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source: palm/trunk/SOURCE/pres.f90 @ 2195

Last change on this file since 2195 was 2119, checked in by raasch, 8 years ago
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[1682]	1	!> @file pres.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1212]	21	! ------------------
[1932]	22	!
[2119]	23	!
[1919]	24	! Former revisions:
	25	! -----------------
	26	! $Id: pres.f90 2119 2017-01-17 16:51:50Z raasch $
	27	!
[2119]	28	! 2118 2017-01-17 16:38:49Z raasch
	29	! OpenACC directives and related code removed
	30	!
[2074]	31	! 2073 2016-11-30 14:34:05Z raasch
	32	! openmp bugfix for calculation of new divergence
	33	!
[2038]	34	! 2037 2016-10-26 11:15:40Z knoop
	35	! Anelastic approximation implemented
	36	!
[2001]	37	! 2000 2016-08-20 18:09:15Z knoop
	38	! Forced header and separation lines into 80 columns
	39	!
[1933]	40	! 1932 2016-06-10 12:09:21Z suehring
	41	! Initial version of purely vertical nesting introduced.
	42	!
[1932]	43	! 1931 2016-06-10 12:06:59Z suehring
	44	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
	45	!
[1930]	46	! 1929 2016-06-09 16:25:25Z suehring
	47	! Bugfix: weight_substep for initial call, replace by local variable
	48	!
[1919]	49	! 1918 2016-05-27 14:35:57Z raasch
[1918]	50	! sum of divergence is also calculated when pres is called before the initial
	51	! first time step,
	52	! stearing is modified by using intermediate_timestep_count = 0 in order to
	53	! determine if pres is called before the first initial timestep,
	54	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
	55	! mean vertical velocity is also removed for the first time step
	56	! bugfix for calculating divergences
[1321]	57	!
[1909]	58	! 1908 2016-05-25 17:22:32Z suehring
	59	! New divergence for output into RUN_CONTROL file is calculated only at last
	60	! Runge-Kutta step
	61	!
[1846]	62	! 1845 2016-04-08 08:29:13Z raasch
	63	! nzb_2d replace by nzb_u\|v_inner
	64	!
[1800]	65	! 1799 2016-04-05 08:35:55Z gronemeier
	66	! Bugfix: excluded third dimension from horizontal volume flow calculation
	67	!
[1763]	68	! 1762 2016-02-25 12:31:13Z hellstea
	69	! Introduction of nested domain feature
	70	!
[1683]	71	! 1682 2015-10-07 23:56:08Z knoop
	72	! Code annotations made doxygen readable
	73	!
[1576]	74	! 1575 2015-03-27 09:56:27Z raasch
	75	! poismg_fast + respective module added, adjustments for psolver-queries
	76	!
[1343]	77	! 1342 2014-03-26 17:04:47Z kanani
	78	! REAL constants defined as wp-kind
	79	!
[1321]	80	! 1320 2014-03-20 08:40:49Z raasch
[1320]	81	! ONLY-attribute added to USE-statements,
	82	! kind-parameters added to all INTEGER and REAL declaration statements,
	83	! kinds are defined in new module kinds,
	84	! old module precision_kind is removed,
	85	! revision history before 2012 removed,
	86	! comment fields (!:) to be used for variable explanations added to
	87	! all variable declaration statements
[708]	88	!
[1319]	89	! 1318 2014-03-17 13:35:16Z raasch
	90	! module interfaces removed
	91	!
[1307]	92	! 1306 2014-03-13 14:30:59Z raasch
	93	! second argument removed from routine poisfft
	94	!
[1258]	95	! 1257 2013-11-08 15:18:40Z raasch
	96	! openacc loop and loop vector clauses removed, independent clauses added,
	97	! end parallel replaced by end parallel loop
	98	!
[1222]	99	! 1221 2013-09-10 08:59:13Z raasch
	100	! openACC porting of reduction operations, loops for calculating d are
	101	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	102	!
[1213]	103	! 1212 2013-08-15 08:46:27Z raasch
	104	! call of poisfft_hybrid removed
	105	!
[1118]	106	! 1117 2013-03-27 11:15:36Z suehring
	107	! Bugfix in OpenMP parallelization.
