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source: palm/trunk/SOURCE/pres.f90 @ 4539

Last change on this file since 4539 was 4457, checked in by raasch, 5 years ago
ghost point exchange modularized, bugfix for wrong 2d-exchange
Property svn:keywords set to `Id`
File size: 30.3 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	!
[4360]	17	! Copyright 1997-2020 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 4457 2020-03-11 14:20:43Z raasch $
[4457]	27	! use statement for exchange horiz added
	28	!
	29	! 4360 2020-01-07 11:25:50Z suehring
[4346]	30	! Introduction of wall_flags_total_0, which currently sets bits based on static
	31	! topography information used in wall_flags_static_0
	32	!
	33	! 4329 2019-12-10 15:46:36Z motisi
[4329]	34	! Renamed wall_flags_0 to wall_flags_static_0
	35	!
	36	! 4182 2019-08-22 15:20:23Z scharf
[4182]	37	! Corrected "Former revisions" section
	38	!
	39	! 4015 2019-06-05 13:25:35Z raasch
[4015]	40	! variable child_domain_nvn eliminated
	41	!
	42	! 3849 2019-04-01 16:35:16Z knoop
[3634]	43	! OpenACC port for SPEC
[1919]	44	!
[4182]	45	! Revision 1.1 1997/07/24 11:24:44 raasch
	46	! Initial revision
	47	!
	48	!
[1]	49	! Description:
	50	! ------------
[1682]	51	!> Compute the divergence of the provisional velocity field. Solve the Poisson
	52	!> equation for the perturbation pressure. Compute the final velocities using
	53	!> this perturbation pressure. Compute the remaining divergence.
[1]	54	!------------------------------------------------------------------------------!
[1682]	55	SUBROUTINE pres
	56
[1]	57
[1320]	58	USE arrays_3d, &
[2037]	59	ONLY: d, ddzu, ddzu_pres, ddzw, dzw, p, p_loc, rho_air, rho_air_zw, &
	60	tend, u, v, w
[1320]	61
	62	USE control_parameters, &
[3182]	63	ONLY: bc_lr_cyc, bc_ns_cyc, bc_radiation_l, bc_radiation_n, &
	64	bc_radiation_r, bc_radiation_s, child_domain, &
	65	conserve_volume_flow, coupling_mode, &
[3012]	66	dt_3d, gathered_size, ibc_p_b, ibc_p_t, &
	67	intermediate_timestep_count, intermediate_timestep_count_max, &
[3347]	68	mg_switch_to_pe0_level, nesting_offline, &
	69	psolver, subdomain_size, &
[3182]	70	topography, volume_flow, volume_flow_area, volume_flow_initial
[1320]	71
	72	USE cpulog, &
	73	ONLY: cpu_log, log_point, log_point_s
	74
[4457]	75	USE exchange_horiz_mod, &
	76	ONLY: exchange_horiz
	77
[1320]	78	USE grid_variables, &
	79	ONLY: ddx, ddy
	80
	81	USE indices, &
	82	ONLY: nbgp, ngp_2dh_outer, nx, nxl, nxlg, nxl_mg, nxr, nxrg, nxr_mg, &
[2232]	83	ny, nys, nysg, nys_mg, nyn, nyng, nyn_mg, nzb, nzt, nzt_mg, &
[4346]	84	wall_flags_total_0
[1320]	85
	86	USE kinds
	87
[1]	88	USE pegrid
[1933]	89
	90	USE pmc_interface, &
	91	ONLY: nesting_mode
[1]	92
[1320]	93	USE poisfft_mod, &
	94	ONLY: poisfft
	95
[1575]	96	USE poismg_mod
	97
[2696]	98	USE poismg_noopt_mod
	99
[1320]	100	USE statistics, &
	101	ONLY: statistic_regions, sums_divnew_l, sums_divold_l, weight_pres, &
	102	weight_substep
	103
[2232]	104	USE surface_mod, &
	105	ONLY : bc_h
	106
[1]	107	IMPLICIT NONE
	108
[1682]	109	INTEGER(iwp) :: i !<
	110	INTEGER(iwp) :: j !<
	111	INTEGER(iwp) :: k !<
[2232]	112	INTEGER(iwp) :: m !<
[1]	113
[1682]	114	REAL(wp) :: ddt_3d !<
[1918]	115	REAL(wp) :: d_weight_pres !<
[1682]	116	REAL(wp) :: localsum !<
	117	REAL(wp) :: threadsum !<
[1918]	118	REAL(wp) :: weight_pres_l !<
[1929]	119	REAL(wp) :: weight_substep_l !<
[1]	120
[1762]	121	REAL(wp), DIMENSION(1:3) :: volume_flow_l !<
	122	REAL(wp), DIMENSION(1:3) :: volume_flow_offset !<
[1682]	123	REAL(wp), DIMENSION(1:nzt) :: w_l !<
	124	REAL(wp), DIMENSION(1:nzt) :: w_l_l !<
[1]	125
	126
	127	CALL cpu_log( log_point(8), 'pres', 'start' )
	128
[1918]	129	!
