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source: palm/trunk/SOURCE/pres.f90 @ 2834

Last change on this file since 2834 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
File size: 30.6 KB

Rev	Line
[1682]	1	!> @file pres.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	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	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1212]	21	! ------------------
[1932]	22	!
[2233]	23	!
[1919]	24	! Former revisions:
	25	! -----------------
[2716]	26	! Id: pres.f90 2696 2017-12-14 17:12:51Z kanani $
	27	! Corrected "Former revisions" section
[2696]	28	!
[2716]	29	! 2696 2017-12-14 17:12:51Z kanani
	30	! Change in file header (GPL part)
	31	! poismg_noopt modularized (MS)
	32	!
[2696]	33	! 2298 2017-06-29 09:28:18Z raasch
[2298]	34	! comment changed + some formatting
	35	!
	36	! 2233 2017-05-30 18:08:54Z suehring
[1919]	37	!
[2233]	38	! 2232 2017-05-30 17:47:52Z suehring
	39	! Adjustments to new topography and surface concept
	40	!
[2119]	41	! 2118 2017-01-17 16:38:49Z raasch
	42	! OpenACC directives and related code removed
	43	!
[2074]	44	! 2073 2016-11-30 14:34:05Z raasch
	45	! openmp bugfix for calculation of new divergence
	46	!
[2038]	47	! 2037 2016-10-26 11:15:40Z knoop
	48	! Anelastic approximation implemented
	49	!
[2001]	50	! 2000 2016-08-20 18:09:15Z knoop
	51	! Forced header and separation lines into 80 columns
	52	!
[1933]	53	! 1932 2016-06-10 12:09:21Z suehring
	54	! Initial version of purely vertical nesting introduced.
	55	!
[1932]	56	! 1931 2016-06-10 12:06:59Z suehring
	57	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
	58	!
[1930]	59	! 1929 2016-06-09 16:25:25Z suehring
	60	! Bugfix: weight_substep for initial call, replace by local variable
	61	!
[1919]	62	! 1918 2016-05-27 14:35:57Z raasch
[1918]	63	! sum of divergence is also calculated when pres is called before the initial
	64	! first time step,
	65	! stearing is modified by using intermediate_timestep_count = 0 in order to
	66	! determine if pres is called before the first initial timestep,
	67	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
	68	! mean vertical velocity is also removed for the first time step
	69	! bugfix for calculating divergences
[1321]	70	!
[1909]	71	! 1908 2016-05-25 17:22:32Z suehring
	72	! New divergence for output into RUN_CONTROL file is calculated only at last
	73	! Runge-Kutta step
	74	!
[1846]	75	! 1845 2016-04-08 08:29:13Z raasch
	76	! nzb_2d replace by nzb_u\|v_inner
	77	!
[1800]	78	! 1799 2016-04-05 08:35:55Z gronemeier
	79	! Bugfix: excluded third dimension from horizontal volume flow calculation
	80	!
[1763]	81	! 1762 2016-02-25 12:31:13Z hellstea
	82	! Introduction of nested domain feature
	83	!
[1683]	84	! 1682 2015-10-07 23:56:08Z knoop
	85	! Code annotations made doxygen readable
	86	!
[1576]	87	! 1575 2015-03-27 09:56:27Z raasch
	88	! poismg_fast + respective module added, adjustments for psolver-queries
	89	!
[1343]	90	! 1342 2014-03-26 17:04:47Z kanani
	91	! REAL constants defined as wp-kind
	92	!
[1321]	93	! 1320 2014-03-20 08:40:49Z raasch
[1320]	94	! ONLY-attribute added to USE-statements,
	95	! kind-parameters added to all INTEGER and REAL declaration statements,
	96	! kinds are defined in new module kinds,
	97	! old module precision_kind is removed,
	98	! revision history before 2012 removed,
	99	! comment fields (!:) to be used for variable explanations added to
	100	! all variable declaration statements
[708]	101	!
[1319]	102	! 1318 2014-03-17 13:35:16Z raasch
	103	! module interfaces removed
	104	!
[1307]	105	! 1306 2014-03-13 14:30:59Z raasch
	106	! second argument removed from routine poisfft
	107	!
