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source: palm/trunk/SOURCE/pres.f90 @ 4015

Last change on this file since 4015 was 4015, checked in by raasch, 5 years ago
all reals changed to double precision in order to work with 32-bit working precision, otherwise calculated time intervals would mostly give zero; variable child_domain_nvn eliminated
Property svn:keywords set to `Id`
File size: 33.7 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 4015 2019-06-05 13:25:35Z raasch $
[4015]	27	! variable child_domain_nvn eliminated
	28	!
	29	! 3849 2019-04-01 16:35:16Z knoop
[3634]	30	! OpenACC port for SPEC
	31	!
	32	! 3347 2018-10-15 14:21:08Z suehring
[3347]	33	! Bugfixes in offline nesting.
	34	! Add comment.
	35	!
	36	! 3341 2018-10-15 10:31:27Z suehring
[3183]	37	! Rename variables for boundary flags and nesting
	38	!
	39	! 3182 2018-07-27 13:36:03Z suehring
[3016]	40	! Dollar sign added before Id
	41	!
	42	! 2696 2017-12-14 17:12:51Z kanani
[3013]	43	! To avoid jumps while plotting w-profiles w level nzt+1 is set to w level nzt
	44	! after velocity modifications through the pressure solver were carried out
	45	!
	46	! 2696 2017-12-14 17:12:51Z kanani
[2716]	47	! Corrected "Former revisions" section
[2696]	48	!
[2716]	49	! 2696 2017-12-14 17:12:51Z kanani
	50	! Change in file header (GPL part)
	51	! poismg_noopt modularized (MS)
	52	!
[2696]	53	! 2298 2017-06-29 09:28:18Z raasch
[2298]	54	! comment changed + some formatting
	55	!
	56	! 2233 2017-05-30 18:08:54Z suehring
[1919]	57	!
[2233]	58	! 2232 2017-05-30 17:47:52Z suehring
	59	! Adjustments to new topography and surface concept
	60	!
[2119]	61	! 2118 2017-01-17 16:38:49Z raasch
	62	! OpenACC directives and related code removed
	63	!
[2074]	64	! 2073 2016-11-30 14:34:05Z raasch
	65	! openmp bugfix for calculation of new divergence
	66	!
[2038]	67	! 2037 2016-10-26 11:15:40Z knoop
	68	! Anelastic approximation implemented
	69	!
[2001]	70	! 2000 2016-08-20 18:09:15Z knoop
	71	! Forced header and separation lines into 80 columns
	72	!
[1933]	73	! 1932 2016-06-10 12:09:21Z suehring
	74	! Initial version of purely vertical nesting introduced.
	75	!
[1932]	76	! 1931 2016-06-10 12:06:59Z suehring
	77	! Rename multigrid into multigrid_noopt and multigrid_fast into multigrid
	78	!
[1930]	79	! 1929 2016-06-09 16:25:25Z suehring
	80	! Bugfix: weight_substep for initial call, replace by local variable
	81	!
[1919]	82	! 1918 2016-05-27 14:35:57Z raasch
[1918]	83	! sum of divergence is also calculated when pres is called before the initial
	84	! first time step,
	85	! stearing is modified by using intermediate_timestep_count = 0 in order to
	86	! determine if pres is called before the first initial timestep,
	87	! bugfix: in case of Neumann conditions for pressure both at bottom and top,
	88	! mean vertical velocity is also removed for the first time step
	89	! bugfix for calculating divergences
[1321]	90	!
[1909]	91	! 1908 2016-05-25 17:22:32Z suehring
	92	! New divergence for output into RUN_CONTROL file is calculated only at last
	93	! Runge-Kutta step
	94	!
[1846]	95	! 1845 2016-04-08 08:29:13Z raasch
	96	! nzb_2d replace by nzb_u\|v_inner
	97	!
[1800]	98	! 1799 2016-04-05 08:35:55Z gronemeier
	99	! Bugfix: excluded third dimension from horizontal volume flow calculation
	100	!
[1763]	101	! 1762 2016-02-25 12:31:13Z hellstea
	102	! Introduction of nested domain feature
	103	!
[1683]	104	! 1682 2015-10-07 23:56:08Z knoop
	105	! Code annotations made doxygen readable
	106	!
[1576]	107	! 1575 2015-03-27 09:56:27Z raasch
	108	! poismg_fast + respective module added, adjustments for psolver-queries
	109	!
[1343]	110	! 1342 2014-03-26 17:04:47Z kanani
	111	! REAL constants defined as wp-kind
	112	!