	130	!-- Calculate quantities to be used locally
[1342]	131	ddt_3d = 1.0_wp / dt_3d
[1918]	132	IF ( intermediate_timestep_count == 0 ) THEN
	133	!
	134	!-- If pres is called before initial time step
[1929]	135	weight_pres_l = 1.0_wp
	136	d_weight_pres = 1.0_wp
	137	weight_substep_l = 1.0_wp
[1918]	138	ELSE
[1929]	139	weight_pres_l = weight_pres(intermediate_timestep_count)
	140	d_weight_pres = 1.0_wp / weight_pres(intermediate_timestep_count)
	141	weight_substep_l = weight_substep(intermediate_timestep_count)
[1918]	142	ENDIF
[85]	143
[1]	144	!
[707]	145	!-- Multigrid method expects array d to have one ghost layer.
	146	!--
[1575]	147	IF ( psolver(1:9) == 'multigrid' ) THEN
[667]	148
[1]	149	DEALLOCATE( d )
[667]	150	ALLOCATE( d(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1) )
[707]	151
	152	!
	153	!-- Since p is later used to hold the weighted average of the substeps, it
	154	!-- cannot be used in the iterative solver. Therefore, its initial value is
	155	!-- stored on p_loc, which is then iteratively advanced in every substep.
[1762]	156	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	157	DO i = nxl-1, nxr+1
	158	DO j = nys-1, nyn+1
	159	DO k = nzb, nzt+1
	160	p_loc(k,j,i) = p(k,j,i)
	161	ENDDO
	162	ENDDO
	163	ENDDO
[667]	164	ENDIF
	165
[1918]	166	ELSEIF ( psolver == 'sor' .AND. intermediate_timestep_count <= 1 ) THEN
[707]	167
	168	!
	169	!-- Since p is later used to hold the weighted average of the substeps, it
	170	!-- cannot be used in the iterative solver. Therefore, its initial value is
	171	!-- stored on p_loc, which is then iteratively advanced in every substep.
	172	p_loc = p
	173
[1]	174	ENDIF
	175
	176	!
[75]	177	!-- Conserve the volume flow at the outflow in case of non-cyclic lateral
	178	!-- boundary conditions
[106]	179	!-- WARNING: so far, this conservation does not work at the left/south
	180	!-- boundary if the topography at the inflow differs from that at the
	181	!-- outflow! For this case, volume_flow_area needs adjustment!
	182	!
	183	!-- Left/right
[3182]	184	IF ( conserve_volume_flow .AND. ( bc_radiation_l .OR. &
	185	bc_radiation_r ) ) THEN
[680]	186
[1342]	187	volume_flow(1) = 0.0_wp
	188	volume_flow_l(1) = 0.0_wp
[106]	189
[3182]	190	IF ( bc_radiation_l ) THEN
[106]	191	i = 0
[3182]	192	ELSEIF ( bc_radiation_r ) THEN
[106]	193	i = nx+1
	194	ENDIF
	195
	196	DO j = nys, nyn
	197	!
	198	!-- Sum up the volume flow through the south/north boundary
[2232]	199	DO k = nzb+1, nzt
	200	volume_flow_l(1) = volume_flow_l(1) + u(k,j,i) * dzw(k) &
	201	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	202	BTEST( wall_flags_total_0(k,j,i), 1 ) &
[2232]	203	)
[106]	204	ENDDO
	205	ENDDO
	206
	207	#if defined( __parallel )
[680]	208	IF ( collective_wait ) CALL MPI_BARRIER( comm1dy, ierr )
[106]	209	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 1, MPI_REAL, &
	210	MPI_SUM, comm1dy, ierr )
	211	#else
	212	volume_flow = volume_flow_l
	213	#endif
[709]	214	volume_flow_offset(1) = ( volume_flow_initial(1) - volume_flow(1) ) &
[106]	215	/ volume_flow_area(1)
	216
[667]	217	DO j = nysg, nyng
[2232]	218	DO k = nzb+1, nzt
	219	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	220	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	221	BTEST( wall_flags_total_0(k,j,i), 1 ) &
[2232]	222	)
[106]	223	ENDDO
	224	ENDDO
	225
	226	ENDIF
	227
	228	!
