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source: palm/trunk/SOURCE/poismg.f90 @ 1547

Last change on this file since 1547 was 1354, checked in by heinze, 11 years ago
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1	SUBROUTINE poismg( r )
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 1997-2014 Leibniz Universitaet Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Attention: Loop unrolling and cache optimization in SOR-Red/Black method
21	! still does not give the expected speedup! Further work required.
22	!
23	! Current revisions:
24	! -----------------
25	!
26	!
27	! Former revisions:
28	! -----------------
29	! $Id: poismg.f90 1354 2014-04-08 15:22:57Z witha $
30	!
31	! 1353 2014-04-08 15:21:23Z heinze
32	! REAL constants provided with KIND-attribute
33	!
34	! 1322 2014-03-20 16:38:49Z raasch
35	! REAL constants defined as wp-kind
36	!
37	! 1320 2014-03-20 08:40:49Z raasch
38	! ONLY-attribute added to USE-statements,
39	! kind-parameters added to all INTEGER and REAL declaration statements,
40	! kinds are defined in new module kinds,
41	! old module precision_kind is removed,
42	! revision history before 2012 removed,
43	! comment fields (!:) to be used for variable explanations added to
44	! all variable declaration statements
45	!
46	! 1318 2014-03-17 13:35:16Z raasch
47	! module interfaces removed
48	!
49	! 1159 2013-05-21 11:58:22Z fricke
50	! bc_lr/ns_dirneu/neudir removed
51	!
52	! 1092 2013-02-02 11:24:22Z raasch
53	! unused variables removed
54	!
55	! 1056 2012-11-16 15:28:04Z raasch
56	! Bugfix: all ghost points have to be used for allocating p3
57	! arrays p2, f2, and f2_l changed from allocatable to automatic
58	!
59	! 1036 2012-10-22 13:43:42Z raasch
60	! code put under GPL (PALM 3.9)
61	!
62	! 996 2012-09-07 10:41:47Z raasch
63	! little reformatting
64	!
65	! 978 2012-08-09 08:28:32Z fricke
66	! bc_lr/ns_dirneu/neudir added
67	!
68	! 880 2012-04-13 06:28:59Z raasch
69	! Bugfix: preprocessor statements for parallel execution added
70	!
71	! 778 2011-11-07 14:18:25Z fricke
72	! Allocation of p3 changes when multigrid is used and the collected field on PE0
73	! has more grid points than the subdomain of an PE.
74	!
75	! 707 2011-03-29 11:39:40Z raasch
76	! p_loc is used instead of p in the main routine (poismg).
77	! On coarse grid levels, gathered data are identically processed on all PEs
78	! (before, on PE0 only), so that the subsequent scattering of data is not
79	! neccessary any more.
80	! bc_lr/ns replaced by bc_lr/ns_cyc/dirrad/raddir
81	! Bugfix: bottom (nzb) and top (nzt+1) boundary conditions set in routines
82	! resid and restrict. They were missed before which may have led to
83	! unpredictable results.
84	!
85	! 667 2010-12-23 12:06:00Z suehring/gryschka
86	! Calls of exchange_horiz are modified.
87	!
88	! 622 2010-12-10 08:08:13Z raasch
89	! optional barriers included in order to speed up collective operations
90	!
91	! 257 2009-03-11 15:17:42Z heinze
92	! Output of messages replaced by message handling routine.
93	!
94	! 181 2008-07-30 07:07:47Z raasch
95	! Bugfix: grid_level+1 has to be used in restrict for flags-array
96	!
97	! 114 2007-10-10 00:03:15Z raasch
98	! Boundary conditions at walls are implicitly set using flag arrays. Only
99	! Neumann BC is allowed. Upper walls are still not realized.
100	! Bottom and top BCs for array f_mg in restrict removed because boundary
101	! values are not needed (right hand side of SOR iteration).
102	!
103	! 75 2007-03-22 09:54:05Z raasch
104	! 2nd+3rd argument removed from exchange horiz
105	!
106	! RCS Log replace by Id keyword, revision history cleaned up
107	!
108	! Revision 1.6 2005/03/26 20:55:54 raasch
109	! Implementation of non-cyclic (Neumann) horizontal boundary conditions,
110	! routine prolong simplified (one call of exchange_horiz spared)
111	!
112	! Revision 1.1 2001/07/20 13:10:51 raasch
113	! Initial revision
114	!
115	!
116	! Description:
117	! ------------
118	! Solves the Poisson equation for the perturbation pressure with a multigrid
119	! V- or W-Cycle scheme.
120	!
121	! This multigrid method was originally developed for PALM by Joerg Uhlenbrock,
122	! September 2000 - July 2001.
123	!------------------------------------------------------------------------------!
124
125	USE arrays_3d, &
126	ONLY: d, p_loc
127
128	USE control_parameters, &
129	ONLY: gathered_size, grid_level, grid_level_count, &
130	maximum_grid_level, message_string, mgcycles, mg_cycles, &
131	mg_switch_to_pe0_level, residual_limit, subdomain_size
132
133	USE cpulog, &
134	ONLY: cpu_log, log_point_s
135
136	USE indices, &
137	ONLY: nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, nys, nysg, nys_mg, nyn, &
138	nyng, nyn_mg, nzb, nzt, nzt_mg
139
140	USE kinds
141
142	USE pegrid
143
144	IMPLICIT NONE
145
146	REAL(wp) :: maxerror !:
147	REAL(wp) :: maximum_mgcycles !:
148	REAL(wp) :: residual_norm !:
149
150	REAL(wp), DIMENSION(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) :: r !:
151
152	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: p3 !:
153
154
155	CALL cpu_log( log_point_s(29), 'poismg', 'start' )
156	!
157	!-- Initialize arrays and variables used in this subroutine
158
159	!-- If the number of grid points of the gathered grid, which is collected
160	!-- on PE0, is larger than the number of grid points of an PE, than array
161	!-- p3 will be enlarged.
162	IF ( gathered_size > subdomain_size ) THEN
163	ALLOCATE( p3(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
164	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
165	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
166	mg_switch_to_pe0_level)+1) )
167	ELSE
168	ALLOCATE ( p3(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
169	ENDIF
170
171	p3 = 0.0_wp
172
173	!
174	!-- Ghost boundaries have to be added to divergence array.
175	!-- Exchange routine needs to know the grid level!
176	grid_level = maximum_grid_level
177	CALL exchange_horiz( d, 1)
178	d(nzb,:,:) = d(nzb+1,:,:)
179
180	!
181	!-- Initiation of the multigrid scheme. Does n cycles until the
182	!-- residual is smaller than the given limit. The accuracy of the solution
183	!-- of the poisson equation will increase with the number of cycles.
184	!-- If the number of cycles is preset by the user, this number will be
185	!-- carried out regardless of the accuracy.
186	grid_level_count = 0
187	mgcycles = 0
188	IF ( mg_cycles == -1 ) THEN
189	maximum_mgcycles = 0
190	residual_norm = 1.0_wp
191	ELSE
192	maximum_mgcycles = mg_cycles
193	residual_norm = 0.0_wp
194	ENDIF
195
196	DO WHILE ( residual_norm > residual_limit .OR. &
197	mgcycles < maximum_mgcycles )
198
199	CALL next_mg_level( d, p_loc, p3, r)
200
201	!
202	!-- Calculate the residual if the user has not preset the number of
203	!-- cycles to be performed
204	IF ( maximum_mgcycles == 0 ) THEN
205	CALL resid( d, p_loc, r )
206	maxerror = SUM( r(nzb+1:nzt,nys:nyn,nxl:nxr)**2 )
207
208	#if defined( __parallel )
209	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
210	CALL MPI_ALLREDUCE( maxerror, residual_norm, 1, MPI_REAL, MPI_SUM, &
211	comm2d, ierr)
212	#else
213	residual_norm = maxerror
214	#endif
215	residual_norm = SQRT( residual_norm )
216	ENDIF
217
218	mgcycles = mgcycles + 1
219
220	!