[1258]	108	! 1257 2013-11-08 15:18:40Z raasch
	109	! openacc loop and loop vector clauses removed, independent clauses added,
	110	! end parallel replaced by end parallel loop
	111	!
[1222]	112	! 1221 2013-09-10 08:59:13Z raasch
	113	! openACC porting of reduction operations, loops for calculating d are
	114	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	115	!
[1213]	116	! 1212 2013-08-15 08:46:27Z raasch
	117	! call of poisfft_hybrid removed
	118	!
[1118]	119	! 1117 2013-03-27 11:15:36Z suehring
	120	! Bugfix in OpenMP parallelization.
	121	!
[1114]	122	! 1113 2013-03-10 02:48:14Z raasch
	123	! GPU-porting of several loops, some loops rearranged
	124	!
[1112]	125	! 1111 2013-03-08 23:54:10Z
	126	! openACC statements added,
	127	! ibc_p_b = 2 removed
	128	!
[1093]	129	! 1092 2013-02-02 11:24:22Z raasch
	130	! unused variables removed
	131	!
[1037]	132	! 1036 2012-10-22 13:43:42Z raasch
	133	! code put under GPL (PALM 3.9)
	134	!
[1004]	135	! 1003 2012-09-14 14:35:53Z raasch
	136	! adjustment of array tend for cases with unequal subdomain sizes removed
	137	!
[1]	138	! Revision 1.1 1997/07/24 11:24:44 raasch
	139	! Initial revision
	140	!
	141	!
	142	! Description:
	143	! ------------
[1682]	144	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	145	!> equation for the perturbation pressure. Compute the final velocities using
	146	!> this perturbation pressure. Compute the remaining divergence.
[1]	147	!------------------------------------------------------------------------------!
[1682]	148	SUBROUTINE pres
	149
[1]	150
[1320]	151	USE arrays_3d, &
[2037]	152	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
	153	tend, u, v, w
[1320]	154
	155	USE control_parameters, &
	156	ONLY: bc_lr_cyc, bc_ns_cyc, conserve_volume_flow, dt_3d, &
	157	gathered_size, ibc_p_b, ibc_p_t, intermediate_timestep_count, &
[1908]	158	intermediate_timestep_count_max, mg_switch_to_pe0_level, &
[2118]	159	nest_domain, outflow_l, outflow_n, outflow_r, &
[1918]	160	outflow_s, psolver, subdomain_size, topography, volume_flow, &
	161	volume_flow_area, volume_flow_initial
[1320]	162
	163	USE cpulog, &
	164	ONLY: cpu_log, log_point, log_point_s
	165
	166	USE grid_variables, &
	167	ONLY: ddx, ddy
	168
	169	USE indices, &
	170	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
[2232]	171	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzt, nzt_mg, &
	172	wall_flags_0
[1320]	173
	174	USE kinds
	175
[1]	176	USE pegrid
[1933]	177
	178	USE pmc_interface, &
	179	ONLY: nesting_mode
[1]	180
[1320]	181	USE poisfft_mod, &
	182	ONLY: poisfft
	183
[1575]	184	USE poismg_mod
	185
[2696]	186	USE poismg_noopt_mod
	187
[1320]	188	USE statistics, &
	189	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	190	weight_substep
	191
[2232]	192	USE surface_mod, &
	193	ONLY : bc_h
	194
[1]	195	IMPLICIT NONE
	196
[1682]	197	INTEGER(iwp) :: i !<
	198	INTEGER(iwp) :: j !<
	199	INTEGER(iwp) :: k !<
[2232]	200	INTEGER(iwp) :: m !<
[1]	201
[1682]	202	REAL(wp) :: ddt_3d !<
[1918]	203	REAL(wp) :: d_weight_pres !<
[1682]	204	REAL(wp) :: localsum !<
	205	REAL(wp) :: threadsum !<
[1918]	206	REAL(wp) :: weight_pres_l !<
[1929]	207	REAL(wp) :: weight_substep_l !<
[1]	208
[1762]	209	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	210	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	211	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	212	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	213
[1933]	214	LOGICAL :: nest_domain_nvn !<
[1]	215
[1933]	216
[1]	217	CALL cpu_log( log_point(8), 'pres', 'start' )
	218
[85]	219
[1918]	220	!
