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source: palm/trunk/SOURCE/pres.f90 @ 1071

Last change on this file since 1071 was 1037, checked in by raasch, 12 years ago
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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 1037 2012-10-22 14:10:22Z franke $
27	!
28	! 1036 2012-10-22 13:43:42Z raasch
29	! code put under GPL (PALM 3.9)
30	!
31	! 1003 2012-09-14 14:35:53Z raasch
32	! adjustment of array tend for cases with unequal subdomain sizes removed
33	!
34	! 778 2011-11-07 14:18:25Z fricke
35	! New allocation of tend when multigrid is used and the collected field on PE0
36	! has more grid points than the subdomain of an PE.
37	!
38	! 719 2011-04-06 13:05:23Z gryschka
39	! Bugfix in volume flow control for double cyclic boundary conditions
40	!
41	! 709 2011-03-30 09:31:40Z raasch
42	! formatting adjustments
43	!
44	! 707 2011-03-29 11:39:40Z raasch
45	! Calculation of weighted average of p is now handled in the same way
46	! regardless of the number of ghost layers (advection scheme),
47	! multigrid and sor method are using p_loc for iterative advancements of
48	! pressure,
49	! localsum calculation modified for proper OpenMP reduction,
50	! bc_lr/ns replaced by bc_lr/ns_cyc
51	!
52	! 693 2011-03-08 09:..:..Z raasch
53	! bugfix: weighting coefficient added to ibm branch
54	!
55	! 680 2011-02-04 23:16:06Z gryschka
56	! bugfix: collective_wait
57	!
58	! 675 2011-01-19 10:56:55Z suehring
59	! Removed bugfix while copying tend.
60	!
61	! 673 2011-01-18 16:19:48Z suehring
62	! Weighting coefficients added for right computation of the pressure during
63	! Runge-Kutta substeps.
64	!
65	! 667 2010-12-23 12:06:00Z suehring/gryschka
66	! New allocation of tend when ws-scheme and multigrid is used. This is due to
67	! reasons of perforance of the data_exchange. The same is done with p after
68	! poismg is called.
69	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng when no
70	! multigrid is used. Calls of exchange_horiz are modified.
71	! bugfix: After pressure correction no volume flow correction in case of
72	! non-cyclic boundary conditions
73	! (has to be done only before pressure correction)
74	! Call of SOR routine is referenced with ddzu_pres.
75	!
76	! 622 2010-12-10 08:08:13Z raasch
77	! optional barriers included in order to speed up collective operations
78	!
79	! 151 2008-03-07 13:42:18Z raasch
80	! Bugfix in volume flow control for non-cyclic boundary conditions
81	!
82	! 106 2007-08-16 14:30:26Z raasch
83	! Volume flow conservation added for the remaining three outflow boundaries
84	!
85	! 85 2007-05-11 09:35:14Z raasch
86	! Division through dt_3d replaced by multiplication of the inverse.
87	! For performance optimisation, this is done in the loop calculating the
88	! divergence instead of using a seperate loop.
89	!
90	! 75 2007-03-22 09:54:05Z raasch
91	! Volume flow control for non-cyclic boundary conditions added (currently only
92	! for the north boundary!!), 2nd+3rd argument removed from exchange horiz,
93	! mean vertical velocity is removed in case of Neumann boundary conditions
94	! both at the bottom and the top
95	!
96	! RCS Log replace by Id keyword, revision history cleaned up
97	!
98	! Revision 1.25 2006/04/26 13:26:12 raasch
99	! OpenMP optimization (+localsum, threadsum)
100	!
101	! Revision 1.1 1997/07/24 11:24:44 raasch
102	! Initial revision
103	!
104	!
105	! Description:
106	! ------------
107	! Compute the divergence of the provisional velocity field. Solve the Poisson
108	! equation for the perturbation pressure. Compute the final velocities using
109	! this perturbation pressure. Compute the remaining divergence.
110	!------------------------------------------------------------------------------!
