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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1320

Last change on this file since 1320 was 1320, checked in by raasch, 10 years ago
ONLY-attribute added to USE-statements, kind-parameters added to all INTEGER and REAL declaration statements, kinds are defined in new module kinds, old module precision_kind is removed, revision history before 2012 removed, comment fields (!:) to be used for variable explanations added to all variable declaration statements
Property svn:keywords set to `Id`
File size: 26.9 KB

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

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