	229	!-- South/north
[3182]	230	IF ( conserve_volume_flow .AND. ( bc_radiation_n .OR. bc_radiation_s ) ) THEN
[106]	231
[1342]	232	volume_flow(2) = 0.0_wp
	233	volume_flow_l(2) = 0.0_wp
[75]	234
[3182]	235	IF ( bc_radiation_s ) THEN
[106]	236	j = 0
[3182]	237	ELSEIF ( bc_radiation_n ) THEN
[75]	238	j = ny+1
[106]	239	ENDIF
	240
	241	DO i = nxl, nxr
[75]	242	!
[106]	243	!-- Sum up the volume flow through the south/north boundary
[2232]	244	DO k = nzb+1, nzt
	245	volume_flow_l(2) = volume_flow_l(2) + v(k,j,i) * dzw(k) &
	246	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	247	BTEST( wall_flags_total_0(k,j,i), 2 ) &
[2232]	248	)
[75]	249	ENDDO
[106]	250	ENDDO
	251
[75]	252	#if defined( __parallel )
[680]	253	IF ( collective_wait ) CALL MPI_BARRIER( comm1dx, ierr )
[75]	254	CALL MPI_ALLREDUCE( volume_flow_l(2), volume_flow(2), 1, MPI_REAL, &
	255	MPI_SUM, comm1dx, ierr )
	256	#else
	257	volume_flow = volume_flow_l
	258	#endif
	259	volume_flow_offset(2) = ( volume_flow_initial(2) - volume_flow(2) ) &
[106]	260	/ volume_flow_area(2)
[75]	261
[667]	262	DO i = nxlg, nxrg
[2232]	263	DO k = nzb+1, nzt
	264	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	265	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	266	BTEST( wall_flags_total_0(k,j,i), 2 ) &
[2232]	267	)
[75]	268	ENDDO
[106]	269	ENDDO
[75]	270
	271	ENDIF
	272
[76]	273	!
[4015]	274	!-- Remove mean vertical velocity in case that Neumann conditions are used both at bottom and top
	275	!-- boundary. With Neumann conditions at both vertical boundaries, the solver cannot remove
	276	!-- mean vertical velocities. They should be removed, because incompressibility requires that
	277	!-- the vertical gradient of vertical velocity is zero. Since w=0 at the solid surface, it must be
	278	!-- zero everywhere.
	279	!-- This must not be done in case of a 3d-nesting child domain, because a mean vertical velocity
	280	!-- can physically exist in such a domain.
	281	!-- Also in case of offline nesting, mean vertical velocities may exist (and must not be removed),
	282	!-- caused by horizontal divergence/convergence of the large scale flow that is prescribed at the
	283	!-- side boundaries.
	284	!-- The removal cannot be done before the first initial time step because ngp_2dh_outer
[1918]	285	!-- is not yet known then.
[4015]	286	IF ( ibc_p_b == 1 .AND. ibc_p_t == 1 .AND. .NOT. nesting_offline &
	287	.AND. .NOT. ( child_domain .AND. nesting_mode /= 'vertical' ) &
	288	.AND. intermediate_timestep_count /= 0 ) &
[1918]	289	THEN
	290	w_l = 0.0_wp; w_l_l = 0.0_wp
	291	DO i = nxl, nxr
	292	DO j = nys, nyn
[2232]	293	DO k = nzb+1, nzt
[4015]	294	w_l_l(k) = w_l_l(k) + w(k,j,i) &
[4346]	295	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
[76]	296	ENDDO
	297	ENDDO
[1918]	298	ENDDO
[76]	299	#if defined( __parallel )
[1918]	300	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[4015]	301	CALL MPI_ALLREDUCE( w_l_l(1), w_l(1), nzt, MPI_REAL, MPI_SUM, comm2d, ierr )
[76]	302	#else
[1918]	303	w_l = w_l_l
[76]	304	#endif
[1918]	305	DO k = 1, nzt
	306	w_l(k) = w_l(k) / ngp_2dh_outer(k,0)
	307	ENDDO
	308	DO i = nxlg, nxrg
	309	DO j = nysg, nyng
[2232]	310	DO k = nzb+1, nzt
[4015]	311	w(k,j,i) = w(k,j,i) - w_l(k) &
[4346]	312	* MERGE( 1.0_wp, 0.0_wp, BTEST( wall_flags_total_0(k,j,i), 3 ) )
[76]	313	ENDDO
	314	ENDDO
[1918]	315	ENDDO
[76]	316	ENDIF
[75]	317
	318	!
[1]	319	!-- Compute the divergence of the provisional velocity field.