	221	!-- Calculate quantities to be used locally
[1342]	222	ddt_3d = 1.0_wp / dt_3d
[1918]	223	IF ( intermediate_timestep_count == 0 ) THEN
	224	!
	225	!-- If pres is called before initial time step
[1929]	226	weight_pres_l = 1.0_wp
	227	d_weight_pres = 1.0_wp
	228	weight_substep_l = 1.0_wp
[1918]	229	ELSE
[1929]	230	weight_pres_l = weight_pres(intermediate_timestep_count)
	231	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	232	weight_substep_l = weight_substep(intermediate_timestep_count)
[1918]	233	ENDIF
[85]	234
[1]	235	!
[707]	236	!-- Multigrid method expects array d to have one ghost layer.
	237	!--
[1575]	238	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	239
[1]	240	DEALLOCATE( d )
[667]	241	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	242
	243	!
	244	!-- Since p is later used to hold the weighted average of the substeps, it
	245	!-- cannot be used in the iterative solver. Therefore, its initial value is
	246	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	247	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	248	DO i = nxl-1, nxr+1
	249	DO j = nys-1, nyn+1
	250	DO k = nzb, nzt+1
	251	p_loc(k,j,i) = p(k,j,i)
	252	ENDDO
	253	ENDDO
	254	ENDDO
[667]	255	ENDIF
	256
[1918]	257	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	258
	259	!
	260	!-- Since p is later used to hold the weighted average of the substeps, it
	261	!-- cannot be used in the iterative solver. Therefore, its initial value is
	262	!-- stored on p_loc, which is then iteratively advanced in every substep.
	263	p_loc = p
	264
[1]	265	ENDIF
	266
	267	!
[75]	268	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	269	!-- boundary conditions
[106]	270	!-- WARNING: so far, this conservation does not work at the left/south
	271	!-- boundary if the topography at the inflow differs from that at the
	272	!-- outflow! For this case, volume_flow_area needs adjustment!
	273	!
	274	!-- Left/right
[709]	275	IF ( conserve_volume_flow .AND. ( outflow_l .OR. outflow_r ) ) THEN
[680]	276
[1342]	277	volume_flow(1) = 0.0_wp
	278	volume_flow_l(1) = 0.0_wp
[106]	279
	280	IF ( outflow_l ) THEN
	281	i = 0
	282	ELSEIF ( outflow_r ) THEN
	283	i = nx+1
	284	ENDIF
	285
	286	DO j = nys, nyn
	287	!
	288	!-- Sum up the volume flow through the south/north boundary
[2232]	289	DO k = nzb+1, nzt
	290	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k) &
	291	* MERGE( 1.0_wp, 0.0_wp, &
	292	BTEST( wall_flags_0(k,j,i), 1 ) &
	293	)
[106]	294	ENDDO
	295	ENDDO
	296
	297	#if defined( __parallel )
[680]	298	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	299	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	300	MPI_SUM, comm1dy, ierr )
	301	#else
	302	volume_flow = volume_flow_l
	303	#endif
[709]	304	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	305	/ volume_flow_area(1)
	306
[667]	307	DO j = nysg, nyng
[2232]	308	DO k = nzb+1, nzt
	309	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	310	* MERGE( 1.0_wp, 0.0_wp, &
	311	BTEST( wall_flags_0(k,j,i), 1 ) &
	312	)
[106]	313	ENDDO
	314	ENDDO
	315
	316	ENDIF
	317
	318	!
	319	!-- South/north
[709]	320	IF ( conserve_volume_flow .AND. ( outflow_n .OR. outflow_s ) ) THEN
[106]	321
[1342]	322	volume_flow(2) = 0.0_wp
	323	volume_flow_l(2) = 0.0_wp
[75]	324
[106]	325	IF ( outflow_s ) THEN
	326	j = 0
	327	ELSEIF ( outflow_n ) THEN
[75]	328	j = ny+1
[106]	329	ENDIF
	330
	331	DO i = nxl, nxr
[75]	332	!
