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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1791

Last change on this file since 1791 was 1741, checked in by raasch, 9 years ago
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[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	! -----------------
[1341]	21	!
[1741]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_v.f90 1741 2016-01-13 08:32:52Z raasch $
	26	!
[1741]	27	! 1740 2016-01-13 08:19:40Z raasch
	28	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	29	!
[1683]	30	! 1682 2015-10-07 23:56:08Z knoop
	31	! Code annotations made doxygen readable
	32	!
[1341]	33	! 1340 2014-03-25 19:45:13Z kanani
	34	! REAL constants defined as wp-kind
	35	!
[1321]	36	! 1320 2014-03-20 08:40:49Z raasch
[1320]	37	! ONLY-attribute added to USE-statements,
	38	! kind-parameters added to all INTEGER and REAL declaration statements,
	39	! kinds are defined in new module kinds,
	40	! revision history before 2012 removed,
	41	! comment fields (!:) to be used for variable explanations added to
	42	! all variable declaration statements
[1321]	43	!
[1258]	44	! 1257 2013-11-08 15:18:40Z raasch
	45	! openacc loop and loop vector clauses removed, declare create moved after
	46	! the FORTRAN declaration statement
	47	!
[1132]	48	! 1128 2013-04-12 06:19:32Z raasch
	49	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	50	! j_north
	51	!
[1037]	52	! 1036 2012-10-22 13:43:42Z raasch
	53	! code put under GPL (PALM 3.9)
	54	!
[1017]	55	! 1015 2012-09-27 09:23:24Z raasch
	56	! accelerator version (*_acc) added
	57	!
[1002]	58	! 1001 2012-09-13 14:08:46Z raasch
	59	! arrays comunicated by module instead of parameter list
	60	!
[979]	61	! 978 2012-08-09 08:28:32Z fricke
	62	! outflow damping layer removed
	63	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	64	!
[1]	65	! Revision 1.1 1997/09/12 06:24:01 raasch
	66	! Initial revision
	67	!
	68	!
	69	! Description:
	70	! ------------
[1682]	71	!> Diffusion term of the v-component
[1]	72	!------------------------------------------------------------------------------!
[1682]	73	MODULE diffusion_v_mod
	74
[1]	75
[56]	76	USE wall_fluxes_mod
	77
[1]	78	PRIVATE
[1015]	79	PUBLIC diffusion_v, diffusion_v_acc
[1]	80
	81	INTERFACE diffusion_v
	82	MODULE PROCEDURE diffusion_v
	83	MODULE PROCEDURE diffusion_v_ij
	84	END INTERFACE diffusion_v
	85
[1015]	86	INTERFACE diffusion_v_acc
	87	MODULE PROCEDURE diffusion_v_acc
	88	END INTERFACE diffusion_v_acc
	89
[1]	90	CONTAINS
	91
	92
	93	!------------------------------------------------------------------------------!
[1682]	94	! Description:
	95	! ------------
	96	!> Call for all grid points
[1]	97	!------------------------------------------------------------------------------!
[1001]	98	SUBROUTINE diffusion_v
[1]	99
[1320]	100	USE arrays_3d, &
	101	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	102
	103	USE control_parameters, &
	104	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	105	use_top_fluxes
	106
	107	USE grid_variables, &
	108	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	109
	110	USE indices, &
	111	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	112	nzb_v_outer, nzt, nzt_diff
	113
	114	USE kinds
[1]	115
	116	IMPLICIT NONE
	117
[1682]	118	INTEGER(iwp) :: i !<
	119	INTEGER(iwp) :: j !<
	120	INTEGER(iwp) :: k !<
	121	REAL(wp) :: kmxm !<
	122	REAL(wp) :: kmxp !<
	123	REAL(wp) :: kmzm !<
	124	REAL(wp) :: kmzp !<
[1001]	125
[1682]	126	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1]	127
[56]	128	!
	129	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	130	!-- if neccessary
	131	IF ( topography /= 'flat' ) THEN
[1320]	132	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	133	nzb_v_outer, wall_v )
	134	ENDIF
	135
[1]	136	DO i = nxl, nxr
[106]	137	DO j = nysv, nyn
[1]	138	!
	139	!-- Compute horizontal diffusion
	140	DO k = nzb_v_outer(j,i)+1, nzt
	141	!
