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source: palm/trunk/SOURCE/pres.f90 @ 3741

Last change on this file since 3741 was 3655, checked in by knoop, 6 years ago
Bugfix: made "unit" and "found" intend INOUT in module interface subroutines + automatic copyright update
Property svn:keywords set to `Id`
File size: 33.9 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	!
[3655]	17	! Copyright 1997-2019 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1212]	21	! ------------------
[1932]	22	!
[3183]	23	!
[1919]	24	! Former revisions:
	25	! -----------------
[3016]	26	! $Id: pres.f90 3655 2019-01-07 16:51:22Z hellstea $
[3634]	27	! OpenACC port for SPEC
	28	!
	29	! 3347 2018-10-15 14:21:08Z suehring
[3347]	30	! Bugfixes in offline nesting.
	31	! Add comment.
	32	!
	33	! 3341 2018-10-15 10:31:27Z suehring
[3183]	34	! Rename variables for boundary flags and nesting
	35	!
	36	! 3182 2018-07-27 13:36:03Z suehring
[3016]	37	! Dollar sign added before Id
	38	!
	39	! 2696 2017-12-14 17:12:51Z kanani
[3013]	40	! To avoid jumps while plotting w-profiles w level nzt+1 is set to w level nzt
	41	! after velocity modifications through the pressure solver were carried out
	42	!
	43	! 2696 2017-12-14 17:12:51Z kanani
[2716]	44	! Corrected "Former revisions" section
[2696]	45	!
[2716]	46	! 2696 2017-12-14 17:12:51Z kanani
	47	! Change in file header (GPL part)
	48	! poismg_noopt modularized (MS)
	49	!
[2696]	50	! 2298 2017-06-29 09:28:18Z raasch
[2298]	51	! comment changed + some formatting
	52	!
	53	! 2233 2017-05-30 18:08:54Z suehring
[1919]	54	!
[2233]	55	! 2232 2017-05-30 17:47:52Z suehring
	56	! Adjustments to new topography and surface concept
	57	!
[2119]	58	! 2118 2017-01-17 16:38:49Z raasch
	59	! OpenACC directives and related code removed
	60	!
[2074]	61	! 2073 2016-11-30 14:34:05Z raasch
	62	! openmp bugfix for calculation of new divergence
	63	!
[2038]	64	! 2037 2016-10-26 11:15:40Z knoop
	65	! Anelastic approximation implemented
	66	!
[2001]	67	! 2000 2016-08-20 18:09:15Z knoop
	68	! Forced header and separation lines into 80 columns
	69	!
[1933]	70	! 1932 2016-06-10 12:09:21Z suehring
	71	! Initial version of purely vertical nesting introduced.
	72	!
[1932]	73	! 1931 2016-06-10 12:06:59Z suehring
	74	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
	75	!
[1930]	76	! 1929 2016-06-09 16:25:25Z suehring
	77	! Bugfix: weight_substep for initial call, replace by local variable
	78	!
[1919]	79	! 1918 2016-05-27 14:35:57Z raasch
[1918]	80	! sum of divergence is also calculated when pres is called before the initial
	81	! first time step,
	82	! stearing is modified by using intermediate_timestep_count = 0 in order to
	83	! determine if pres is called before the first initial timestep,
	84	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
	85	! mean vertical velocity is also removed for the first time step
	86	! bugfix for calculating divergences
[1321]	87	!
[1909]	88	! 1908 2016-05-25 17:22:32Z suehring
	89	! New divergence for output into RUN_CONTROL file is calculated only at last
	90	! Runge-Kutta step
	91	!
[1846]	92	! 1845 2016-04-08 08:29:13Z raasch
	93	! nzb_2d replace by nzb_u\|v_inner
	94	!
[1800]	95	! 1799 2016-04-05 08:35:55Z gronemeier
	96	! Bugfix: excluded third dimension from horizontal volume flow calculation
	97	!
[1763]	98	! 1762 2016-02-25 12:31:13Z hellstea
	99	! Introduction of nested domain feature
	100	!
[1683]	101	! 1682 2015-10-07 23:56:08Z knoop
	102	! Code annotations made doxygen readable
	103	!
[1576]	104	! 1575 2015-03-27 09:56:27Z raasch
	105	! poismg_fast + respective module added, adjustments for psolver-queries
	106	!
[1343]	107	! 1342 2014-03-26 17:04:47Z kanani
	108	! REAL constants defined as wp-kind
	109	!
[1321]	110	! 1320 2014-03-20 08:40:49Z raasch
[1320]	111	! ONLY-attribute added to USE-statements,
	112	! kind-parameters added to all INTEGER and REAL declaration statements,
	113	! kinds are defined in new module kinds,
	114	! old module precision_kind is removed,
	115	! revision history before 2012 removed,
	116	! comment fields (!:) to be used for variable explanations added to
	117	! all variable declaration statements
[708]	118	!
