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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1740

Last change on this file since 1740 was 1740, checked in by raasch, 9 years ago
unnecessary calculations of kmzm and kmzp removed from wall bounded parts
Property svn:keywords set to `Id`
File size: 26.5 KB

Rev	Line
[1682]	1	!> @file diffusion_v.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1310]	16	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[484]	19	! Current revisions:
[1]	20	! -----------------
[1740]	21	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
[1341]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_v.f90 1740 2016-01-13 08:19:40Z raasch $
	26	!
[1683]	27	! 1682 2015-10-07 23:56:08Z knoop
	28	! Code annotations made doxygen readable
	29	!
[1341]	30	! 1340 2014-03-25 19:45:13Z kanani
	31	! REAL constants defined as wp-kind
	32	!
[1321]	33	! 1320 2014-03-20 08:40:49Z raasch
[1320]	34	! ONLY-attribute added to USE-statements,
	35	! kind-parameters added to all INTEGER and REAL declaration statements,
	36	! kinds are defined in new module kinds,
	37	! revision history before 2012 removed,
	38	! comment fields (!:) to be used for variable explanations added to
	39	! all variable declaration statements
[1321]	40	!
[1258]	41	! 1257 2013-11-08 15:18:40Z raasch
	42	! openacc loop and loop vector clauses removed, declare create moved after
	43	! the FORTRAN declaration statement
	44	!
[1132]	45	! 1128 2013-04-12 06:19:32Z raasch
	46	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	47	! j_north
	48	!
[1037]	49	! 1036 2012-10-22 13:43:42Z raasch
	50	! code put under GPL (PALM 3.9)
	51	!
[1017]	52	! 1015 2012-09-27 09:23:24Z raasch
	53	! accelerator version (*_acc) added
	54	!
[1002]	55	! 1001 2012-09-13 14:08:46Z raasch
	56	! arrays comunicated by module instead of parameter list
	57	!
[979]	58	! 978 2012-08-09 08:28:32Z fricke
	59	! outflow damping layer removed
	60	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	61	!
[1]	62	! Revision 1.1 1997/09/12 06:24:01 raasch
	63	! Initial revision
	64	!
	65	!
	66	! Description:
	67	! ------------
[1682]	68	!> Diffusion term of the v-component
[1]	69	!------------------------------------------------------------------------------!
[1682]	70	MODULE diffusion_v_mod
	71
[1]	72
[56]	73	USE wall_fluxes_mod
	74
[1]	75	PRIVATE
[1015]	76	PUBLIC diffusion_v, diffusion_v_acc
[1]	77
	78	INTERFACE diffusion_v
	79	MODULE PROCEDURE diffusion_v
	80	MODULE PROCEDURE diffusion_v_ij
	81	END INTERFACE diffusion_v
	82
[1015]	83	INTERFACE diffusion_v_acc
	84	MODULE PROCEDURE diffusion_v_acc
	85	END INTERFACE diffusion_v_acc
	86
[1]	87	CONTAINS
	88
	89
	90	!------------------------------------------------------------------------------!
[1682]	91	! Description:
	92	! ------------
	93	!> Call for all grid points
[1]	94	!------------------------------------------------------------------------------!
[1001]	95	SUBROUTINE diffusion_v
[1]	96
[1320]	97	USE arrays_3d, &
	98	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	99
	100	USE control_parameters, &
	101	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	102	use_top_fluxes
	103
	104	USE grid_variables, &
	105	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	106
	107	USE indices, &
	108	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	109	nzb_v_outer, nzt, nzt_diff
	110
	111	USE kinds
[1]	112
	113	IMPLICIT NONE
	114
[1682]	115	INTEGER(iwp) :: i !<
	116	INTEGER(iwp) :: j !<
	117	INTEGER(iwp) :: k !<
	118	REAL(wp) :: kmxm !<
	119	REAL(wp) :: kmxp !<
	120	REAL(wp) :: kmzm !<
	121	REAL(wp) :: kmzp !<
[1001]	122
[1682]	123	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1]	124
[56]	125	!
	126	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	127	!-- if neccessary
	128	IF ( topography /= 'flat' ) THEN
[1320]	129	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	130	nzb_v_outer, wall_v )
	131	ENDIF
	132
[1]	133	DO i = nxl, nxr
[106]	134	DO j = nysv, nyn
[1]	135	!
	136	!-- Compute horizontal diffusion
	137	DO k = nzb_v_outer(j,i)+1, nzt
	138	!