	320	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	321
[1575]	322	IF ( psolver(1:9) == 'multigrid' ) THEN
[2232]	323	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[1]	324	DO i = nxl-1, nxr+1
	325	DO j = nys-1, nyn+1
	326	DO k = nzb, nzt+1
[1342]	327	d(k,j,i) = 0.0_wp
[1]	328	ENDDO
	329	ENDDO
	330	ENDDO
	331	ELSE
[2232]	332	!$OMP PARALLEL DO SCHEDULE( STATIC ) PRIVATE (i,j,k)
[3634]	333	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	334	!$ACC PRESENT(d)
[1003]	335	DO i = nxl, nxr
	336	DO j = nys, nyn
	337	DO k = nzb+1, nzt
[1342]	338	d(k,j,i) = 0.0_wp
[1]	339	ENDDO
	340	ENDDO
	341	ENDDO
	342	ENDIF
	343
[1342]	344	localsum = 0.0_wp
	345	threadsum = 0.0_wp
[1]	346
	347	#if defined( __ibm )
	348	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	349	!$OMP DO SCHEDULE( STATIC )
	350	DO i = nxl, nxr
	351	DO j = nys, nyn
[2232]	352	DO k = nzb+1, nzt
[2037]	353	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	354	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	355	( w(k,j,i) * rho_air_zw(k) - &
	356	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	357	) * ddt_3d * d_weight_pres &
	358	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	359	BTEST( wall_flags_total_0(k,j,i), 0 ) &
[2232]	360	)
[1]	361	ENDDO
	362	!
	363	!-- Compute possible PE-sum of divergences for flow_statistics
[2232]	364	DO k = nzb+1, nzt
	365	threadsum = threadsum + ABS( d(k,j,i) ) &
	366	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	367	BTEST( wall_flags_total_0(k,j,i), 0 ) &
[2232]	368	)
[1]	369	ENDDO
	370
	371	ENDDO
	372	ENDDO
	373
[1918]	374	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	375	intermediate_timestep_count == 0 ) THEN
	376	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	377	ENDIF
[1]	378	!$OMP END PARALLEL
	379	#else
	380
[1111]	381	!$OMP PARALLEL PRIVATE (i,j,k)
	382	!$OMP DO SCHEDULE( STATIC )
[3634]	383	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
[4346]	384	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_total_0) &
[3634]	385	!$ACC PRESENT(d)
[1111]	386	DO i = nxl, nxr
	387	DO j = nys, nyn
	388	DO k = 1, nzt
[2037]	389	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	390	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	391	( w(k,j,i) * rho_air_zw(k) - &
	392	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	393	) * ddt_3d * d_weight_pres &
	394	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	395	BTEST( wall_flags_total_0(k,j,i), 0 ) &
[2232]	396	)
[1]	397	ENDDO
	398	ENDDO
[1111]	399	ENDDO
	400	!$OMP END PARALLEL
[1]	401
	402	!
[1908]	403	!-- Compute possible PE-sum of divergences for flow_statistics. Carry out
	404	!-- computation only at last Runge-Kutta substep.
[1918]	405	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	406	intermediate_timestep_count == 0 ) THEN
[1908]	407	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
	408	!$OMP DO SCHEDULE( STATIC )
[3634]	409	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i,j,k) &
	410	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	411	!$ACC PRESENT(d)
[1908]	412	DO i = nxl, nxr
	413	DO j = nys, nyn
	414	DO k = nzb+1, nzt
	415	threadsum = threadsum + ABS( d(k,j,i) )
	416	ENDDO
[1]	417	ENDDO
	418	ENDDO
[1918]	419	localsum = localsum + threadsum * dt_3d * weight_pres_l
[1908]	420	!$OMP END PARALLEL
	421	ENDIF
[1]	422	#endif
	423
	424	!
	425	!-- For completeness, set the divergence sum of all statistic regions to those
	426	!-- of the total domain
[1918]	427	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	428	intermediate_timestep_count == 0 ) THEN
[1908]	429	sums_divold_l(0:statistic_regions) = localsum
[1918]	430	ENDIF
[1]	431
	432	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
	433
	434	!
	435	!-- Compute the pressure perturbation solving the Poisson equation
[1575]	436	IF ( psolver == 'poisfft' ) THEN
[1]	437
	438	!
	439	!-- Solve Poisson equation via FFT and solution of tridiagonal matrices
[1575]	440	CALL poisfft( d )
[1212]	441
[1]	442	!
	443	!-- Store computed perturbation pressure and set boundary condition in
	444	!-- z-direction
[2232]	445	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	446	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	447	!$ACC PRESENT(d, tend)
[1]	448	DO i = nxl, nxr
	449	DO j = nys, nyn
	450	DO k = nzb+1, nzt
	451	tend(k,j,i) = d(k,j,i)
	452	ENDDO
	453	ENDDO
	454	ENDDO
	455
	456	!