[1319]	119	! 1318 2014-03-17 13:35:16Z raasch
	120	! module interfaces removed
	121	!
[1307]	122	! 1306 2014-03-13 14:30:59Z raasch
	123	! second argument removed from routine poisfft
	124	!
[1258]	125	! 1257 2013-11-08 15:18:40Z raasch
	126	! openacc loop and loop vector clauses removed, independent clauses added,
	127	! end parallel replaced by end parallel loop
	128	!
[1222]	129	! 1221 2013-09-10 08:59:13Z raasch
	130	! openACC porting of reduction operations, loops for calculating d are
	131	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	132	!
[1213]	133	! 1212 2013-08-15 08:46:27Z raasch
	134	! call of poisfft_hybrid removed
	135	!
[1118]	136	! 1117 2013-03-27 11:15:36Z suehring
	137	! Bugfix in OpenMP parallelization.
	138	!
[1114]	139	! 1113 2013-03-10 02:48:14Z raasch
	140	! GPU-porting of several loops, some loops rearranged
	141	!
[1112]	142	! 1111 2013-03-08 23:54:10Z
	143	! openACC statements added,
	144	! ibc_p_b = 2 removed
	145	!
[1093]	146	! 1092 2013-02-02 11:24:22Z raasch
	147	! unused variables removed
	148	!
[1037]	149	! 1036 2012-10-22 13:43:42Z raasch
	150	! code put under GPL (PALM 3.9)
	151	!
[1004]	152	! 1003 2012-09-14 14:35:53Z raasch
	153	! adjustment of array tend for cases with unequal subdomain sizes removed
	154	!
[1]	155	! Revision 1.1 1997/07/24 11:24:44 raasch
	156	! Initial revision
	157	!
	158	!
	159	! Description:
	160	! ------------
[1682]	161	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	162	!> equation for the perturbation pressure. Compute the final velocities using
	163	!> this perturbation pressure. Compute the remaining divergence.
[1]	164	!------------------------------------------------------------------------------!
[1682]	165	SUBROUTINE pres
	166
[1]	167
[1320]	168	USE arrays_3d, &
[2037]	169	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
	170	tend, u, v, w
[1320]	171
	172	USE control_parameters, &
[3182]	173	ONLY: bc_lr_cyc, bc_ns_cyc, bc_radiation_l, bc_radiation_n, &
	174	bc_radiation_r, bc_radiation_s, child_domain, &
	175	conserve_volume_flow, coupling_mode, &
[3012]	176	dt_3d, gathered_size, ibc_p_b, ibc_p_t, &
	177	intermediate_timestep_count, intermediate_timestep_count_max, &
[3347]	178	mg_switch_to_pe0_level, nesting_offline, &
	179	psolver, subdomain_size, &
[3182]	180	topography, volume_flow, volume_flow_area, volume_flow_initial
[1320]	181
	182	USE cpulog, &
	183	ONLY: cpu_log, log_point, log_point_s
	184
	185	USE grid_variables, &
	186	ONLY: ddx, ddy
	187
	188	USE indices, &
	189	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
[2232]	190	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzt, nzt_mg, &
	191	wall_flags_0
[1320]	192
	193	USE kinds
	194
[1]	195	USE pegrid
[1933]	196
	197	USE pmc_interface, &
	198	ONLY: nesting_mode
[1]	199
[1320]	200	USE poisfft_mod, &
	201	ONLY: poisfft
	202
[1575]	203	USE poismg_mod
	204
[2696]	205	USE poismg_noopt_mod
	206
[1320]	207	USE statistics, &
	208	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	209	weight_substep
	210
[2232]	211	USE surface_mod, &
	212	ONLY : bc_h
	213
[1]	214	IMPLICIT NONE
	215
[1682]	216	INTEGER(iwp) :: i !<
	217	INTEGER(iwp) :: j !<
	218	INTEGER(iwp) :: k !<
[2232]	219	INTEGER(iwp) :: m !<
[1]	220
[1682]	221	REAL(wp) :: ddt_3d !<
[1918]	222	REAL(wp) :: d_weight_pres !<
[1682]	223	REAL(wp) :: localsum !<
	224	REAL(wp) :: threadsum !<
[1918]	225	REAL(wp) :: weight_pres_l !<
[1929]	226	REAL(wp) :: weight_substep_l !<
[1]	227
[1762]	228	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	229	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	230	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	231	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	232
[3182]	233	LOGICAL :: child_domain_nvn !<
[1]	234
[1933]	235
[1]	236	CALL cpu_log( log_point(8), 'pres', 'start' )
	237
[3634]	238	!$ACC DATA COPYOUT(d, tend) &
	239	!$ACC COPY(u, v, w, p) &
	240	!$ACC COPYIN(rho_air, rho_air_zw, ddzu, ddzw, wall_flags_0)
[85]	241
[3634]	242	!$ACC DATA &
	243	!$ACC COPYIN(bc_h(0:1)) &
	244	!$ACC COPYIN(bc_h(0)%i(1:bc_h(0)%ns)) &
	245	!$ACC COPYIN(bc_h(0)%j(1:bc_h(0)%ns)) &
	246	!$ACC COPYIN(bc_h(0)%k(1:bc_h(0)%ns)) &
	247	!$ACC COPYIN(bc_h(1)%i(1:bc_h(1)%ns)) &
	248	!$ACC COPYIN(bc_h(1)%j(1:bc_h(1)%ns)) &
	249	!$ACC COPYIN(bc_h(1)%k(1:bc_h(1)%ns))
	250
	251
[1918]	252	!