221	!-- If the user has not limited the number of cycles, stop the run in case
222	!-- of insufficient convergence
223	IF ( mgcycles > 1000 .AND. mg_cycles == -1 ) THEN
224	message_string = 'no sufficient convergence within 1000 cycles'
225	CALL message( 'poismg', 'PA0283', 1, 2, 0, 6, 0 )
226	ENDIF
227
228	ENDDO
229
230	DEALLOCATE( p3 )
231
232	!
233	!-- Unset the grid level. Variable is used to determine the MPI datatypes for
234	!-- ghost point exchange
235	grid_level = 0
236
237	CALL cpu_log( log_point_s(29), 'poismg', 'stop' )
238
239	END SUBROUTINE poismg
240
241
242
243	SUBROUTINE resid( f_mg, p_mg, r )
244
245	!------------------------------------------------------------------------------!
246	! Description:
247	! ------------
248	! Computes the residual of the perturbation pressure.
249	!------------------------------------------------------------------------------!
250
251	USE arrays_3d, &
252	ONLY: f1_mg, f2_mg, f3_mg
253
254	USE control_parameters, &
255	ONLY: bc_lr_cyc, bc_ns_cyc, grid_level, ibc_p_b, ibc_p_t, inflow_l, &
256	inflow_n, inflow_r, inflow_s, outflow_l, outflow_n, outflow_r, &
257	outflow_s
258
259	USE grid_variables, &
260	ONLY: ddx2_mg, ddy2_mg
261
262	USE indices, &
263	ONLY: flags, wall_flags_1, wall_flags_2, wall_flags_3, wall_flags_4, &
264	wall_flags_5, wall_flags_6, wall_flags_7, wall_flags_8, &
265	wall_flags_9, wall_flags_10, nxl_mg, nxr_mg, nys_mg, nyn_mg, &
266	nzb, nzt_mg
267
268	USE kinds
269
270	IMPLICIT NONE
271
272	INTEGER(iwp) :: i
273	INTEGER(iwp) :: j
274	INTEGER(iwp) :: k
275	INTEGER(iwp) :: l
276
277	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
278	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
279	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f_mg !:
280	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
281	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
282	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: p_mg !:
283	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
284	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
285	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: r !:
286
287	!
288	!-- Calculate the residual
289	l = grid_level
290
291	!
292	!-- Choose flag array of this level
293	SELECT CASE ( l )
294	CASE ( 1 )
295	flags => wall_flags_1
296	CASE ( 2 )
297	flags => wall_flags_2
298	CASE ( 3 )
299	flags => wall_flags_3
300	CASE ( 4 )
301	flags => wall_flags_4
302	CASE ( 5 )
303	flags => wall_flags_5
304	CASE ( 6 )
305	flags => wall_flags_6
306	CASE ( 7 )
307	flags => wall_flags_7
308	CASE ( 8 )
309	flags => wall_flags_8
310	CASE ( 9 )
311	flags => wall_flags_9
312	CASE ( 10 )
313	flags => wall_flags_10
314	END SELECT
315
316	!$OMP PARALLEL PRIVATE (i,j,k)
317	!$OMP DO
318	DO i = nxl_mg(l), nxr_mg(l)
319	DO j = nys_mg(l), nyn_mg(l)
320	DO k = nzb+1, nzt_mg(l)
321	r(k,j,i) = f_mg(k,j,i) &
322	- ddx2_mg(l) * &
323	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
324	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
325	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
326	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
327	- ddy2_mg(l) * &
328	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
329	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
330	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
331	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
332	- f2_mg(k,l) * p_mg(k+1,j,i) &
333	- f3_mg(k,l) * &
334	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
335	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
336	+ f1_mg(k,l) * p_mg(k,j,i)
337	!
338	!-- Residual within topography should be zero
339	r(k,j,i) = r(k,j,i) * ( 1.0_wp - IBITS( flags(k,j,i), 6, 1 ) )
340	ENDDO
341	ENDDO
342	ENDDO
343	!$OMP END PARALLEL
344
345	!
346	!-- Horizontal boundary conditions
347	CALL exchange_horiz( r, 1)
348
349	IF ( .NOT. bc_lr_cyc ) THEN
350	IF ( inflow_l .OR. outflow_l ) r(:,:,nxl_mg(l)-1) = r(:,:,nxl_mg(l))
351	IF ( inflow_r .OR. outflow_r ) r(:,:,nxr_mg(l)+1) = r(:,:,nxr_mg(l))
352	ENDIF
353
354	IF ( .NOT. bc_ns_cyc ) THEN
355	IF ( inflow_n .OR. outflow_n ) r(:,nyn_mg(l)+1,:) = r(:,nyn_mg(l),:)
356	IF ( inflow_s .OR. outflow_s ) r(:,nys_mg(l)-1,:) = r(:,nys_mg(l),:)
357	ENDIF
358
359	!
360	!-- Boundary conditions at bottom and top of the domain.
361	!-- These points are not handled by the above loop. Points may be within
362	!-- buildings, but that doesn't matter.
363	IF ( ibc_p_b == 1 ) THEN
364	r(nzb,:,: ) = r(nzb+1,:,:)
365	ELSE
366	r(nzb,:,: ) = 0.0_wp
367	ENDIF
368
369	IF ( ibc_p_t == 1 ) THEN
370	r(nzt_mg(l)+1,:,: ) = r(nzt_mg(l),:,:)
371	ELSE
372	r(nzt_mg(l)+1,:,: ) = 0.0_wp
373	ENDIF
374
375
376	END SUBROUTINE resid
377
378
379
380	SUBROUTINE restrict( f_mg, r )
381
382	!------------------------------------------------------------------------------!
383	! Description:
384	! ------------
385	! Interpolates the residual on the next coarser grid with "full weighting"
386	! scheme
387	!------------------------------------------------------------------------------!
388
389	USE control_parameters, &
390	ONLY: bc_lr_cyc, bc_ns_cyc, grid_level, ibc_p_b, ibc_p_t, inflow_l, &
391	inflow_n, inflow_r, inflow_s, outflow_l, outflow_n, outflow_r, &
392	outflow_s
393
394	USE indices, &
395	ONLY: flags, wall_flags_1, wall_flags_2, wall_flags_3, wall_flags_4, &
396	wall_flags_5, wall_flags_6, wall_flags_7, wall_flags_8, &
397	wall_flags_9, wall_flags_10, nxl_mg, nxr_mg, nys_mg, nyn_mg, &
398	nzb, nzt_mg
399
400	USE kinds
401
402	IMPLICIT NONE
403
404	INTEGER(iwp) :: i !:
405	INTEGER(iwp) :: ic !:
406	INTEGER(iwp) :: j !:
407	INTEGER(iwp) :: jc !:
408	INTEGER(iwp) :: k !:
409	INTEGER(iwp) :: kc !:
410	INTEGER(iwp) :: l !:
411
412	REAL(wp) :: rkjim !:
413	REAL(wp) :: rkjip !:
414	REAL(wp) :: rkjmi !:
415	REAL(wp) :: rkjmim !:
416	REAL(wp) :: rkjmip !:
417	REAL(wp) :: rkjpi !:
418	REAL(wp) :: rkjpim !:
419	REAL(wp) :: rkjpip !:
420	REAL(wp) :: rkmji !:
421	REAL(wp) :: rkmjim !:
422	REAL(wp) :: rkmjip !:
423	REAL(wp) :: rkmjmi !:
424	REAL(wp) :: rkmjmim !:
425	REAL(wp) :: rkmjmip !:
426	REAL(wp) :: rkmjpi !:
427	REAL(wp) :: rkmjpim !:
428	REAL(wp) :: rkmjpip !:
429
430	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
431	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
432	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f_mg !:
433
434	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level+1)+1, &
435	nys_mg(grid_level+1)-1:nyn_mg(grid_level+1)+1, &
436	nxl_mg(grid_level+1)-1:nxr_mg(grid_level+1)+1) :: r !:
437
438	!
439	!-- Interpolate the residual
440	l = grid_level
441
442	!