	108	!
[1114]	109	! 1113 2013-03-10 02:48:14Z raasch
	110	! GPU-porting of several loops, some loops rearranged
	111	!
[1112]	112	! 1111 2013-03-08 23:54:10Z
	113	! openACC statements added,
	114	! ibc_p_b = 2 removed
	115	!
[1093]	116	! 1092 2013-02-02 11:24:22Z raasch
	117	! unused variables removed
	118	!
[1037]	119	! 1036 2012-10-22 13:43:42Z raasch
	120	! code put under GPL (PALM 3.9)
	121	!
[1004]	122	! 1003 2012-09-14 14:35:53Z raasch
	123	! adjustment of array tend for cases with unequal subdomain sizes removed
	124	!
[1]	125	! Revision 1.1 1997/07/24 11:24:44 raasch
	126	! Initial revision
	127	!
	128	!
	129	! Description:
	130	! ------------
[1682]	131	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	132	!> equation for the perturbation pressure. Compute the final velocities using
	133	!> this perturbation pressure. Compute the remaining divergence.
[1]	134	!------------------------------------------------------------------------------!
[1682]	135	SUBROUTINE pres
	136
[1]	137
[1320]	138	USE arrays_3d, &
[2037]	139	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
	140	tend, u, v, w
[1320]	141
	142	USE control_parameters, &
	143	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
	144	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
[1908]	145	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
[2118]	146	nest_domain, outflow_l, outflow_n, outflow_r, &
[1918]	147	outflow_s, psolver, subdomain_size, topography, volume_flow, &
	148	volume_flow_area, volume_flow_initial
[1320]	149
	150	USE cpulog, &
	151	ONLY: cpu_log, log_point, log_point_s
	152
	153	USE grid_variables, &
	154	ONLY: ddx, ddy
	155
	156	USE indices, &
	157	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
	158	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzb_s_inner, &
[1845]	159	nzb_u_inner, nzb_v_inner, nzb_w_inner, nzt, nzt_mg, &
[1320]	160	rflags_s_inner
	161
	162	USE kinds
	163
[1]	164	USE pegrid
[1933]	165
	166	USE pmc_interface, &
	167	ONLY: nesting_mode
[1]	168
[1320]	169	USE poisfft_mod, &
	170	ONLY: poisfft
	171
[1575]	172	USE poismg_mod
	173
[1320]	174	USE statistics, &
	175	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	176	weight_substep
	177
[1]	178	IMPLICIT NONE
	179
[1682]	180	INTEGER(iwp) :: i !<
	181	INTEGER(iwp) :: j !<
	182	INTEGER(iwp) :: k !<
[1]	183
[1682]	184	REAL(wp) :: ddt_3d !<
[1918]	185	REAL(wp) :: d_weight_pres !<
[1682]	186	REAL(wp) :: localsum !<
	187	REAL(wp) :: threadsum !<
[1918]	188	REAL(wp) :: weight_pres_l !<
[1929]	189	REAL(wp) :: weight_substep_l !<
[1]	190
[1762]	191	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	192	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	193	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	194	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	195
[1933]	196	LOGICAL :: nest_domain_nvn !<
[1]	197
[1933]	198
[1]	199	CALL cpu_log( log_point(8), 'pres', 'start' )
	200
[85]	201
[1918]	202	!
	203	!-- Calculate quantities to be used locally
[1342]	204	ddt_3d = 1.0_wp / dt_3d
[1918]	205	IF ( intermediate_timestep_count == 0 ) THEN
	206	!
	207	!-- If pres is called before initial time step
[1929]	208	weight_pres_l = 1.0_wp
	209	d_weight_pres = 1.0_wp
	210	weight_substep_l = 1.0_wp
[1918]	211	ELSE
[1929]	212	weight_pres_l = weight_pres(intermediate_timestep_count)
	213	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	214	weight_substep_l = weight_substep(intermediate_timestep_count)
[1918]	215	ENDIF
[85]	216
[1]	217	!
[707]	218	!-- Multigrid method expects array d to have one ghost layer.
	219	!--
[1575]	220	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	221
[1]	222	DEALLOCATE( d )
[667]	223	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	224
	225	!