	253	!-- Calculate quantities to be used locally
[1342]	254	ddt_3d = 1.0_wp / dt_3d
[1918]	255	IF ( intermediate_timestep_count == 0 ) THEN
	256	!
	257	!-- If pres is called before initial time step
[1929]	258	weight_pres_l = 1.0_wp
	259	d_weight_pres = 1.0_wp
	260	weight_substep_l = 1.0_wp
[1918]	261	ELSE
[1929]	262	weight_pres_l = weight_pres(intermediate_timestep_count)
	263	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	264	weight_substep_l = weight_substep(intermediate_timestep_count)
[1918]	265	ENDIF
[85]	266
[1]	267	!
[707]	268	!-- Multigrid method expects array d to have one ghost layer.
	269	!--
[1575]	270	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	271
[1]	272	DEALLOCATE( d )
[667]	273	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	274
	275	!
	276	!-- Since p is later used to hold the weighted average of the substeps, it
	277	!-- cannot be used in the iterative solver. Therefore, its initial value is
	278	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	279	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	280	DO i = nxl-1, nxr+1
	281	DO j = nys-1, nyn+1
	282	DO k = nzb, nzt+1
	283	p_loc(k,j,i) = p(k,j,i)
	284	ENDDO
	285	ENDDO
	286	ENDDO
[667]	287	ENDIF
	288
[1918]	289	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	290
	291	!
	292	!-- Since p is later used to hold the weighted average of the substeps, it
	293	!-- cannot be used in the iterative solver. Therefore, its initial value is
	294	!-- stored on p_loc, which is then iteratively advanced in every substep.
	295	p_loc = p
	296
[1]	297	ENDIF
	298
	299	!
[75]	300	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	301	!-- boundary conditions
[106]	302	!-- WARNING: so far, this conservation does not work at the left/south
	303	!-- boundary if the topography at the inflow differs from that at the
	304	!-- outflow! For this case, volume_flow_area needs adjustment!
	305	!
	306	!-- Left/right
[3182]	307	IF ( conserve_volume_flow .AND. ( bc_radiation_l .OR. &
	308	bc_radiation_r ) ) THEN
[680]	309
[1342]	310	volume_flow(1) = 0.0_wp
	311	volume_flow_l(1) = 0.0_wp
[106]	312
[3182]	313	IF ( bc_radiation_l ) THEN
[106]	314	i = 0
[3182]	315	ELSEIF ( bc_radiation_r ) THEN
[106]	316	i = nx+1
	317	ENDIF
	318
	319	DO j = nys, nyn
	320	!
	321	!-- Sum up the volume flow through the south/north boundary
[2232]	322	DO k = nzb+1, nzt
	323	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k) &
	324	* MERGE( 1.0_wp, 0.0_wp, &
	325	BTEST( wall_flags_0(k,j,i), 1 ) &
	326	)
[106]	327	ENDDO
	328	ENDDO
	329
	330	#if defined( __parallel )
[680]	331	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	332	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	333	MPI_SUM, comm1dy, ierr )
	334	#else
	335	volume_flow = volume_flow_l
	336	#endif
[709]	337	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	338	/ volume_flow_area(1)
	339
[667]	340	DO j = nysg, nyng
[2232]	341	DO k = nzb+1, nzt
	342	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	343	* MERGE( 1.0_wp, 0.0_wp, &
	344	BTEST( wall_flags_0(k,j,i), 1 ) &
	345	)
[106]	346	ENDDO
	347	ENDDO
	348
	349	ENDIF
	350
	351	!
