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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1884

Last change on this file since 1884 was 1874, checked in by maronga, 9 years ago
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[1873]	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	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[484]	19	! Current revisions:
[1]	20	! -----------------
[1341]	21	!
[1851]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_v.f90 1874 2016-04-18 14:51:10Z hoffmann $
	26	!
[1874]	27	! 1873 2016-04-18 14:50:06Z maronga
	28	! Module renamed (removed _mod)
	29	!
	30	!
[1851]	31	! 1850 2016-04-08 13:29:27Z maronga
	32	! Module renamed
	33	!
	34	!
[1741]	35	! 1740 2016-01-13 08:19:40Z raasch
	36	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	37	!
[1683]	38	! 1682 2015-10-07 23:56:08Z knoop
	39	! Code annotations made doxygen readable
	40	!
[1341]	41	! 1340 2014-03-25 19:45:13Z kanani
	42	! REAL constants defined as wp-kind
	43	!
[1321]	44	! 1320 2014-03-20 08:40:49Z raasch
[1320]	45	! ONLY-attribute added to USE-statements,
	46	! kind-parameters added to all INTEGER and REAL declaration statements,
	47	! kinds are defined in new module kinds,
	48	! revision history before 2012 removed,
	49	! comment fields (!:) to be used for variable explanations added to
	50	! all variable declaration statements
[1321]	51	!
[1258]	52	! 1257 2013-11-08 15:18:40Z raasch
	53	! openacc loop and loop vector clauses removed, declare create moved after
	54	! the FORTRAN declaration statement
	55	!
[1132]	56	! 1128 2013-04-12 06:19:32Z raasch
	57	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	58	! j_north
	59	!
[1037]	60	! 1036 2012-10-22 13:43:42Z raasch
	61	! code put under GPL (PALM 3.9)
	62	!
[1017]	63	! 1015 2012-09-27 09:23:24Z raasch
	64	! accelerator version (*_acc) added
	65	!
[1002]	66	! 1001 2012-09-13 14:08:46Z raasch
	67	! arrays comunicated by module instead of parameter list
	68	!
[979]	69	! 978 2012-08-09 08:28:32Z fricke
	70	! outflow damping layer removed
	71	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	72	!
[1]	73	! Revision 1.1 1997/09/12 06:24:01 raasch
	74	! Initial revision
	75	!
	76	!
	77	! Description:
	78	! ------------
[1682]	79	!> Diffusion term of the v-component
[1]	80	!------------------------------------------------------------------------------!
[1682]	81	MODULE diffusion_v_mod
	82
[1]	83
[56]	84	USE wall_fluxes_mod
	85
[1]	86	PRIVATE
[1015]	87	PUBLIC diffusion_v, diffusion_v_acc
[1]	88
	89	INTERFACE diffusion_v
	90	MODULE PROCEDURE diffusion_v
	91	MODULE PROCEDURE diffusion_v_ij
	92	END INTERFACE diffusion_v
	93
[1015]	94	INTERFACE diffusion_v_acc
	95	MODULE PROCEDURE diffusion_v_acc
	96	END INTERFACE diffusion_v_acc
	97
[1]	98	CONTAINS
	99
	100
	101	!------------------------------------------------------------------------------!
[1682]	102	! Description:
	103	! ------------
	104	!> Call for all grid points
[1]	105	!------------------------------------------------------------------------------!
[1001]	106	SUBROUTINE diffusion_v
[1]	107
[1320]	108	USE arrays_3d, &
	109	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	110
	111	USE control_parameters, &
	112	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	113	use_top_fluxes
	114
	115	USE grid_variables, &
	116	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	117
	118	USE indices, &
	119	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	120	nzb_v_outer, nzt, nzt_diff
	121
	122	USE kinds
[1]	123
	124	IMPLICIT NONE
	125
[1682]	126	INTEGER(iwp) :: i !<
	127	INTEGER(iwp) :: j !<
	128	INTEGER(iwp) :: k !<
	129	REAL(wp) :: kmxm !<
	130	REAL(wp) :: kmxp !<
	131	REAL(wp) :: kmzm !<
	132	REAL(wp) :: kmzp !<
[1001]	133
[1682]	134	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1]	135
[56]	136	!
	137	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	138	!-- if neccessary
	139	IF ( topography /= 'flat' ) THEN
[1320]	140	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	141	nzb_v_outer, wall_v )
	142	ENDIF
	143
[1]	144	DO i = nxl, nxr
[106]	145	DO j = nysv, nyn
[1]	146	!