[1321]	113	! 1320 2014-03-20 08:40:49Z raasch
[1320]	114	! ONLY-attribute added to USE-statements,
	115	! kind-parameters added to all INTEGER and REAL declaration statements,
	116	! kinds are defined in new module kinds,
	117	! old module precision_kind is removed,
	118	! revision history before 2012 removed,
	119	! comment fields (!:) to be used for variable explanations added to
	120	! all variable declaration statements
[708]	121	!
[1319]	122	! 1318 2014-03-17 13:35:16Z raasch
	123	! module interfaces removed
	124	!
[1307]	125	! 1306 2014-03-13 14:30:59Z raasch
	126	! second argument removed from routine poisfft
	127	!
[1258]	128	! 1257 2013-11-08 15:18:40Z raasch
	129	! openacc loop and loop vector clauses removed, independent clauses added,
	130	! end parallel replaced by end parallel loop
	131	!
[1222]	132	! 1221 2013-09-10 08:59:13Z raasch
	133	! openACC porting of reduction operations, loops for calculating d are
	134	! using the rflags_s_inner multiply flag instead of the nzb_s_inner loop index
	135	!
[1213]	136	! 1212 2013-08-15 08:46:27Z raasch
	137	! call of poisfft_hybrid removed
	138	!
[1118]	139	! 1117 2013-03-27 11:15:36Z suehring
	140	! Bugfix in OpenMP parallelization.
	141	!
[1114]	142	! 1113 2013-03-10 02:48:14Z raasch
	143	! GPU-porting of several loops, some loops rearranged
	144	!
[1112]	145	! 1111 2013-03-08 23:54:10Z
	146	! openACC statements added,
	147	! ibc_p_b = 2 removed
	148	!
[1093]	149	! 1092 2013-02-02 11:24:22Z raasch
	150	! unused variables removed
	151	!
[1037]	152	! 1036 2012-10-22 13:43:42Z raasch
	153	! code put under GPL (PALM 3.9)
	154	!
[1004]	155	! 1003 2012-09-14 14:35:53Z raasch
	156	! adjustment of array tend for cases with unequal subdomain sizes removed
	157	!
[1]	158	! Revision 1.1 1997/07/24 11:24:44 raasch
	159	! Initial revision
	160	!
	161	!
	162	! Description:
	163	! ------------
[1682]	164	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	165	!> equation for the perturbation pressure. Compute the final velocities using
	166	!> this perturbation pressure. Compute the remaining divergence.
[1]	167	!------------------------------------------------------------------------------!
[1682]	168	SUBROUTINE pres
	169
[1]	170
[1320]	171	USE arrays_3d, &
[2037]	172	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
	173	tend, u, v, w
[1320]	174
	175	USE control_parameters, &
[3182]	176	ONLY: bc_lr_cyc, bc_ns_cyc, bc_radiation_l, bc_radiation_n, &
	177	bc_radiation_r, bc_radiation_s, child_domain, &
	178	conserve_volume_flow, coupling_mode, &
[3012]	179	dt_3d, gathered_size, ibc_p_b, ibc_p_t, &
	180	intermediate_timestep_count, intermediate_timestep_count_max, &
[3347]	181	mg_switch_to_pe0_level, nesting_offline, &
	182	psolver, subdomain_size, &
[3182]	183	topography, volume_flow, volume_flow_area, volume_flow_initial
[1320]	184
	185	USE cpulog, &
	186	ONLY: cpu_log, log_point, log_point_s
	187
	188	USE grid_variables, &
	189	ONLY: ddx, ddy
	190
	191	USE indices, &
	192	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
[2232]	193	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzt, nzt_mg, &
	194	wall_flags_0
[1320]	195
	196	USE kinds
	197
[1]	198	USE pegrid
[1933]	199
	200	USE pmc_interface, &
	201	ONLY: nesting_mode
[1]	202
[1320]	203	USE poisfft_mod, &
	204	ONLY: poisfft
	205
[1575]	206	USE poismg_mod
	207
[2696]	208	USE poismg_noopt_mod
	209
[1320]	210	USE statistics, &
	211	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	212	weight_substep
	213
[2232]	214	USE surface_mod, &
	215	ONLY : bc_h
	216
[1]	217	IMPLICIT NONE
	218
[1682]	219	INTEGER(iwp) :: i !<
	220	INTEGER(iwp) :: j !<
	221	INTEGER(iwp) :: k !<
[2232]	222	INTEGER(iwp) :: m !<
[1]	223
[1682]	224	REAL(wp) :: ddt_3d !<
[1918]	225	REAL(wp) :: d_weight_pres !<
[1682]	226	REAL(wp) :: localsum !<
	227	REAL(wp) :: threadsum !<
[1918]	228	REAL(wp) :: weight_pres_l !<
[1929]	229	REAL(wp) :: weight_substep_l !<
[1]	230
[1762]	231	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	232	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	233	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	234	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	235
	236
	237	CALL cpu_log( log_point(8), 'pres', 'start' )
	238
[1918]	239	!