	457	!-- Bottom boundary:
	458	!-- This condition is only required for internal output. The pressure
	459	!-- gradient (dp(nzb+1)-dp(nzb))/dz is not used anywhere else.
	460	IF ( ibc_p_b == 1 ) THEN
	461	!
[2232]	462	!-- Neumann (dp/dz = 0). Using surfae data type, first for non-natural
	463	!-- surfaces, then for natural and urban surfaces
	464	!-- Upward facing
	465	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	466	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	467	!$ACC PRESENT(bc_h, tend)
[2232]	468	DO m = 1, bc_h(0)%ns
[2298]	469	i = bc_h(0)%i(m)
	470	j = bc_h(0)%j(m)
	471	k = bc_h(0)%k(m)
[2232]	472	tend(k-1,j,i) = tend(k,j,i)
[1]	473	ENDDO
[2232]	474	!
	475	!-- Downward facing
	476	!$OMP PARALLEL DO PRIVATE( i, j, k )
[3634]	477	!$ACC PARALLEL LOOP PRIVATE(i, j, k) &
	478	!$ACC PRESENT(bc_h, tend)
[2232]	479	DO m = 1, bc_h(1)%ns
[2298]	480	i = bc_h(1)%i(m)
	481	j = bc_h(1)%j(m)
	482	k = bc_h(1)%k(m)
[2232]	483	tend(k+1,j,i) = tend(k,j,i)
	484	ENDDO
[1]	485
	486	ELSE
	487	!
[2232]	488	!-- Dirichlet. Using surface data type, first for non-natural
	489	!-- surfaces, then for natural and urban surfaces
	490	!-- Upward facing
	491	!$OMP PARALLEL DO PRIVATE( i, j, k )
	492	DO m = 1, bc_h(0)%ns
[2298]	493	i = bc_h(0)%i(m)
	494	j = bc_h(0)%j(m)
	495	k = bc_h(0)%k(m)
[2232]	496	tend(k-1,j,i) = 0.0_wp
[1]	497	ENDDO
[2232]	498	!
	499	!-- Downward facing
	500	!$OMP PARALLEL DO PRIVATE( i, j, k )
	501	DO m = 1, bc_h(1)%ns
[2298]	502	i = bc_h(1)%i(m)
	503	j = bc_h(1)%j(m)
	504	k = bc_h(1)%k(m)
[2232]	505	tend(k+1,j,i) = 0.0_wp
	506	ENDDO
[1]	507
	508	ENDIF
	509
	510	!
	511	!-- Top boundary
	512	IF ( ibc_p_t == 1 ) THEN
	513	!
	514	!-- Neumann
[2232]	515	!$OMP PARALLEL DO PRIVATE (i,j,k)
[667]	516	DO i = nxlg, nxrg
	517	DO j = nysg, nyng
[1]	518	tend(nzt+1,j,i) = tend(nzt,j,i)
	519	ENDDO
	520	ENDDO
	521
	522	ELSE
	523	!
	524	!-- Dirichlet
[2232]	525	!$OMP PARALLEL DO PRIVATE (i,j,k)
[3634]	526	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j) &
	527	!$ACC PRESENT(tend)
[667]	528	DO i = nxlg, nxrg
	529	DO j = nysg, nyng
[1342]	530	tend(nzt+1,j,i) = 0.0_wp
[1]	531	ENDDO
	532	ENDDO
	533
	534	ENDIF
	535
	536	!
	537	!-- Exchange boundaries for p
[667]	538	CALL exchange_horiz( tend, nbgp )
[1]	539
	540	ELSEIF ( psolver == 'sor' ) THEN
	541
	542	!
	543	!-- Solve Poisson equation for perturbation pressure using SOR-Red/Black
	544	!-- scheme
[707]	545	CALL sor( d, ddzu_pres, ddzw, p_loc )
	546	tend = p_loc
[1]	547
[1575]	548	ELSEIF ( psolver(1:9) == 'multigrid' ) THEN
[1]	549
	550	!
	551	!-- Solve Poisson equation for perturbation pressure using Multigrid scheme,
[2298]	552	!-- array tend is used to store the residuals.
[778]	553
	554	!-- If the number of grid points of the gathered grid, which is collected
	555	!-- on PE0, is larger than the number of grid points of an PE, than array
	556	!-- tend will be enlarged.