	147	!-- Compute horizontal diffusion
	148	DO k = nzb_v_outer(j,i)+1, nzt
	149	!
	150	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	151	kmxp = 0.25_wp * &
[978]	152	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	153	kmxm = 0.25_wp * &
[978]	154	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	155
[1320]	156	tend(k,j,i) = tend(k,j,i) &
	157	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	158	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	159	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	160	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	161	& ) * ddx &
[1340]	162	& + 2.0_wp * ( &
[1320]	163	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	164	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	165	& ) * ddy2
[1]	166	ENDDO
	167
	168	!
	169	!-- Wall functions at the left and right walls, respectively
[1340]	170	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	171
[1]	172	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	173	kmxp = 0.25_wp * &
[978]	174	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	175	kmxm = 0.25_wp * &
[978]	176	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	177
[1]	178	tend(k,j,i) = tend(k,j,i) &
[1340]	179	+ 2.0_wp * ( &
[1]	180	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	181	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	182	) * ddy2 &
[1]	183	+ ( fxp(j,i) * ( &
[978]	184	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	185	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	186	) &
	187	- fxm(j,i) * ( &
[978]	188	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	189	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	190	) &
[56]	191	+ wall_v(j,i) * vsus(k,j,i) &
[1]	192	) * ddx
	193	ENDDO
	194	ENDIF
	195
	196	!
	197	!-- Compute vertical diffusion. In case of simulating a Prandtl
	198	!-- layer, index k starts at nzb_v_inner+2.
[102]	199	DO k = nzb_diff_v(j,i), nzt_diff
[1]	200	!
	201	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	202	kmzp = 0.25_wp * &
[1]	203	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	204	kmzm = 0.25_wp * &
[1]	205	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	206
[1320]	207	tend(k,j,i) = tend(k,j,i) &
	208	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	209	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	210	& ) &
	211	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	212	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	213	& ) &
[1]	214	& ) * ddzw(k)
	215	ENDDO
	216
	217	!
	218	!-- Vertical diffusion at the first grid point above the surface,
	219	!-- if the momentum flux at the bottom is given by the Prandtl law
	220	!-- or if it is prescribed by the user.
	221	!-- Difference quotient of the momentum flux is not formed over
	222	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	223	!-- comparison with other (LES) models showed that the values of
[1]	224	!-- the momentum flux becomes too large in this case.
	225	!-- The term containing w(k-1,..) (see above equation) is removed here
	226	!-- because the vertical velocity is assumed to be zero at the surface.
	227	IF ( use_surface_fluxes ) THEN
	228	k = nzb_v_inner(j,i)+1
	229	!
	230	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	231	kmzp = 0.25_wp * &
[1]	232	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	233
[1320]	234	tend(k,j,i) = tend(k,j,i) &
	235	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	236	& ) * ddzw(k) &
	237	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	238	& + vsws(j,i) &
[1]	239	& ) * ddzw(k)
	240	ENDIF
	241
[102]	242	!
	243	!-- Vertical diffusion at the first gridpoint below the top boundary,
	244	!-- if the momentum flux at the top is prescribed by the user
[103]	245	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	246	k = nzt
	247	!
	248	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	249	kmzm = 0.25_wp * &
[102]	250	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	251
[1320]	252	tend(k,j,i) = tend(k,j,i) &
	253	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	254	& ) * ddzw(k) &
	255	& + ( -vswst(j,i) &
	256	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	257	& ) * ddzw(k)
	258	ENDIF
	259
[1]	260	ENDDO
	261	ENDDO
	262
	263	END SUBROUTINE diffusion_v
	264
	265
	266	!------------------------------------------------------------------------------!
[1682]	267	! Description:
	268	! ------------
	269	!> Call for all grid points - accelerator version
[1015]	270	!------------------------------------------------------------------------------!
	271	SUBROUTINE diffusion_v_acc
	272
[1320]	273	USE arrays_3d, &
	274	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	275
	276	USE control_parameters, &
	277	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	278	use_top_fluxes
	279
	280	USE grid_variables, &
	281	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	282
	283	USE indices, &
	284	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	285	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	286
	287	USE kinds
[1015]	288
	289	IMPLICIT NONE
	290
[1682]	291	INTEGER(iwp) :: i !<
	292	INTEGER(iwp) :: j !<
	293	INTEGER(iwp) :: k !<
	294	REAL(wp) :: kmxm !<
	295	REAL(wp) :: kmxp !<
	296	REAL(wp) :: kmzm !<
	297	REAL(wp) :: kmzp !<
[1015]	298
[1682]	299	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1015]	300	!$acc declare create ( vsus )
	301
	302	!