	240	!-- Calculate quantities to be used locally
[1342]	241	ddt_3d = 1.0_wp / dt_3d
[1918]	242	IF ( intermediate_timestep_count == 0 ) THEN
	243	!
	244	!-- If pres is called before initial time step
[1929]	245	weight_pres_l = 1.0_wp
	246	d_weight_pres = 1.0_wp
	247	weight_substep_l = 1.0_wp
[1918]	248	ELSE
[1929]	249	weight_pres_l = weight_pres(intermediate_timestep_count)
	250	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	251	weight_substep_l = weight_substep(intermediate_timestep_count)
[1918]	252	ENDIF
[85]	253
[1]	254	!
[707]	255	!-- Multigrid method expects array d to have one ghost layer.
	256	!--
[1575]	257	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	258
[1]	259	DEALLOCATE( d )
[667]	260	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	261
	262	!
	263	!-- Since p is later used to hold the weighted average of the substeps, it
	264	!-- cannot be used in the iterative solver. Therefore, its initial value is
	265	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	266	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	267	DO i = nxl-1, nxr+1
	268	DO j = nys-1, nyn+1
	269	DO k = nzb, nzt+1
	270	p_loc(k,j,i) = p(k,j,i)
	271	ENDDO
	272	ENDDO
	273	ENDDO
[667]	274	ENDIF
	275
[1918]	276	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	277
	278	!
	279	!-- Since p is later used to hold the weighted average of the substeps, it
	280	!-- cannot be used in the iterative solver. Therefore, its initial value is
	281	!-- stored on p_loc, which is then iteratively advanced in every substep.
	282	p_loc = p
	283
[1]	284	ENDIF
	285
	286	!
[75]	287	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	288	!-- boundary conditions
[106]	289	!-- WARNING: so far, this conservation does not work at the left/south
	290	!-- boundary if the topography at the inflow differs from that at the
	291	!-- outflow! For this case, volume_flow_area needs adjustment!
	292	!
	293	!-- Left/right
[3182]	294	IF ( conserve_volume_flow .AND. ( bc_radiation_l .OR. &
	295	bc_radiation_r ) ) THEN
[680]	296
[1342]	297	volume_flow(1) = 0.0_wp
	298	volume_flow_l(1) = 0.0_wp
[106]	299
[3182]	300	IF ( bc_radiation_l ) THEN
[106]	301	i = 0
[3182]	302	ELSEIF ( bc_radiation_r ) THEN
[106]	303	i = nx+1
	304	ENDIF
	305
	306	DO j = nys, nyn
	307	!
	308	!-- Sum up the volume flow through the south/north boundary
[2232]	309	DO k = nzb+1, nzt
	310	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k) &
	311	* MERGE( 1.0_wp, 0.0_wp, &
	312	BTEST( wall_flags_0(k,j,i), 1 ) &
	313	)
[106]	314	ENDDO
	315	ENDDO
	316
	317	#if defined( __parallel )
[680]	318	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	319	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	320	MPI_SUM, comm1dy, ierr )
	321	#else
	322	volume_flow = volume_flow_l
	323	#endif
[709]	324	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	325	/ volume_flow_area(1)
	326
[667]	327	DO j = nysg, nyng
[2232]	328	DO k = nzb+1, nzt
	329	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	330	* MERGE( 1.0_wp, 0.0_wp, &
	331	BTEST( wall_flags_0(k,j,i), 1 ) &
	332	)
[106]	333	ENDDO
	334	ENDDO
	335
	336	ENDIF
	337
	338	!
	339	!-- South/north
[3182]	340	IF ( conserve_volume_flow .AND. ( bc_radiation_n .OR. bc_radiation_s ) ) THEN
[106]	341
[1342]	342	volume_flow(2) = 0.0_wp
	343	volume_flow_l(2) = 0.0_wp
[75]	344
[3182]	345	IF ( bc_radiation_s ) THEN
[106]	346	j = 0
[3182]	347	ELSEIF ( bc_radiation_n ) THEN
[75]	348	j = ny+1
[106]	349	ENDIF
	350
	351	DO i = nxl, nxr
[75]	352	!