	139	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	140	kmxp = 0.25_wp * &
[978]	141	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	142	kmxm = 0.25_wp * &
[978]	143	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	144
[1320]	145	tend(k,j,i) = tend(k,j,i) &
	146	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	147	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	148	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	149	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	150	& ) * ddx &
[1340]	151	& + 2.0_wp * ( &
[1320]	152	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	153	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	154	& ) * ddy2
[1]	155	ENDDO
	156
	157	!
	158	!-- Wall functions at the left and right walls, respectively
[1340]	159	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	160
[1]	161	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	162	kmxp = 0.25_wp * &
[978]	163	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	164	kmxm = 0.25_wp * &
[978]	165	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	166
[1]	167	tend(k,j,i) = tend(k,j,i) &
[1340]	168	+ 2.0_wp * ( &
[1]	169	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	170	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	171	) * ddy2 &
[1]	172	+ ( fxp(j,i) * ( &
[978]	173	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	174	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	175	) &
	176	- fxm(j,i) * ( &
[978]	177	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	178	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	179	) &
[56]	180	+ wall_v(j,i) * vsus(k,j,i) &
[1]	181	) * ddx
	182	ENDDO
	183	ENDIF
	184
	185	!
	186	!-- Compute vertical diffusion. In case of simulating a Prandtl
	187	!-- layer, index k starts at nzb_v_inner+2.
[102]	188	DO k = nzb_diff_v(j,i), nzt_diff
[1]	189	!
	190	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	191	kmzp = 0.25_wp * &
[1]	192	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	193	kmzm = 0.25_wp * &
[1]	194	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	195
[1320]	196	tend(k,j,i) = tend(k,j,i) &
	197	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	198	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	199	& ) &
	200	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	201	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	202	& ) &
[1]	203	& ) * ddzw(k)
	204	ENDDO
	205
	206	!
	207	!-- Vertical diffusion at the first grid point above the surface,
	208	!-- if the momentum flux at the bottom is given by the Prandtl law
	209	!-- or if it is prescribed by the user.
	210	!-- Difference quotient of the momentum flux is not formed over
	211	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	212	!-- comparison with other (LES) models showed that the values of
[1]	213	!-- the momentum flux becomes too large in this case.
	214	!-- The term containing w(k-1,..) (see above equation) is removed here
	215	!-- because the vertical velocity is assumed to be zero at the surface.
	216	IF ( use_surface_fluxes ) THEN
	217	k = nzb_v_inner(j,i)+1
	218	!
	219	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	220	kmzp = 0.25_wp * &
[1]	221	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	222
[1320]	223	tend(k,j,i) = tend(k,j,i) &
	224	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	225	& ) * ddzw(k) &
	226	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	227	& + vsws(j,i) &
[1]	228	& ) * ddzw(k)
	229	ENDIF
	230
[102]	231	!
	232	!-- Vertical diffusion at the first gridpoint below the top boundary,
	233	!-- if the momentum flux at the top is prescribed by the user
[103]	234	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	235	k = nzt
	236	!
	237	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	238	kmzm = 0.25_wp * &
[102]	239	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	240
[1320]	241	tend(k,j,i) = tend(k,j,i) &
	242	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	243	& ) * ddzw(k) &
	244	& + ( -vswst(j,i) &
	245	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	246	& ) * ddzw(k)
	247	ENDIF
	248
[1]	249	ENDDO
	250	ENDDO
	251
	252	END SUBROUTINE diffusion_v
	253
	254
	255	!------------------------------------------------------------------------------!
[1682]	256	! Description:
	257	! ------------
	258	!> Call for all grid points - accelerator version
[1015]	259	!------------------------------------------------------------------------------!
	260	SUBROUTINE diffusion_v_acc
	261
[1320]	262	USE arrays_3d, &
	263	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	264
	265	USE control_parameters, &
	266	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	267	use_top_fluxes
	268
	269	USE grid_variables, &
	270	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	271
	272	USE indices, &
	273	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	274	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	275
	276	USE kinds
[1015]	277
	278	IMPLICIT NONE
	279
[1682]	280	INTEGER(iwp) :: i !<
	281	INTEGER(iwp) :: j !<
	282	INTEGER(iwp) :: k !<
	283	REAL(wp) :: kmxm !<
	284	REAL(wp) :: kmxp !<
	285	REAL(wp) :: kmzm !<
	286	REAL(wp) :: kmzp !<
[1015]	287
[1682]	288	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1015]	289	!$acc declare create ( vsus )
	290
	291	!