	352	!-- South/north
[3182]	353	IF ( conserve_volume_flow .AND. ( bc_radiation_n .OR. bc_radiation_s ) ) THEN
[106]	354
[1342]	355	volume_flow(2) = 0.0_wp
	356	volume_flow_l(2) = 0.0_wp
[75]	357
[3182]	358	IF ( bc_radiation_s ) THEN
[106]	359	j = 0
[3182]	360	ELSEIF ( bc_radiation_n ) THEN
[75]	361	j = ny+1
[106]	362	ENDIF
	363
	364	DO i = nxl, nxr
[75]	365	!
[106]	366	!-- Sum up the volume flow through the south/north boundary
[2232]	367	DO k = nzb+1, nzt
	368	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k) &
	369	* MERGE( 1.0_wp, 0.0_wp, &
	370	BTEST( wall_flags_0(k,j,i), 2 ) &
	371	)
[75]	372	ENDDO
[106]	373	ENDDO
	374
[75]	375	#if defined( __parallel )
[680]	376	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	377	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	378	MPI_SUM, comm1dx, ierr )
	379	#else
	380	volume_flow = volume_flow_l
	381	#endif
	382	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	383	/ volume_flow_area(2)
[75]	384
[667]	385	DO i = nxlg, nxrg
[2232]	386	DO k = nzb+1, nzt
	387	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	388	* MERGE( 1.0_wp, 0.0_wp, &
	389	BTEST( wall_flags_0(k,j,i), 2 ) &
	390	)
[75]	391	ENDDO
[106]	392	ENDDO
[75]	393
	394	ENDIF
	395
[76]	396	!
[1762]	397	!-- Remove mean vertical velocity in case that Neumann conditions are
[1933]	398	!-- used both at bottom and top boundary, and if not a nested domain in a
	399	!-- normal nesting run. In case of vertical nesting, this must be done.
[3182]	400	!-- Therefore an auxiliary logical variable child_domain_nvn is used here, and
[1933]	401	!-- nvn stands for non-vertical nesting.
[1918]	402	!-- This cannot be done before the first initial time step because ngp_2dh_outer
	403	!-- is not yet known then.
[3182]	404	child_domain_nvn = child_domain
	405	IF ( child_domain .AND. nesting_mode == 'vertical' ) THEN
	406	child_domain_nvn = .FALSE.
[1933]	407	ENDIF
	408
[3347]	409	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nesting_offline .AND. &
[3182]	410	.NOT. child_domain_nvn .AND. intermediate_timestep_count /= 0 ) &
[1918]	411	THEN
	412	w_l = 0.0_wp; w_l_l = 0.0_wp
	413	DO i = nxl, nxr
	414	DO j = nys, nyn
[2232]	415	DO k = nzb+1, nzt
	416	w_l_l(k) = w_l_l(k) + w(k,j,i) &
	417	* MERGE( 1.0_wp, 0.0_wp, &
	418	BTEST( wall_flags_0(k,j,i), 3 ) &
	419	)
[76]	420	ENDDO
	421	ENDDO
[1918]	422	ENDDO
[76]	423	#if defined( __parallel )
[1918]	424	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
	425	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, &
	426	comm2d, ierr )
[76]	427	#else
[1918]	428	w_l = w_l_l
[76]	429	#endif
[1918]	430	DO k = 1, nzt
	431	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	432	ENDDO
	433	DO i = nxlg, nxrg
	434	DO j = nysg, nyng
[2232]	435	DO k = nzb+1, nzt
	436	w(k,j,i) = w(k,j,i) - w_l(k) &
	437	* MERGE( 1.0_wp, 0.0_wp, &
	438	BTEST( wall_flags_0(k,j,i), 3 ) &
	439	)
[76]	440	ENDDO
	441	ENDDO
[1918]	442	ENDDO
[76]	443	ENDIF
[75]	444
	445	!
[1]	446	!-- Compute the divergence of the provisional velocity field.
	447	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	448
[1575]	449	IF ( psolver(1:9) == 'multigrid' ) THEN
[2232]	450	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[1]	451	DO i = nxl-1, nxr+1
	452	DO j = nys-1, nyn+1
	453	DO k = nzb, nzt+1
[1342]	454	d(k,j,i) = 0.0_wp
[1]	455	ENDDO
	456	ENDDO
	457	ENDDO
	458	ELSE
[2232]	459	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[3634]	460	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	461	!$ACC PRESENT(d)
[1003]	462	DO i = nxl, nxr
	463	DO j = nys, nyn
	464	DO k = nzb+1, nzt
[1342]	465	d(k,j,i) = 0.0_wp
[1]	466	ENDDO
	467	ENDDO
	468	ENDDO
	469	ENDIF
	470
[1342]	471	localsum = 0.0_wp
	472	threadsum = 0.0_wp
[1]	473
	474	#if defined( __ibm )
	475	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	476	!$OMP DO SCHEDULE( STATIC )
	477	DO i = nxl, nxr
	478	DO j = nys, nyn
[2232]	479	DO k = nzb+1, nzt
[2037]	480	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	481	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	482	( w(k,j,i) * rho_air_zw(k) - &
	483	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	484	) * ddt_3d * d_weight_pres &
	485	* MERGE( 1.0_wp, 0.0_wp, &
	486	BTEST( wall_flags_0(k,j,i), 0 ) &
	487	)
[1]	488	ENDDO
	489	!