443	!-- Choose flag array of the upper level
444	SELECT CASE ( l+1 )
445	CASE ( 1 )
446	flags => wall_flags_1
447	CASE ( 2 )
448	flags => wall_flags_2
449	CASE ( 3 )
450	flags => wall_flags_3
451	CASE ( 4 )
452	flags => wall_flags_4
453	CASE ( 5 )
454	flags => wall_flags_5
455	CASE ( 6 )
456	flags => wall_flags_6
457	CASE ( 7 )
458	flags => wall_flags_7
459	CASE ( 8 )
460	flags => wall_flags_8
461	CASE ( 9 )
462	flags => wall_flags_9
463	CASE ( 10 )
464	flags => wall_flags_10
465	END SELECT
466
467	!$OMP PARALLEL PRIVATE (i,j,k,ic,jc,kc)
468	!$OMP DO
469	DO ic = nxl_mg(l), nxr_mg(l)
470	i = 2*ic
471	DO jc = nys_mg(l), nyn_mg(l)
472	j = 2*jc
473	DO kc = nzb+1, nzt_mg(l)
474	k = 2*kc-1
475	!
476	!-- Use implicit Neumann BCs if the respective gridpoint is inside
477	!-- the building
478	rkjim = r(k,j,i-1) + IBITS( flags(k,j,i-1), 6, 1 ) * &
479	( r(k,j,i) - r(k,j,i-1) )
480	rkjip = r(k,j,i+1) + IBITS( flags(k,j,i+1), 6, 1 ) * &
481	( r(k,j,i) - r(k,j,i+1) )
482	rkjpi = r(k,j+1,i) + IBITS( flags(k,j+1,i), 6, 1 ) * &
483	( r(k,j,i) - r(k,j+1,i) )
484	rkjmi = r(k,j-1,i) + IBITS( flags(k,j-1,i), 6, 1 ) * &
485	( r(k,j,i) - r(k,j-1,i) )
486	rkjmim = r(k,j-1,i-1) + IBITS( flags(k,j-1,i-1), 6, 1 ) * &
487	( r(k,j,i) - r(k,j-1,i-1) )
488	rkjpim = r(k,j+1,i-1) + IBITS( flags(k,j+1,i-1), 6, 1 ) * &
489	( r(k,j,i) - r(k,j+1,i-1) )
490	rkjmip = r(k,j-1,i+1) + IBITS( flags(k,j-1,i+1), 6, 1 ) * &
491	( r(k,j,i) - r(k,j-1,i+1) )
492	rkjpip = r(k,j+1,i+1) + IBITS( flags(k,j+1,i+1), 6, 1 ) * &
493	( r(k,j,i) - r(k,j+1,i+1) )
494	rkmji = r(k-1,j,i) + IBITS( flags(k-1,j,i), 6, 1 ) * &
495	( r(k,j,i) - r(k-1,j,i) )
496	rkmjim = r(k-1,j,i-1) + IBITS( flags(k-1,j,i-1), 6, 1 ) * &
497	( r(k,j,i) - r(k-1,j,i-1) )
498	rkmjip = r(k-1,j,i+1) + IBITS( flags(k-1,j,i+1), 6, 1 ) * &
499	( r(k,j,i) - r(k-1,j,i+1) )
500	rkmjpi = r(k-1,j+1,i) + IBITS( flags(k-1,j+1,i), 6, 1 ) * &
501	( r(k,j,i) - r(k-1,j+1,i) )
502	rkmjmi = r(k-1,j-1,i) + IBITS( flags(k-1,j-1,i), 6, 1 ) * &
503	( r(k,j,i) - r(k-1,j-1,i) )
504	rkmjmim = r(k-1,j-1,i-1) + IBITS( flags(k-1,j-1,i-1), 6, 1 ) * &
505	( r(k,j,i) - r(k-1,j-1,i-1) )
506	rkmjpim = r(k-1,j+1,i-1) + IBITS( flags(k-1,j+1,i-1), 6, 1 ) * &
507	( r(k,j,i) - r(k-1,j+1,i-1) )
508	rkmjmip = r(k-1,j-1,i+1) + IBITS( flags(k-1,j-1,i+1), 6, 1 ) * &
509	( r(k,j,i) - r(k-1,j-1,i+1) )
510	rkmjpip = r(k-1,j+1,i+1) + IBITS( flags(k-1,j+1,i+1), 6, 1 ) * &
511	( r(k,j,i) - r(k-1,j+1,i+1) )
512
513	f_mg(kc,jc,ic) = 1.0_wp / 64.0_wp * ( &
514	8.0_wp * r(k,j,i) &
515	+ 4.0_wp * ( rkjim + rkjip + &
516	rkjpi + rkjmi ) &
517	+ 2.0_wp * ( rkjmim + rkjpim + &
518	rkjmip + rkjpip ) &
519	+ 4.0_wp * rkmji &
520	+ 2.0_wp * ( rkmjim + rkmjim + &
521	rkmjpi + rkmjmi ) &
522	+ ( rkmjmim + rkmjpim + &
523	rkmjmip + rkmjpip ) &
524	+ 4.0_wp * r(k+1,j,i) &
525	+ 2.0_wp * ( r(k+1,j,i-1) + r(k+1,j,i+1) + &
526	r(k+1,j+1,i) + r(k+1,j-1,i) ) &
527	+ ( r(k+1,j-1,i-1) + r(k+1,j+1,i-1) + &
528	r(k+1,j-1,i+1) + r(k+1,j+1,i+1) ) &
529	)
530
531	! f_mg(kc,jc,ic) = 1.0_wp / 64.0_wp * ( &
532	! 8.0_wp * r(k,j,i) &
533	! + 4.0_wp * ( r(k,j,i-1) + r(k,j,i+1) + &
534	! r(k,j+1,i) + r(k,j-1,i) ) &
535	! + 2.0_wp * ( r(k,j-1,i-1) + r(k,j+1,i-1) + &
536	! r(k,j-1,i+1) + r(k,j+1,i+1) ) &
537	! + 4.0_wp * r(k-1,j,i) &
538	! + 2.0_wp * ( r(k-1,j,i-1) + r(k-1,j,i+1) + &
539	! r(k-1,j+1,i) + r(k-1,j-1,i) ) &
540	! + ( r(k-1,j-1,i-1) + r(k-1,j+1,i-1) + &
541	! r(k-1,j-1,i+1) + r(k-1,j+1,i+1) ) &
542	! + 4.0_wp * r(k+1,j,i) &
543	! + 2.0_wp * ( r(k+1,j,i-1) + r(k+1,j,i+1) + &
544	! r(k+1,j+1,i) + r(k+1,j-1,i) ) &
545	! + ( r(k+1,j-1,i-1) + r(k+1,j+1,i-1) + &
546	! r(k+1,j-1,i+1) + r(k+1,j+1,i+1) ) &
547	! )
548	ENDDO
549	ENDDO
550	ENDDO
551	!$OMP END PARALLEL
552
553	!
554	!-- Horizontal boundary conditions
555	CALL exchange_horiz( f_mg, 1)
556
557	IF ( .NOT. bc_lr_cyc ) THEN
558	IF (inflow_l .OR. outflow_l) f_mg(:,:,nxl_mg(l)-1) = f_mg(:,:,nxl_mg(l))
559	IF (inflow_r .OR. outflow_r) f_mg(:,:,nxr_mg(l)+1) = f_mg(:,:,nxr_mg(l))
560	ENDIF
561
562	IF ( .NOT. bc_ns_cyc ) THEN
563	IF (inflow_n .OR. outflow_n) f_mg(:,nyn_mg(l)+1,:) = f_mg(:,nyn_mg(l),:)
564	IF (inflow_s .OR. outflow_s) f_mg(:,nys_mg(l)-1,:) = f_mg(:,nys_mg(l),:)
565	ENDIF
566
567	!
568	!-- Boundary conditions at bottom and top of the domain.
569	!-- These points are not handled by the above loop. Points may be within
570	!-- buildings, but that doesn't matter.
