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source: palm/trunk/SOURCE/diffusion_v.f90 @ 2037

Last change on this file since 2037 was 2037, checked in by knoop, 7 years ago
Anelastic approximation implemented
Property svn:keywords set to `Id`
File size: 27.1 KB

Rev	Line
[1873]	1	!> @file diffusion_v.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[1818]	17	! Copyright 1997-2016 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[2037]	22	! Anelastic approximation implemented
[1341]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_v.f90 2037 2016-10-26 11:15:40Z knoop $
	27	!
[2001]	28	! 2000 2016-08-20 18:09:15Z knoop
	29	! Forced header and separation lines into 80 columns
	30	!
[1874]	31	! 1873 2016-04-18 14:50:06Z maronga
	32	! Module renamed (removed _mod)
	33	!
	34	!
[1851]	35	! 1850 2016-04-08 13:29:27Z maronga
	36	! Module renamed
	37	!
	38	!
[1741]	39	! 1740 2016-01-13 08:19:40Z raasch
	40	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	41	!
[1683]	42	! 1682 2015-10-07 23:56:08Z knoop
	43	! Code annotations made doxygen readable
	44	!
[1341]	45	! 1340 2014-03-25 19:45:13Z kanani
	46	! REAL constants defined as wp-kind
	47	!
[1321]	48	! 1320 2014-03-20 08:40:49Z raasch
[1320]	49	! ONLY-attribute added to USE-statements,
	50	! kind-parameters added to all INTEGER and REAL declaration statements,
	51	! kinds are defined in new module kinds,
	52	! revision history before 2012 removed,
	53	! comment fields (!:) to be used for variable explanations added to
	54	! all variable declaration statements
[1321]	55	!
[1258]	56	! 1257 2013-11-08 15:18:40Z raasch
	57	! openacc loop and loop vector clauses removed, declare create moved after
	58	! the FORTRAN declaration statement
	59	!
[1132]	60	! 1128 2013-04-12 06:19:32Z raasch
	61	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	62	! j_north
	63	!
[1037]	64	! 1036 2012-10-22 13:43:42Z raasch
	65	! code put under GPL (PALM 3.9)
	66	!
[1017]	67	! 1015 2012-09-27 09:23:24Z raasch
	68	! accelerator version (*_acc) added
	69	!
[1002]	70	! 1001 2012-09-13 14:08:46Z raasch
	71	! arrays comunicated by module instead of parameter list
	72	!
[979]	73	! 978 2012-08-09 08:28:32Z fricke
	74	! outflow damping layer removed
	75	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	76	!
[1]	77	! Revision 1.1 1997/09/12 06:24:01 raasch
	78	! Initial revision
	79	!
	80	!
	81	! Description:
	82	! ------------
[1682]	83	!> Diffusion term of the v-component
[1]	84	!------------------------------------------------------------------------------!
[1682]	85	MODULE diffusion_v_mod
	86
[1]	87
[56]	88	USE wall_fluxes_mod
	89
[1]	90	PRIVATE
[1015]	91	PUBLIC diffusion_v, diffusion_v_acc
[1]	92
	93	INTERFACE diffusion_v
	94	MODULE PROCEDURE diffusion_v
	95	MODULE PROCEDURE diffusion_v_ij
	96	END INTERFACE diffusion_v
	97
[1015]	98	INTERFACE diffusion_v_acc
	99	MODULE PROCEDURE diffusion_v_acc
	100	END INTERFACE diffusion_v_acc
	101
[1]	102	CONTAINS
	103
	104
	105	!------------------------------------------------------------------------------!
[1682]	106	! Description:
	107	! ------------
	108	!> Call for all grid points
[1]	109	!------------------------------------------------------------------------------!
[1001]	110	SUBROUTINE diffusion_v
[1]	111
[1320]	112	USE arrays_3d, &
[2037]	113	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, &
	114	drho_air, rho_air_zw
[1320]	115
	116	USE control_parameters, &
	117	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	118	use_top_fluxes
	119
	120	USE grid_variables, &
	121	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	122
	123	USE indices, &
	124	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	125	nzb_v_outer, nzt, nzt_diff
	126
	127	USE kinds
[1]	128
	129	IMPLICIT NONE
	130
[1682]	131	INTEGER(iwp) :: i !<
	132	INTEGER(iwp) :: j !<
	133	INTEGER(iwp) :: k !<
	134	REAL(wp) :: kmxm !<
	135	REAL(wp) :: kmxp !<
	136	REAL(wp) :: kmzm !<
	137	REAL(wp) :: kmzp !<
[1001]	138
[1682]	139	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1]	140
[56]	141	!
