suehring
59	! New divergence for output into RUN_CONTROL file is calculated only at last
60	! Runge-Kutta step
61	!
62	! 1845 2016-04-08 08:29:13Z raasch
63	! nzb_2d replace by nzb_u\|v_inner
64	!
65	! 1799 2016-04-05 08:35:55Z gronemeier
66	! Bugfix: excluded third dimension from horizontal volume flow calculation
67	!
68	! 1762 2016-02-25 12:31:13Z hellstea
69	! Introduction of nested domain feature
70	!
71	! 1682 2015-10-07 23:56:08Z knoop
72	! Code annotations made doxygen readable
73	!
74	! 1575 2015-03-27 09:56:27Z raasch
75	! poismg_fast + respective module added, adjustments for psolver-queries
76	!
77	! 1342 2014-03-26 17:04:47Z kanani
78	! REAL constants defined as wp-kind
79	!
80	! 1320 2014-03-20 08:40:49Z raasch
81	! ONLY-attribute added to USE-statements,
82	! kind-parameters added to all INTEGER and REAL declaration statements,
83	! kinds are defined in new module kinds,
84	! old module precision_kind is removed,
85	! revision history before 2012 removed,
86	! comment fields (!:) to be used for variable explanations added to
87	! all variable declaration statements
88	!
89	! 1318 2014-03-17 13:35:16Z raasch
90	! module interfaces removed
91	!
92	! 1306 2014-03-13 14:30:59Z raasch
93	! second argument removed from routine poisfft
94	!
95	! 1257 2013-11-08 15:18:40Z raasch
96	! openacc loop and loop vector clauses removed, independent clauses added,
97	! end parallel replaced by end parallel loop
98	!
99	! 1221 2013-09-10 08:59:13Z raasch
100	! openACC porting of reduction operations, loops for calculating d are
101	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
102	!
103	! 1212 2013-08-15 08:46:27Z raasch
104	! call of poisfft_hybrid removed
105	!
106	! 1117 2013-03-27 11:15:36Z suehring
107	! Bugfix in OpenMP parallelization.
108	!
109	! 1113 2013-03-10 02:48:14Z raasch
110	! GPU-porting of several loops, some loops rearranged
111	!
112	! 1111 2013-03-08 23:54:10Z
113	! openACC statements added,
114	! ibc_p_b = 2 removed
115	!
116	! 1092 2013-02-02 11:24:22Z raasch
117	! unused variables removed
118	!
119	! 1036 2012-10-22 13:43:42Z raasch
120	! code put under GPL (PALM 3.9)
121	!
122	! 1003 2012-09-14 14:35:53Z raasch
123	! adjustment of array tend for cases with unequal subdomain sizes removed
124	!
125	! Revision 1.1 1997/07/24 11:24:44 raasch
126	! Initial revision
127	!
128	!
129	! Description:
130	! ------------
131	!> Compute the divergence of the provisional velocity field. Solve the Poisson
132	!> equation for the perturbation pressure. Compute the final velocities using
133	!> this perturbation pressure. Compute the remaining divergence.
134	!------------------------------------------------------------------------------!