571	IF ( ibc_p_b == 1 ) THEN
572	f_mg(nzb,:,: ) = f_mg(nzb+1,:,:)
573	ELSE
574	f_mg(nzb,:,: ) = 0.0_wp
575	ENDIF
576
577	IF ( ibc_p_t == 1 ) THEN
578	f_mg(nzt_mg(l)+1,:,: ) = f_mg(nzt_mg(l),:,:)
579	ELSE
580	f_mg(nzt_mg(l)+1,:,: ) = 0.0_wp
581	ENDIF
582
583
584	END SUBROUTINE restrict
585
586
587
588	SUBROUTINE prolong( p, temp )
589
590	!------------------------------------------------------------------------------!
591	! Description:
592	! ------------
593	! Interpolates the correction of the perturbation pressure
594	! to the next finer grid.
595	!------------------------------------------------------------------------------!
596
597	USE control_parameters, &
598	ONLY: bc_lr_cyc, bc_ns_cyc, grid_level, ibc_p_b, ibc_p_t, inflow_l, &
599	inflow_n, inflow_r, inflow_s, outflow_l, outflow_n, outflow_r, &
600	outflow_s
601
602	USE indices, &
603	ONLY: nxl_mg, nxr_mg, nys_mg, nyn_mg, nzb, nzt_mg
604
605	USE kinds
606
607	IMPLICIT NONE
608
609	INTEGER(iwp) :: i !:
610	INTEGER(iwp) :: j !:
611	INTEGER(iwp) :: k !:
612	INTEGER(iwp) :: l !:
613
614	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level-1)+1, &
615	nys_mg(grid_level-1)-1:nyn_mg(grid_level-1)+1, &
616	nxl_mg(grid_level-1)-1:nxr_mg(grid_level-1)+1 ) :: p !:
617
618	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
619	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
620	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: temp !:
621
622
623	!
624	!-- First, store elements of the coarser grid on the next finer grid
625	l = grid_level
626
627	!$OMP PARALLEL PRIVATE (i,j,k)
628	!$OMP DO
629	DO i = nxl_mg(l-1), nxr_mg(l-1)
630	DO j = nys_mg(l-1), nyn_mg(l-1)
631	!CDIR NODEP
632	DO k = nzb+1, nzt_mg(l-1)
633	!
634	!-- Points of the coarse grid are directly stored on the next finer
635	!-- grid
636	temp(2k-1,2j,2*i) = p(k,j,i)
637	!
638	!-- Points between two coarse-grid points
639	temp(2k-1,2j,2i+1) = 0.5_wp ( p(k,j,i) + p(k,j,i+1) )
640	temp(2k-1,2j+1,2i) = 0.5_wp ( p(k,j,i) + p(k,j+1,i) )
641	temp(2k,2j,2i) = 0.5_wp ( p(k,j,i) + p(k+1,j,i) )
642	!
643	!-- Points in the center of the planes stretched by four points
644	!-- of the coarse grid cube
645	temp(2k-1,2j+1,2i+1) = 0.25_wp ( p(k,j,i) + p(k,j,i+1) + &
646	p(k,j+1,i) + p(k,j+1,i+1) )
647	temp(2k,2j,2i+1) = 0.25_wp ( p(k,j,i) + p(k,j,i+1) + &
648	p(k+1,j,i) + p(k+1,j,i+1) )
649	temp(2k,2j+1,2i) = 0.25_wp ( p(k,j,i) + p(k,j+1,i) + &
650	p(k+1,j,i) + p(k+1,j+1,i) )
651	!
652	!-- Points in the middle of coarse grid cube
653	temp(2k,2j+1,2i+1) = 0.125_wp ( p(k,j,i) + p(k,j,i+1) + &
654	p(k,j+1,i) + p(k,j+1,i+1) + &
655	p(k+1,j,i) + p(k+1,j,i+1) + &
656	p(k+1,j+1,i) + p(k+1,j+1,i+1) )
657	ENDDO
658	ENDDO
659	ENDDO
660	!$OMP END PARALLEL
661
662	!
663	!-- Horizontal boundary conditions
664	CALL exchange_horiz( temp, 1)
665
666	IF ( .NOT. bc_lr_cyc ) THEN
667	IF (inflow_l .OR. outflow_l) temp(:,:,nxl_mg(l)-1) = temp(:,:,nxl_mg(l))
668	IF (inflow_r .OR. outflow_r) temp(:,:,nxr_mg(l)+1) = temp(:,:,nxr_mg(l))
669	ENDIF
670
671	IF ( .NOT. bc_ns_cyc ) THEN
672	IF (inflow_n .OR. outflow_n) temp(:,nyn_mg(l)+1,:) = temp(:,nyn_mg(l),:)
673	IF (inflow_s .OR. outflow_s) temp(:,nys_mg(l)-1,:) = temp(:,nys_mg(l),:)
674	ENDIF
675
676	!
677	!-- Bottom and top boundary conditions
678	IF ( ibc_p_b == 1 ) THEN
679	temp(nzb,:,: ) = temp(nzb+1,:,:)
680	ELSE
681	temp(nzb,:,: ) = 0.0_wp
682	ENDIF
683
684	IF ( ibc_p_t == 1 ) THEN
685	temp(nzt_mg(l)+1,:,: ) = temp(nzt_mg(l),:,:)
686	ELSE
687	temp(nzt_mg(l)+1,:,: ) = 0.0_wp
688	ENDIF
689
690
691	END SUBROUTINE prolong
692
693
694	SUBROUTINE redblack( f_mg, p_mg )
695
696	!------------------------------------------------------------------------------!
697	! Description:
698	! ------------
699	! Relaxation method for the multigrid scheme. A Gauss-Seidel iteration with
700	! 3D-Red-Black decomposition (GS-RB) is used.
701	!------------------------------------------------------------------------------!
702
703	USE arrays_3d, &
704	ONLY: f1_mg, f2_mg, f3_mg
705
706	USE control_parameters, &
707	ONLY: bc_lr_cyc, bc_ns_cyc, grid_level, ibc_p_b, ibc_p_t, inflow_l, &
708	inflow_n, inflow_r, inflow_s, ngsrb, outflow_l, outflow_n, &
709	outflow_r, outflow_s
710
711	USE cpulog, &
712	ONLY: cpu_log, log_point_s
713
714	USE grid_variables, &
715	ONLY: ddx2_mg, ddy2_mg
716
717	USE indices, &
718	ONLY: flags, wall_flags_1, wall_flags_2, wall_flags_3, wall_flags_4, &
719	wall_flags_5, wall_flags_6, wall_flags_7, wall_flags_8, &
720	wall_flags_9, wall_flags_10, nxl_mg, nxr_mg, nys_mg, nyn_mg, &
721	nzb, nzt_mg
722
723	USE kinds
724
725	IMPLICIT NONE
726
727	INTEGER(iwp) :: color !:
728	INTEGER(iwp) :: i !:
729	INTEGER(iwp) :: ic !:
730	INTEGER(iwp) :: j !:
731	INTEGER(iwp) :: jc !:
732	INTEGER(iwp) :: jj !:
733	INTEGER(iwp) :: k !:
734	INTEGER(iwp) :: l !:
735	INTEGER(iwp) :: n !:
736
737	LOGICAL :: unroll !:
738
739	REAL(wp) :: wall_left !:
740	REAL(wp) :: wall_north !:
741	REAL(wp) :: wall_right !:
742	REAL(wp) :: wall_south !:
743	REAL(wp) :: wall_total !:
744	REAL(wp) :: wall_top !:
745
746	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
747	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
748	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f_mg !:
749	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
750	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
751	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: p_mg !:
752
753	l = grid_level
754
755	!