	490	!-- Compute possible PE-sum of divergences for flow_statistics
[2232]	491	DO k = nzb+1, nzt
	492	threadsum = threadsum + ABS( d(k,j,i) ) &
	493	* MERGE( 1.0_wp, 0.0_wp, &
	494	BTEST( wall_flags_0(k,j,i), 0 ) &
	495	)
[1]	496	ENDDO
	497
	498	ENDDO
	499	ENDDO
	500
[1918]	501	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	502	intermediate_timestep_count == 0 ) THEN
	503	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	504	ENDIF
[1]	505	!$OMP END PARALLEL
	506	#else
	507
[1111]	508	!$OMP PARALLEL PRIVATE (i,j,k)
	509	!$OMP DO SCHEDULE( STATIC )
[3634]	510	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	511	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_0) &
	512	!$ACC PRESENT(d)
[1111]	513	DO i = nxl, nxr
	514	DO j = nys, nyn
	515	DO k = 1, nzt
[2037]	516	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	517	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	518	( w(k,j,i) * rho_air_zw(k) - &
	519	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	520	) * ddt_3d * d_weight_pres &
	521	* MERGE( 1.0_wp, 0.0_wp, &
	522	BTEST( wall_flags_0(k,j,i), 0 ) &
	523	)
[1]	524	ENDDO
	525	ENDDO
[1111]	526	ENDDO
	527	!$OMP END PARALLEL
[1]	528
	529	!
[1908]	530	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	531	!-- computation only at last Runge-Kutta substep.
[1918]	532	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	533	intermediate_timestep_count == 0 ) THEN
[1908]	534	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	535	!$OMP DO SCHEDULE( STATIC )
[3634]	536	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
	537	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	538	!$ACC PRESENT(d)
[1908]	539	DO i = nxl, nxr
	540	DO j = nys, nyn
	541	DO k = nzb+1, nzt
	542	threadsum = threadsum + ABS( d(k,j,i) )
	543	ENDDO
[1]	544	ENDDO
	545	ENDDO
[1918]	546	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	547	!$OMP END PARALLEL
	548	ENDIF
[1]	549	#endif
	550
	551	!
	552	!-- For completeness, set the divergence sum of all statistic regions to those
	553	!-- of the total domain
[1918]	554	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	555	intermediate_timestep_count == 0 ) THEN
[1908]	556	sums_divold_l(0:statistic_regions) = localsum
[1918]	557	ENDIF
[1]	558
	559	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	560
	561	!
	562	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	563	IF ( psolver == 'poisfft' ) THEN
[1]	564
	565	!
	566	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	567	CALL poisfft( d )
[1212]	568
[1]	569	!
	570	!-- Store computed perturbation pressure and set boundary condition in
	571	!-- z-direction
[2232]	572	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	573	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	574	!$ACC PRESENT(d, tend)
[1]	575	DO i = nxl, nxr
	576	DO j = nys, nyn
	577	DO k = nzb+1, nzt
	578	tend(k,j,i) = d(k,j,i)
	579	ENDDO
	580	ENDDO
	581	ENDDO
	582
	583	!
	584	!-- Bottom boundary:
	585	!-- This condition is only required for internal output. The pressure
	586	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	587	IF ( ibc_p_b == 1 ) THEN
	588	!
[2232]	589	!-- Neumann (dp/dz = 0). Using surfae data type, first for non-natural
	590	!-- surfaces, then for natural and urban surfaces
	591	!-- Upward facing
	592	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	593	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	594	!$ACC PRESENT(bc_h, tend)
[2232]	595	DO m = 1, bc_h(0)%ns
[2298]	596	i = bc_h(0)%i(m)
	597	j = bc_h(0)%j(m)
	598	k = bc_h(0)%k(m)
[2232]	599	tend(k-1,j,i) = tend(k,j,i)
[1]	600	ENDDO
[2232]	601	!
	602	!-- Downward facing
	603	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	604	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	605	!$ACC PRESENT(bc_h, tend)
[2232]	606	DO m = 1, bc_h(1)%ns
[2298]	607	i = bc_h(1)%i(m)
	608	j = bc_h(1)%j(m)
	609	k = bc_h(1)%k(m)
[2232]	610	tend(k+1,j,i) = tend(k,j,i)
	611	ENDDO
[1]	612
	613	ELSE
	614	!