[106]	353	!-- Sum up the volume flow through the south/north boundary
[2232]	354	DO k = nzb+1, nzt
	355	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k) &
	356	* MERGE( 1.0_wp, 0.0_wp, &
	357	BTEST( wall_flags_0(k,j,i), 2 ) &
	358	)
[75]	359	ENDDO
[106]	360	ENDDO
	361
[75]	362	#if defined( __parallel )
[680]	363	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	364	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	365	MPI_SUM, comm1dx, ierr )
	366	#else
	367	volume_flow = volume_flow_l
	368	#endif
	369	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	370	/ volume_flow_area(2)
[75]	371
[667]	372	DO i = nxlg, nxrg
[2232]	373	DO k = nzb+1, nzt
	374	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	375	* MERGE( 1.0_wp, 0.0_wp, &
	376	BTEST( wall_flags_0(k,j,i), 2 ) &
	377	)
[75]	378	ENDDO
[106]	379	ENDDO
[75]	380
	381	ENDIF
	382
[76]	383	!
[4015]	384	!-- Remove mean vertical velocity in case that Neumann conditions are used both at bottom and top
	385	!-- boundary. With Neumann conditions at both vertical boundaries, the solver cannot remove
	386	!-- mean vertical velocities. They should be removed, because incompressibility requires that
	387	!-- the vertical gradient of vertical velocity is zero. Since w=0 at the solid surface, it must be
	388	!-- zero everywhere.
	389	!-- This must not be done in case of a 3d-nesting child domain, because a mean vertical velocity
	390	!-- can physically exist in such a domain.
	391	!-- Also in case of offline nesting, mean vertical velocities may exist (and must not be removed),
	392	!-- caused by horizontal divergence/convergence of the large scale flow that is prescribed at the
	393	!-- side boundaries.
	394	!-- The removal cannot be done before the first initial time step because ngp_2dh_outer
[1918]	395	!-- is not yet known then.
[4015]	396	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nesting_offline &
	397	.AND. .NOT. ( child_domain .AND. nesting_mode /= 'vertical' ) &
	398	.AND. intermediate_timestep_count /= 0 ) &
[1918]	399	THEN
	400	w_l = 0.0_wp; w_l_l = 0.0_wp
	401	DO i = nxl, nxr
	402	DO j = nys, nyn
[2232]	403	DO k = nzb+1, nzt
[4015]	404	w_l_l(k) = w_l_l(k) + w(k,j,i) &
	405	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 3 ) )
[76]	406	ENDDO
	407	ENDDO
[1918]	408	ENDDO
[76]	409	#if defined( __parallel )
[1918]	410	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[4015]	411	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, comm2d, ierr )
[76]	412	#else
[1918]	413	w_l = w_l_l
[76]	414	#endif
[1918]	415	DO k = 1, nzt
	416	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	417	ENDDO
	418	DO i = nxlg, nxrg
	419	DO j = nysg, nyng
[2232]	420	DO k = nzb+1, nzt
[4015]	421	w(k,j,i) = w(k,j,i) - w_l(k) &
	422	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_0(k,j,i), 3 ) )
[76]	423	ENDDO
	424	ENDDO
[1918]	425	ENDDO
[76]	426	ENDIF
[75]	427
	428	!
[1]	429	!-- Compute the divergence of the provisional velocity field.
	430	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	431
[1575]	432	IF ( psolver(1:9) == 'multigrid' ) THEN
[2232]	433	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[1]	434	DO i = nxl-1, nxr+1
	435	DO j = nys-1, nyn+1
	436	DO k = nzb, nzt+1
[1342]	437	d(k,j,i) = 0.0_wp
[1]	438	ENDDO
	439	ENDDO
	440	ENDDO
	441	ELSE
[2232]	442	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[3634]	443	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	444	!$ACC PRESENT(d)
[1003]	445	DO i = nxl, nxr
	446	DO j = nys, nyn
	447	DO k = nzb+1, nzt
[1342]	448	d(k,j,i) = 0.0_wp
[1]	449	ENDDO
	450	ENDDO
	451	ENDDO
	452	ENDIF
	453
[1342]	454	localsum = 0.0_wp
	455	threadsum = 0.0_wp
[1]	456
	457	#if defined( __ibm )
	458	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	459	!$OMP DO SCHEDULE( STATIC )
	460	DO i = nxl, nxr
	461	DO j = nys, nyn
[2232]	462	DO k = nzb+1, nzt
[2037]	463	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	464	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	465	( w(k,j,i) * rho_air_zw(k) - &
	466	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	467	) * ddt_3d * d_weight_pres &
	468	* MERGE( 1.0_wp, 0.0_wp, &
	469	BTEST( wall_flags_0(k,j,i), 0 ) &
	470	)
[1]	471	ENDDO
	472	!