135	SUBROUTINE pres
136
137
138	USE arrays_3d, &
139	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
140	tend, u, v, w
141
142	USE control_parameters, &
143	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
144	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
145	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
146	nest_domain, outflow_l, outflow_n, outflow_r, &
147	outflow_s, psolver, subdomain_size, topography, volume_flow, &
148	volume_flow_area, volume_flow_initial
149
150	USE cpulog, &
151	ONLY: cpu_log, log_point, log_point_s
152
153	USE grid_variables, &
154	ONLY: ddx, ddy
155
156	USE indices, &
157	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
158	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
159	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
160	rflags_s_inner
161
162	USE kinds
163
164	USE pegrid
165
166	USE pmc_interface, &
167	ONLY: nesting_mode
168
169	USE poisfft_mod, &
170	ONLY: poisfft
171
172	USE poismg_mod
173
174	USE statistics, &
175	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
176	weight_substep
177
178	IMPLICIT NONE
179
180	INTEGER(iwp) :: i !<
181	INTEGER(iwp) :: j !<
182	INTEGER(iwp) :: k !<
183
184	REAL(wp) :: ddt_3d !<
185	REAL(wp) :: d_weight_pres !<
186	REAL(wp) :: localsum !<
187	REAL(wp) :: threadsum !<
188	REAL(wp) :: weight_pres_l !<
189	REAL(wp) :: weight_substep_l !<
190
191	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
192	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
193	REAL(wp), DIMENSION(1:nzt) :: w_l !<
194	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
195
196	LOGICAL :: nest_domain_nvn !<
197
198
199	CALL cpu_log( log_point(8), 'pres', 'start' )
200
201
202	!
203	!-- Calculate quantities to be used locally
204	ddt_3d = 1.0_wp / dt_3d
205	IF ( intermediate_timestep_count == 0 ) THEN
206	!
207	!-- If pres is called before initial time step
208	weight_pres_l = 1.0_wp
209	d_weight_pres = 1.0_wp
210	weight_substep_l = 1.0_wp
211	ELSE
212	weight_pres_l = weight_pres(intermediate_timestep_count)
213	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
214	weight_substep_l = weight_substep(intermediate_timestep_count)
215	ENDIF
216
217	!
218	!-- Multigrid method expects array d to have one ghost layer.
219	!--
220	IF ( psolver(1:9) == 'multigrid' ) THEN
221
222	DEALLOCATE( d )
223	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
224
225	!
226	!-- Since p is later used to hold the weighted average of the substeps, it
227	!-- cannot be used in the iterative solver. Therefore, its initial value is
228	!-- stored on p_loc, which is then iteratively advanced in every substep.
229	IF ( intermediate_timestep_count <= 1 ) THEN
230	DO i = nxl-1, nxr+1
231	DO j = nys-1, nyn+1
232	DO k = nzb, nzt+1
233	p_loc(k,j,i) = p(k,j,i)
234	ENDDO
235	ENDDO
236	ENDDO
237	ENDIF
238
239	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
240
241	!
242	!-- Since p is later used to hold the weighted average of the substeps, it
243	!-- cannot be used in the iterative solver. Therefore, its initial value is
244	!-- stored on p_loc, which is then iteratively advanced in every substep.
245	p_loc = p
246
247	ENDIF
248
249	!
250	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
251	!-- boundary conditions
252	!-- WARNING: so far, this conservation does not work at the left/south
253	!-- boundary if the topography at the inflow differs from that at the
254	!-- outflow! For this case, volume_flow_area needs adjustment!
255	!
256	!-- Left/right
257	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
258
259	volume_flow(1) = 0.0_wp
260	volume_flow_l(1) = 0.0_wp
261
262	IF ( outflow_l ) THEN
263	i = 0
264	ELSEIF ( outflow_r ) THEN
265	i = nx+1
266	ENDIF
267
268	DO j = nys, nyn
269	!
270	!-- Sum up the volume flow through the south/north boundary
271	DO k = nzb_u_inner(j,i)+1, nzt
272	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
273	ENDDO
274	ENDDO
275
276	#if defined( __parallel )
277	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
278	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
279	MPI_SUM, comm1dy, ierr )
280	#else
281	volume_flow = volume_flow_l
282	#endif
283	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
284	/ volume_flow_area(1)
285
286	DO j = nysg, nyng
287	DO k = nzb_u_inner(j,i)+1, nzt
288	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
289	ENDDO
290	ENDDO
291
292	ENDIF
293
294	!