	142	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	143	kmxp = 0.25_wp * &
[978]	144	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	145	kmxm = 0.25_wp * &
[978]	146	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	147
[1320]	148	tend(k,j,i) = tend(k,j,i) &
	149	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	150	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	151	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	152	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	153	& ) * ddx &
[1340]	154	& + 2.0_wp * ( &
[1320]	155	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	156	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	157	& ) * ddy2
[1]	158	ENDDO
	159
	160	!
	161	!-- Wall functions at the left and right walls, respectively
[1340]	162	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	163
[1]	164	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	165	kmxp = 0.25_wp * &
[978]	166	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	167	kmxm = 0.25_wp * &
[978]	168	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	169
[1]	170	tend(k,j,i) = tend(k,j,i) &
[1340]	171	+ 2.0_wp * ( &
[1]	172	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	173	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	174	) * ddy2 &
[1]	175	+ ( fxp(j,i) * ( &
[978]	176	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	177	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	178	) &
	179	- fxm(j,i) * ( &
[978]	180	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	181	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	182	) &
[56]	183	+ wall_v(j,i) * vsus(k,j,i) &
[1]	184	) * ddx
	185	ENDDO
	186	ENDIF
	187
	188	!
	189	!-- Compute vertical diffusion. In case of simulating a Prandtl
	190	!-- layer, index k starts at nzb_v_inner+2.
[102]	191	DO k = nzb_diff_v(j,i), nzt_diff
[1]	192	!
	193	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	194	kmzp = 0.25_wp * &
[1]	195	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	196	kmzm = 0.25_wp * &
[1]	197	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	198
[1320]	199	tend(k,j,i) = tend(k,j,i) &
	200	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	201	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	202	& ) &
	203	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	204	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	205	& ) &
[1]	206	& ) * ddzw(k)
	207	ENDDO
	208
	209	!
	210	!-- Vertical diffusion at the first grid point above the surface,
	211	!-- if the momentum flux at the bottom is given by the Prandtl law
	212	!-- or if it is prescribed by the user.
	213	!-- Difference quotient of the momentum flux is not formed over
	214	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	215	!-- comparison with other (LES) models showed that the values of
[1]	216	!-- the momentum flux becomes too large in this case.
	217	!-- The term containing w(k-1,..) (see above equation) is removed here
	218	!-- because the vertical velocity is assumed to be zero at the surface.
	219	IF ( use_surface_fluxes ) THEN
	220	k = nzb_v_inner(j,i)+1
	221	!
	222	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	223	kmzp = 0.25_wp * &
[1]	224	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	225
[1320]	226	tend(k,j,i) = tend(k,j,i) &
	227	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	228	& ) * ddzw(k) &
	229	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	230	& + vsws(j,i) &
[1]	231	& ) * ddzw(k)
	232	ENDIF
	233
[102]	234	!
	235	!-- Vertical diffusion at the first gridpoint below the top boundary,
	236	!-- if the momentum flux at the top is prescribed by the user
[103]	237	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	238	k = nzt
	239	!
	240	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	241	kmzm = 0.25_wp * &
[102]	242	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	243
[1320]	244	tend(k,j,i) = tend(k,j,i) &
	245	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	246	& ) * ddzw(k) &
	247	& + ( -vswst(j,i) &
	248	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	249	& ) * ddzw(k)
	250	ENDIF
	251
[1]	252	ENDDO
	253	ENDDO
	254
	255	END SUBROUTINE diffusion_v
	256
	257
	258	!------------------------------------------------------------------------------!
[1682]	259	! Description:
	260	! ------------
	261	!> Call for all grid points - accelerator version
[1015]	262	!------------------------------------------------------------------------------!
	263	SUBROUTINE diffusion_v_acc
	264
[1320]	265	USE arrays_3d, &
	266	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	267
	268	USE control_parameters, &
	269	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	270	use_top_fluxes
	271
	272	USE grid_variables, &
	273	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	274
	275	USE indices, &
	276	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	277	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	278
	279	USE kinds
[1015]	280
	281	IMPLICIT NONE
	282
[1682]	283	INTEGER(iwp) :: i !<
	284	INTEGER(iwp) :: j !<
	285	INTEGER(iwp) :: k !<
	286	REAL(wp) :: kmxm !<
	287	REAL(wp) :: kmxp !<
	288	REAL(wp) :: kmzm !<
	289	REAL(wp) :: kmzp !<
[1015]	290
[1682]	291	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1015]	292	!$acc declare create ( vsus )
	293
	294	!