	292	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	293	!-- if neccessary
	294	IF ( topography /= 'flat' ) THEN
[1320]	295	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	296	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	297	ENDIF
	298
[1320]	299	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	300	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	301	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	302	DO i = i_left, i_right
	303	DO j = j_south, j_north
[1015]	304	!
	305	!-- Compute horizontal diffusion
	306	DO k = 1, nzt
	307	IF ( k > nzb_v_outer(j,i) ) THEN
	308	!
	309	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	310	kmxp = 0.25_wp * &
[1015]	311	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	312	kmxm = 0.25_wp * &
[1015]	313	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	314
	315	tend(k,j,i) = tend(k,j,i) &
	316	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	317	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	318	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	319	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	320	& ) * ddx &
[1340]	321	& + 2.0_wp * ( &
[1015]	322	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	323	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	324	& ) * ddy2
[1015]	325	ENDIF
	326	ENDDO
	327
	328	!
	329	!-- Wall functions at the left and right walls, respectively
	330	DO k = 1, nzt
[1320]	331	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1340]	332	wall_v(j,i) /= 0.0_wp ) THEN
[1015]	333
[1340]	334	kmxp = 0.25_wp * &
[1015]	335	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	336	kmxm = 0.25_wp * &
[1015]	337	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	338
	339	tend(k,j,i) = tend(k,j,i) &
[1340]	340	+ 2.0_wp * ( &
[1015]	341	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	342	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	343	) * ddy2 &
[1015]	344	+ ( fxp(j,i) * ( &
	345	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	346	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	347	) &
	348	- fxm(j,i) * ( &
	349	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	350	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	351	) &
	352	+ wall_v(j,i) * vsus(k,j,i) &
	353	) * ddx
	354	ENDIF
	355	ENDDO
	356
	357	!
	358	!-- Compute vertical diffusion. In case of simulating a Prandtl
	359	!-- layer, index k starts at nzb_v_inner+2.
	360	DO k = 1, nzt_diff
	361	IF ( k >= nzb_diff_v(j,i) ) THEN
	362	!
	363	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	364	kmzp = 0.25_wp * &
[1015]	365	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	366	kmzm = 0.25_wp * &
[1015]	367	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	368
	369	tend(k,j,i) = tend(k,j,i) &
	370	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	371	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	372	& ) &
	373	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	374	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	375	& ) &
	376	& ) * ddzw(k)
	377	ENDIF
	378	ENDDO
	379
	380	ENDDO
	381	ENDDO
	382
	383	!
	384	!-- Vertical diffusion at the first grid point above the surface,
	385	!-- if the momentum flux at the bottom is given by the Prandtl law
	386	!-- or if it is prescribed by the user.
	387	!-- Difference quotient of the momentum flux is not formed over
	388	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	389	!-- comparison with other (LES) models showed that the values of
[1015]	390	!-- the momentum flux becomes too large in this case.
	391	!-- The term containing w(k-1,..) (see above equation) is removed here
	392	!-- because the vertical velocity is assumed to be zero at the surface.
	393	IF ( use_surface_fluxes ) THEN
	394
[1128]	395	DO i = i_left, i_right
	396	DO j = j_south, j_north
[1015]	397
	398	k = nzb_v_inner(j,i)+1
	399	!
	400	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	401	kmzp = 0.25_wp * &
[1015]	402	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	403
[1320]	404	tend(k,j,i) = tend(k,j,i) &
	405	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	406	& ) * ddzw(k) &
	407	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	408	& + vsws(j,i) &
[1015]	409	& ) * ddzw(k)
	410	ENDDO
	411	ENDDO
	412
	413	ENDIF
	414
	415	!
	416	!-- Vertical diffusion at the first gridpoint below the top boundary,
	417	!-- if the momentum flux at the top is prescribed by the user
	418	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	419
	420	k = nzt
	421
[1128]	422	DO i = i_left, i_right
	423	DO j = j_south, j_north
[1015]	424
	425	!
	426	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	427	kmzm = 0.25_wp * &
[1015]	428	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	429
[1320]	430	tend(k,j,i) = tend(k,j,i) &
	431	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	432	& ) * ddzw(k) &
	433	& + ( -vswst(j,i) &
	434	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[1015]	435	& ) * ddzw(k)
	436	ENDDO
	437	ENDDO
	438
	439	ENDIF
	440	!$acc end kernels
	441
	442	END SUBROUTINE diffusion_v_acc
	443
	444
	445	!------------------------------------------------------------------------------!