	226	!-- Since p is later used to hold the weighted average of the substeps, it
	227	!-- cannot be used in the iterative solver. Therefore, its initial value is
	228	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	229	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	230	DO i = nxl-1, nxr+1
	231	DO j = nys-1, nyn+1
	232	DO k = nzb, nzt+1
	233	p_loc(k,j,i) = p(k,j,i)
	234	ENDDO
	235	ENDDO
	236	ENDDO
[667]	237	ENDIF
	238
[1918]	239	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	240
	241	!
	242	!-- Since p is later used to hold the weighted average of the substeps, it
	243	!-- cannot be used in the iterative solver. Therefore, its initial value is
	244	!-- stored on p_loc, which is then iteratively advanced in every substep.
	245	p_loc = p
	246
[1]	247	ENDIF
	248
	249	!
[75]	250	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	251	!-- boundary conditions
[106]	252	!-- WARNING: so far, this conservation does not work at the left/south
	253	!-- boundary if the topography at the inflow differs from that at the
	254	!-- outflow! For this case, volume_flow_area needs adjustment!
	255	!
	256	!-- Left/right
[709]	257	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
[680]	258
[1342]	259	volume_flow(1) = 0.0_wp
	260	volume_flow_l(1) = 0.0_wp
[106]	261
	262	IF ( outflow_l ) THEN
	263	i = 0
	264	ELSEIF ( outflow_r ) THEN
	265	i = nx+1
	266	ENDIF
	267
	268	DO j = nys, nyn
	269	!
	270	!-- Sum up the volume flow through the south/north boundary
[1845]	271	DO k = nzb_u_inner(j,i)+1, nzt
[667]	272	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k)
[106]	273	ENDDO
	274	ENDDO
	275
	276	#if defined( __parallel )
[680]	277	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	278	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	279	MPI_SUM, comm1dy, ierr )
	280	#else
	281	volume_flow = volume_flow_l
	282	#endif
[709]	283	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	284	/ volume_flow_area(1)
	285
[667]	286	DO j = nysg, nyng
[1845]	287	DO k = nzb_u_inner(j,i)+1, nzt
[106]	288	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
	289	ENDDO
	290	ENDDO
	291
	292	ENDIF
	293
	294	!
	295	!-- South/north
[709]	296	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
[106]	297
[1342]	298	volume_flow(2) = 0.0_wp
	299	volume_flow_l(2) = 0.0_wp
[75]	300
[106]	301	IF ( outflow_s ) THEN
	302	j = 0
	303	ELSEIF ( outflow_n ) THEN
[75]	304	j = ny+1
[106]	305	ENDIF
	306
	307	DO i = nxl, nxr
[75]	308	!
[106]	309	!-- Sum up the volume flow through the south/north boundary
[1845]	310	DO k = nzb_v_inner(j,i)+1, nzt
[667]	311	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k)
[75]	312	ENDDO
[106]	313	ENDDO
	314
[75]	315	#if defined( __parallel )
[680]	316	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	317	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	318	MPI_SUM, comm1dx, ierr )
	319	#else
	320	volume_flow = volume_flow_l
	321	#endif
	322	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	323	/ volume_flow_area(2)
[75]	324
[667]	325	DO i = nxlg, nxrg
[709]	326	DO k = nzb_v_inner(j,i)+1, nzt
[106]	327	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
[75]	328	ENDDO
[106]	329	ENDDO
[75]	330
	331	ENDIF
	332
[76]	333	!
[1762]	334	!-- Remove mean vertical velocity in case that Neumann conditions are
[1933]	335	!-- used both at bottom and top boundary, and if not a nested domain in a
	336	!-- normal nesting run. In case of vertical nesting, this must be done.
	337	!-- Therefore an auxiliary logical variable nest_domain_nvn is used here, and
	338	!-- nvn stands for non-vertical nesting.
[1918]	339	!-- This cannot be done before the first initial time step because ngp_2dh_outer
	340	!-- is not yet known then.
[1933]	341	nest_domain_nvn = nest_domain
	342	IF ( nest_domain .AND. nesting_mode == 'vertical' ) THEN
	343	nest_domain_nvn = .FALSE.