	142	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	143	!-- if neccessary
	144	IF ( topography /= 'flat' ) THEN
[1320]	145	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	146	nzb_v_outer, wall_v )
	147	ENDIF
	148
[1]	149	DO i = nxl, nxr
[106]	150	DO j = nysv, nyn
[1]	151	!
	152	!-- Compute horizontal diffusion
	153	DO k = nzb_v_outer(j,i)+1, nzt
	154	!
	155	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	156	kmxp = 0.25_wp * &
[978]	157	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	158	kmxm = 0.25_wp * &
[978]	159	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	160
[1320]	161	tend(k,j,i) = tend(k,j,i) &
	162	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	163	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	164	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	165	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	166	& ) * ddx &
[1340]	167	& + 2.0_wp * ( &
[1320]	168	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	169	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	170	& ) * ddy2
[1]	171	ENDDO
	172
	173	!
	174	!-- Wall functions at the left and right walls, respectively
[1340]	175	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	176
[1]	177	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	178	kmxp = 0.25_wp * &
[978]	179	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	180	kmxm = 0.25_wp * &
[978]	181	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	182
[1]	183	tend(k,j,i) = tend(k,j,i) &
[1340]	184	+ 2.0_wp * ( &
[1]	185	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	186	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	187	) * ddy2 &
[1]	188	+ ( fxp(j,i) * ( &
[978]	189	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	190	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	191	) &
	192	- fxm(j,i) * ( &
[978]	193	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	194	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	195	) &
[56]	196	+ wall_v(j,i) * vsus(k,j,i) &
[1]	197	) * ddx
	198	ENDDO
	199	ENDIF
	200
	201	!
	202	!-- Compute vertical diffusion. In case of simulating a Prandtl
	203	!-- layer, index k starts at nzb_v_inner+2.
[102]	204	DO k = nzb_diff_v(j,i), nzt_diff
[1]	205	!
	206	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	207	kmzp = 0.25_wp * &
[1]	208	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	209	kmzm = 0.25_wp * &
[1]	210	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	211
[1320]	212	tend(k,j,i) = tend(k,j,i) &
	213	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	214	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2037]	215	& ) * rho_air_zw(k) &
[1320]	216	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	217	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2037]	218	& ) * rho_air_zw(k-1) &
	219	& ) * ddzw(k) * drho_air(k)
[1]	220	ENDDO
	221
	222	!
	223	!-- Vertical diffusion at the first grid point above the surface,
	224	!-- if the momentum flux at the bottom is given by the Prandtl law
	225	!-- or if it is prescribed by the user.
	226	!-- Difference quotient of the momentum flux is not formed over
	227	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	228	!-- comparison with other (LES) models showed that the values of
[1]	229	!-- the momentum flux becomes too large in this case.
	230	!-- The term containing w(k-1,..) (see above equation) is removed here
	231	!-- because the vertical velocity is assumed to be zero at the surface.
	232	IF ( use_surface_fluxes ) THEN
	233	k = nzb_v_inner(j,i)+1
	234	!
	235	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	236	kmzp = 0.25_wp * &
[1]	237	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	238
[1320]	239	tend(k,j,i) = tend(k,j,i) &
[2037]	240	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	241	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	242	& ) * rho_air_zw(k) &
	243	& - ( -vsws(j,i) ) &
	244	& ) * ddzw(k) * drho_air(k)
[1]	245	ENDIF
	246
[102]	247	!
	248	!-- Vertical diffusion at the first gridpoint below the top boundary,
	249	!-- if the momentum flux at the top is prescribed by the user
[103]	250	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	251	k = nzt
	252	!
	253	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	254	kmzm = 0.25_wp * &
[102]	255	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	256
[1320]	257	tend(k,j,i) = tend(k,j,i) &
[2037]	258	& + ( ( -vswst(j,i) ) &
	259	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	260	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	261	& ) * rho_air_zw(k-1) &
	262	& ) * ddzw(k) * drho_air(k)
[102]	263	ENDIF
	264
[1]	265	ENDDO
	266	ENDDO
	267
	268	END SUBROUTINE diffusion_v
	269
	270
	271	!------------------------------------------------------------------------------!
[1682]	272	! Description:
	273	! ------------
	274	!> Call for all grid points - accelerator version
[1015]	275	!------------------------------------------------------------------------------!
	276	SUBROUTINE diffusion_v_acc
	277
[1320]	278	USE arrays_3d, &
[2037]	279	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, &
	280	drho_air, rho_air_zw
[1320]	281
	282	USE control_parameters, &
	283	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	284	use_top_fluxes
	285
	286	USE grid_variables, &
	287	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	288
	289	USE indices, &
	290	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	291	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	292
	293	USE kinds
[1015]	294
	295	IMPLICIT NONE
	296
[1682]	297	INTEGER(iwp) :: i !<
	298	INTEGER(iwp) :: j !<
	299	INTEGER(iwp) :: k !<
	300	REAL(wp) :: kmxm !<
	301	REAL(wp) :: kmxp !<
	302	REAL(wp) :: kmzm !<
	303	REAL(wp) :: kmzp !<
[1015]	304
[1682]	305	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1015]	306	!$acc declare create ( vsus )
	307
	308	!