295	!-- South/north
296	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
297
298	volume_flow(2) = 0.0_wp
299	volume_flow_l(2) = 0.0_wp
300
301	IF ( outflow_s ) THEN
302	j = 0
303	ELSEIF ( outflow_n ) THEN
304	j = ny+1
305	ENDIF
306
307	DO i = nxl, nxr
308	!
309	!-- Sum up the volume flow through the south/north boundary
310	DO k = nzb_v_inner(j,i)+1, nzt
311	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
312	ENDDO
313	ENDDO
314
315	#if defined( __parallel )
316	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
317	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
318	MPI_SUM, comm1dx, ierr )
319	#else
320	volume_flow = volume_flow_l
321	#endif
322	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
323	/ volume_flow_area(2)
324
325	DO i = nxlg, nxrg
326	DO k = nzb_v_inner(j,i)+1, nzt
327	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
328	ENDDO
329	ENDDO
330
331	ENDIF
332
333	!
334	!-- Remove mean vertical velocity in case that Neumann conditions are
335	!-- used both at bottom and top boundary, and if not a nested domain in a
336	!-- normal nesting run. In case of vertical nesting, this must be done.
337	!-- Therefore an auxiliary logical variable nest_domain_nvn is used here, and
338	!-- nvn stands for non-vertical nesting.
339	!-- This cannot be done before the first initial time step because ngp_2dh_outer
340	!-- is not yet known then.
341	nest_domain_nvn = nest_domain
342	IF ( nest_domain .AND. nesting_mode == 'vertical' ) THEN
343	nest_domain_nvn = .FALSE.
344	ENDIF
345
346	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. &
347	.NOT. nest_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
348	THEN
349	w_l = 0.0_wp; w_l_l = 0.0_wp
350	DO i = nxl, nxr
351	DO j = nys, nyn
352	DO k = nzb_w_inner(j,i)+1, nzt
353	w_l_l(k) = w_l_l(k) + w(k,j,i)
354	ENDDO
355	ENDDO
356	ENDDO
357	#if defined( __parallel )
358	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
359	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
360	comm2d, ierr )
361	#else
362	w_l = w_l_l
363	#endif
364	DO k = 1, nzt
365	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
366	ENDDO
367	DO i = nxlg, nxrg
368	DO j = nysg, nyng
369	DO k = nzb_w_inner(j,i)+1, nzt
370	w(k,j,i) = w(k,j,i) - w_l(k)
371	ENDDO
372	ENDDO
373	ENDDO
374	ENDIF
375
376	!
377	!-- Compute the divergence of the provisional velocity field.
378	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
379
380	IF ( psolver(1:9) == 'multigrid' ) THEN
381	!$OMP PARALLEL DO SCHEDULE( STATIC )
382	DO i = nxl-1, nxr+1
383	DO j = nys-1, nyn+1
384	DO k = nzb, nzt+1
385	d(k,j,i) = 0.0_wp
386	ENDDO
387	ENDDO
388	ENDDO
389	ELSE
390	!$OMP PARALLEL DO SCHEDULE( STATIC )
391	DO i = nxl, nxr
392	DO j = nys, nyn
393	DO k = nzb+1, nzt
394	d(k,j,i) = 0.0_wp
395	ENDDO
396	ENDDO
397	ENDDO
398	ENDIF
399
400	localsum = 0.0_wp
401	threadsum = 0.0_wp
402
403	#if defined( __ibm )
404	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
405	!$OMP DO SCHEDULE( STATIC )
406	DO i = nxl, nxr
407	DO j = nys, nyn
408	DO k = nzb_s_inner(j,i)+1, nzt
409	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
410	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
411	( w(k,j,i) * rho_air_zw(k) - &
412	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
413	) * ddt_3d * d_weight_pres
414	ENDDO
415	!