111
112	USE arrays_3d
113	USE constants
114	USE control_parameters
115	USE cpulog
116	USE grid_variables
117	USE indices
118	USE interfaces
119	USE pegrid
120	USE poisfft_mod
121	USE poisfft_hybrid_mod
122	USE statistics
123
124	IMPLICIT NONE
125
126	INTEGER :: i, j, k, sr
127
128	REAL :: ddt_3d, localsum, threadsum, d_weight_pres
129
130	REAL, DIMENSION(1:2) :: volume_flow_l, volume_flow_offset
131	REAL, DIMENSION(1:nzt) :: w_l, w_l_l
132
133
134	CALL cpu_log( log_point(8), 'pres', 'start' )
135
136
137	ddt_3d = 1.0 / dt_3d
138	d_weight_pres = 1.0 / weight_pres(intermediate_timestep_count)
139
140	!
141	!-- Multigrid method expects array d to have one ghost layer.
142	!--
143	IF ( psolver == 'multigrid' ) THEN
144
145	DEALLOCATE( d )
146	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
147
148	!
149	!-- Since p is later used to hold the weighted average of the substeps, it
150	!-- cannot be used in the iterative solver. Therefore, its initial value is
151	!-- stored on p_loc, which is then iteratively advanced in every substep.
152	IF ( intermediate_timestep_count == 1 ) THEN
153	DO i = nxl-1, nxr+1
154	DO j = nys-1, nyn+1
155	DO k = nzb, nzt+1
156	p_loc(k,j,i) = p(k,j,i)
157	ENDDO
158	ENDDO
159	ENDDO
160	ENDIF
161
162	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count == 1 ) THEN
163
164	!
165	!-- Since p is later used to hold the weighted average of the substeps, it
166	!-- cannot be used in the iterative solver. Therefore, its initial value is
167	!-- stored on p_loc, which is then iteratively advanced in every substep.
168	p_loc = p
169
170	ENDIF
171
172	!
173	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
174	!-- boundary conditions
175	!-- WARNING: so far, this conservation does not work at the left/south
176	!-- boundary if the topography at the inflow differs from that at the
177	!-- outflow! For this case, volume_flow_area needs adjustment!
178	!
179	!-- Left/right
180	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
181
182	volume_flow(1) = 0.0
183	volume_flow_l(1) = 0.0
184
185	IF ( outflow_l ) THEN
186	i = 0
187	ELSEIF ( outflow_r ) THEN
188	i = nx+1
189	ENDIF
190
191	DO j = nys, nyn
192	!
193	!-- Sum up the volume flow through the south/north boundary
194	DO k = nzb_2d(j,i)+1, nzt
195	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
196	ENDDO
197	ENDDO
198
199	#if defined( __parallel )
200	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
201	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
202	MPI_SUM, comm1dy, ierr )
203	#else
204	volume_flow = volume_flow_l
205	#endif
206	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
207	/ volume_flow_area(1)
208
209	DO j = nysg, nyng
210	DO k = nzb_2d(j,i)+1, nzt
211	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
212	ENDDO
213	ENDDO
214
215	ENDIF
216
217	!
218	!-- South/north
219	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
220
221	volume_flow(2) = 0.0
222	volume_flow_l(2) = 0.0
223
224	IF ( outflow_s ) THEN
225	j = 0
226	ELSEIF ( outflow_n ) THEN
227	j = ny+1
228	ENDIF
229
230	DO i = nxl, nxr
231	!
232	!-- Sum up the volume flow through the south/north boundary
233	DO k = nzb_2d(j,i)+1, nzt
234	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
235	ENDDO
236	ENDDO
237
238	#if defined( __parallel )
239	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
240	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
241	MPI_SUM, comm1dx, ierr )
242	#else
243	volume_flow = volume_flow_l
244	#endif
245	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
246	/ volume_flow_area(2)
247
248	DO i = nxlg, nxrg
249	DO k = nzb_v_inner(j,i)+1, nzt
250	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
251	ENDDO
252	ENDDO
253
254	ENDIF
255
256	!