[2232]	615	!-- Dirichlet. Using surface data type, first for non-natural
	616	!-- surfaces, then for natural and urban surfaces
	617	!-- Upward facing
	618	!$OMP PARALLEL DO PRIVATE( i, j, k )
	619	DO m = 1, bc_h(0)%ns
[2298]	620	i = bc_h(0)%i(m)
	621	j = bc_h(0)%j(m)
	622	k = bc_h(0)%k(m)
[2232]	623	tend(k-1,j,i) = 0.0_wp
[1]	624	ENDDO
[2232]	625	!
	626	!-- Downward facing
	627	!$OMP PARALLEL DO PRIVATE( i, j, k )
	628	DO m = 1, bc_h(1)%ns
[2298]	629	i = bc_h(1)%i(m)
	630	j = bc_h(1)%j(m)
	631	k = bc_h(1)%k(m)
[2232]	632	tend(k+1,j,i) = 0.0_wp
	633	ENDDO
[1]	634
	635	ENDIF
	636
	637	!
	638	!-- Top boundary
	639	IF ( ibc_p_t == 1 ) THEN
	640	!
	641	!-- Neumann
[2232]	642	!$OMP PARALLEL DO PRIVATE (i,j,k)
[667]	643	DO i = nxlg, nxrg
	644	DO j = nysg, nyng
[1]	645	tend(nzt+1,j,i) = tend(nzt,j,i)
	646	ENDDO
	647	ENDDO
	648
	649	ELSE
	650	!
	651	!-- Dirichlet
[2232]	652	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	653	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j) &
	654	!$ACC PRESENT(tend)
[667]	655	DO i = nxlg, nxrg
	656	DO j = nysg, nyng
[1342]	657	tend(nzt+1,j,i) = 0.0_wp
[1]	658	ENDDO
	659	ENDDO
	660
	661	ENDIF
	662
	663	!
	664	!-- Exchange boundaries for p
[667]	665	CALL exchange_horiz( tend, nbgp )
[1]	666
	667	ELSEIF ( psolver == 'sor' ) THEN
	668
	669	!
	670	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	671	!-- scheme
[707]	672	CALL sor( d, ddzu_pres, ddzw, p_loc )
	673	tend = p_loc
[1]	674
[1575]	675	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	676
	677	!
	678	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[2298]	679	!-- array tend is used to store the residuals.
[778]	680
	681	!-- If the number of grid points of the gathered grid, which is collected
	682	!-- on PE0, is larger than the number of grid points of an PE, than array
	683	!-- tend will be enlarged.
	684	IF ( gathered_size > subdomain_size ) THEN
	685	DEALLOCATE( tend )
	686	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	687	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	688	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	689	mg_switch_to_pe0_level)+1) )
	690	ENDIF
	691
[1575]	692	IF ( psolver == 'multigrid' ) THEN
	693	CALL poismg( tend )
	694	ELSE
[1931]	695	CALL poismg_noopt( tend )
[1575]	696	ENDIF
[707]	697
[778]	698	IF ( gathered_size > subdomain_size ) THEN
	699	DEALLOCATE( tend )
	700	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	701	ENDIF
	702
[1]	703	!
	704	!-- Restore perturbation pressure on tend because this array is used
	705	!-- further below to correct the velocity fields
[707]	706	DO i = nxl-1, nxr+1
	707	DO j = nys-1, nyn+1
	708	DO k = nzb, nzt+1
	709	tend(k,j,i) = p_loc(k,j,i)
	710	ENDDO
	711	ENDDO
	712	ENDDO
[667]	713
[1]	714	ENDIF
	715
	716	!
[707]	717	!-- Store perturbation pressure on array p, used for pressure data output.
	718	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	719	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	720	!$OMP PARALLEL PRIVATE (i,j,k)
	721	!$OMP DO
[3634]	722	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	723	!$ACC PRESENT(p, tend)
[707]	724	DO i = nxl-1, nxr+1
	725	DO j = nys-1, nyn+1
	726	DO k = nzb, nzt+1
	727	p(k,j,i) = tend(k,j,i) * &
[1929]	728	weight_substep_l
[673]	729	ENDDO
[1]	730	ENDDO
[707]	731	ENDDO
	732	!$OMP END PARALLEL
	733
[1762]	734	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	735	!$OMP PARALLEL PRIVATE (i,j,k)
	736	!$OMP DO
[3634]	737	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	738	!$ACC PRESENT(p, tend)
[707]	739	DO i = nxl-1, nxr+1
	740	DO j = nys-1, nyn+1
	741	DO k = nzb, nzt+1
	742	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
[1929]	743	weight_substep_l
[673]	744	ENDDO
	745	ENDDO
[707]	746	ENDDO
	747	!$OMP END PARALLEL
	748
	749	ENDIF
[673]	750
[707]	751	!