[106]	333	!-- Sum up the volume flow through the south/north boundary
[2232]	334	DO k = nzb+1, nzt
	335	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k) &
	336	* MERGE( 1.0_wp, 0.0_wp, &
	337	BTEST( wall_flags_0(k,j,i), 2 ) &
	338	)
[75]	339	ENDDO
[106]	340	ENDDO
	341
[75]	342	#if defined( __parallel )
[680]	343	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	344	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	345	MPI_SUM, comm1dx, ierr )
	346	#else
	347	volume_flow = volume_flow_l
	348	#endif
	349	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	350	/ volume_flow_area(2)
[75]	351
[667]	352	DO i = nxlg, nxrg
[2232]	353	DO k = nzb+1, nzt
	354	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	355	* MERGE( 1.0_wp, 0.0_wp, &
	356	BTEST( wall_flags_0(k,j,i), 2 ) &
	357	)
[75]	358	ENDDO
[106]	359	ENDDO
[75]	360
	361	ENDIF
	362
[76]	363	!
[1762]	364	!-- Remove mean vertical velocity in case that Neumann conditions are
[1933]	365	!-- used both at bottom and top boundary, and if not a nested domain in a
	366	!-- normal nesting run. In case of vertical nesting, this must be done.
	367	!-- Therefore an auxiliary logical variable nest_domain_nvn is used here, and
	368	!-- nvn stands for non-vertical nesting.
[1918]	369	!-- This cannot be done before the first initial time step because ngp_2dh_outer
	370	!-- is not yet known then.
[1933]	371	nest_domain_nvn = nest_domain
	372	IF ( nest_domain .AND. nesting_mode == 'vertical' ) THEN
	373	nest_domain_nvn = .FALSE.
	374	ENDIF
	375
	376	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. &
	377	.NOT. nest_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
[1918]	378	THEN
	379	w_l = 0.0_wp; w_l_l = 0.0_wp
	380	DO i = nxl, nxr
	381	DO j = nys, nyn
[2232]	382	DO k = nzb+1, nzt
	383	w_l_l(k) = w_l_l(k) + w(k,j,i) &
	384	* MERGE( 1.0_wp, 0.0_wp, &
	385	BTEST( wall_flags_0(k,j,i), 3 ) &
	386	)
[76]	387	ENDDO
	388	ENDDO
[1918]	389	ENDDO
[76]	390	#if defined( __parallel )
[1918]	391	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	392	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
	393	comm2d, ierr )
[76]	394	#else
[1918]	395	w_l = w_l_l
[76]	396	#endif
[1918]	397	DO k = 1, nzt
	398	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	399	ENDDO
	400	DO i = nxlg, nxrg
	401	DO j = nysg, nyng
[2232]	402	DO k = nzb+1, nzt
	403	w(k,j,i) = w(k,j,i) - w_l(k) &
	404	* MERGE( 1.0_wp, 0.0_wp, &
	405	BTEST( wall_flags_0(k,j,i), 3 ) &
	406	)
[76]	407	ENDDO
	408	ENDDO
[1918]	409	ENDDO
[76]	410	ENDIF
[75]	411
	412	!
[1]	413	!-- Compute the divergence of the provisional velocity field.
	414	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	415
[1575]	416	IF ( psolver(1:9) == 'multigrid' ) THEN
[2232]	417	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[1]	418	DO i = nxl-1, nxr+1
	419	DO j = nys-1, nyn+1
	420	DO k = nzb, nzt+1
[1342]	421	d(k,j,i) = 0.0_wp
[1]	422	ENDDO
	423	ENDDO
	424	ENDDO
	425	ELSE
[2232]	426	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[1003]	427	DO i = nxl, nxr
	428	DO j = nys, nyn
	429	DO k = nzb+1, nzt
[1342]	430	d(k,j,i) = 0.0_wp
[1]	431	ENDDO
	432	ENDDO
	433	ENDDO
	434	ENDIF
	435
[1342]	436	localsum = 0.0_wp
	437	threadsum = 0.0_wp
[1]	438
	439	#if defined( __ibm )
	440	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	441	!$OMP DO SCHEDULE( STATIC )
	442	DO i = nxl, nxr
	443	DO j = nys, nyn
[2232]	444	DO k = nzb+1, nzt
[2037]	445	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	446	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	447	( w(k,j,i) * rho_air_zw(k) - &
	448	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	449	) * ddt_3d * d_weight_pres &
	450	* MERGE( 1.0_wp, 0.0_wp, &
	451	BTEST( wall_flags_0(k,j,i), 0 ) &
	452	)
[1]	453	ENDDO
	454	!