	557	IF ( gathered_size > subdomain_size ) THEN
	558	DEALLOCATE( tend )
	559	ALLOCATE( tend(nzb:nzt_mg(mg_switch_to_pe0_level)+1,nys_mg( &
	560	mg_switch_to_pe0_level)-1:nyn_mg(mg_switch_to_pe0_level)+1,&
	561	nxl_mg(mg_switch_to_pe0_level)-1:nxr_mg( &
	562	mg_switch_to_pe0_level)+1) )
	563	ENDIF
	564
[1575]	565	IF ( psolver == 'multigrid' ) THEN
	566	CALL poismg( tend )
	567	ELSE
[1931]	568	CALL poismg_noopt( tend )
[1575]	569	ENDIF
[707]	570
[778]	571	IF ( gathered_size > subdomain_size ) THEN
	572	DEALLOCATE( tend )
	573	ALLOCATE( tend(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
	574	ENDIF
	575
[1]	576	!
	577	!-- Restore perturbation pressure on tend because this array is used
	578	!-- further below to correct the velocity fields
[707]	579	DO i = nxl-1, nxr+1
	580	DO j = nys-1, nyn+1
	581	DO k = nzb, nzt+1
	582	tend(k,j,i) = p_loc(k,j,i)
	583	ENDDO
	584	ENDDO
	585	ENDDO
[667]	586
[1]	587	ENDIF
	588
	589	!
[707]	590	!-- Store perturbation pressure on array p, used for pressure data output.
	591	!-- Ghost layers are added in the output routines (except sor-method: see below)
[1918]	592	IF ( intermediate_timestep_count <= 1 ) THEN
[707]	593	!$OMP PARALLEL PRIVATE (i,j,k)
	594	!$OMP DO
[3634]	595	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	596	!$ACC PRESENT(p, tend)
[707]	597	DO i = nxl-1, nxr+1
	598	DO j = nys-1, nyn+1
	599	DO k = nzb, nzt+1
	600	p(k,j,i) = tend(k,j,i) * &
[1929]	601	weight_substep_l
[673]	602	ENDDO
[1]	603	ENDDO
[707]	604	ENDDO
	605	!$OMP END PARALLEL
	606
[1762]	607	ELSEIF ( intermediate_timestep_count > 1 ) THEN
[707]	608	!$OMP PARALLEL PRIVATE (i,j,k)
	609	!$OMP DO
[3634]	610	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	611	!$ACC PRESENT(p, tend)
[707]	612	DO i = nxl-1, nxr+1
	613	DO j = nys-1, nyn+1
	614	DO k = nzb, nzt+1
	615	p(k,j,i) = p(k,j,i) + tend(k,j,i) * &
[1929]	616	weight_substep_l
[673]	617	ENDDO
	618	ENDDO
[707]	619	ENDDO
	620	!$OMP END PARALLEL
	621
	622	ENDIF
[673]	623
[707]	624	!
	625	!-- SOR-method needs ghost layers for the next timestep
	626	IF ( psolver == 'sor' ) CALL exchange_horiz( p, nbgp )
[682]	627
[1]	628	!
	629	!-- Correction of the provisional velocities with the current perturbation
	630	!-- pressure just computed
[709]	631	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .OR. bc_ns_cyc ) ) THEN
[1342]	632	volume_flow_l(1) = 0.0_wp
	633	volume_flow_l(2) = 0.0_wp
[1]	634	ENDIF
[3347]	635	!
	636	!-- Add pressure gradients to the velocity components. Note, the loops are
	637	!-- running over the entire model domain, even though, in case of non-cyclic
	638	!-- boundaries u- and v-component are not prognostic at i=0 and j=0,
	639	!-- respectiveley. However, in case of Dirichlet boundary conditions for the
	640	!-- velocities, zero-gradient conditions for the pressure are set, so that
	641	!-- no modification is imposed at the boundaries.
[1]	642	!$OMP PARALLEL PRIVATE (i,j,k)
	643	!$OMP DO
[3634]	644	!$ACC PARALLEL LOOP COLLAPSE(2) PRIVATE(i, j, k) &
[4346]	645	!$ACC PRESENT(u, v, w, tend, ddzu, wall_flags_total_0)
[673]	646	DO i = nxl, nxr
[1]	647	DO j = nys, nyn
[2118]	648
[2232]	649	DO k = nzb+1, nzt
	650	w(k,j,i) = w(k,j,i) - dt_3d * &
	651	( tend(k+1,j,i) - tend(k,j,i) ) * ddzu(k+1) &
	652	* weight_pres_l &
	653	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	654	BTEST( wall_flags_total_0(k,j,i), 3 ) &
[2232]	655	)
[1]	656	ENDDO
[2118]	657
[2232]	658	DO k = nzb+1, nzt
	659	u(k,j,i) = u(k,j,i) - dt_3d * &
	660	( tend(k,j,i) - tend(k,j,i-1) ) * ddx &
	661	* weight_pres_l &
	662	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	663	BTEST( wall_flags_total_0(k,j,i), 1 ) &
[2232]	664	)
[1]	665	ENDDO
[2118]	666
[2232]	667	DO k = nzb+1, nzt
	668	v(k,j,i) = v(k,j,i) - dt_3d * &
	669	( tend(k,j,i) - tend(k,j-1,i) ) * ddy &
	670	* weight_pres_l &
	671	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	672	BTEST( wall_flags_total_0(k,j,i), 2 ) &
[2232]	673	)
[673]	674	ENDDO
[1]	675
	676	ENDDO
	677	ENDDO
	678	!$OMP END PARALLEL
[1113]	679
	680	!