	752	!-- SOR-method needs ghost layers for the next timestep
	753	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	754
[1]	755	!
	756	!-- Correction of the provisional velocities with the current perturbation
	757	!-- pressure just computed
[709]	758	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	759	volume_flow_l(1) = 0.0_wp
	760	volume_flow_l(2) = 0.0_wp
[1]	761	ENDIF
[3347]	762	!
	763	!-- Add pressure gradients to the velocity components. Note, the loops are
	764	!-- running over the entire model domain, even though, in case of non-cyclic
	765	!-- boundaries u- and v-component are not prognostic at i=0 and j=0,
	766	!-- respectiveley. However, in case of Dirichlet boundary conditions for the
	767	!-- velocities, zero-gradient conditions for the pressure are set, so that
	768	!-- no modification is imposed at the boundaries.
[1]	769	!$OMP PARALLEL PRIVATE (i,j,k)
	770	!$OMP DO
[3634]	771	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k) &
	772	!$ACC PRESENT(u, v, w, tend, ddzu, wall_flags_0)
[673]	773	DO i = nxl, nxr
[1]	774	DO j = nys, nyn
[2118]	775
[2232]	776	DO k = nzb+1, nzt
	777	w(k,j,i) = w(k,j,i) - dt_3d * &
	778	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) &
	779	* weight_pres_l &
	780	* MERGE( 1.0_wp, 0.0_wp, &
	781	BTEST( wall_flags_0(k,j,i), 3 ) &
	782	)
[1]	783	ENDDO
[2118]	784
[2232]	785	DO k = nzb+1, nzt
	786	u(k,j,i) = u(k,j,i) - dt_3d * &
	787	( tend(k,j,i) - tend(k,j,i-1) ) * ddx &
	788	* weight_pres_l &
	789	* MERGE( 1.0_wp, 0.0_wp, &
	790	BTEST( wall_flags_0(k,j,i), 1 ) &
	791	)
[1]	792	ENDDO
[2118]	793
[2232]	794	DO k = nzb+1, nzt
	795	v(k,j,i) = v(k,j,i) - dt_3d * &
	796	( tend(k,j,i) - tend(k,j-1,i) ) * ddy &
	797	* weight_pres_l &
	798	* MERGE( 1.0_wp, 0.0_wp, &
	799	BTEST( wall_flags_0(k,j,i), 2 ) &
	800	)
[673]	801	ENDDO
[1]	802
	803	ENDDO
	804	ENDDO
	805	!$OMP END PARALLEL
[1113]	806
	807	!
[3012]	808	!-- The vertical velocity is not set to zero at nzt + 1 for nested domains
	809	!-- Instead it is set to the values of nzt (see routine vnest_boundary_conds
	810	!-- or pmci_interp_tril_t) BEFORE calling the pressure solver. To avoid jumps
	811	!-- while plotting profiles w at the top has to be set to the values in the
	812	!-- height nzt after above modifications. Hint: w level nzt+1 does not impact
	813	!-- results.
[3182]	814	IF ( child_domain .OR. coupling_mode == 'vnested_fine' ) THEN
[3012]	815	w(nzt+1,:,:) = w(nzt,:,:)
	816	ENDIF
	817
	818	!
[1113]	819	!-- Sum up the volume flow through the right and north boundary
[2232]	820	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
[1113]	821	nxr == nx ) THEN
	822
	823	!$OMP PARALLEL PRIVATE (j,k)
	824	!$OMP DO
	825	DO j = nys, nyn
	826	!$OMP CRITICAL
[2232]	827	DO k = nzb+1, nzt
	828	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nxr) * dzw(k) &
	829	* MERGE( 1.0_wp, 0.0_wp, &
	830	BTEST( wall_flags_0(k,j,nxr), 1 )&
	831	)
[1113]	832	ENDDO
	833	!$OMP END CRITICAL
	834	ENDDO
	835	!$OMP END PARALLEL
	836
	837	ENDIF
	838
[2232]	839	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
[1113]	840	nyn == ny ) THEN
	841
	842	!$OMP PARALLEL PRIVATE (i,k)
	843	!$OMP DO
	844	DO i = nxl, nxr
	845	!$OMP CRITICAL
[2232]	846	DO k = nzb+1, nzt
	847	volume_flow_l(2) = volume_flow_l(2) + v(k,nyn,i) * dzw(k) &
	848	* MERGE( 1.0_wp, 0.0_wp, &
	849	BTEST( wall_flags_0(k,nyn,i), 2 )&
	850	)
[1113]	851	ENDDO
	852	!$OMP END CRITICAL
	853	ENDDO
	854	!$OMP END PARALLEL
	855
	856	ENDIF
[673]	857
[1]	858	!