	473	!-- Compute possible PE-sum of divergences for flow_statistics
[2232]	474	DO k = nzb+1, nzt
	475	threadsum = threadsum + ABS( d(k,j,i) ) &
	476	* MERGE( 1.0_wp, 0.0_wp, &
	477	BTEST( wall_flags_0(k,j,i), 0 ) &
	478	)
[1]	479	ENDDO
	480
	481	ENDDO
	482	ENDDO
	483
[1918]	484	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	485	intermediate_timestep_count == 0 ) THEN
	486	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	487	ENDIF
[1]	488	!$OMP END PARALLEL
	489	#else
	490
[1111]	491	!$OMP PARALLEL PRIVATE (i,j,k)
	492	!$OMP DO SCHEDULE( STATIC )
[3634]	493	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	494	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_0) &
	495	!$ACC PRESENT(d)
[1111]	496	DO i = nxl, nxr
	497	DO j = nys, nyn
	498	DO k = 1, nzt
[2037]	499	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	500	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	501	( w(k,j,i) * rho_air_zw(k) - &
	502	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	503	) * ddt_3d * d_weight_pres &
	504	* MERGE( 1.0_wp, 0.0_wp, &
	505	BTEST( wall_flags_0(k,j,i), 0 ) &
	506	)
[1]	507	ENDDO
	508	ENDDO
[1111]	509	ENDDO
	510	!$OMP END PARALLEL
[1]	511
	512	!
[1908]	513	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	514	!-- computation only at last Runge-Kutta substep.
[1918]	515	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	516	intermediate_timestep_count == 0 ) THEN
[1908]	517	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	518	!$OMP DO SCHEDULE( STATIC )
[3634]	519	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
	520	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	521	!$ACC PRESENT(d)
[1908]	522	DO i = nxl, nxr
	523	DO j = nys, nyn
	524	DO k = nzb+1, nzt
	525	threadsum = threadsum + ABS( d(k,j,i) )
	526	ENDDO
[1]	527	ENDDO
	528	ENDDO
[1918]	529	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	530	!$OMP END PARALLEL
	531	ENDIF
[1]	532	#endif
	533
	534	!
	535	!-- For completeness, set the divergence sum of all statistic regions to those
	536	!-- of the total domain
[1918]	537	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	538	intermediate_timestep_count == 0 ) THEN
[1908]	539	sums_divold_l(0:statistic_regions) = localsum
[1918]	540	ENDIF
[1]	541
	542	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	543
	544	!
	545	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	546	IF ( psolver == 'poisfft' ) THEN
[1]	547
	548	!
	549	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	550	CALL poisfft( d )
[1212]	551
[1]	552	!
	553	!-- Store computed perturbation pressure and set boundary condition in
	554	!-- z-direction
[2232]	555	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	556	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	557	!$ACC PRESENT(d, tend)
[1]	558	DO i = nxl, nxr
	559	DO j = nys, nyn
	560	DO k = nzb+1, nzt
	561	tend(k,j,i) = d(k,j,i)
	562	ENDDO
	563	ENDDO
	564	ENDDO
	565
	566	!
	567	!-- Bottom boundary:
	568	!-- This condition is only required for internal output. The pressure
	569	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	570	IF ( ibc_p_b == 1 ) THEN
	571	!
[2232]	572	!-- Neumann (dp/dz = 0). Using surfae data type, first for non-natural
	573	!-- surfaces, then for natural and urban surfaces
	574	!-- Upward facing
	575	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	576	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	577	!$ACC PRESENT(bc_h, tend)
[2232]	578	DO m = 1, bc_h(0)%ns
[2298]	579	i = bc_h(0)%i(m)
	580	j = bc_h(0)%j(m)
	581	k = bc_h(0)%k(m)
[2232]	582	tend(k-1,j,i) = tend(k,j,i)
[1]	583	ENDDO
[2232]	584	!
	585	!-- Downward facing
	586	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	587	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	588	!$ACC PRESENT(bc_h, tend)
[2232]	589	DO m = 1, bc_h(1)%ns
[2298]	590	i = bc_h(1)%i(m)
	591	j = bc_h(1)%j(m)
	592	k = bc_h(1)%k(m)
[2232]	593	tend(k+1,j,i) = tend(k,j,i)
	594	ENDDO
[1]	595
	596	ELSE
	597	!