756	!-- Choose flag array of this level
757	SELECT CASE ( l )
758	CASE ( 1 )
759	flags => wall_flags_1
760	CASE ( 2 )
761	flags => wall_flags_2
762	CASE ( 3 )
763	flags => wall_flags_3
764	CASE ( 4 )
765	flags => wall_flags_4
766	CASE ( 5 )
767	flags => wall_flags_5
768	CASE ( 6 )
769	flags => wall_flags_6
770	CASE ( 7 )
771	flags => wall_flags_7
772	CASE ( 8 )
773	flags => wall_flags_8
774	CASE ( 9 )
775	flags => wall_flags_9
776	CASE ( 10 )
777	flags => wall_flags_10
778	END SELECT
779
780	unroll = ( MOD( nyn_mg(l)-nys_mg(l)+1, 4 ) == 0 .AND. &
781	MOD( nxr_mg(l)-nxl_mg(l)+1, 2 ) == 0 )
782
783	DO n = 1, ngsrb
784
785	DO color = 1, 2
786
787	IF ( .NOT. unroll ) THEN
788
789	CALL cpu_log( log_point_s(36), 'redblack_no_unroll', 'start' )
790
791	!
792	!-- Without unrolling of loops, no cache optimization
793	DO i = nxl_mg(l), nxr_mg(l), 2
794	DO j = nys_mg(l) + 2 - color, nyn_mg(l), 2
795	DO k = nzb+1, nzt_mg(l), 2
796	! p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
797	! ddx2_mg(l) * ( p_mg(k,j,i+1) + p_mg(k,j,i-1) ) &
798	! + ddy2_mg(l) * ( p_mg(k,j+1,i) + p_mg(k,j-1,i) ) &
799	! + f2_mg(k,l) * p_mg(k+1,j,i) &
800	! + f3_mg(k,l) * p_mg(k-1,j,i) - f_mg(k,j,i) &
801	! )
802
803	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
804	ddx2_mg(l) * &
805	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
806	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
807	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
808	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
809	+ ddy2_mg(l) * &
810	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
811	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
812	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
813	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
814	+ f2_mg(k,l) * p_mg(k+1,j,i) &
815	+ f3_mg(k,l) * &
816	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
817	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
818	- f_mg(k,j,i) )
819	ENDDO
820	ENDDO
821	ENDDO
822
823	DO i = nxl_mg(l)+1, nxr_mg(l), 2
824	DO j = nys_mg(l) + (color-1), nyn_mg(l), 2
825	DO k = nzb+1, nzt_mg(l), 2
826	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
827	ddx2_mg(l) * &
828	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
829	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
830	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
831	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
832	+ ddy2_mg(l) * &
833	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
834	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
835	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
836	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
837	+ f2_mg(k,l) * p_mg(k+1,j,i) &
838	+ f3_mg(k,l) * &
839	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
840	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
841	- f_mg(k,j,i) )
842	ENDDO
843	ENDDO
844	ENDDO
845
846	DO i = nxl_mg(l), nxr_mg(l), 2
847	DO j = nys_mg(l) + (color-1), nyn_mg(l), 2
848	DO k = nzb+2, nzt_mg(l), 2
849	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
850	ddx2_mg(l) * &
851	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
852	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
853	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
854	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
855	+ ddy2_mg(l) * &
856	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
857	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
858	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
859	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
860	+ f2_mg(k,l) * p_mg(k+1,j,i) &
861	+ f3_mg(k,l) * &
862	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
863	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
864	- f_mg(k,j,i) )
865	ENDDO
866	ENDDO
867	ENDDO
868
869	DO i = nxl_mg(l)+1, nxr_mg(l), 2
870	DO j = nys_mg(l) + 2 - color, nyn_mg(l), 2
871	DO k = nzb+2, nzt_mg(l), 2
872	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
873	ddx2_mg(l) * &
874	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
875	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
876	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
877	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
878	+ ddy2_mg(l) * &
879	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
880	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
881	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
882	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
883	+ f2_mg(k,l) * p_mg(k+1,j,i) &
884	+ f3_mg(k,l) * &
885	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
886	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
887	- f_mg(k,j,i) )
888	ENDDO
889	ENDDO
890	ENDDO
891	CALL cpu_log( log_point_s(36), 'redblack_no_unroll', 'stop' )
892
893	ELSE
894
895	!
896	!-- Loop unrolling along y, only one i loop for better cache use
897	CALL cpu_log( log_point_s(38), 'redblack_unroll', 'start' )
898	DO ic = nxl_mg(l), nxr_mg(l), 2
899	DO jc = nys_mg(l), nyn_mg(l), 4
900	i = ic
901	jj = jc+2-color
902	DO k = nzb+1, nzt_mg(l), 2
903	j = jj
904	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
905	ddx2_mg(l) * &
906	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
907	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
908	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
909	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
910	+ ddy2_mg(l) * &
911	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
912	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
913	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
914	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
915	+ f2_mg(k,l) * p_mg(k+1,j,i) &
916	+ f3_mg(k,l) * &
917	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
918	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
919	- f_mg(k,j,i) )
920	j = jj+2
921	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
922	ddx2_mg(l) * &
923	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
924	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
925	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
926	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
927	+ ddy2_mg(l) * &
928	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
929	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
930	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
931	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
932	+ f2_mg(k,l) * p_mg(k+1,j,i) &
933	+ f3_mg(k,l) * &
934	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
935	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
936	- f_mg(k,j,i) )
937	ENDDO
938
939	i = ic+1
940	jj = jc+color-1
941	DO k = nzb+1, nzt_mg(l), 2
942	j =jj
943	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
944	ddx2_mg(l) * &
945	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
946	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
947	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
948	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
949	+ ddy2_mg(l) * &
950	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
951	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
952	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
953	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
954	+ f2_mg(k,l) * p_mg(k+1,j,i) &
955	+ f3_mg(k,l) * &
956	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
957	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
958	- f_mg(k,j,i) )
959	j = jj+2
960	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
961	ddx2_mg(l) * &
962	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
963	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
964	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
965	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
966	+ ddy2_mg(l) * &
967	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
968	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
969	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
970	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
971	+ f2_mg(k,l) * p_mg(k+1,j,i) &
972	+ f3_mg(k,l) * &
973	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
974	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
975	- f_mg(k,j,i) )
976	ENDDO
977
978	i = ic
979	jj = jc+color-1
980	DO k = nzb+2, nzt_mg(l), 2
981	j =jj
982	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
983	ddx2_mg(l) * &
984	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
985	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
986	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
987	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
988	+ ddy2_mg(l) * &
989	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
990	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
991	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
992	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
993	+ f2_mg(k,l) * p_mg(k+1,j,i) &
994	+ f3_mg(k,l) * &
995	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
996	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
997	- f_mg(k,j,i) )
998	j = jj+2
999	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
1000	ddx2_mg(l) * &
1001	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
1002	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
1003	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
1004	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
1005	+ ddy2_mg(l) * &
1006	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
1007	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
1008	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
1009	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
1010	+ f2_mg(k,l) * p_mg(k+1,j,i) &
1011	+ f3_mg(k,l) * &
1012	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
1013	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
1014	- f_mg(k,j,i) )
1015	ENDDO
1016
1017	i = ic+1
1018	jj = jc+2-color
1019	DO k = nzb+2, nzt_mg(l), 2
1020	j =jj
1021	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
1022	ddx2_mg(l) * &
1023	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
1024	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
1025	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
1026	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
1027	+ ddy2_mg(l) * &
1028	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
1029	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
1030	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
1031	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
1032	+ f2_mg(k,l) * p_mg(k+1,j,i) &
1033	+ f3_mg(k,l) * &
1034	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
1035	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
1036	- f_mg(k,j,i) )
1037	j = jj+2
1038	p_mg(k,j,i) = 1.0_wp / f1_mg(k,l) * ( &
1039	ddx2_mg(l) * &
1040	( p_mg(k,j,i+1) + IBITS( flags(k,j,i), 5, 1 ) * &
1041	( p_mg(k,j,i) - p_mg(k,j,i+1) ) + &
1042	p_mg(k,j,i-1) + IBITS( flags(k,j,i), 4, 1 ) * &
1043	( p_mg(k,j,i) - p_mg(k,j,i-1) ) ) &
1044	+ ddy2_mg(l) * &
1045	( p_mg(k,j+1,i) + IBITS( flags(k,j,i), 3, 1 ) * &
1046	( p_mg(k,j,i) - p_mg(k,j+1,i) ) + &
1047	p_mg(k,j-1,i) + IBITS( flags(k,j,i), 2, 1 ) * &
1048	( p_mg(k,j,i) - p_mg(k,j-1,i) ) ) &
1049	+ f2_mg(k,l) * p_mg(k+1,j,i) &
1050	+ f3_mg(k,l) * &
1051	( p_mg(k-1,j,i) + IBITS( flags(k,j,i), 0, 1 ) * &
1052	( p_mg(k,j,i) - p_mg(k-1,j,i) ) ) &
1053	- f_mg(k,j,i) )
1054	ENDDO
1055
1056	ENDDO
1057	ENDDO
1058	CALL cpu_log( log_point_s(38), 'redblack_unroll', 'stop' )
1059
1060	ENDIF
1061
1062	!