	309	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	310	!-- if neccessary
	311	IF ( topography /= 'flat' ) THEN
[1320]	312	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	313	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	314	ENDIF
	315
[1320]	316	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	317	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	318	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	319	DO i = i_left, i_right
	320	DO j = j_south, j_north
[1015]	321	!
	322	!-- Compute horizontal diffusion
	323	DO k = 1, nzt
	324	IF ( k > nzb_v_outer(j,i) ) THEN
	325	!
	326	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	327	kmxp = 0.25_wp * &
[1015]	328	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	329	kmxm = 0.25_wp * &
[1015]	330	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	331
	332	tend(k,j,i) = tend(k,j,i) &
	333	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	334	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	335	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	336	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	337	& ) * ddx &
[1340]	338	& + 2.0_wp * ( &
[1015]	339	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	340	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	341	& ) * ddy2
[1015]	342	ENDIF
	343	ENDDO
	344
	345	!
	346	!-- Wall functions at the left and right walls, respectively
	347	DO k = 1, nzt
[1320]	348	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1340]	349	wall_v(j,i) /= 0.0_wp ) THEN
[1015]	350
[1340]	351	kmxp = 0.25_wp * &
[1015]	352	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	353	kmxm = 0.25_wp * &
[1015]	354	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	355
	356	tend(k,j,i) = tend(k,j,i) &
[1340]	357	+ 2.0_wp * ( &
[1015]	358	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	359	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	360	) * ddy2 &
[1015]	361	+ ( fxp(j,i) * ( &
	362	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	363	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	364	) &
	365	- fxm(j,i) * ( &
	366	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	367	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	368	) &
	369	+ wall_v(j,i) * vsus(k,j,i) &
	370	) * ddx
	371	ENDIF
	372	ENDDO
	373
	374	!
	375	!-- Compute vertical diffusion. In case of simulating a Prandtl
	376	!-- layer, index k starts at nzb_v_inner+2.
	377	DO k = 1, nzt_diff
	378	IF ( k >= nzb_diff_v(j,i) ) THEN
	379	!
	380	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	381	kmzp = 0.25_wp * &
[1015]	382	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	383	kmzm = 0.25_wp * &
[1015]	384	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	385
	386	tend(k,j,i) = tend(k,j,i) &
	387	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	388	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2037]	389	& ) * rho_air_zw(k) &
[1015]	390	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	391	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2037]	392	& ) * rho_air_zw(k-1) &
	393	& ) * ddzw(k) * drho_air(k)
[1015]	394	ENDIF
	395	ENDDO
	396
	397	ENDDO
	398	ENDDO
	399
	400	!
	401	!-- Vertical diffusion at the first grid point above the surface,
	402	!-- if the momentum flux at the bottom is given by the Prandtl law
	403	!-- or if it is prescribed by the user.
	404	!-- Difference quotient of the momentum flux is not formed over
	405	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	406	!-- comparison with other (LES) models showed that the values of
[1015]	407	!-- the momentum flux becomes too large in this case.
	408	!-- The term containing w(k-1,..) (see above equation) is removed here
	409	!-- because the vertical velocity is assumed to be zero at the surface.
	410	IF ( use_surface_fluxes ) THEN
	411
[1128]	412	DO i = i_left, i_right
	413	DO j = j_south, j_north
[1015]	414
	415	k = nzb_v_inner(j,i)+1
	416	!
	417	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	418	kmzp = 0.25_wp * &
[1015]	419	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	420
[1320]	421	tend(k,j,i) = tend(k,j,i) &
[2037]	422	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	423	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	424	& ) * rho_air_zw(k) &
	425	& - ( -vsws(j,i) ) &
	426	& ) * ddzw(k) * drho_air(k)
[1015]	427	ENDDO
	428	ENDDO
	429
	430	ENDIF
	431
	432	!
	433	!-- Vertical diffusion at the first gridpoint below the top boundary,
	434	!-- if the momentum flux at the top is prescribed by the user
	435	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	436
	437	k = nzt
	438
[1128]	439	DO i = i_left, i_right
	440	DO j = j_south, j_north
[1015]	441
	442	!
	443	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	444	kmzm = 0.25_wp * &
[1015]	445	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	446
[1320]	447	tend(k,j,i) = tend(k,j,i) &
[2037]	448	& + ( ( -vswst(j,i) ) &
	449	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	450	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	451	& ) * rho_air_zw(k-1) &
	452	& ) * ddzw(k) * drho_air(k)
[1015]	453	ENDDO
	454	ENDDO
	455
	456	ENDIF
	457	!$acc end kernels
	458
	459	END SUBROUTINE diffusion_v_acc
	460
	461
	462	!------------------------------------------------------------------------------!