257	!-- Remove mean vertical velocity
258	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 ) THEN
259	IF ( simulated_time > 0.0 ) THEN ! otherwise nzb_w_inner not yet known
260	w_l = 0.0; w_l_l = 0.0
261	DO i = nxl, nxr
262	DO j = nys, nyn
263	DO k = nzb_w_inner(j,i)+1, nzt
264	w_l_l(k) = w_l_l(k) + w(k,j,i)
265	ENDDO
266	ENDDO
267	ENDDO
268	#if defined( __parallel )
269	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
270	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
271	comm2d, ierr )
272	#else
273	w_l = w_l_l
274	#endif
275	DO k = 1, nzt
276	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
277	ENDDO
278	DO i = nxlg, nxrg
279	DO j = nysg, nyng
280	DO k = nzb_w_inner(j,i)+1, nzt
281	w(k,j,i) = w(k,j,i) - w_l(k)
282	ENDDO
283	ENDDO
284	ENDDO
285	ENDIF
286	ENDIF
287
288	!
289	!-- Compute the divergence of the provisional velocity field.
290	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
291
292	IF ( psolver == 'multigrid' ) THEN
293	!$OMP PARALLEL DO SCHEDULE( STATIC )
294	DO i = nxl-1, nxr+1
295	DO j = nys-1, nyn+1
296	DO k = nzb, nzt+1
297	d(k,j,i) = 0.0
298	ENDDO
299	ENDDO
300	ENDDO
301	ELSE
302	!$OMP PARALLEL DO SCHEDULE( STATIC )
303	DO i = nxl, nxr
304	DO j = nys, nyn
305	DO k = nzb+1, nzt
306	d(k,j,i) = 0.0
307	ENDDO
308	ENDDO
309	ENDDO
310	ENDIF
311
312	localsum = 0.0
313	threadsum = 0.0
314
315	#if defined( __ibm )
316	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
317	!$OMP DO SCHEDULE( STATIC )
318	DO i = nxl, nxr
319	DO j = nys, nyn
320	DO k = nzb_s_inner(j,i)+1, nzt
321	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
322	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
323	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
324	* d_weight_pres
325	ENDDO
326	!
327	!-- Additional pressure boundary condition at the bottom boundary for
328	!-- inhomogeneous Prandtl layer heat fluxes and temperatures, respectively
329	!-- dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0.
330	!-- This condition must not be applied at the start of a run, because then
331	!-- flow_statistics has not yet been called and thus sums = 0.
332	IF ( ibc_p_b == 2 .AND. sums(nzb+1,4) /= 0.0 ) THEN
333	k = nzb_s_inner(j,i)
334	d(k+1,j,i) = d(k+1,j,i) + ( &
335	( usws(j,i+1) - usws(j,i) ) * ddx &
336	+ ( vsws(j+1,i) - vsws(j,i) ) * ddy &
337	- g * ( pt(k+1,j,i) - sums(k+1,4) ) / &
338	sums(k+1,4) &
339	) * ddzw(k+1) * ddt_3d * d_weight_pres
340	ENDIF
341
342	!
343	!-- Compute possible PE-sum of divergences for flow_statistics
344	DO k = nzb_s_inner(j,i)+1, nzt
345	threadsum = threadsum + ABS( d(k,j,i) )
346	ENDDO
347
348	ENDDO
349	ENDDO
350
351	localsum = localsum + threadsum * dt_3d * &
352	weight_pres(intermediate_timestep_count)
353
354	!$OMP END PARALLEL
355	#else
356	IF ( ibc_p_b == 2 .AND. sums(nzb+1,4) /= 0.0 ) THEN
357	!$OMP PARALLEL PRIVATE (i,j,k)
358	!$OMP DO SCHEDULE( STATIC )
359	DO i = nxl, nxr
360	DO j = nys, nyn
361	DO k = nzb_s_inner(j,i)+1, nzt
362	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
363	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
364	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
365	* d_weight_pres
366	ENDDO
367	ENDDO
368	!