	344	ENDIF
	345
	346	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. &
	347	.NOT. nest_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
[1918]	348	THEN
	349	w_l = 0.0_wp; w_l_l = 0.0_wp
	350	DO i = nxl, nxr
	351	DO j = nys, nyn
	352	DO k = nzb_w_inner(j,i)+1, nzt
	353	w_l_l(k) = w_l_l(k) + w(k,j,i)
[76]	354	ENDDO
	355	ENDDO
[1918]	356	ENDDO
[76]	357	#if defined( __parallel )
[1918]	358	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	359	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
	360	comm2d, ierr )
[76]	361	#else
[1918]	362	w_l = w_l_l
[76]	363	#endif
[1918]	364	DO k = 1, nzt
	365	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	366	ENDDO
	367	DO i = nxlg, nxrg
	368	DO j = nysg, nyng
	369	DO k = nzb_w_inner(j,i)+1, nzt
	370	w(k,j,i) = w(k,j,i) - w_l(k)
[76]	371	ENDDO
	372	ENDDO
[1918]	373	ENDDO
[76]	374	ENDIF
[75]	375
	376	!
[1]	377	!-- Compute the divergence of the provisional velocity field.
	378	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	379
[1575]	380	IF ( psolver(1:9) == 'multigrid' ) THEN
[1]	381	!$OMP PARALLEL DO SCHEDULE( STATIC )
	382	DO i = nxl-1, nxr+1
	383	DO j = nys-1, nyn+1
	384	DO k = nzb, nzt+1
[1342]	385	d(k,j,i) = 0.0_wp
[1]	386	ENDDO
	387	ENDDO
	388	ENDDO
	389	ELSE
	390	!$OMP PARALLEL DO SCHEDULE( STATIC )
[1003]	391	DO i = nxl, nxr
	392	DO j = nys, nyn
	393	DO k = nzb+1, nzt
[1342]	394	d(k,j,i) = 0.0_wp
[1]	395	ENDDO
	396	ENDDO
	397	ENDDO
	398	ENDIF
	399
[1342]	400	localsum = 0.0_wp
	401	threadsum = 0.0_wp
[1]	402
	403	#if defined( __ibm )
	404	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	405	!$OMP DO SCHEDULE( STATIC )
	406	DO i = nxl, nxr
	407	DO j = nys, nyn
	408	DO k = nzb_s_inner(j,i)+1, nzt
[2037]	409	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	410	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	411	( w(k,j,i) * rho_air_zw(k) - &
	412	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	413	) * ddt_3d * d_weight_pres
[1]	414	ENDDO
	415	!
	416	!-- Compute possible PE-sum of divergences for flow_statistics
	417	DO k = nzb_s_inner(j,i)+1, nzt
	418	threadsum = threadsum + ABS( d(k,j,i) )
	419	ENDDO
	420
	421	ENDDO
	422	ENDDO
	423
[1918]	424	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	425	intermediate_timestep_count == 0 ) THEN
	426	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	427	ENDIF
[1]	428	!$OMP END PARALLEL
	429	#else
	430
[1111]	431	!$OMP PARALLEL PRIVATE (i,j,k)
	432	!$OMP DO SCHEDULE( STATIC )
	433	DO i = nxl, nxr
	434	DO j = nys, nyn
	435	DO k = 1, nzt
[2037]	436	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	437	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	438	( w(k,j,i) * rho_air_zw(k) - &
	439	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	440	) * ddt_3d * d_weight_pres * rflags_s_inner(k,j,i)
[1]	441	ENDDO
	442	ENDDO
[1111]	443	ENDDO
	444	!$OMP END PARALLEL
[1]	445
	446	!
[1908]	447	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	448	!-- computation only at last Runge-Kutta substep.
[1918]	449	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	450	intermediate_timestep_count == 0 ) THEN
[1908]	451	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	452	!$OMP DO SCHEDULE( STATIC )
	453	DO i = nxl, nxr
	454	DO j = nys, nyn
	455	DO k = nzb+1, nzt
	456	threadsum = threadsum + ABS( d(k,j,i) )
	457	ENDDO
[1]	458	ENDDO
	459	ENDDO
[1918]	460	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	461	!$OMP END PARALLEL
	462	ENDIF
[1]	463	#endif
	464
	465	!
