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source: palm/trunk/SOURCE/poismg.f90 @ 1318

Last change on this file since 1318 was 1318, checked in by raasch, 10 years ago
former files/routines cpu_log and cpu_statistics combined to one module, which also includes the former data module cpulog from the modules-file, module interfaces removed
Property svn:keywords set to `Id`
File size: 56.1 KB

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

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