[2232]	598	!-- Dirichlet. Using surface data type, first for non-natural
	599	!-- surfaces, then for natural and urban surfaces
	600	!-- Upward facing
	601	!$OMP PARALLEL DO PRIVATE( i, j, k )
	602	DO m = 1, bc_h(0)%ns
[2298]	603	i = bc_h(0)%i(m)
	604	j = bc_h(0)%j(m)
	605	k = bc_h(0)%k(m)
[2232]	606	tend(k-1,j,i) = 0.0_wp
[1]	607	ENDDO
[2232]	608	!
	609	!-- Downward facing
	610	!$OMP PARALLEL DO PRIVATE( i, j, k )
	611	DO m = 1, bc_h(1)%ns
[2298]	612	i = bc_h(1)%i(m)
	613	j = bc_h(1)%j(m)
	614	k = bc_h(1)%k(m)
[2232]	615	tend(k+1,j,i) = 0.0_wp
	616	ENDDO
[1]	617
	618	ENDIF
	619
	620	!
	621	!-- Top boundary
	622	IF ( ibc_p_t == 1 ) THEN
	623	!
	624	!-- Neumann
[2232]	625	!$OMP PARALLEL DO PRIVATE (i,j,k)
[667]	626	DO i = nxlg, nxrg
	627	DO j = nysg, nyng
[1]	628	tend(nzt+1,j,i) = tend(nzt,j,i)
	629	ENDDO
	630	ENDDO
	631
	632	ELSE
	633	!
	634	!-- Dirichlet
[2232]	635	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	636	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j) &
	637	!$ACC PRESENT(tend)
[667]	638	DO i = nxlg, nxrg
	639	DO j = nysg, nyng
[1342]	640	tend(nzt+1,j,i) = 0.0_wp
[1]	641	ENDDO
	642	ENDDO
	643
	644	ENDIF
	645
	646	!
	647	!-- Exchange boundaries for p
[667]	648	CALL exchange_horiz( tend, nbgp )
[1]	649
	650	ELSEIF ( psolver == 'sor' ) THEN
	651
	652	!
	653	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	654	!-- scheme
[707]	655	CALL sor( d, ddzu_pres, ddzw, p_loc )
	656	tend = p_loc
[1]	657
[1575]	658	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	659
	660	!
	661	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[2298]	662	!-- array tend is used to store the residuals.
[778]	663
	664	!-- If the number of grid points of the gathered grid, which is collected
	665	!-- on PE0, is larger than the number of grid points of an PE, than array
	666	!-- tend will be enlarged.
	667	IF ( gathered_size > subdomain_size ) THEN
	668	DEALLOCATE( tend )
	669	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	670	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	671	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	672	mg_switch_to_pe0_level)+1) )
	673	ENDIF
	674
[1575]	675	IF ( psolver == 'multigrid' ) THEN
	676	CALL poismg( tend )
	677	ELSE
[1931]	678	CALL poismg_noopt( tend )
[1575]	679	ENDIF
[707]	680
[778]	681	IF ( gathered_size > subdomain_size ) THEN
	682	DEALLOCATE( tend )
	683	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	684	ENDIF
	685
[1]	686	!
	687	!-- Restore perturbation pressure on tend because this array is used
	688	!-- further below to correct the velocity fields
[707]	689	DO i = nxl-1, nxr+1
	690	DO j = nys-1, nyn+1
	691	DO k = nzb, nzt+1
	692	tend(k,j,i) = p_loc(k,j,i)
	693	ENDDO
	694	ENDDO
	695	ENDDO
[667]	696
[1]	697	ENDIF
	698
	699	!
[707]	700	!-- Store perturbation pressure on array p, used for pressure data output.
	701	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	702	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	703	!$OMP PARALLEL PRIVATE (i,j,k)
	704	!$OMP DO
[3634]	705	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	706	!$ACC PRESENT(p, tend)
[707]	707	DO i = nxl-1, nxr+1
	708	DO j = nys-1, nyn+1
	709	DO k = nzb, nzt+1
	710	p(k,j,i) = tend(k,j,i) * &
[1929]	711	weight_substep_l
[673]	712	ENDDO
[1]	713	ENDDO
[707]	714	ENDDO
	715	!$OMP END PARALLEL
	716
[1762]	717	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	718	!$OMP PARALLEL PRIVATE (i,j,k)
	719	!$OMP DO
[3634]	720	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	721	!$ACC PRESENT(p, tend)
[707]	722	DO i = nxl-1, nxr+1
	723	DO j = nys-1, nyn+1
	724	DO k = nzb, nzt+1
	725	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
[1929]	726	weight_substep_l
[673]	727	ENDDO
	728	ENDDO
[707]	729	ENDDO
	730	!$OMP END PARALLEL
	731
	732	ENDIF
[673]	733
[707]	734	!