	303	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	304	!-- if neccessary
	305	IF ( topography /= 'flat' ) THEN
[1320]	306	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	307	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	308	ENDIF
	309
[1320]	310	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	311	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	312	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	313	DO i = i_left, i_right
	314	DO j = j_south, j_north
[1015]	315	!
	316	!-- Compute horizontal diffusion
	317	DO k = 1, nzt
	318	IF ( k > nzb_v_outer(j,i) ) THEN
	319	!
	320	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	321	kmxp = 0.25_wp * &
[1015]	322	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	323	kmxm = 0.25_wp * &
[1015]	324	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	325
	326	tend(k,j,i) = tend(k,j,i) &
	327	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	328	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	329	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	330	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	331	& ) * ddx &
[1340]	332	& + 2.0_wp * ( &
[1015]	333	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	334	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	335	& ) * ddy2
[1015]	336	ENDIF
	337	ENDDO
	338
	339	!
	340	!-- Wall functions at the left and right walls, respectively
	341	DO k = 1, nzt
[1320]	342	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1340]	343	wall_v(j,i) /= 0.0_wp ) THEN
[1015]	344
[1340]	345	kmxp = 0.25_wp * &
[1015]	346	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	347	kmxm = 0.25_wp * &
[1015]	348	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	349
	350	tend(k,j,i) = tend(k,j,i) &
[1340]	351	+ 2.0_wp * ( &
[1015]	352	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	353	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	354	) * ddy2 &
[1015]	355	+ ( fxp(j,i) * ( &
	356	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	357	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	358	) &
	359	- fxm(j,i) * ( &
	360	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	361	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	362	) &
	363	+ wall_v(j,i) * vsus(k,j,i) &
	364	) * ddx
	365	ENDIF
	366	ENDDO
	367
	368	!
	369	!-- Compute vertical diffusion. In case of simulating a Prandtl
	370	!-- layer, index k starts at nzb_v_inner+2.
	371	DO k = 1, nzt_diff
	372	IF ( k >= nzb_diff_v(j,i) ) THEN
	373	!
	374	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	375	kmzp = 0.25_wp * &
[1015]	376	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	377	kmzm = 0.25_wp * &
[1015]	378	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	379
	380	tend(k,j,i) = tend(k,j,i) &
	381	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	382	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	383	& ) &
	384	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	385	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	386	& ) &
	387	& ) * ddzw(k)
	388	ENDIF
	389	ENDDO
	390
	391	ENDDO
	392	ENDDO
	393
	394	!
	395	!-- Vertical diffusion at the first grid point above the surface,
	396	!-- if the momentum flux at the bottom is given by the Prandtl law
	397	!-- or if it is prescribed by the user.
	398	!-- Difference quotient of the momentum flux is not formed over
	399	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	400	!-- comparison with other (LES) models showed that the values of
[1015]	401	!-- the momentum flux becomes too large in this case.
	402	!-- The term containing w(k-1,..) (see above equation) is removed here
	403	!-- because the vertical velocity is assumed to be zero at the surface.
	404	IF ( use_surface_fluxes ) THEN
	405
[1128]	406	DO i = i_left, i_right
	407	DO j = j_south, j_north
[1015]	408
	409	k = nzb_v_inner(j,i)+1
	410	!
	411	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	412	kmzp = 0.25_wp * &
[1015]	413	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	414
[1320]	415	tend(k,j,i) = tend(k,j,i) &
	416	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	417	& ) * ddzw(k) &
	418	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	419	& + vsws(j,i) &
[1015]	420	& ) * ddzw(k)
	421	ENDDO
	422	ENDDO
	423
	424	ENDIF
	425
	426	!
	427	!-- Vertical diffusion at the first gridpoint below the top boundary,
	428	!-- if the momentum flux at the top is prescribed by the user
	429	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	430
	431	k = nzt
	432
[1128]	433	DO i = i_left, i_right
	434	DO j = j_south, j_north
[1015]	435
	436	!