1063	!-- Horizontal boundary conditions
1064	CALL exchange_horiz( p_mg, 1 )
1065
1066	IF ( .NOT. bc_lr_cyc ) THEN
1067	IF ( inflow_l .OR. outflow_l ) THEN
1068	p_mg(:,:,nxl_mg(l)-1) = p_mg(:,:,nxl_mg(l))
1069	ENDIF
1070	IF ( inflow_r .OR. outflow_r ) THEN
1071	p_mg(:,:,nxr_mg(l)+1) = p_mg(:,:,nxr_mg(l))
1072	ENDIF
1073	ENDIF
1074
1075	IF ( .NOT. bc_ns_cyc ) THEN
1076	IF ( inflow_n .OR. outflow_n ) THEN
1077	p_mg(:,nyn_mg(l)+1,:) = p_mg(:,nyn_mg(l),:)
1078	ENDIF
1079	IF ( inflow_s .OR. outflow_s ) THEN
1080	p_mg(:,nys_mg(l)-1,:) = p_mg(:,nys_mg(l),:)
1081	ENDIF
1082	ENDIF
1083
1084	!
1085	!-- Bottom and top boundary conditions
1086	IF ( ibc_p_b == 1 ) THEN
1087	p_mg(nzb,:,: ) = p_mg(nzb+1,:,:)
1088	ELSE
1089	p_mg(nzb,:,: ) = 0.0_wp
1090	ENDIF
1091
1092	IF ( ibc_p_t == 1 ) THEN
1093	p_mg(nzt_mg(l)+1,:,: ) = p_mg(nzt_mg(l),:,:)
1094	ELSE
1095	p_mg(nzt_mg(l)+1,:,: ) = 0.0_wp
1096	ENDIF
1097
1098	ENDDO
1099
1100	ENDDO
1101
1102	!
1103	!-- Set pressure within topography and at the topography surfaces
1104	!$OMP PARALLEL PRIVATE (i,j,k,wall_left,wall_north,wall_right,wall_south,wall_top,wall_total)
1105	!$OMP DO
1106	DO i = nxl_mg(l), nxr_mg(l)
1107	DO j = nys_mg(l), nyn_mg(l)
1108	DO k = nzb, nzt_mg(l)
1109	!
1110	!-- First, set pressure inside topography to zero
1111	p_mg(k,j,i) = p_mg(k,j,i) * ( 1.0_wp - IBITS( flags(k,j,i), 6, 1 ) )
1112	!
1113	!-- Second, determine if the gridpoint inside topography is adjacent
1114	!-- to a wall and set its value to a value given by the average of
1115	!-- those values obtained from Neumann boundary condition
1116	wall_left = IBITS( flags(k,j,i-1), 5, 1 )
1117	wall_right = IBITS( flags(k,j,i+1), 4, 1 )
1118	wall_south = IBITS( flags(k,j-1,i), 3, 1 )
1119	wall_north = IBITS( flags(k,j+1,i), 2, 1 )
1120	wall_top = IBITS( flags(k+1,j,i), 0, 1 )
1121	wall_total = wall_left + wall_right + wall_south + wall_north + &
1122	wall_top
1123
1124	IF ( wall_total > 0.0_wp ) THEN
1125	p_mg(k,j,i) = 1.0_wp / wall_total * &
1126	( wall_left * p_mg(k,j,i-1) + &
1127	wall_right * p_mg(k,j,i+1) + &
1128	wall_south * p_mg(k,j-1,i) + &
1129	wall_north * p_mg(k,j+1,i) + &
1130	wall_top * p_mg(k+1,j,i) )
1131	ENDIF
1132	ENDDO
1133	ENDDO
1134	ENDDO
1135	!$OMP END PARALLEL
1136
1137	!
1138	!-- One more time horizontal boundary conditions
1139	CALL exchange_horiz( p_mg, 1)
1140
1141
1142	END SUBROUTINE redblack
1143
1144
1145
1146	SUBROUTINE mg_gather( f2, f2_sub )
1147
1148	USE control_parameters, &
1149	ONLY: grid_level
1150
1151	USE cpulog, &
1152	ONLY: cpu_log, log_point_s
1153
1154	USE indices, &
1155	ONLY: mg_loc_ind, nxl_mg, nxr_mg, nys_mg, nyn_mg, nzb, nzt_mg
1156
1157	USE kinds
1158
1159	USE pegrid
1160
1161	IMPLICIT NONE
1162
1163	INTEGER(iwp) :: i !:
1164	INTEGER(iwp) :: il !:
1165	INTEGER(iwp) :: ir !:
1166	INTEGER(iwp) :: j !:
1167	INTEGER(iwp) :: jn !:
1168	INTEGER(iwp) :: js !:
1169	INTEGER(iwp) :: k !:
1170	INTEGER(iwp) :: nwords !:
1171
1172	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1173	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1174	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f2 !:
1175	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1176	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1177	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f2_l !:
1178
1179	REAL(wp), DIMENSION(nzb:mg_loc_ind(5,myid)+1, &
1180	mg_loc_ind(3,myid)-1:mg_loc_ind(4,myid)+1, &
1181	mg_loc_ind(1,myid)-1:mg_loc_ind(2,myid)+1) :: f2_sub !:
1182
1183
1184	#if defined( __parallel )
1185	CALL cpu_log( log_point_s(34), 'mg_gather', 'start' )
1186
1187	f2_l = 0.0_wp
1188
1189	!
1190	!-- Store the local subdomain array on the total array
1191	js = mg_loc_ind(3,myid)
1192	IF ( south_border_pe ) js = js - 1
1193	jn = mg_loc_ind(4,myid)
1194	IF ( north_border_pe ) jn = jn + 1
1195	il = mg_loc_ind(1,myid)
1196	IF ( left_border_pe ) il = il - 1
1197	ir = mg_loc_ind(2,myid)
1198	IF ( right_border_pe ) ir = ir + 1
1199	DO i = il, ir
1200	DO j = js, jn
1201	DO k = nzb, nzt_mg(grid_level)+1
1202	f2_l(k,j,i) = f2_sub(k,j,i)
1203	ENDDO
1204	ENDDO
1205	ENDDO
1206
1207	!
1208	!-- Find out the number of array elements of the total array
1209	nwords = SIZE( f2 )
1210
1211	!
1212	!-- Gather subdomain data from all PEs
1213	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
1214	CALL MPI_ALLREDUCE( f2_l(nzb,nys_mg(grid_level)-1,nxl_mg(grid_level)-1), &
1215	f2(nzb,nys_mg(grid_level)-1,nxl_mg(grid_level)-1), &
1216	nwords, MPI_REAL, MPI_SUM, comm2d, ierr )
1217
1218	CALL cpu_log( log_point_s(34), 'mg_gather', 'stop' )
1219	#endif
1220
1221	END SUBROUTINE mg_gather
1222
1223
1224
1225	SUBROUTINE mg_scatter( p2, p2_sub )
1226	!