[1682]	463	! Description:
	464	! ------------
	465	!> Call for grid point i,j
[1]	466	!------------------------------------------------------------------------------!
[1001]	467	SUBROUTINE diffusion_v_ij( i, j )
[1]	468
[1320]	469	USE arrays_3d, &
[2037]	470	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, &
	471	drho_air, rho_air_zw
[1320]	472
	473	USE control_parameters, &
	474	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	475
	476	USE grid_variables, &
	477	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	478
	479	USE indices, &
	480	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	481
	482	USE kinds
[1]	483
	484	IMPLICIT NONE
	485
[1682]	486	INTEGER(iwp) :: i !<
	487	INTEGER(iwp) :: j !<
	488	INTEGER(iwp) :: k !<
	489	REAL(wp) :: kmxm !<
	490	REAL(wp) :: kmxp !<
	491	REAL(wp) :: kmzm !<
	492	REAL(wp) :: kmzp !<
[1]	493
[1682]	494	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	495
[1]	496	!
	497	!-- Compute horizontal diffusion
	498	DO k = nzb_v_outer(j,i)+1, nzt
	499	!
	500	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	501	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	502	kmxm = 0.25_wp * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	503
[1320]	504	tend(k,j,i) = tend(k,j,i) &
	505	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	506	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	507	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	508	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	509	& ) * ddx &
[1340]	510	& + 2.0_wp * ( &
[1320]	511	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	512	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	513	& ) * ddy2
[1]	514	ENDDO
	515
	516	!
	517	!-- Wall functions at the left and right walls, respectively
[1340]	518	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	519
	520	!
	521	!-- Calculate the horizontal momentum flux v'u'
[1320]	522	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	523	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	524
[1]	525	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	526	kmxp = 0.25_wp * &
[978]	527	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	528	kmxm = 0.25_wp * &
[978]	529	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	530
	531	tend(k,j,i) = tend(k,j,i) &
[1340]	532	+ 2.0_wp * ( &
[1]	533	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	534	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	535	) * ddy2 &
[1]	536	+ ( fxp(j,i) * ( &
[978]	537	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	538	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	539	) &
	540	- fxm(j,i) * ( &
[978]	541	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	542	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	543	) &
[51]	544	+ wall_v(j,i) * vsus(k) &
[1]	545	) * ddx
	546	ENDDO
	547	ENDIF
	548
	549	!
	550	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	551	!-- index k starts at nzb_v_inner+2.
[102]	552	DO k = nzb_diff_v(j,i), nzt_diff
[1]	553	!
	554	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	555	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	556	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
[1]	557
[1320]	558	tend(k,j,i) = tend(k,j,i) &
	559	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	560	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2037]	561	& ) * rho_air_zw(k) &
[1320]	562	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	563	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2037]	564	& ) * rho_air_zw(k-1) &
	565	& ) * ddzw(k) * drho_air(k)
[1]	566	ENDDO
	567
	568	!
	569	!-- Vertical diffusion at the first grid point above the surface, if the
	570	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	571	!-- prescribed by the user.
	572	!-- Difference quotient of the momentum flux is not formed over half of
	573	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	574	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	575	!-- too large in this case.
	576	!-- The term containing w(k-1,..) (see above equation) is removed here
	577	!-- because the vertical velocity is assumed to be zero at the surface.
	578	IF ( use_surface_fluxes ) THEN
	579	k = nzb_v_inner(j,i)+1
	580	!
	581	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	582	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1]	583
[1320]	584	tend(k,j,i) = tend(k,j,i) &
[2037]	585	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	586	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	587	& ) * rho_air_zw(k) &
	588	& - ( -vsws(j,i) ) &
	589	& ) * ddzw(k) * drho_air(k)
[1]	590	ENDIF
	591
[102]	592	!
	593	!-- Vertical diffusion at the first gridpoint below the top boundary,
	594	!-- if the momentum flux at the top is prescribed by the user
[103]	595	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	596	k = nzt
	597	!
	598	!-- Interpolate eddy diffusivities on staggered gridpoints
[2037]	599	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
[102]	600
[1320]	601	tend(k,j,i) = tend(k,j,i) &
[2037]	602	& + ( ( -vswst(j,i) ) &
	603	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	604	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	605	& ) * rho_air_zw(k-1) &
	606	& ) * ddzw(k) * drho_air(k)
[102]	607	ENDIF
	608
[1]	609	END SUBROUTINE diffusion_v_ij
	610
[1321]	611	END MODULE diffusion_v_mod

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