	437	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	438	kmzm = 0.25_wp * &
[1015]	439	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	440
[1320]	441	tend(k,j,i) = tend(k,j,i) &
	442	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	443	& ) * ddzw(k) &
	444	& + ( -vswst(j,i) &
	445	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[1015]	446	& ) * ddzw(k)
	447	ENDDO
	448	ENDDO
	449
	450	ENDIF
	451	!$acc end kernels
	452
	453	END SUBROUTINE diffusion_v_acc
	454
	455
	456	!------------------------------------------------------------------------------!
[1682]	457	! Description:
	458	! ------------
	459	!> Call for grid point i,j
[1]	460	!------------------------------------------------------------------------------!
[1001]	461	SUBROUTINE diffusion_v_ij( i, j )
[1]	462
[1320]	463	USE arrays_3d, &
	464	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	465
	466	USE control_parameters, &
	467	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	468
	469	USE grid_variables, &
	470	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	471
	472	USE indices, &
	473	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	474
	475	USE kinds
[1]	476
	477	IMPLICIT NONE
	478
[1682]	479	INTEGER(iwp) :: i !<
	480	INTEGER(iwp) :: j !<
	481	INTEGER(iwp) :: k !<
	482	REAL(wp) :: kmxm !<
	483	REAL(wp) :: kmxp !<
	484	REAL(wp) :: kmzm !<
	485	REAL(wp) :: kmzp !<
[1]	486
[1682]	487	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	488
[1]	489	!
	490	!-- Compute horizontal diffusion
	491	DO k = nzb_v_outer(j,i)+1, nzt
	492	!
	493	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	494	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	495	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]	496
[1320]	497	tend(k,j,i) = tend(k,j,i) &
	498	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	499	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	500	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	501	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	502	& ) * ddx &
[1340]	503	& + 2.0_wp * ( &
[1320]	504	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	505	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	506	& ) * ddy2
[1]	507	ENDDO
	508
	509	!
	510	!-- Wall functions at the left and right walls, respectively
[1340]	511	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	512
	513	!
	514	!-- Calculate the horizontal momentum flux v'u'
[1320]	515	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	516	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	517
[1]	518	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	519	kmxp = 0.25_wp * &
[978]	520	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	521	kmxm = 0.25_wp * &
[978]	522	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	523
	524	tend(k,j,i) = tend(k,j,i) &
[1340]	525	+ 2.0_wp * ( &
[1]	526	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	527	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	528	) * ddy2 &
[1]	529	+ ( fxp(j,i) * ( &
[978]	530	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	531	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	532	) &
	533	- fxm(j,i) * ( &
[978]	534	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	535	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	536	) &
[51]	537	+ wall_v(j,i) * vsus(k) &
[1]	538	) * ddx
	539	ENDDO
	540	ENDIF
	541
	542	!
	543	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	544	!-- index k starts at nzb_v_inner+2.
[102]	545	DO k = nzb_diff_v(j,i), nzt_diff
[1]	546	!
	547	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	548	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	549	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]	550
[1320]	551	tend(k,j,i) = tend(k,j,i) &
	552	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	553	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	554	& ) &
	555	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	556	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	557	& ) &
[1]	558	& ) * ddzw(k)
	559	ENDDO
	560
	561	!
	562	!-- Vertical diffusion at the first grid point above the surface, if the
	563	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	564	!-- prescribed by the user.
	565	!-- Difference quotient of the momentum flux is not formed over half of
	566	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	567	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	568	!-- too large in this case.
	569	!-- The term containing w(k-1,..) (see above equation) is removed here
	570	!-- because the vertical velocity is assumed to be zero at the surface.
	571	IF ( use_surface_fluxes ) THEN
	572	k = nzb_v_inner(j,i)+1
	573	!
	574	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	575	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]	576
[1320]	577	tend(k,j,i) = tend(k,j,i) &
	578	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	579	& ) * ddzw(k) &
	580	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	581	& + vsws(j,i) &
[1]	582	& ) * ddzw(k)
	583	ENDIF
	584
[102]	585	!
	586	!-- Vertical diffusion at the first gridpoint below the top boundary,
	587	!-- if the momentum flux at the top is prescribed by the user
[103]	588	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	589	k = nzt
	590	!
	591	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	592	kmzm = 0.25_wp * &
[102]	593	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	594
[1320]	595	tend(k,j,i) = tend(k,j,i) &
	596	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	597	& ) * ddzw(k) &
	598	& + ( -vswst(j,i) &
	599	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	600	& ) * ddzw(k)
	601	ENDIF
	602
[1]	603	END SUBROUTINE diffusion_v_ij
	604
[1321]	605	END MODULE diffusion_v_mod

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