1227	!-- TODO: It may be possible to improve the speed of this routine by using
1228	!-- non-blocking communication
1229
1230	USE control_parameters, &
1231	ONLY: grid_level
1232
1233	USE cpulog, &
1234	ONLY: cpu_log, log_point_s
1235
1236	USE indices, &
1237	ONLY: mg_loc_ind, nxl_mg, nxr_mg, nys_mg, nyn_mg, nzb, nzt_mg
1238
1239	USE kinds
1240
1241	USE pegrid
1242
1243	IMPLICIT NONE
1244
1245	INTEGER(iwp) :: nwords !:
1246
1247	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level-1)+1, &
1248	nys_mg(grid_level-1)-1:nyn_mg(grid_level-1)+1, &
1249	nxl_mg(grid_level-1)-1:nxr_mg(grid_level-1)+1) :: p2 !:
1250
1251	REAL(wp), DIMENSION(nzb:mg_loc_ind(5,myid)+1, &
1252	mg_loc_ind(3,myid)-1:mg_loc_ind(4,myid)+1, &
1253	mg_loc_ind(1,myid)-1:mg_loc_ind(2,myid)+1) :: p2_sub !:
1254
1255	!
1256	!-- Find out the number of array elements of the subdomain array
1257	nwords = SIZE( p2_sub )
1258
1259	#if defined( __parallel )
1260	CALL cpu_log( log_point_s(35), 'mg_scatter', 'start' )
1261
1262	p2_sub = p2(:,mg_loc_ind(3,myid)-1:mg_loc_ind(4,myid)+1, &
1263	mg_loc_ind(1,myid)-1:mg_loc_ind(2,myid)+1)
1264
1265	CALL cpu_log( log_point_s(35), 'mg_scatter', 'stop' )
1266	#endif
1267
1268	END SUBROUTINE mg_scatter
1269
1270
1271
1272	RECURSIVE SUBROUTINE next_mg_level( f_mg, p_mg, p3, r )
1273
1274	!------------------------------------------------------------------------------!
1275	! Description:
1276	! ------------
1277	! This is where the multigrid technique takes place. V- and W- Cycle are
1278	! implemented and steered by the parameter "gamma". Parameter "nue" determines
1279	! the convergence of the multigrid iterative solution. There are nue times
1280	! RB-GS iterations. It should be set to "1" or "2", considering the time effort
1281	! one would like to invest. Last choice shows a very good converging factor,
1282	! but leads to an increase in computing time.
1283	!------------------------------------------------------------------------------!
1284
1285	USE control_parameters, &
1286	ONLY: bc_lr_dirrad, bc_lr_raddir, bc_ns_dirrad, bc_ns_raddir, &
1287	gamma_mg, grid_level, grid_level_count, ibc_p_b, ibc_p_t, &
1288	inflow_l, inflow_n, inflow_r, inflow_s, maximum_grid_level, &
1289	mg_switch_to_pe0_level, mg_switch_to_pe0, ngsrb, outflow_l, &
1290	outflow_n, outflow_r, outflow_s
1291
1292
1293	USE indices, &
1294	ONLY: mg_loc_ind, nxl, nxl_mg, nxr, nxr_mg, nys, nys_mg, nyn, &
1295	nyn_mg, nzb, nzt, nzt_mg
1296
1297	USE kinds
1298
1299	USE pegrid
1300
1301	IMPLICIT NONE
1302
1303	INTEGER(iwp) :: i !:
1304	INTEGER(iwp) :: j !:
1305	INTEGER(iwp) :: k !:
1306	INTEGER(iwp) :: nxl_mg_save !:
1307	INTEGER(iwp) :: nxr_mg_save !:
1308	INTEGER(iwp) :: nyn_mg_save !:
1309	INTEGER(iwp) :: nys_mg_save !:
1310	INTEGER(iwp) :: nzt_mg_save !:
1311
1312	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1313	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1314	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: f_mg !:
1315	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1316	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1317	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: p_mg !:
1318	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1319	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1320	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: p3 !:
1321	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level)+1, &
1322	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1323	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) :: r !:
1324
1325	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level-1)+1, &
1326	nys_mg(grid_level-1)-1:nyn_mg(grid_level-1)+1, &
1327	nxl_mg(grid_level-1)-1:nxr_mg(grid_level-1)+1) :: f2 !:
1328	REAL(wp), DIMENSION(nzb:nzt_mg(grid_level-1)+1, &
1329	nys_mg(grid_level-1)-1:nyn_mg(grid_level-1)+1, &
1330	nxl_mg(grid_level-1)-1:nxr_mg(grid_level-1)+1) :: p2 !:
1331
1332	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: f2_sub !:
1333	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: p2_sub !:
1334
1335	!
1336	!-- Restriction to the coarsest grid
1337	10 IF ( grid_level == 1 ) THEN
1338
1339	!
1340	!-- Solution on the coarsest grid. Double the number of Gauss-Seidel
1341	!-- iterations in order to get a more accurate solution.
1342	ngsrb = 2 * ngsrb
1343
1344	CALL redblack( f_mg, p_mg )
1345
1346	ngsrb = ngsrb / 2
1347
1348
1349	ELSEIF ( grid_level /= 1 ) THEN
1350
1351	grid_level_count(grid_level) = grid_level_count(grid_level) + 1
1352
1353	!
1354	!-- Solution on the actual grid level
1355	CALL redblack( f_mg, p_mg )
1356
1357	!
1358	!-- Determination of the actual residual
1359	CALL resid( f_mg, p_mg, r )
1360
1361	!
1362	!-- Restriction of the residual (finer grid values!) to the next coarser
1363	!-- grid. Therefore, the grid level has to be decremented now. nxl..nzt have
1364	!-- to be set to the coarse grid values, because these variables are needed
1365	!-- for the exchange of ghost points in routine exchange_horiz
1366	grid_level = grid_level - 1
1367	nxl = nxl_mg(grid_level)
1368	nys = nys_mg(grid_level)
1369	nxr = nxr_mg(grid_level)
1370	nyn = nyn_mg(grid_level)
1371	nzt = nzt_mg(grid_level)
1372
1373	IF ( grid_level == mg_switch_to_pe0_level ) THEN
1374
1375	!
1376	!-- From this level on, calculations are done on PE0 only.
1377	!-- First, carry out restriction on the subdomain.
1378	!-- Therefore, indices of the level have to be changed to subdomain values
1379	!-- in between (otherwise, the restrict routine would expect
1380	!-- the gathered array)
1381
1382	nxl_mg_save = nxl_mg(grid_level)
1383	nxr_mg_save = nxr_mg(grid_level)
1384	nys_mg_save = nys_mg(grid_level)
1385	nyn_mg_save = nyn_mg(grid_level)
1386	nzt_mg_save = nzt_mg(grid_level)
1387	nxl_mg(grid_level) = mg_loc_ind(1,myid)
1388	nxr_mg(grid_level) = mg_loc_ind(2,myid)
1389	nys_mg(grid_level) = mg_loc_ind(3,myid)
1390	nyn_mg(grid_level) = mg_loc_ind(4,myid)
1391	nzt_mg(grid_level) = mg_loc_ind(5,myid)
1392	nxl = mg_loc_ind(1,myid)
1393	nxr = mg_loc_ind(2,myid)
1394	nys = mg_loc_ind(3,myid)
1395	nyn = mg_loc_ind(4,myid)
1396	nzt = mg_loc_ind(5,myid)
1397
1398	ALLOCATE( f2_sub(nzb:nzt_mg(grid_level)+1, &
1399	nys_mg(grid_level)-1:nyn_mg(grid_level)+1, &
1400	nxl_mg(grid_level)-1:nxr_mg(grid_level)+1) )
1401
1402	CALL restrict( f2_sub, r )
1403
1404	!
1405	!-- Restore the correct indices of this level
1406	nxl_mg(grid_level) = nxl_mg_save
1407	nxr_mg(grid_level) = nxr_mg_save
1408	nys_mg(grid_level) = nys_mg_save
1409	nyn_mg(grid_level) = nyn_mg_save
1410	nzt_mg(grid_level) = nzt_mg_save
1411	nxl = nxl_mg(grid_level)
1412	nxr = nxr_mg(grid_level)
1413	nys = nys_mg(grid_level)
1414	nyn = nyn_mg(grid_level)
1415	nzt = nzt_mg(grid_level)
1416	!