[3012]	681	!-- The vertical velocity is not set to zero at nzt + 1 for nested domains
	682	!-- Instead it is set to the values of nzt (see routine vnest_boundary_conds
	683	!-- or pmci_interp_tril_t) BEFORE calling the pressure solver. To avoid jumps
	684	!-- while plotting profiles w at the top has to be set to the values in the
	685	!-- height nzt after above modifications. Hint: w level nzt+1 does not impact
	686	!-- results.
[3182]	687	IF ( child_domain .OR. coupling_mode == 'vnested_fine' ) THEN
[3012]	688	w(nzt+1,:,:) = w(nzt,:,:)
	689	ENDIF
	690
	691	!
[1113]	692	!-- Sum up the volume flow through the right and north boundary
[2232]	693	IF ( conserve_volume_flow .AND. bc_lr_cyc .AND. bc_ns_cyc .AND. &
[1113]	694	nxr == nx ) THEN
	695
	696	!$OMP PARALLEL PRIVATE (j,k)
	697	!$OMP DO
	698	DO j = nys, nyn
	699	!$OMP CRITICAL
[2232]	700	DO k = nzb+1, nzt
	701	volume_flow_l(1) = volume_flow_l(1) + u(k,j,nxr) * dzw(k) &
	702	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	703	BTEST( wall_flags_total_0(k,j,nxr), 1 )&
[2232]	704	)
[1113]	705	ENDDO
	706	!$OMP END CRITICAL
	707	ENDDO
	708	!$OMP END PARALLEL
	709
	710	ENDIF
	711
[2232]	712	IF ( conserve_volume_flow .AND. bc_ns_cyc .AND. bc_lr_cyc .AND. &
[1113]	713	nyn == ny ) THEN
	714
	715	!$OMP PARALLEL PRIVATE (i,k)
	716	!$OMP DO
	717	DO i = nxl, nxr
	718	!$OMP CRITICAL
[2232]	719	DO k = nzb+1, nzt
	720	volume_flow_l(2) = volume_flow_l(2) + v(k,nyn,i) * dzw(k) &
	721	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	722	BTEST( wall_flags_total_0(k,nyn,i), 2 )&
[2232]	723	)
[1113]	724	ENDDO
	725	!$OMP END CRITICAL
	726	ENDDO
	727	!$OMP END PARALLEL
	728
	729	ENDIF
[673]	730
[1]	731	!
	732	!-- Conserve the volume flow
[707]	733	IF ( conserve_volume_flow .AND. ( bc_lr_cyc .AND. bc_ns_cyc ) ) THEN
[1]	734
	735	#if defined( __parallel )
[622]	736	IF ( collective_wait ) CALL MPI_BARRIER( comm2d, ierr )
[1]	737	CALL MPI_ALLREDUCE( volume_flow_l(1), volume_flow(1), 2, MPI_REAL, &
	738	MPI_SUM, comm2d, ierr )
	739	#else
	740	volume_flow = volume_flow_l
	741	#endif
	742
[1799]	743	volume_flow_offset(1:2) = ( volume_flow_initial(1:2) - volume_flow(1:2) ) / &
	744	volume_flow_area(1:2)
[1]	745
	746	!$OMP PARALLEL PRIVATE (i,j,k)
	747	!$OMP DO
	748	DO i = nxl, nxr
	749	DO j = nys, nyn
[2232]	750	DO k = nzb+1, nzt
	751	u(k,j,i) = u(k,j,i) + volume_flow_offset(1) &
	752	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	753	BTEST( wall_flags_total_0(k,j,i), 1 ) &
[2232]	754	)
[719]	755	ENDDO
[2232]	756	DO k = nzb+1, nzt
	757	v(k,j,i) = v(k,j,i) + volume_flow_offset(2) &
	758	* MERGE( 1.0_wp, 0.0_wp, &
[4346]	759	BTEST( wall_flags_total_0(k,j,i), 2 ) &
[2232]	760	)
[667]	761	ENDDO
[1]	762	ENDDO
	763	ENDDO
[667]	764
[1]	765	!$OMP END PARALLEL
	766
	767	ENDIF
	768
	769	!