416	!-- Compute possible PE-sum of divergences for flow_statistics
417	DO k = nzb_s_inner(j,i)+1, nzt
418	threadsum = threadsum + ABS( d(k,j,i) )
419	ENDDO
420
421	ENDDO
422	ENDDO
423
424	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
425	intermediate_timestep_count == 0 ) THEN
426	localsum = localsum + threadsum * dt_3d * weight_pres_l
427	ENDIF
428	!$OMP END PARALLEL
429	#else
430
431	!$OMP PARALLEL PRIVATE (i,j,k)
432	!$OMP DO SCHEDULE( STATIC )
433	DO i = nxl, nxr
434	DO j = nys, nyn
435	DO k = 1, nzt
436	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
437	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
438	( w(k,j,i) * rho_air_zw(k) - &
439	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
440	) * ddt_3d * d_weight_pres * rflags_s_inner(k,j,i)
441	ENDDO
442	ENDDO
443	ENDDO
444	!$OMP END PARALLEL
445
446	!
447	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
448	!-- computation only at last Runge-Kutta substep.
449	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
450	intermediate_timestep_count == 0 ) THEN
451	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
452	!$OMP DO SCHEDULE( STATIC )
453	DO i = nxl, nxr
454	DO j = nys, nyn
455	DO k = nzb+1, nzt
456	threadsum = threadsum + ABS( d(k,j,i) )
457	ENDDO
458	ENDDO
459	ENDDO
460	localsum = localsum + threadsum * dt_3d * weight_pres_l
461	!$OMP END PARALLEL
462	ENDIF
463	#endif
464
465	!
466	!-- For completeness, set the divergence sum of all statistic regions to those
467	!-- of the total domain
468	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
469	intermediate_timestep_count == 0 ) THEN
470	sums_divold_l(0:statistic_regions) = localsum
471	ENDIF
472
473	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
474
475	!
476	!-- Compute the pressure perturbation solving the Poisson equation
477	IF ( psolver == 'poisfft' ) THEN
478
479	!
480	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
481	CALL poisfft( d )
482
483	!
484	!-- Store computed perturbation pressure and set boundary condition in
485	!-- z-direction
486	!$OMP PARALLEL DO
487	DO i = nxl, nxr
488	DO j = nys, nyn
489	DO k = nzb+1, nzt
490	tend(k,j,i) = d(k,j,i)
491	ENDDO
492	ENDDO
493	ENDDO
494
495	!
496	!-- Bottom boundary:
497	!-- This condition is only required for internal output. The pressure
498	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
499	IF ( ibc_p_b == 1 ) THEN
500	!
501	!-- Neumann (dp/dz = 0)
502	!$OMP PARALLEL DO
503	DO i = nxlg, nxrg
504	DO j = nysg, nyng
505	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
506	ENDDO
507	ENDDO
508
509	ELSE
510	!
511	!-- Dirichlet
512	!$OMP PARALLEL DO
513	DO i = nxlg, nxrg
514	DO j = nysg, nyng
515	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
516	ENDDO
517	ENDDO
518
519	ENDIF
520
521	!
522	!-- Top boundary
523	IF ( ibc_p_t == 1 ) THEN
524	!
525	!-- Neumann
526	!$OMP PARALLEL DO
527	DO i = nxlg, nxrg
528	DO j = nysg, nyng
529	tend(nzt+1,j,i) = tend(nzt,j,i)
530	ENDDO
531	ENDDO
532
533	ELSE
534	!
535	!-- Dirichlet
536	!$OMP PARALLEL DO
537	DO i = nxlg, nxrg
538	DO j = nysg, nyng
539	tend(nzt+1,j,i) = 0.0_wp
540	ENDDO
541	ENDDO
542
543	ENDIF
544
545	!
546	!-- Exchange boundaries for p
547	CALL exchange_horiz( tend, nbgp )
548
549	ELSEIF ( psolver == 'sor' ) THEN
550
551	!
552	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
553	!-- scheme
554	CALL sor( d, ddzu_pres, ddzw, p_loc )
555	tend = p_loc
556
557	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
558
559	!