	466	!-- For completeness, set the divergence sum of all statistic regions to those
	467	!-- of the total domain
[1918]	468	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	469	intermediate_timestep_count == 0 ) THEN
[1908]	470	sums_divold_l(0:statistic_regions) = localsum
[1918]	471	ENDIF
[1]	472
	473	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	474
	475	!
	476	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	477	IF ( psolver == 'poisfft' ) THEN
[1]	478
	479	!
	480	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	481	CALL poisfft( d )
[1212]	482
[1]	483	!
	484	!-- Store computed perturbation pressure and set boundary condition in
	485	!-- z-direction
	486	!$OMP PARALLEL DO
	487	DO i = nxl, nxr
	488	DO j = nys, nyn
	489	DO k = nzb+1, nzt
	490	tend(k,j,i) = d(k,j,i)
	491	ENDDO
	492	ENDDO
	493	ENDDO
	494
	495	!
	496	!-- Bottom boundary:
	497	!-- This condition is only required for internal output. The pressure
	498	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	499	IF ( ibc_p_b == 1 ) THEN
	500	!
	501	!-- Neumann (dp/dz = 0)
	502	!$OMP PARALLEL DO
[667]	503	DO i = nxlg, nxrg
	504	DO j = nysg, nyng
[1]	505	tend(nzb_s_inner(j,i),j,i) = tend(nzb_s_inner(j,i)+1,j,i)
	506	ENDDO
	507	ENDDO
	508
	509	ELSE
	510	!
	511	!-- Dirichlet
	512	!$OMP PARALLEL DO
[667]	513	DO i = nxlg, nxrg
	514	DO j = nysg, nyng
[1342]	515	tend(nzb_s_inner(j,i),j,i) = 0.0_wp
[1]	516	ENDDO
	517	ENDDO
	518
	519	ENDIF
	520
	521	!
	522	!-- Top boundary
	523	IF ( ibc_p_t == 1 ) THEN
	524	!
	525	!-- Neumann
	526	!$OMP PARALLEL DO
[667]	527	DO i = nxlg, nxrg
	528	DO j = nysg, nyng
[1]	529	tend(nzt+1,j,i) = tend(nzt,j,i)
	530	ENDDO
	531	ENDDO
	532
	533	ELSE
	534	!
	535	!-- Dirichlet
	536	!$OMP PARALLEL DO
[667]	537	DO i = nxlg, nxrg
	538	DO j = nysg, nyng
[1342]	539	tend(nzt+1,j,i) = 0.0_wp
[1]	540	ENDDO
	541	ENDDO
	542
	543	ENDIF
	544
	545	!
	546	!-- Exchange boundaries for p
[667]	547	CALL exchange_horiz( tend, nbgp )
[1]	548
	549	ELSEIF ( psolver == 'sor' ) THEN
	550
	551	!
	552	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	553	!-- scheme
[707]	554	CALL sor( d, ddzu_pres, ddzw, p_loc )
	555	tend = p_loc
[1]	556
[1575]	557	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	558
	559	!
	560	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[667]	561	!-- array tend is used to store the residuals, logical exchange_mg is used
	562	!-- to discern data exchange in multigrid ( 1 ghostpoint ) and normal grid
	563	!-- ( nbgp ghost points ).
[778]	564
	565	!-- If the number of grid points of the gathered grid, which is collected
	566	!-- on PE0, is larger than the number of grid points of an PE, than array
	567	!-- tend will be enlarged.
	568	IF ( gathered_size > subdomain_size ) THEN
	569	DEALLOCATE( tend )
	570	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	571	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	572	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	573	mg_switch_to_pe0_level)+1) )
	574	ENDIF
	575
[1575]	576	IF ( psolver == 'multigrid' ) THEN
	577	CALL poismg( tend )
	578	ELSE
[1931]	579	CALL poismg_noopt( tend )
[1575]	580	ENDIF
[707]	581
[778]	582	IF ( gathered_size > subdomain_size ) THEN
	583	DEALLOCATE( tend )
	584	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	585	ENDIF
	586
[1]	587	!