369	!-- Additional pressure boundary condition at the bottom boundary for
370	!-- inhomogeneous Prandtl layer heat fluxes and temperatures, respectively
371	!-- dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0.
372	!-- This condition must not be applied at the start of a run, because then
373	!-- flow_statistics has not yet been called and thus sums = 0.
374	DO j = nys, nyn
375	k = nzb_s_inner(j,i)
376	d(k+1,j,i) = d(k+1,j,i) + ( &
377	( usws(j,i+1) - usws(j,i) ) * ddx &
378	+ ( vsws(j+1,i) - vsws(j,i) ) * ddy &
379	- g * ( pt(k+1,j,i) - sums(k+1,4) ) / &
380	sums(k+1,4) &
381	) * ddzw(k+1) * ddt_3d &
382	* d_weight_pres
383	ENDDO
384	ENDDO
385	!$OMP END PARALLEL
386
387	ELSE
388
389	!$OMP PARALLEL PRIVATE (i,j,k)
390	!$OMP DO SCHEDULE( STATIC )
391	DO i = nxl, nxr
392	DO j = nys, nyn
393	DO k = nzb_s_inner(j,i)+1, nzt
394	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
395	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
396	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k) ) * ddt_3d &
397	* d_weight_pres
398	ENDDO
399	ENDDO
400	ENDDO
401	!$OMP END PARALLEL
402
403	ENDIF
404
405	!
406	!-- Compute possible PE-sum of divergences for flow_statistics
407	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
408	!$OMP DO SCHEDULE( STATIC )
409	DO i = nxl, nxr
410	DO j = nys, nyn
411	DO k = nzb+1, nzt
412	threadsum = threadsum + ABS( d(k,j,i) )
413	ENDDO
414	ENDDO
415	ENDDO
416	localsum = localsum + threadsum * dt_3d * &
417	weight_pres(intermediate_timestep_count)
418	!$OMP END PARALLEL
419	#endif
420
421	!
422	!-- For completeness, set the divergence sum of all statistic regions to those
423	!-- of the total domain
424	sums_divold_l(0:statistic_regions) = localsum
425
426	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
427
428	!
429	!-- Compute the pressure perturbation solving the Poisson equation
430	IF ( psolver(1:7) == 'poisfft' ) THEN
431
432	!
433	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
434	IF ( psolver == 'poisfft' ) THEN
435	!
436	!-- Solver for 2d-decomposition
437	CALL poisfft( d, tend )
438	ELSEIF ( psolver == 'poisfft_hybrid' ) THEN
439	!
440	!-- Solver for 1d-decomposition (using MPI and OpenMP).
441	!-- The old hybrid-solver is still included here, as long as there
442	!-- are some optimization problems in poisfft
443	CALL poisfft_hybrid( d )
444	ENDIF
445
446	!
447	!-- Store computed perturbation pressure and set boundary condition in
448	!-- z-direction
449	!$OMP PARALLEL DO
450	DO i = nxl, nxr
451	DO j = nys, nyn
452	DO k = nzb+1, nzt
453	tend(k,j,i) = d(k,j,i)
454	ENDDO
455	ENDDO
456	ENDDO
457
458	!
459	!-- Bottom boundary:
460	!-- This condition is only required for internal output. The pressure
461	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
462	IF ( ibc_p_b == 1 ) THEN
463	!
464	!-- Neumann (dp/dz = 0)
465	!$OMP PARALLEL DO
466	DO i = nxlg, nxrg
467	DO j = nysg, nyng
468	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
469	ENDDO
470	ENDDO
471
472	ELSEIF ( ibc_p_b == 2 ) THEN
473	!
474	!-- Neumann condition for inhomogeneous surfaces,
475	!-- here currently still in the form of a zero gradient. Actually
476	!-- dp/dz = -(dtau13/dx + dtau23/dy) + g*pt'/pt0 would have to be used for
477	!-- the computation (cf. above: computation of divergences).
478	!$OMP PARALLEL DO
479	DO i = nxlg, nxrg
480	DO j = nysg, nyng
481	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
482	ENDDO
483	ENDDO
484
485	ELSE
486	!