	295	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	296	!-- if neccessary
	297	IF ( topography /= 'flat' ) THEN
[1320]	298	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	299	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	300	ENDIF
	301
[1320]	302	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	303	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	304	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	305	DO i = i_left, i_right
	306	DO j = j_south, j_north
[1015]	307	!
	308	!-- Compute horizontal diffusion
	309	DO k = 1, nzt
	310	IF ( k > nzb_v_outer(j,i) ) THEN
	311	!
	312	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	313	kmxp = 0.25_wp * &
[1015]	314	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	315	kmxm = 0.25_wp * &
[1015]	316	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	317
	318	tend(k,j,i) = tend(k,j,i) &
	319	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	320	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	321	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	322	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	323	& ) * ddx &
[1340]	324	& + 2.0_wp * ( &
[1015]	325	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	326	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	327	& ) * ddy2
[1015]	328	ENDIF
	329	ENDDO
	330
	331	!
	332	!-- Wall functions at the left and right walls, respectively
	333	DO k = 1, nzt
[1320]	334	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1340]	335	wall_v(j,i) /= 0.0_wp ) THEN
[1015]	336
[1340]	337	kmxp = 0.25_wp * &
[1015]	338	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	339	kmxm = 0.25_wp * &
[1015]	340	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	341
	342	tend(k,j,i) = tend(k,j,i) &
[1340]	343	+ 2.0_wp * ( &
[1015]	344	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	345	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	346	) * ddy2 &
[1015]	347	+ ( fxp(j,i) * ( &
	348	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	349	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	350	) &
	351	- fxm(j,i) * ( &
	352	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	353	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	354	) &
	355	+ wall_v(j,i) * vsus(k,j,i) &
	356	) * ddx
	357	ENDIF
	358	ENDDO
	359
	360	!
	361	!-- Compute vertical diffusion. In case of simulating a Prandtl
	362	!-- layer, index k starts at nzb_v_inner+2.
	363	DO k = 1, nzt_diff
	364	IF ( k >= nzb_diff_v(j,i) ) THEN
	365	!
	366	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	367	kmzp = 0.25_wp * &
[1015]	368	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	369	kmzm = 0.25_wp * &
[1015]	370	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	371
	372	tend(k,j,i) = tend(k,j,i) &
	373	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	374	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	375	& ) &
	376	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	377	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	378	& ) &
	379	& ) * ddzw(k)
	380	ENDIF
	381	ENDDO
	382
	383	ENDDO
	384	ENDDO
	385
	386	!
	387	!-- Vertical diffusion at the first grid point above the surface,
	388	!-- if the momentum flux at the bottom is given by the Prandtl law
	389	!-- or if it is prescribed by the user.
	390	!-- Difference quotient of the momentum flux is not formed over
	391	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	392	!-- comparison with other (LES) models showed that the values of
[1015]	393	!-- the momentum flux becomes too large in this case.
	394	!-- The term containing w(k-1,..) (see above equation) is removed here
	395	!-- because the vertical velocity is assumed to be zero at the surface.
	396	IF ( use_surface_fluxes ) THEN
	397
[1128]	398	DO i = i_left, i_right
	399	DO j = j_south, j_north
[1015]	400
	401	k = nzb_v_inner(j,i)+1
	402	!
	403	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	404	kmzp = 0.25_wp * &
[1015]	405	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	406
[1320]	407	tend(k,j,i) = tend(k,j,i) &
	408	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	409	& ) * ddzw(k) &
	410	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	411	& + vsws(j,i) &
[1015]	412	& ) * ddzw(k)
	413	ENDDO
	414	ENDDO
	415
	416	ENDIF
	417
	418	!
	419	!-- Vertical diffusion at the first gridpoint below the top boundary,
	420	!-- if the momentum flux at the top is prescribed by the user
	421	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	422
	423	k = nzt
	424
[1128]	425	DO i = i_left, i_right
	426	DO j = j_south, j_north
[1015]	427
	428	!
	429	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	430	kmzm = 0.25_wp * &
[1015]	431	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	432
[1320]	433	tend(k,j,i) = tend(k,j,i) &
	434	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	435	& ) * ddzw(k) &
	436	& + ( -vswst(j,i) &
	437	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[1015]	438	& ) * ddzw(k)
	439	ENDDO
	440	ENDDO
	441
	442	ENDIF
	443	!$acc end kernels
	444
	445	END SUBROUTINE diffusion_v_acc
	446
	447
	448	!------------------------------------------------------------------------------!