	588	!-- Restore perturbation pressure on tend because this array is used
	589	!-- further below to correct the velocity fields
[707]	590	DO i = nxl-1, nxr+1
	591	DO j = nys-1, nyn+1
	592	DO k = nzb, nzt+1
	593	tend(k,j,i) = p_loc(k,j,i)
	594	ENDDO
	595	ENDDO
	596	ENDDO
[667]	597
[1]	598	ENDIF
	599
	600	!
[707]	601	!-- Store perturbation pressure on array p, used for pressure data output.
	602	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	603	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	604	!$OMP PARALLEL PRIVATE (i,j,k)
	605	!$OMP DO
	606	DO i = nxl-1, nxr+1
	607	DO j = nys-1, nyn+1
	608	DO k = nzb, nzt+1
	609	p(k,j,i) = tend(k,j,i) * &
[1929]	610	weight_substep_l
[673]	611	ENDDO
[1]	612	ENDDO
[707]	613	ENDDO
	614	!$OMP END PARALLEL
	615
[1762]	616	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	617	!$OMP PARALLEL PRIVATE (i,j,k)
	618	!$OMP DO
	619	DO i = nxl-1, nxr+1
	620	DO j = nys-1, nyn+1
	621	DO k = nzb, nzt+1
	622	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
[1929]	623	weight_substep_l
[673]	624	ENDDO
	625	ENDDO
[707]	626	ENDDO
	627	!$OMP END PARALLEL
	628
	629	ENDIF
[673]	630
[707]	631	!
	632	!-- SOR-method needs ghost layers for the next timestep
	633	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	634
[1]	635	!
	636	!-- Correction of the provisional velocities with the current perturbation
	637	!-- pressure just computed
[709]	638	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	639	volume_flow_l(1) = 0.0_wp
	640	volume_flow_l(2) = 0.0_wp
[1]	641	ENDIF
[707]	642
[1]	643	!$OMP PARALLEL PRIVATE (i,j,k)
	644	!$OMP DO
[673]	645	DO i = nxl, nxr
[1]	646	DO j = nys, nyn
[2118]	647
[1113]	648	DO k = 1, nzt
	649	IF ( k > nzb_w_inner(j,i) ) THEN
	650	w(k,j,i) = w(k,j,i) - dt_3d * &
	651	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) * &
[1918]	652	weight_pres_l
[1113]	653	ENDIF
[1]	654	ENDDO
[2118]	655
[1113]	656	DO k = 1, nzt
	657	IF ( k > nzb_u_inner(j,i) ) THEN
	658	u(k,j,i) = u(k,j,i) - dt_3d * &
	659	( tend(k,j,i) - tend(k,j,i-1) ) * ddx * &
[1918]	660	weight_pres_l
[1113]	661	ENDIF
[1]	662	ENDDO
[2118]	663
[1113]	664	DO k = 1, nzt
	665	IF ( k > nzb_v_inner(j,i) ) THEN
	666	v(k,j,i) = v(k,j,i) - dt_3d * &
	667	( tend(k,j,i) - tend(k,j-1,i) ) * ddy * &
[1918]	668	weight_pres_l
[1113]	669	ENDIF
[673]	670	ENDDO
[1]	671
	672	ENDDO
	673	ENDDO
	674	!$OMP END PARALLEL
[1113]	675
	676	!
	677	!-- Sum up the volume flow through the right and north boundary
	678	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
	679	nxr == nx ) THEN
	680
	681	!$OMP PARALLEL PRIVATE (j,k)
	682	!$OMP DO
	683	DO j = nys, nyn
	684	!$OMP CRITICAL
[1845]	685	DO k = nzb_u_inner(j,nx) + 1, nzt
[1113]	686	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nx) * dzw(k)
	687	ENDDO
	688	!$OMP END CRITICAL
	689	ENDDO
	690	!$OMP END PARALLEL
	691
	692	ENDIF
	693
	694	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
	695	nyn == ny ) THEN
	696
	697	!$OMP PARALLEL PRIVATE (i,k)
	698	!$OMP DO
	699	DO i = nxl, nxr
	700	!$OMP CRITICAL
[1845]	701	DO k = nzb_v_inner(ny,i) + 1, nzt
[1113]	702	volume_flow_l(2) = volume_flow_l(2) + v(k,ny,i) * dzw(k)
	703	ENDDO
	704	!$OMP END CRITICAL
	705	ENDDO
	706	!$OMP END PARALLEL
	707
	708	ENDIF
[673]	709
[1]	710	!