	455	!-- Compute possible PE-sum of divergences for flow_statistics
[2232]	456	DO k = nzb+1, nzt
	457	threadsum = threadsum + ABS( d(k,j,i) ) &
	458	* MERGE( 1.0_wp, 0.0_wp, &
	459	BTEST( wall_flags_0(k,j,i), 0 ) &
	460	)
[1]	461	ENDDO
	462
	463	ENDDO
	464	ENDDO
	465
[1918]	466	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	467	intermediate_timestep_count == 0 ) THEN
	468	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	469	ENDIF
[1]	470	!$OMP END PARALLEL
	471	#else
	472
[1111]	473	!$OMP PARALLEL PRIVATE (i,j,k)
	474	!$OMP DO SCHEDULE( STATIC )
	475	DO i = nxl, nxr
	476	DO j = nys, nyn
	477	DO k = 1, nzt
[2037]	478	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	479	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	480	( w(k,j,i) * rho_air_zw(k) - &
	481	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	482	) * ddt_3d * d_weight_pres &
	483	* MERGE( 1.0_wp, 0.0_wp, &
	484	BTEST( wall_flags_0(k,j,i), 0 ) &
	485	)
[1]	486	ENDDO
	487	ENDDO
[1111]	488	ENDDO
	489	!$OMP END PARALLEL
[1]	490
	491	!
[1908]	492	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	493	!-- computation only at last Runge-Kutta substep.
[1918]	494	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	495	intermediate_timestep_count == 0 ) THEN
[1908]	496	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	497	!$OMP DO SCHEDULE( STATIC )
	498	DO i = nxl, nxr
	499	DO j = nys, nyn
	500	DO k = nzb+1, nzt
	501	threadsum = threadsum + ABS( d(k,j,i) )
	502	ENDDO
[1]	503	ENDDO
	504	ENDDO
[1918]	505	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	506	!$OMP END PARALLEL
	507	ENDIF
[1]	508	#endif
	509
	510	!
	511	!-- For completeness, set the divergence sum of all statistic regions to those
	512	!-- of the total domain
[1918]	513	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	514	intermediate_timestep_count == 0 ) THEN
[1908]	515	sums_divold_l(0:statistic_regions) = localsum
[1918]	516	ENDIF
[1]	517
	518	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	519
	520	!
	521	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	522	IF ( psolver == 'poisfft' ) THEN
[1]	523
	524	!
	525	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	526	CALL poisfft( d )
[1212]	527
[1]	528	!
	529	!-- Store computed perturbation pressure and set boundary condition in
	530	!-- z-direction
[2232]	531	!$OMP PARALLEL DO PRIVATE (i,j,k)
[1]	532	DO i = nxl, nxr
	533	DO j = nys, nyn
	534	DO k = nzb+1, nzt
	535	tend(k,j,i) = d(k,j,i)
	536	ENDDO
	537	ENDDO
	538	ENDDO
	539
	540	!
	541	!-- Bottom boundary:
	542	!-- This condition is only required for internal output. The pressure
	543	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	544	IF ( ibc_p_b == 1 ) THEN
	545	!
[2232]	546	!-- Neumann (dp/dz = 0). Using surfae data type, first for non-natural
	547	!-- surfaces, then for natural and urban surfaces
	548	!-- Upward facing
	549	!$OMP PARALLEL DO PRIVATE( i, j, k )
	550	DO m = 1, bc_h(0)%ns
[2298]	551	i = bc_h(0)%i(m)
	552	j = bc_h(0)%j(m)
	553	k = bc_h(0)%k(m)
[2232]	554	tend(k-1,j,i) = tend(k,j,i)
[1]	555	ENDDO
[2232]	556	!
	557	!-- Downward facing
	558	!$OMP PARALLEL DO PRIVATE( i, j, k )
	559	DO m = 1, bc_h(1)%ns
[2298]	560	i = bc_h(1)%i(m)
	561	j = bc_h(1)%j(m)
	562	k = bc_h(1)%k(m)
[2232]	563	tend(k+1,j,i) = tend(k,j,i)
	564	ENDDO
[1]	565
	566	ELSE
	567	!