[1682]	449	! Description:
	450	! ------------
	451	!> Call for grid point i,j
[1]	452	!------------------------------------------------------------------------------!
[1001]	453	SUBROUTINE diffusion_v_ij( i, j )
[1]	454
[1320]	455	USE arrays_3d, &
	456	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	457
	458	USE control_parameters, &
	459	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	460
	461	USE grid_variables, &
	462	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	463
	464	USE indices, &
	465	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	466
	467	USE kinds
[1]	468
	469	IMPLICIT NONE
	470
[1682]	471	INTEGER(iwp) :: i !<
	472	INTEGER(iwp) :: j !<
	473	INTEGER(iwp) :: k !<
	474	REAL(wp) :: kmxm !<
	475	REAL(wp) :: kmxp !<
	476	REAL(wp) :: kmzm !<
	477	REAL(wp) :: kmzp !<
[1]	478
[1682]	479	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	480
[1]	481	!
	482	!-- Compute horizontal diffusion
	483	DO k = nzb_v_outer(j,i)+1, nzt
	484	!
	485	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	486	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	487	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]	488
[1320]	489	tend(k,j,i) = tend(k,j,i) &
	490	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	491	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	492	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	493	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	494	& ) * ddx &
[1340]	495	& + 2.0_wp * ( &
[1320]	496	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	497	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	498	& ) * ddy2
[1]	499	ENDDO
	500
	501	!
	502	!-- Wall functions at the left and right walls, respectively
[1340]	503	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	504
	505	!
	506	!-- Calculate the horizontal momentum flux v'u'
[1320]	507	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	508	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	509
[1]	510	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	511	kmxp = 0.25_wp * &
[978]	512	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	513	kmxm = 0.25_wp * &
[978]	514	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	515
	516	tend(k,j,i) = tend(k,j,i) &
[1340]	517	+ 2.0_wp * ( &
[1]	518	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	519	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	520	) * ddy2 &
[1]	521	+ ( fxp(j,i) * ( &
[978]	522	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	523	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	524	) &
	525	- fxm(j,i) * ( &
[978]	526	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	527	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	528	) &
[51]	529	+ wall_v(j,i) * vsus(k) &
[1]	530	) * ddx
	531	ENDDO
	532	ENDIF
	533
	534	!
	535	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	536	!-- index k starts at nzb_v_inner+2.
[102]	537	DO k = nzb_diff_v(j,i), nzt_diff
[1]	538	!
	539	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	540	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	541	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]	542
[1320]	543	tend(k,j,i) = tend(k,j,i) &
	544	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	545	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	546	& ) &
	547	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	548	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	549	& ) &
[1]	550	& ) * ddzw(k)
	551	ENDDO
	552
	553	!
	554	!-- Vertical diffusion at the first grid point above the surface, if the
	555	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	556	!-- prescribed by the user.
	557	!-- Difference quotient of the momentum flux is not formed over half of
	558	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	559	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	560	!-- too large in this case.
	561	!-- The term containing w(k-1,..) (see above equation) is removed here
	562	!-- because the vertical velocity is assumed to be zero at the surface.
	563	IF ( use_surface_fluxes ) THEN
	564	k = nzb_v_inner(j,i)+1
	565	!
	566	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	567	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]	568
[1320]	569	tend(k,j,i) = tend(k,j,i) &
	570	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	571	& ) * ddzw(k) &
	572	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	573	& + vsws(j,i) &
[1]	574	& ) * ddzw(k)
	575	ENDIF
	576
[102]	577	!
	578	!-- Vertical diffusion at the first gridpoint below the top boundary,
	579	!-- if the momentum flux at the top is prescribed by the user
[103]	580	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	581	k = nzt
	582	!
	583	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	584	kmzm = 0.25_wp * &
[102]	585	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	586
[1320]	587	tend(k,j,i) = tend(k,j,i) &
	588	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	589	& ) * ddzw(k) &
	590	& + ( -vswst(j,i) &
	591	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	592	& ) * ddzw(k)
	593	ENDIF
	594
[1]	595	END SUBROUTINE diffusion_v_ij
	596
[1321]	597	END MODULE diffusion_v_mod

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