	711	!-- Conserve the volume flow
[707]	712	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	713
	714	#if defined( __parallel )
[622]	715	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	716	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	717	MPI_SUM, comm2d, ierr )
	718	#else
	719	volume_flow = volume_flow_l
	720	#endif
	721
[1799]	722	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	723	volume_flow_area(1:2)
[1]	724
	725	!$OMP PARALLEL PRIVATE (i,j,k)
	726	!$OMP DO
	727	DO i = nxl, nxr
	728	DO j = nys, nyn
[667]	729	DO k = nzb_u_inner(j,i) + 1, nzt
	730	u(k,j,i) = u(k,j,i) + volume_flow_offset(1)
[719]	731	ENDDO
[1845]	732	DO k = nzb_v_inner(j,i) + 1, nzt
[667]	733	v(k,j,i) = v(k,j,i) + volume_flow_offset(2)
	734	ENDDO
[1]	735	ENDDO
	736	ENDDO
[667]	737
[1]	738	!$OMP END PARALLEL
	739
	740	ENDIF
	741
	742	!
	743	!-- Exchange of boundaries for the velocities
[667]	744	CALL exchange_horiz( u, nbgp )
	745	CALL exchange_horiz( v, nbgp )
	746	CALL exchange_horiz( w, nbgp )
[1]	747
	748	!
	749	!-- Compute the divergence of the corrected velocity field,
[1908]	750	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	751	!-- only at last Runge-Kutta step.
[1918]	752	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	753	intermediate_timestep_count == 0 ) THEN
[1908]	754	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	755	sums_divnew_l = 0.0_wp
[1]	756
	757	!
[1908]	758	!-- d must be reset to zero because it can contain nonzero values below the
	759	!-- topography
	760	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	761
[1908]	762	localsum = 0.0_wp
	763	threadsum = 0.0_wp
[1]	764
[1908]	765	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
[2073]	766	#if defined( __ibm )
[1908]	767	!$OMP DO SCHEDULE( STATIC )
	768	DO i = nxl, nxr
	769	DO j = nys, nyn
	770	DO k = nzb_s_inner(j,i)+1, nzt
[2037]	771	d(k,j,i) = ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	772	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	773	( w(k,j,i) * rho_air_zw(k) - &
	774	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k)
[1908]	775	ENDDO
	776	DO k = nzb+1, nzt
	777	threadsum = threadsum + ABS( d(k,j,i) )
	778	ENDDO
[1]	779	ENDDO
	780	ENDDO
	781	#else
[2073]	782	!$OMP DO SCHEDULE( STATIC )
[1908]	783	DO i = nxl, nxr
	784	DO j = nys, nyn
	785	DO k = 1, nzt
[2037]	786	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	787	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	788	( w(k,j,i) * rho_air_zw(k) - &
	789	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	790	) * rflags_s_inner(k,j,i)
[1908]	791	ENDDO
[1113]	792	ENDDO
	793	ENDDO
	794	!
[1908]	795	!-- Compute possible PE-sum of divergences for flow_statistics
[2073]	796	!$OMP DO SCHEDULE( STATIC )
[1908]	797	DO i = nxl, nxr
	798	DO j = nys, nyn
	799	DO k = nzb+1, nzt
	800	threadsum = threadsum + ABS( d(k,j,i) )
	801	ENDDO
[1]	802	ENDDO
	803	ENDDO
	804	#endif
[667]	805
[1908]	806	localsum = localsum + threadsum
	807	!$OMP END PARALLEL
[1]	808
	809	!
[1908]	810	!-- For completeness, set the divergence sum of all statistic regions to those
	811	!-- of the total domain
	812	sums_divnew_l(0:statistic_regions) = localsum
[1]	813
[1908]	814	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	815
[1908]	816	ENDIF
	817
[1]	818	CALL cpu_log( log_point(8), 'pres', 'stop' )
	819
	820
	821	END SUBROUTINE pres

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