1417	!-- Gather all arrays from the subdomains on PE0
1418	CALL mg_gather( f2, f2_sub )
1419
1420	!
1421	!-- Set switch for routine exchange_horiz, that no ghostpoint exchange
1422	!-- has to be carried out from now on
1423	mg_switch_to_pe0 = .TRUE.
1424
1425	!
1426	!-- In case of non-cyclic lateral boundary conditions, both in- and
1427	!-- outflow conditions have to be used on all PEs after the switch,
1428	!-- because then they have the total domain.
1429	IF ( bc_lr_dirrad ) THEN
1430	inflow_l = .TRUE.
1431	inflow_r = .FALSE.
1432	outflow_l = .FALSE.
1433	outflow_r = .TRUE.
1434	ELSEIF ( bc_lr_raddir ) THEN
1435	inflow_l = .FALSE.
1436	inflow_r = .TRUE.
1437	outflow_l = .TRUE.
1438	outflow_r = .FALSE.
1439	ENDIF
1440
1441	IF ( bc_ns_dirrad ) THEN
1442	inflow_n = .TRUE.
1443	inflow_s = .FALSE.
1444	outflow_n = .FALSE.
1445	outflow_s = .TRUE.
1446	ELSEIF ( bc_ns_raddir ) THEN
1447	inflow_n = .FALSE.
1448	inflow_s = .TRUE.
1449	outflow_n = .TRUE.
1450	outflow_s = .FALSE.
1451	ENDIF
1452
1453	DEALLOCATE( f2_sub )
1454
1455	ELSE
1456
1457	CALL restrict( f2, r )
1458
1459	ENDIF
1460
1461	p2 = 0.0_wp
1462
1463	!
1464	!-- Repeat the same procedure till the coarsest grid is reached
1465	CALL next_mg_level( f2, p2, p3, r )
1466
1467	ENDIF
1468
1469	!
1470	!-- Now follows the prolongation
1471	IF ( grid_level >= 2 ) THEN
1472
1473	!
1474	!-- Prolongation of the new residual. The values are transferred
1475	!-- from the coarse to the next finer grid.
1476	IF ( grid_level == mg_switch_to_pe0_level+1 ) THEN
1477
1478	#if defined( __parallel )
1479	!
1480	!-- At this level, the new residual first has to be scattered from
1481	!-- PE0 to the other PEs
1482	ALLOCATE( p2_sub(nzb:mg_loc_ind(5,myid)+1, &
1483	mg_loc_ind(3,myid)-1:mg_loc_ind(4,myid)+1, &
1484	mg_loc_ind(1,myid)-1:mg_loc_ind(2,myid)+1) )
1485
1486	CALL mg_scatter( p2, p2_sub )
1487
1488	!
1489	!-- Therefore, indices of the previous level have to be changed to
1490	!-- subdomain values in between (otherwise, the prolong routine would
1491	!-- expect the gathered array)
1492	nxl_mg_save = nxl_mg(grid_level-1)
1493	nxr_mg_save = nxr_mg(grid_level-1)
1494	nys_mg_save = nys_mg(grid_level-1)
1495	nyn_mg_save = nyn_mg(grid_level-1)
1496	nzt_mg_save = nzt_mg(grid_level-1)
1497	nxl_mg(grid_level-1) = mg_loc_ind(1,myid)
1498	nxr_mg(grid_level-1) = mg_loc_ind(2,myid)
1499	nys_mg(grid_level-1) = mg_loc_ind(3,myid)
1500	nyn_mg(grid_level-1) = mg_loc_ind(4,myid)
1501	nzt_mg(grid_level-1) = mg_loc_ind(5,myid)
1502
1503	!
1504	!-- Set switch for routine exchange_horiz, that ghostpoint exchange
1505	!-- has to be carried again out from now on
1506	mg_switch_to_pe0 = .FALSE.
1507
1508	!
1509	!-- For non-cyclic lateral boundary conditions, restore the
1510	!-- in-/outflow conditions
1511	inflow_l = .FALSE.; inflow_r = .FALSE.
1512	inflow_n = .FALSE.; inflow_s = .FALSE.
1513	outflow_l = .FALSE.; outflow_r = .FALSE.
1514	outflow_n = .FALSE.; outflow_s = .FALSE.
1515
1516	IF ( pleft == MPI_PROC_NULL ) THEN
1517	IF ( bc_lr_dirrad ) THEN
1518	inflow_l = .TRUE.
1519	ELSEIF ( bc_lr_raddir ) THEN
1520	outflow_l = .TRUE.
1521	ENDIF
1522	ENDIF
1523
1524	IF ( pright == MPI_PROC_NULL ) THEN
1525	IF ( bc_lr_dirrad ) THEN
1526	outflow_r = .TRUE.
1527	ELSEIF ( bc_lr_raddir ) THEN
1528	inflow_r = .TRUE.
1529	ENDIF
1530	ENDIF
1531
1532	IF ( psouth == MPI_PROC_NULL ) THEN
1533	IF ( bc_ns_dirrad ) THEN
1534	outflow_s = .TRUE.
1535	ELSEIF ( bc_ns_raddir ) THEN
1536	inflow_s = .TRUE.
1537	ENDIF
1538	ENDIF
1539
1540	IF ( pnorth == MPI_PROC_NULL ) THEN
1541	IF ( bc_ns_dirrad ) THEN
1542	inflow_n = .TRUE.
1543	ELSEIF ( bc_ns_raddir ) THEN
1544	outflow_n = .TRUE.
1545	ENDIF
1546	ENDIF
1547
1548	CALL prolong( p2_sub, p3 )
1549
1550	!
1551	!-- Restore the correct indices of the previous level
1552	nxl_mg(grid_level-1) = nxl_mg_save
1553	nxr_mg(grid_level-1) = nxr_mg_save
1554	nys_mg(grid_level-1) = nys_mg_save
1555	nyn_mg(grid_level-1) = nyn_mg_save
1556	nzt_mg(grid_level-1) = nzt_mg_save
1557
1558	DEALLOCATE( p2_sub )
1559	#endif
1560
1561	ELSE
1562
1563	CALL prolong( p2, p3 )
1564
1565	ENDIF
1566
1567	!
1568	!-- Computation of the new pressure correction. Therefore,
1569	!-- values from prior grids are added up automatically stage by stage.
1570	DO i = nxl_mg(grid_level)-1, nxr_mg(grid_level)+1
1571	DO j = nys_mg(grid_level)-1, nyn_mg(grid_level)+1
1572	DO k = nzb, nzt_mg(grid_level)+1
1573	p_mg(k,j,i) = p_mg(k,j,i) + p3(k,j,i)
1574	ENDDO
1575	ENDDO
1576	ENDDO
1577
1578	!
1579	!-- Relaxation of the new solution
1580	CALL redblack( f_mg, p_mg )
1581
1582	ENDIF
1583
1584
1585	!
1586	!-- The following few lines serve the steering of the multigrid scheme
1587	IF ( grid_level == maximum_grid_level ) THEN
1588
1589	GOTO 20
1590
1591	ELSEIF ( grid_level /= maximum_grid_level .AND. grid_level /= 1 .AND. &
1592	grid_level_count(grid_level) /= gamma_mg ) THEN
1593
1594	GOTO 10
1595
1596	ENDIF
1597
1598	!
1599	!-- Reset counter for the next call of poismg
1600	grid_level_count(grid_level) = 0
1601
1602	!
1603	!-- Continue with the next finer level. nxl..nzt have to be
1604	!-- set to the finer grid values, because these variables are needed for the
1605	!-- exchange of ghost points in routine exchange_horiz
1606	grid_level = grid_level + 1
1607	nxl = nxl_mg(grid_level)
1608	nxr = nxr_mg(grid_level)
1609	nys = nys_mg(grid_level)
1610	nyn = nyn_mg(grid_level)
1611	nzt = nzt_mg(grid_level)
1612
1613	20 CONTINUE
1614
1615	END SUBROUTINE next_mg_level

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