	735	!-- SOR-method needs ghost layers for the next timestep
	736	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	737
[1]	738	!
	739	!-- Correction of the provisional velocities with the current perturbation
	740	!-- pressure just computed
[709]	741	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	742	volume_flow_l(1) = 0.0_wp
	743	volume_flow_l(2) = 0.0_wp
[1]	744	ENDIF
[3347]	745	!
	746	!-- Add pressure gradients to the velocity components. Note, the loops are
	747	!-- running over the entire model domain, even though, in case of non-cyclic
	748	!-- boundaries u- and v-component are not prognostic at i=0 and j=0,
	749	!-- respectiveley. However, in case of Dirichlet boundary conditions for the
	750	!-- velocities, zero-gradient conditions for the pressure are set, so that
	751	!-- no modification is imposed at the boundaries.
[1]	752	!$OMP PARALLEL PRIVATE (i,j,k)
	753	!$OMP DO
[3634]	754	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k) &
	755	!$ACC PRESENT(u, v, w, tend, ddzu, wall_flags_0)
[673]	756	DO i = nxl, nxr
[1]	757	DO j = nys, nyn
[2118]	758
[2232]	759	DO k = nzb+1, nzt
	760	w(k,j,i) = w(k,j,i) - dt_3d * &
	761	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) &
	762	* weight_pres_l &
	763	* MERGE( 1.0_wp, 0.0_wp, &
	764	BTEST( wall_flags_0(k,j,i), 3 ) &
	765	)
[1]	766	ENDDO
[2118]	767
[2232]	768	DO k = nzb+1, nzt
	769	u(k,j,i) = u(k,j,i) - dt_3d * &
	770	( tend(k,j,i) - tend(k,j,i-1) ) * ddx &
	771	* weight_pres_l &
	772	* MERGE( 1.0_wp, 0.0_wp, &
	773	BTEST( wall_flags_0(k,j,i), 1 ) &
	774	)
[1]	775	ENDDO
[2118]	776
[2232]	777	DO k = nzb+1, nzt
	778	v(k,j,i) = v(k,j,i) - dt_3d * &
	779	( tend(k,j,i) - tend(k,j-1,i) ) * ddy &
	780	* weight_pres_l &
	781	* MERGE( 1.0_wp, 0.0_wp, &
	782	BTEST( wall_flags_0(k,j,i), 2 ) &
	783	)
[673]	784	ENDDO
[1]	785
	786	ENDDO
	787	ENDDO
	788	!$OMP END PARALLEL
[1113]	789
	790	!
[3012]	791	!-- The vertical velocity is not set to zero at nzt + 1 for nested domains
	792	!-- Instead it is set to the values of nzt (see routine vnest_boundary_conds
	793	!-- or pmci_interp_tril_t) BEFORE calling the pressure solver. To avoid jumps
	794	!-- while plotting profiles w at the top has to be set to the values in the
	795	!-- height nzt after above modifications. Hint: w level nzt+1 does not impact
	796	!-- results.
[3182]	797	IF ( child_domain .OR. coupling_mode == 'vnested_fine' ) THEN
[3012]	798	w(nzt+1,:,:) = w(nzt,:,:)
	799	ENDIF
	800
	801	!
[1113]	802	!-- Sum up the volume flow through the right and north boundary
[2232]	803	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
[1113]	804	nxr == nx ) THEN
	805
	806	!$OMP PARALLEL PRIVATE (j,k)
	807	!$OMP DO
	808	DO j = nys, nyn
	809	!$OMP CRITICAL
[2232]	810	DO k = nzb+1, nzt
	811	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nxr) * dzw(k) &
	812	* MERGE( 1.0_wp, 0.0_wp, &
	813	BTEST( wall_flags_0(k,j,nxr), 1 )&
	814	)
[1113]	815	ENDDO
	816	!$OMP END CRITICAL
	817	ENDDO
	818	!$OMP END PARALLEL
	819
	820	ENDIF
	821
[2232]	822	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
[1113]	823	nyn == ny ) THEN
	824
	825	!$OMP PARALLEL PRIVATE (i,k)
	826	!$OMP DO
	827	DO i = nxl, nxr
	828	!$OMP CRITICAL
[2232]	829	DO k = nzb+1, nzt
	830	volume_flow_l(2) = volume_flow_l(2) + v(k,nyn,i) * dzw(k) &
	831	* MERGE( 1.0_wp, 0.0_wp, &
	832	BTEST( wall_flags_0(k,nyn,i), 2 )&
	833	)
[1113]	834	ENDDO
	835	!$OMP END CRITICAL
	836	ENDDO
	837	!$OMP END PARALLEL
	838
	839	ENDIF
[673]	840
[1]	841	!