[2232]	568	!-- Dirichlet. Using surface data type, first for non-natural
	569	!-- surfaces, then for natural and urban surfaces
	570	!-- Upward facing
	571	!$OMP PARALLEL DO PRIVATE( i, j, k )
	572	DO m = 1, bc_h(0)%ns
[2298]	573	i = bc_h(0)%i(m)
	574	j = bc_h(0)%j(m)
	575	k = bc_h(0)%k(m)
[2232]	576	tend(k-1,j,i) = 0.0_wp
[1]	577	ENDDO
[2232]	578	!
	579	!-- Downward facing
	580	!$OMP PARALLEL DO PRIVATE( i, j, k )
	581	DO m = 1, bc_h(1)%ns
[2298]	582	i = bc_h(1)%i(m)
	583	j = bc_h(1)%j(m)
	584	k = bc_h(1)%k(m)
[2232]	585	tend(k+1,j,i) = 0.0_wp
	586	ENDDO
[1]	587
	588	ENDIF
	589
	590	!
	591	!-- Top boundary
	592	IF ( ibc_p_t == 1 ) THEN
	593	!
	594	!-- Neumann
[2232]	595	!$OMP PARALLEL DO PRIVATE (i,j,k)
[667]	596	DO i = nxlg, nxrg
	597	DO j = nysg, nyng
[1]	598	tend(nzt+1,j,i) = tend(nzt,j,i)
	599	ENDDO
	600	ENDDO
	601
	602	ELSE
	603	!
	604	!-- Dirichlet
[2232]	605	!$OMP PARALLEL DO PRIVATE (i,j,k)
[667]	606	DO i = nxlg, nxrg
	607	DO j = nysg, nyng
[1342]	608	tend(nzt+1,j,i) = 0.0_wp
[1]	609	ENDDO
	610	ENDDO
	611
	612	ENDIF
	613
	614	!
	615	!-- Exchange boundaries for p
[667]	616	CALL exchange_horiz( tend, nbgp )
[1]	617
	618	ELSEIF ( psolver == 'sor' ) THEN
	619
	620	!
	621	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	622	!-- scheme
[707]	623	CALL sor( d, ddzu_pres, ddzw, p_loc )
	624	tend = p_loc
[1]	625
[1575]	626	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	627
	628	!
	629	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[2298]	630	!-- array tend is used to store the residuals.
[778]	631
	632	!-- If the number of grid points of the gathered grid, which is collected
	633	!-- on PE0, is larger than the number of grid points of an PE, than array
	634	!-- tend will be enlarged.
	635	IF ( gathered_size > subdomain_size ) THEN
	636	DEALLOCATE( tend )
	637	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	638	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	639	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	640	mg_switch_to_pe0_level)+1) )
	641	ENDIF
	642
[1575]	643	IF ( psolver == 'multigrid' ) THEN
	644	CALL poismg( tend )
	645	ELSE
[1931]	646	CALL poismg_noopt( tend )
[1575]	647	ENDIF
[707]	648
[778]	649	IF ( gathered_size > subdomain_size ) THEN
	650	DEALLOCATE( tend )
	651	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	652	ENDIF
	653
[1]	654	!
	655	!-- Restore perturbation pressure on tend because this array is used
	656	!-- further below to correct the velocity fields
[707]	657	DO i = nxl-1, nxr+1
	658	DO j = nys-1, nyn+1
	659	DO k = nzb, nzt+1
	660	tend(k,j,i) = p_loc(k,j,i)
	661	ENDDO
	662	ENDDO
	663	ENDDO
[667]	664
[1]	665	ENDIF
	666
	667	!
[707]	668	!-- Store perturbation pressure on array p, used for pressure data output.