487	!-- Dirichlet
488	!$OMP PARALLEL DO
489	DO i = nxlg, nxrg
490	DO j = nysg, nyng
491	tend(nzb_s_inner(j,i),j,i) = 0.0
492	ENDDO
493	ENDDO
494
495	ENDIF
496
497	!
498	!-- Top boundary
499	IF ( ibc_p_t == 1 ) THEN
500	!
501	!-- Neumann
502	!$OMP PARALLEL DO
503	DO i = nxlg, nxrg
504	DO j = nysg, nyng
505	tend(nzt+1,j,i) = tend(nzt,j,i)
506	ENDDO
507	ENDDO
508
509	ELSE
510	!
511	!-- Dirichlet
512	!$OMP PARALLEL DO
513	DO i = nxlg, nxrg
514	DO j = nysg, nyng
515	tend(nzt+1,j,i) = 0.0
516	ENDDO
517	ENDDO
518
519	ENDIF
520
521	!
522	!-- Exchange boundaries for p
523	CALL exchange_horiz( tend, nbgp )
524
525	ELSEIF ( psolver == 'sor' ) THEN
526
527	!
528	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
529	!-- scheme
530	CALL sor( d, ddzu_pres, ddzw, p_loc )
531	tend = p_loc
532
533	ELSEIF ( psolver == 'multigrid' ) THEN
534
535	!
536	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
537	!-- array tend is used to store the residuals, logical exchange_mg is used
538	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
539	!-- ( nbgp ghost points ).
540
541	!-- If the number of grid points of the gathered grid, which is collected
542	!-- on PE0, is larger than the number of grid points of an PE, than array
543	!-- tend will be enlarged.
544	IF ( gathered_size > subdomain_size ) THEN
545	DEALLOCATE( tend )
546	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
547	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
548	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
549	mg_switch_to_pe0_level)+1) )
550	ENDIF
551
552	CALL poismg( tend )
553
554	IF ( gathered_size > subdomain_size ) THEN
555	DEALLOCATE( tend )
556	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
557	ENDIF
558
559	!
560	!-- Restore perturbation pressure on tend because this array is used
561	!-- further below to correct the velocity fields
562	DO i = nxl-1, nxr+1
563	DO j = nys-1, nyn+1
564	DO k = nzb, nzt+1
565	tend(k,j,i) = p_loc(k,j,i)
566	ENDDO
567	ENDDO
568	ENDDO
569
570	ENDIF
571
572	!
573	!-- Store perturbation pressure on array p, used for pressure data output.
574	!-- Ghost layers are added in the output routines (except sor-method: see below)
575	IF ( intermediate_timestep_count == 1 ) THEN
576	!$OMP PARALLEL PRIVATE (i,j,k)
577	!$OMP DO
578	DO i = nxl-1, nxr+1
579	DO j = nys-1, nyn+1
580	DO k = nzb, nzt+1
581	p(k,j,i) = tend(k,j,i) * &
582	weight_substep(intermediate_timestep_count)
583	ENDDO
584	ENDDO
585	ENDDO
586	!$OMP END PARALLEL
587
588	ELSE
589	!$OMP PARALLEL PRIVATE (i,j,k)
590	!$OMP DO
591	DO i = nxl-1, nxr+1
592	DO j = nys-1, nyn+1
593	DO k = nzb, nzt+1
594	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
595	weight_substep(intermediate_timestep_count)
596	ENDDO
597	ENDDO
598	ENDDO
599	!$OMP END PARALLEL
600
601	ENDIF
602
603	!
604	!-- SOR-method needs ghost layers for the next timestep
605	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
606
607	!