560	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
561	!-- array tend is used to store the residuals, logical exchange_mg is used
562	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
563	!-- ( nbgp ghost points ).
564
565	!-- If the number of grid points of the gathered grid, which is collected
566	!-- on PE0, is larger than the number of grid points of an PE, than array
567	!-- tend will be enlarged.
568	IF ( gathered_size > subdomain_size ) THEN
569	DEALLOCATE( tend )
570	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
571	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
572	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
573	mg_switch_to_pe0_level)+1) )
574	ENDIF
575
576	IF ( psolver == 'multigrid' ) THEN
577	CALL poismg( tend )
578	ELSE
579	CALL poismg_noopt( tend )
580	ENDIF
581
582	IF ( gathered_size > subdomain_size ) THEN
583	DEALLOCATE( tend )
584	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
585	ENDIF
586
587	!
588	!-- Restore perturbation pressure on tend because this array is used
589	!-- further below to correct the velocity fields
590	DO i = nxl-1, nxr+1
591	DO j = nys-1, nyn+1
592	DO k = nzb, nzt+1
593	tend(k,j,i) = p_loc(k,j,i)
594	ENDDO
595	ENDDO
596	ENDDO
597
598	ENDIF
599
600	!
601	!-- Store perturbation pressure on array p, used for pressure data output.
602	!-- Ghost layers are added in the output routines (except sor-method: see below)
603	IF ( intermediate_timestep_count <= 1 ) THEN
604	!$OMP PARALLEL PRIVATE (i,j,k)
605	!$OMP DO
606	DO i = nxl-1, nxr+1
607	DO j = nys-1, nyn+1
608	DO k = nzb, nzt+1
609	p(k,j,i) = tend(k,j,i) * &
610	weight_substep_l
611	ENDDO
612	ENDDO
613	ENDDO
614	!$OMP END PARALLEL
615
616	ELSEIF ( intermediate_timestep_count > 1 ) THEN
617	!$OMP PARALLEL PRIVATE (i,j,k)
618	!$OMP DO
619	DO i = nxl-1, nxr+1
620	DO j = nys-1, nyn+1
621	DO k = nzb, nzt+1
622	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
623	weight_substep_l
624	ENDDO
625	ENDDO
626	ENDDO
627	!$OMP END PARALLEL
628
629	ENDIF
630
631	!
632	!-- SOR-method needs ghost layers for the next timestep
633	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
634
635	!
636	!-- Correction of the provisional velocities with the current perturbation
637	!-- pressure just computed
638	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
639	volume_flow_l(1) = 0.0_wp
640	volume_flow_l(2) = 0.0_wp
641	ENDIF
642
643	!$OMP PARALLEL PRIVATE (i,j,k)
644	!$OMP DO
645	DO i = nxl, nxr
646	DO j = nys, nyn
647
648	DO k = 1, nzt
649	IF ( k > nzb_w_inner(j,i) ) THEN
650	w(k,j,i) = w(k,j,i) - dt_3d * &
651	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
652	weight_pres_l
653	ENDIF
654	ENDDO
655
656	DO k = 1, nzt
657	IF ( k > nzb_u_inner(j,i) ) THEN
658	u(k,j,i) = u(k,j,i) - dt_3d * &
659	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
660	weight_pres_l
661	ENDIF
662	ENDDO
663
664	DO k = 1, nzt
665	IF ( k > nzb_v_inner(j,i) ) THEN
666	v(k,j,i) = v(k,j,i) - dt_3d * &
667	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
668	weight_pres_l
669	ENDIF
670	ENDDO
671
672	ENDDO
673	ENDDO
674	!$OMP END PARALLEL
675
676	!