	669	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	670	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	671	!$OMP PARALLEL PRIVATE (i,j,k)
	672	!$OMP DO
	673	DO i = nxl-1, nxr+1
	674	DO j = nys-1, nyn+1
	675	DO k = nzb, nzt+1
	676	p(k,j,i) = tend(k,j,i) * &
[1929]	677	weight_substep_l
[673]	678	ENDDO
[1]	679	ENDDO
[707]	680	ENDDO
	681	!$OMP END PARALLEL
	682
[1762]	683	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	684	!$OMP PARALLEL PRIVATE (i,j,k)
	685	!$OMP DO
	686	DO i = nxl-1, nxr+1
	687	DO j = nys-1, nyn+1
	688	DO k = nzb, nzt+1
	689	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
[1929]	690	weight_substep_l
[673]	691	ENDDO
	692	ENDDO
[707]	693	ENDDO
	694	!$OMP END PARALLEL
	695
	696	ENDIF
[673]	697
[707]	698	!
	699	!-- SOR-method needs ghost layers for the next timestep
	700	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	701
[1]	702	!
	703	!-- Correction of the provisional velocities with the current perturbation
	704	!-- pressure just computed
[709]	705	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	706	volume_flow_l(1) = 0.0_wp
	707	volume_flow_l(2) = 0.0_wp
[1]	708	ENDIF
[707]	709
[1]	710	!$OMP PARALLEL PRIVATE (i,j,k)
	711	!$OMP DO
[673]	712	DO i = nxl, nxr
[1]	713	DO j = nys, nyn
[2118]	714
[2232]	715	DO k = nzb+1, nzt
	716	w(k,j,i) = w(k,j,i) - dt_3d * &
	717	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) &
	718	* weight_pres_l &
	719	* MERGE( 1.0_wp, 0.0_wp, &
	720	BTEST( wall_flags_0(k,j,i), 3 ) &
	721	)
[1]	722	ENDDO
[2118]	723
[2232]	724	DO k = nzb+1, nzt
	725	u(k,j,i) = u(k,j,i) - dt_3d * &
	726	( tend(k,j,i) - tend(k,j,i-1) ) * ddx &
	727	* weight_pres_l &
	728	* MERGE( 1.0_wp, 0.0_wp, &
	729	BTEST( wall_flags_0(k,j,i), 1 ) &
	730	)
[1]	731	ENDDO
[2118]	732
[2232]	733	DO k = nzb+1, nzt
	734	v(k,j,i) = v(k,j,i) - dt_3d * &
	735	( tend(k,j,i) - tend(k,j-1,i) ) * ddy &
	736	* weight_pres_l &
	737	* MERGE( 1.0_wp, 0.0_wp, &
	738	BTEST( wall_flags_0(k,j,i), 2 ) &
	739	)
[673]	740	ENDDO
[1]	741
	742	ENDDO
	743	ENDDO
	744	!$OMP END PARALLEL
[1113]	745
	746	!
	747	!-- Sum up the volume flow through the right and north boundary
[2232]	748	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
[1113]	749	nxr == nx ) THEN
	750
	751	!$OMP PARALLEL PRIVATE (j,k)
	752	!$OMP DO
	753	DO j = nys, nyn
	754	!$OMP CRITICAL
[2232]	755	DO k = nzb+1, nzt
	756	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nxr) * dzw(k) &
	757	* MERGE( 1.0_wp, 0.0_wp, &
	758	BTEST( wall_flags_0(k,j,nxr), 1 )&
	759	)
[1113]	760	ENDDO
	761	!$OMP END CRITICAL
	762	ENDDO
	763	!$OMP END PARALLEL
	764
	765	ENDIF
	766
[2232]	767	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
[1113]	768	nyn == ny ) THEN
	769
	770	!$OMP PARALLEL PRIVATE (i,k)
	771	!$OMP DO
	772	DO i = nxl, nxr
	773	!$OMP CRITICAL
[2232]	774	DO k = nzb+1, nzt
	775	volume_flow_l(2) = volume_flow_l(2) + v(k,nyn,i) * dzw(k) &
	776	* MERGE( 1.0_wp, 0.0_wp, &
	777	BTEST( wall_flags_0(k,nyn,i), 2 )&
	778	)
[1113]	779	ENDDO
	780	!$OMP END CRITICAL
	781	ENDDO
	782	!$OMP END PARALLEL
	783
	784	ENDIF
[673]	785
[1]	786	!
