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source: palm/trunk/SOURCE/pres.f90 @ 1036

Last change on this file since 1036 was 1036, checked in by raasch, 12 years ago
code has been put under the GNU General Public License (v3)
Property svn:keywords set to `Id`
File size: 23.8 KB

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

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