677	!-- Sum up the volume flow through the right and north boundary
678	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
679	nxr == nx ) THEN
680
681	!$OMP PARALLEL PRIVATE (j,k)
682	!$OMP DO
683	DO j = nys, nyn
684	!$OMP CRITICAL
685	DO k = nzb_u_inner(j,nx) + 1, nzt
686	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
687	ENDDO
688	!$OMP END CRITICAL
689	ENDDO
690	!$OMP END PARALLEL
691
692	ENDIF
693
694	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
695	nyn == ny ) THEN
696
697	!$OMP PARALLEL PRIVATE (i,k)
698	!$OMP DO
699	DO i = nxl, nxr
700	!$OMP CRITICAL
701	DO k = nzb_v_inner(ny,i) + 1, nzt
702	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
703	ENDDO
704	!$OMP END CRITICAL
705	ENDDO
706	!$OMP END PARALLEL
707
708	ENDIF
709
710	!
711	!-- Conserve the volume flow
712	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
713
714	#if defined( __parallel )
715	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
716	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
717	MPI_SUM, comm2d, ierr )
718	#else
719	volume_flow = volume_flow_l
720	#endif
721
722	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
723	volume_flow_area(1:2)
724
725	!$OMP PARALLEL PRIVATE (i,j,k)
726	!$OMP DO
727	DO i = nxl, nxr
728	DO j = nys, nyn
729	DO k = nzb_u_inner(j,i) + 1, nzt
730	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
731	ENDDO
732	DO k = nzb_v_inner(j,i) + 1, nzt
733	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
734	ENDDO
735	ENDDO
736	ENDDO
737
738	!$OMP END PARALLEL
739
740	ENDIF
741
742	!
743	!-- Exchange of boundaries for the velocities
744	CALL exchange_horiz( u, nbgp )
745	CALL exchange_horiz( v, nbgp )
746	CALL exchange_horiz( w, nbgp )
747
748	!
749	!-- Compute the divergence of the corrected velocity field,
750	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
751	!-- only at last Runge-Kutta step.
752	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
753	intermediate_timestep_count == 0 ) THEN
754	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
755	sums_divnew_l = 0.0_wp
756
757	!
758	!-- d must be reset to zero because it can contain nonzero values below the
759	!-- topography
760	IF ( topography /= 'flat' ) d = 0.0_wp
761
762	localsum = 0.0_wp
763	threadsum = 0.0_wp
764
765	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
766	#if defined( __ibm )
767	!$OMP DO SCHEDULE( STATIC )
768	DO i = nxl, nxr
769	DO j = nys, nyn
770	DO k = nzb_s_inner(j,i)+1, nzt
771	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
772	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
773	( w(k,j,i) * rho_air_zw(k) - &
774	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k)
775	ENDDO
776	DO k = nzb+1, nzt
777	threadsum = threadsum + ABS( d(k,j,i) )
778	ENDDO
779	ENDDO
780	ENDDO
781	#else
782	!$OMP DO SCHEDULE( STATIC )
783	DO i = nxl, nxr
784	DO j = nys, nyn
785	DO k = 1, nzt
786	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
787	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
788	( w(k,j,i) * rho_air_zw(k) - &
789	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
790	) * rflags_s_inner(k,j,i)
791	ENDDO
792	ENDDO
793	ENDDO
794	!
795	!-- Compute possible PE-sum of divergences for flow_statistics
796	!$OMP DO SCHEDULE( STATIC )
797	DO i = nxl, nxr
798	DO j = nys, nyn
799	DO k = nzb+1, nzt
800	threadsum = threadsum + ABS( d(k,j,i) )
801	ENDDO
802	ENDDO
803	ENDDO
804	#endif
805
806	localsum = localsum + threadsum
807	!$OMP END PARALLEL
808
809	!
810	!-- For completeness, set the divergence sum of all statistic regions to those
811	!-- of the total domain
812	sums_divnew_l(0:statistic_regions) = localsum
813
814	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
815
816	ENDIF
817
818	CALL cpu_log( log_point(8), 'pres', 'stop' )
819
820
821	END SUBROUTINE pres

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