	842	!-- Conserve the volume flow
[707]	843	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	844
	845	#if defined( __parallel )
[622]	846	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	847	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	848	MPI_SUM, comm2d, ierr )
	849	#else
	850	volume_flow = volume_flow_l
	851	#endif
	852
[1799]	853	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	854	volume_flow_area(1:2)
[1]	855
	856	!$OMP PARALLEL PRIVATE (i,j,k)
	857	!$OMP DO
	858	DO i = nxl, nxr
	859	DO j = nys, nyn
[2232]	860	DO k = nzb+1, nzt
	861	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	862	* MERGE( 1.0_wp, 0.0_wp, &
	863	BTEST( wall_flags_0(k,j,i), 1 ) &
	864	)
[719]	865	ENDDO
[2232]	866	DO k = nzb+1, nzt
	867	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	868	* MERGE( 1.0_wp, 0.0_wp, &
	869	BTEST( wall_flags_0(k,j,i), 2 ) &
	870	)
[667]	871	ENDDO
[1]	872	ENDDO
	873	ENDDO
[667]	874
[1]	875	!$OMP END PARALLEL
	876
	877	ENDIF
	878
	879	!
	880	!-- Exchange of boundaries for the velocities
[667]	881	CALL exchange_horiz( u, nbgp )
	882	CALL exchange_horiz( v, nbgp )
	883	CALL exchange_horiz( w, nbgp )
[1]	884
	885	!
	886	!-- Compute the divergence of the corrected velocity field,
[1908]	887	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	888	!-- only at last Runge-Kutta step.
[1918]	889	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	890	intermediate_timestep_count == 0 ) THEN
[1908]	891	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	892	sums_divnew_l = 0.0_wp
[1]	893
	894	!
[1908]	895	!-- d must be reset to zero because it can contain nonzero values below the
	896	!-- topography
	897	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	898
[1908]	899	localsum = 0.0_wp
	900	threadsum = 0.0_wp
[1]	901
[1908]	902	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
[2073]	903	#if defined( __ibm )
[1908]	904	!$OMP DO SCHEDULE( STATIC )
	905	DO i = nxl, nxr
	906	DO j = nys, nyn
[2232]	907	DO k = nzb+1, nzt
	908	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	909	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	910	( w(k,j,i) * rho_air_zw(k) - &
	911	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	912	) * MERGE( 1.0_wp, 0.0_wp, &
	913	BTEST( wall_flags_0(k,j,i), 0 ) &
	914	)
[1908]	915	ENDDO
	916	DO k = nzb+1, nzt
	917	threadsum = threadsum + ABS( d(k,j,i) )
	918	ENDDO
[1]	919	ENDDO
	920	ENDDO
	921	#else
[2073]	922	!$OMP DO SCHEDULE( STATIC )
[3634]	923	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	924	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_0) &
	925	!$ACC PRESENT(d)
[1908]	926	DO i = nxl, nxr
	927	DO j = nys, nyn
[2232]	928	DO k = nzb+1, nzt
[2037]	929	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	930	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	931	( w(k,j,i) * rho_air_zw(k) - &
	932	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	933	) * MERGE( 1.0_wp, 0.0_wp, &
	934	BTEST( wall_flags_0(k,j,i), 0 ) &
	935	)
[1908]	936	ENDDO
[1113]	937	ENDDO
	938	ENDDO
	939	!
[1908]	940	!-- Compute possible PE-sum of divergences for flow_statistics
[2073]	941	!$OMP DO SCHEDULE( STATIC )
[3634]	942	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	943	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	944	!$ACC PRESENT(d)
[1908]	945	DO i = nxl, nxr
	946	DO j = nys, nyn
	947	DO k = nzb+1, nzt
	948	threadsum = threadsum + ABS( d(k,j,i) )
	949	ENDDO
[1]	950	ENDDO
	951	ENDDO
	952	#endif
[667]	953
[1908]	954	localsum = localsum + threadsum
	955	!$OMP END PARALLEL
[1]	956
	957	!
[1908]	958	!-- For completeness, set the divergence sum of all statistic regions to those
	959	!-- of the total domain
	960	sums_divnew_l(0:statistic_regions) = localsum
[1]	961
[1908]	962	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	963
[1908]	964	ENDIF
	965
[1]	966	CALL cpu_log( log_point(8), 'pres', 'stop' )
	967
	968	END SUBROUTINE pres

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