[1682]	446	! Description:
	447	! ------------
	448	!> Call for grid point i,j
[1]	449	!------------------------------------------------------------------------------!
[1001]	450	SUBROUTINE diffusion_v_ij( i, j )
[1]	451
[1320]	452	USE arrays_3d, &
	453	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	454
	455	USE control_parameters, &
	456	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	457
	458	USE grid_variables, &
	459	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	460
	461	USE indices, &
	462	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	463
	464	USE kinds
[1]	465
	466	IMPLICIT NONE
	467
[1682]	468	INTEGER(iwp) :: i !<
	469	INTEGER(iwp) :: j !<
	470	INTEGER(iwp) :: k !<
	471	REAL(wp) :: kmxm !<
	472	REAL(wp) :: kmxp !<
	473	REAL(wp) :: kmzm !<
	474	REAL(wp) :: kmzp !<
[1]	475
[1682]	476	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	477
[1]	478	!
	479	!-- Compute horizontal diffusion
	480	DO k = nzb_v_outer(j,i)+1, nzt
	481	!
	482	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	483	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	484	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]	485
[1320]	486	tend(k,j,i) = tend(k,j,i) &
	487	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	488	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	489	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	490	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	491	& ) * ddx &
[1340]	492	& + 2.0_wp * ( &
[1320]	493	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	494	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	495	& ) * ddy2
[1]	496	ENDDO
	497
	498	!
	499	!-- Wall functions at the left and right walls, respectively
[1340]	500	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	501
	502	!
	503	!-- Calculate the horizontal momentum flux v'u'
[1320]	504	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	505	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	506
[1]	507	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	508	kmxp = 0.25_wp * &
[978]	509	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	510	kmxm = 0.25_wp * &
[978]	511	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	512
	513	tend(k,j,i) = tend(k,j,i) &
[1340]	514	+ 2.0_wp * ( &
[1]	515	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	516	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	517	) * ddy2 &
[1]	518	+ ( fxp(j,i) * ( &
[978]	519	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	520	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	521	) &
	522	- fxm(j,i) * ( &
[978]	523	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	524	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	525	) &
[51]	526	+ wall_v(j,i) * vsus(k) &
[1]	527	) * ddx
	528	ENDDO
	529	ENDIF
	530
	531	!
	532	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	533	!-- index k starts at nzb_v_inner+2.
[102]	534	DO k = nzb_diff_v(j,i), nzt_diff
[1]	535	!
	536	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	537	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	538	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]	539
[1320]	540	tend(k,j,i) = tend(k,j,i) &
	541	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	542	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	543	& ) &
	544	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	545	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	546	& ) &
[1]	547	& ) * ddzw(k)
	548	ENDDO
	549
	550	!
	551	!-- Vertical diffusion at the first grid point above the surface, if the
	552	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	553	!-- prescribed by the user.
	554	!-- Difference quotient of the momentum flux is not formed over half of
	555	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	556	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	557	!-- too large in this case.
	558	!-- The term containing w(k-1,..) (see above equation) is removed here
	559	!-- because the vertical velocity is assumed to be zero at the surface.
	560	IF ( use_surface_fluxes ) THEN
	561	k = nzb_v_inner(j,i)+1
	562	!
	563	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	564	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]	565
[1320]	566	tend(k,j,i) = tend(k,j,i) &
	567	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	568	& ) * ddzw(k) &
	569	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	570	& + vsws(j,i) &
[1]	571	& ) * ddzw(k)
	572	ENDIF
	573
[102]	574	!
	575	!-- Vertical diffusion at the first gridpoint below the top boundary,
	576	!-- if the momentum flux at the top is prescribed by the user
[103]	577	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	578	k = nzt
	579	!
	580	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	581	kmzm = 0.25_wp * &
[102]	582	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	583
[1320]	584	tend(k,j,i) = tend(k,j,i) &
	585	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	586	& ) * ddzw(k) &
	587	& + ( -vswst(j,i) &
	588	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	589	& ) * ddzw(k)
	590	ENDIF
	591
[1]	592	END SUBROUTINE diffusion_v_ij
	593
[1321]	594	END MODULE diffusion_v_mod

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