	787	!-- Conserve the volume flow
[707]	788	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	789
	790	#if defined( __parallel )
[622]	791	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	792	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	793	MPI_SUM, comm2d, ierr )
	794	#else
	795	volume_flow = volume_flow_l
	796	#endif
	797
[1799]	798	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	799	volume_flow_area(1:2)
[1]	800
	801	!$OMP PARALLEL PRIVATE (i,j,k)
	802	!$OMP DO
	803	DO i = nxl, nxr
	804	DO j = nys, nyn
[2232]	805	DO k = nzb+1, nzt
	806	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	807	* MERGE( 1.0_wp, 0.0_wp, &
	808	BTEST( wall_flags_0(k,j,i), 1 ) &
	809	)
[719]	810	ENDDO
[2232]	811	DO k = nzb+1, nzt
	812	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	813	* MERGE( 1.0_wp, 0.0_wp, &
	814	BTEST( wall_flags_0(k,j,i), 2 ) &
	815	)
[667]	816	ENDDO
[1]	817	ENDDO
	818	ENDDO
[667]	819
[1]	820	!$OMP END PARALLEL
	821
	822	ENDIF
	823
	824	!
	825	!-- Exchange of boundaries for the velocities
[667]	826	CALL exchange_horiz( u, nbgp )
	827	CALL exchange_horiz( v, nbgp )
	828	CALL exchange_horiz( w, nbgp )
[1]	829
	830	!
	831	!-- Compute the divergence of the corrected velocity field,
[1908]	832	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	833	!-- only at last Runge-Kutta step.
[1918]	834	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	835	intermediate_timestep_count == 0 ) THEN
[1908]	836	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	837	sums_divnew_l = 0.0_wp
[1]	838
	839	!
[1908]	840	!-- d must be reset to zero because it can contain nonzero values below the
	841	!-- topography
	842	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	843
[1908]	844	localsum = 0.0_wp
	845	threadsum = 0.0_wp
[1]	846
[1908]	847	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
[2073]	848	#if defined( __ibm )
[1908]	849	!$OMP DO SCHEDULE( STATIC )
	850	DO i = nxl, nxr
	851	DO j = nys, nyn
[2232]	852	DO k = nzb+1, nzt
	853	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	854	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	855	( w(k,j,i) * rho_air_zw(k) - &
	856	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	857	) * MERGE( 1.0_wp, 0.0_wp, &
	858	BTEST( wall_flags_0(k,j,i), 0 ) &
	859	)
[1908]	860	ENDDO
	861	DO k = nzb+1, nzt
	862	threadsum = threadsum + ABS( d(k,j,i) )
	863	ENDDO
[1]	864	ENDDO
	865	ENDDO
	866	#else
[2073]	867	!$OMP DO SCHEDULE( STATIC )
[1908]	868	DO i = nxl, nxr
	869	DO j = nys, nyn
[2232]	870	DO k = nzb+1, nzt
[2037]	871	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	872	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	873	( w(k,j,i) * rho_air_zw(k) - &
	874	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	875	) * MERGE( 1.0_wp, 0.0_wp, &
	876	BTEST( wall_flags_0(k,j,i), 0 ) &
	877	)
[1908]	878	ENDDO
[1113]	879	ENDDO
	880	ENDDO
	881	!
[1908]	882	!-- Compute possible PE-sum of divergences for flow_statistics
[2073]	883	!$OMP DO SCHEDULE( STATIC )
[1908]	884	DO i = nxl, nxr
	885	DO j = nys, nyn
	886	DO k = nzb+1, nzt
	887	threadsum = threadsum + ABS( d(k,j,i) )
	888	ENDDO
[1]	889	ENDDO
	890	ENDDO
	891	#endif
[667]	892
[1908]	893	localsum = localsum + threadsum
	894	!$OMP END PARALLEL
[1]	895
	896	!
[1908]	897	!-- For completeness, set the divergence sum of all statistic regions to those
	898	!-- of the total domain
	899	sums_divnew_l(0:statistic_regions) = localsum
[1]	900
[1908]	901	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	902
[1908]	903	ENDIF
	904
[1]	905	CALL cpu_log( log_point(8), 'pres', 'stop' )
	906
	907
	908	END SUBROUTINE pres

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