	859	!-- Conserve the volume flow
[707]	860	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	861
	862	#if defined( __parallel )
[622]	863	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	864	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	865	MPI_SUM, comm2d, ierr )
	866	#else
	867	volume_flow = volume_flow_l
	868	#endif
	869
[1799]	870	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	871	volume_flow_area(1:2)
[1]	872
	873	!$OMP PARALLEL PRIVATE (i,j,k)
	874	!$OMP DO
	875	DO i = nxl, nxr
	876	DO j = nys, nyn
[2232]	877	DO k = nzb+1, nzt
	878	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	879	* MERGE( 1.0_wp, 0.0_wp, &
	880	BTEST( wall_flags_0(k,j,i), 1 ) &
	881	)
[719]	882	ENDDO
[2232]	883	DO k = nzb+1, nzt
	884	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	885	* MERGE( 1.0_wp, 0.0_wp, &
	886	BTEST( wall_flags_0(k,j,i), 2 ) &
	887	)
[667]	888	ENDDO
[1]	889	ENDDO
	890	ENDDO
[667]	891
[1]	892	!$OMP END PARALLEL
	893
	894	ENDIF
	895
	896	!
	897	!-- Exchange of boundaries for the velocities
[667]	898	CALL exchange_horiz( u, nbgp )
	899	CALL exchange_horiz( v, nbgp )
	900	CALL exchange_horiz( w, nbgp )
[1]	901
	902	!
	903	!-- Compute the divergence of the corrected velocity field,
[1908]	904	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	905	!-- only at last Runge-Kutta step.
[1918]	906	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	907	intermediate_timestep_count == 0 ) THEN
[1908]	908	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	909	sums_divnew_l = 0.0_wp
[1]	910
	911	!
[1908]	912	!-- d must be reset to zero because it can contain nonzero values below the
	913	!-- topography
	914	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	915
[1908]	916	localsum = 0.0_wp
	917	threadsum = 0.0_wp
[1]	918
[1908]	919	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
[2073]	920	#if defined( __ibm )
[1908]	921	!$OMP DO SCHEDULE( STATIC )
	922	DO i = nxl, nxr
	923	DO j = nys, nyn
[2232]	924	DO k = nzb+1, nzt
	925	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	926	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	927	( w(k,j,i) * rho_air_zw(k) - &
	928	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	929	) * MERGE( 1.0_wp, 0.0_wp, &
	930	BTEST( wall_flags_0(k,j,i), 0 ) &
	931	)
[1908]	932	ENDDO
	933	DO k = nzb+1, nzt
	934	threadsum = threadsum + ABS( d(k,j,i) )
	935	ENDDO
[1]	936	ENDDO
	937	ENDDO
	938	#else
[2073]	939	!$OMP DO SCHEDULE( STATIC )
[3634]	940	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	941	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_0) &
	942	!$ACC PRESENT(d)
[1908]	943	DO i = nxl, nxr
	944	DO j = nys, nyn
[2232]	945	DO k = nzb+1, nzt
[2037]	946	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	947	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	948	( w(k,j,i) * rho_air_zw(k) - &
	949	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	950	) * MERGE( 1.0_wp, 0.0_wp, &
	951	BTEST( wall_flags_0(k,j,i), 0 ) &
	952	)
[1908]	953	ENDDO
[1113]	954	ENDDO
	955	ENDDO
	956	!
[1908]	957	!-- Compute possible PE-sum of divergences for flow_statistics
[2073]	958	!$OMP DO SCHEDULE( STATIC )
[3634]	959	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	960	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	961	!$ACC PRESENT(d)
[1908]	962	DO i = nxl, nxr
	963	DO j = nys, nyn
	964	DO k = nzb+1, nzt
	965	threadsum = threadsum + ABS( d(k,j,i) )
	966	ENDDO
[1]	967	ENDDO
	968	ENDDO
	969	#endif
[667]	970
[1908]	971	localsum = localsum + threadsum
	972	!$OMP END PARALLEL
[1]	973
	974	!
[1908]	975	!-- For completeness, set the divergence sum of all statistic regions to those
	976	!-- of the total domain
	977	sums_divnew_l(0:statistic_regions) = localsum
[1]	978
[1908]	979	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	980
[1908]	981	ENDIF
	982
[1]	983	CALL cpu_log( log_point(8), 'pres', 'stop' )
	984
[3634]	985	!$ACC END DATA
	986	!$ACC END DATA
[1]	987
	988	END SUBROUTINE pres

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