	770	!-- Exchange of boundaries for the velocities
[667]	771	CALL exchange_horiz( u, nbgp )
	772	CALL exchange_horiz( v, nbgp )
	773	CALL exchange_horiz( w, nbgp )
[1]	774
	775	!
	776	!-- Compute the divergence of the corrected velocity field,
[1908]	777	!-- A possible PE-sum is computed in flow_statistics. Carry out computation
	778	!-- only at last Runge-Kutta step.
[1918]	779	IF ( intermediate_timestep_count == intermediate_timestep_count_max .OR. &
	780	intermediate_timestep_count == 0 ) THEN
[1908]	781	CALL cpu_log( log_point_s(1), 'divergence', 'start' )
	782	sums_divnew_l = 0.0_wp
[1]	783
	784	!
[1908]	785	!-- d must be reset to zero because it can contain nonzero values below the
	786	!-- topography
	787	IF ( topography /= 'flat' ) d = 0.0_wp
[1]	788
[1908]	789	localsum = 0.0_wp
	790	threadsum = 0.0_wp
[1]	791
[1908]	792	!$OMP PARALLEL PRIVATE (i,j,k) FIRSTPRIVATE(threadsum) REDUCTION(+:localsum)
[2073]	793	#if defined( __ibm )
[1908]	794	!$OMP DO SCHEDULE( STATIC )
	795	DO i = nxl, nxr
	796	DO j = nys, nyn
[2232]	797	DO k = nzb+1, nzt
	798	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	799	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	800	( w(k,j,i) * rho_air_zw(k) - &
	801	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
	802	) * MERGE( 1.0_wp, 0.0_wp, &
[4346]	803	BTEST( wall_flags_total_0(k,j,i), 0 ) &
[2232]	804	)
[1908]	805	ENDDO
	806	DO k = nzb+1, nzt
	807	threadsum = threadsum + ABS( d(k,j,i) )
	808	ENDDO
[1]	809	ENDDO
	810	ENDDO
	811	#else
[2073]	812	!$OMP DO SCHEDULE( STATIC )
[3634]	813	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
[4346]	814	!$ACC PRESENT(u, v, w, rho_air, rho_air_zw, ddzw, wall_flags_total_0) &
[3634]	815	!$ACC PRESENT(d)
[1908]	816	DO i = nxl, nxr
	817	DO j = nys, nyn
[2232]	818	DO k = nzb+1, nzt
[2037]	819	d(k,j,i) = ( ( u(k,j,i+1) - u(k,j,i) ) * rho_air(k) * ddx + &
	820	( v(k,j+1,i) - v(k,j,i) ) * rho_air(k) * ddy + &
	821	( w(k,j,i) * rho_air_zw(k) - &
	822	w(k-1,j,i) * rho_air_zw(k-1) ) * ddzw(k) &
[2232]	823	) * MERGE( 1.0_wp, 0.0_wp, &
[4346]	824	BTEST( wall_flags_total_0(k,j,i), 0 ) &
[2232]	825	)
[1908]	826	ENDDO
[1113]	827	ENDDO
	828	ENDDO
	829	!
[1908]	830	!-- Compute possible PE-sum of divergences for flow_statistics
[2073]	831	!$OMP DO SCHEDULE( STATIC )
[3634]	832	!$ACC PARALLEL LOOP COLLAPSE(3) PRIVATE(i, j, k) &
	833	!$ACC REDUCTION(+:threadsum) COPY(threadsum) &
	834	!$ACC PRESENT(d)
[1908]	835	DO i = nxl, nxr
	836	DO j = nys, nyn
	837	DO k = nzb+1, nzt
	838	threadsum = threadsum + ABS( d(k,j,i) )
	839	ENDDO
[1]	840	ENDDO
	841	ENDDO
	842	#endif
[667]	843
[1908]	844	localsum = localsum + threadsum
	845	!$OMP END PARALLEL
[1]	846
	847	!
[1908]	848	!-- For completeness, set the divergence sum of all statistic regions to those
	849	!-- of the total domain
	850	sums_divnew_l(0:statistic_regions) = localsum
[1]	851
[1908]	852	CALL cpu_log( log_point_s(1), 'divergence', 'stop' )
[1]	853
[1908]	854	ENDIF
	855
[1]	856	CALL cpu_log( log_point(8), 'pres', 'stop' )
	857
	858	END SUBROUTINE pres

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