608	!-- Correction of the provisional velocities with the current perturbation
609	!-- pressure just computed
610	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
611	volume_flow_l(1) = 0.0
612	volume_flow_l(2) = 0.0
613	ENDIF
614
615	!$OMP PARALLEL PRIVATE (i,j,k)
616	!$OMP DO
617	DO i = nxl, nxr
618	DO j = nys, nyn
619	DO k = nzb_w_inner(j,i)+1, nzt
620	w(k,j,i) = w(k,j,i) - dt_3d * &
621	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
622	weight_pres(intermediate_timestep_count)
623	ENDDO
624	DO k = nzb_u_inner(j,i)+1, nzt
625	u(k,j,i) = u(k,j,i) - dt_3d * &
626	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
627	weight_pres(intermediate_timestep_count)
628	ENDDO
629	DO k = nzb_v_inner(j,i)+1, nzt
630	v(k,j,i) = v(k,j,i) - dt_3d * &
631	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
632	weight_pres(intermediate_timestep_count)
633	ENDDO
634	!
635	!-- Sum up the volume flow through the right and north boundary
636	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
637	i == nx ) THEN
638	!$OMP CRITICAL
639	DO k = nzb_2d(j,i) + 1, nzt
640	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
641	ENDDO
642	!$OMP END CRITICAL
643	ENDIF
644	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
645	j == ny ) THEN
646	!$OMP CRITICAL
647	DO k = nzb_2d(j,i) + 1, nzt
648	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
649	ENDDO
650	!$OMP END CRITICAL
651	ENDIF
652
653	ENDDO
654	ENDDO
655	!$OMP END PARALLEL
656
657	!
658	!-- Conserve the volume flow
659	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
660
661	#if defined( __parallel )
662	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
663	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
664	MPI_SUM, comm2d, ierr )
665	#else
666	volume_flow = volume_flow_l
667	#endif
668
669	volume_flow_offset = ( volume_flow_initial - volume_flow ) / &
670	volume_flow_area
671
672	!$OMP PARALLEL PRIVATE (i,j,k)
673	!$OMP DO
674	DO i = nxl, nxr
675	DO j = nys, nyn
676	DO k = nzb_u_inner(j,i) + 1, nzt
677	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
678	ENDDO
679	DO k = nzb_v_inner(j,i) + 1, nzt
680	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
681	ENDDO
682	ENDDO
683	ENDDO
684
685	!$OMP END PARALLEL
686
687	ENDIF
688
689	!
690	!-- Exchange of boundaries for the velocities
691	CALL exchange_horiz( u, nbgp )
692	CALL exchange_horiz( v, nbgp )
693	CALL exchange_horiz( w, nbgp )
694
695	!
696	!-- Compute the divergence of the corrected velocity field,
697	!-- a possible PE-sum is computed in flow_statistics
698	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
699	sums_divnew_l = 0.0
700
701	!
702	!-- d must be reset to zero because it can contain nonzero values below the
703	!-- topography
704	IF ( topography /= 'flat' ) d = 0.0
705
706	localsum = 0.0
707	threadsum = 0.0
708
709	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
710	!$OMP DO SCHEDULE( STATIC )
711	#if defined( __ibm )
712	DO i = nxl, nxr
713	DO j = nys, nyn
714	DO k = nzb_s_inner(j,i)+1, nzt
715	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
716	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
717	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
718	ENDDO
719	DO k = nzb+1, nzt
720	threadsum = threadsum + ABS( d(k,j,i) )
721	ENDDO
722	ENDDO
723	ENDDO
724	#else
725	DO i = nxl, nxr
726	DO j = nys, nyn
727	DO k = nzb_s_inner(j,i)+1, nzt
728	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * ddx + &
729	( v(k,j+1,i) - v(k,j,i) ) * ddy + &
730	( w(k,j,i) - w(k-1,j,i) ) * ddzw(k)
731	threadsum = threadsum + ABS( d(k,j,i) )
732	ENDDO
733	ENDDO
734	ENDDO
735	#endif
736
737	localsum = localsum + threadsum
738	!$OMP END PARALLEL
739
740	!
741	!-- For completeness, set the divergence sum of all statistic regions to those
742	!-- of the total domain
743	sums_divnew_l(0:statistic_regions) = localsum
744
745	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
746
747	CALL cpu_log( log_point(8), 'pres', 'stop' )
748
749
750
751	END SUBROUTINE pres

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