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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1339

Last change on this file since 1339 was 1321, checked in by raasch, 11 years ago
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[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	! -----------------
[1321]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_v.f90 1321 2014-03-20 09:40:40Z heinze $
	27	!
	28	! 1320 2014-03-20 08:40:49Z raasch
[1320]	29	! ONLY-attribute added to USE-statements,
	30	! kind-parameters added to all INTEGER and REAL declaration statements,
	31	! kinds are defined in new module kinds,
	32	! revision history before 2012 removed,
	33	! comment fields (!:) to be used for variable explanations added to
	34	! all variable declaration statements
[1321]	35	!
[1258]	36	! 1257 2013-11-08 15:18:40Z raasch
	37	! openacc loop and loop vector clauses removed, declare create moved after
	38	! the FORTRAN declaration statement
	39	!
[1132]	40	! 1128 2013-04-12 06:19:32Z raasch
	41	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	42	! j_north
	43	!
[1037]	44	! 1036 2012-10-22 13:43:42Z raasch
	45	! code put under GPL (PALM 3.9)
	46	!
[1017]	47	! 1015 2012-09-27 09:23:24Z raasch
	48	! accelerator version (*_acc) added
	49	!
[1002]	50	! 1001 2012-09-13 14:08:46Z raasch
	51	! arrays comunicated by module instead of parameter list
	52	!
[979]	53	! 978 2012-08-09 08:28:32Z fricke
	54	! outflow damping layer removed
	55	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	56	!
[1]	57	! Revision 1.1 1997/09/12 06:24:01 raasch
	58	! Initial revision
	59	!
	60	!
	61	! Description:
	62	! ------------
	63	! Diffusion term of the v-component
	64	!------------------------------------------------------------------------------!
	65
[56]	66	USE wall_fluxes_mod
	67
[1]	68	PRIVATE
[1015]	69	PUBLIC diffusion_v, diffusion_v_acc
[1]	70
	71	INTERFACE diffusion_v
	72	MODULE PROCEDURE diffusion_v
	73	MODULE PROCEDURE diffusion_v_ij
	74	END INTERFACE diffusion_v
	75
[1015]	76	INTERFACE diffusion_v_acc
	77	MODULE PROCEDURE diffusion_v_acc
	78	END INTERFACE diffusion_v_acc
	79
[1]	80	CONTAINS
	81
	82
	83	!------------------------------------------------------------------------------!
	84	! Call for all grid points
	85	!------------------------------------------------------------------------------!
[1001]	86	SUBROUTINE diffusion_v
[1]	87
[1320]	88	USE arrays_3d, &
	89	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	90
	91	USE control_parameters, &
	92	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	93	use_top_fluxes
	94
	95	USE grid_variables, &
	96	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	97
	98	USE indices, &
	99	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	100	nzb_v_outer, nzt, nzt_diff
	101
	102	USE kinds
[1]	103
	104	IMPLICIT NONE
	105
[1320]	106	INTEGER(iwp) :: i !:
	107	INTEGER(iwp) :: j !:
	108	INTEGER(iwp) :: k !:
	109	REAL(wp) :: kmxm !:
	110	REAL(wp) :: kmxp !:
	111	REAL(wp) :: kmzm !:
	112	REAL(wp) :: kmzp !:
[1001]	113
[1320]	114	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !:
[1]	115
[56]	116	!
	117	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	118	!-- if neccessary
	119	IF ( topography /= 'flat' ) THEN
[1320]	120	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	121	nzb_v_outer, wall_v )
	122	ENDIF
	123
[1]	124	DO i = nxl, nxr
[106]	125	DO j = nysv, nyn
[1]	126	!
	127	!-- Compute horizontal diffusion
	128	DO k = nzb_v_outer(j,i)+1, nzt
	129	!
	130	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	131	kmxp = 0.25 * &
	132	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	133	kmxm = 0.25 * &
	134	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	135
[1320]	136	tend(k,j,i) = tend(k,j,i) &
	137	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	138	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	139	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	140	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	141	& ) * ddx &
	142	& + 2.0 * ( &
	143	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	144	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1]	145	& ) * ddy2
	146	ENDDO
	147
	148	!
	149	!-- Wall functions at the left and right walls, respectively
	150	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	151
[1]	152	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1320]	153	kmxp = 0.25 * &
[978]	154	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1320]	155	kmxm = 0.25 * &
[978]	156	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	157
[1]	158	tend(k,j,i) = tend(k,j,i) &
	159	+ 2.0 * ( &
	160	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	161	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	162	) * ddy2 &
	163	+ ( fxp(j,i) * ( &
[978]	164	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	165	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	166	) &
	167	- fxm(j,i) * ( &
[978]	168	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	169	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	170	) &
[56]	171	+ wall_v(j,i) * vsus(k,j,i) &
[1]	172	) * ddx
	173	ENDDO
	174	ENDIF
	175
	176	!
	177	!-- Compute vertical diffusion. In case of simulating a Prandtl
	178	!-- layer, index k starts at nzb_v_inner+2.
[102]	179	DO k = nzb_diff_v(j,i), nzt_diff
[1]	180	!
	181	!-- Interpolate eddy diffusivities on staggered gridpoints
	182	kmzp = 0.25 * &
	183	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	184	kmzm = 0.25 * &
	185	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	186
[1320]	187	tend(k,j,i) = tend(k,j,i) &
	188	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	189	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	190	& ) &
	191	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	192	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	193	& ) &
[1]	194	& ) * ddzw(k)
	195	ENDDO
	196
	197	!
	198	!-- Vertical diffusion at the first grid point above the surface,
	199	!-- if the momentum flux at the bottom is given by the Prandtl law
	200	!-- or if it is prescribed by the user.
	201	!-- Difference quotient of the momentum flux is not formed over
	202	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	203	!-- comparison with other (LES) models showed that the values of
[1]	204	!-- the momentum flux becomes too large in this case.
	205	!-- The term containing w(k-1,..) (see above equation) is removed here
	206	!-- because the vertical velocity is assumed to be zero at the surface.
	207	IF ( use_surface_fluxes ) THEN
	208	k = nzb_v_inner(j,i)+1
	209	!
	210	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	211	kmzp = 0.25 * &
[1]	212	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1320]	213	kmzm = 0.25 * &
[1]	214	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	215
[1320]	216	tend(k,j,i) = tend(k,j,i) &
	217	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	218	& ) * ddzw(k) &
	219	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	220	& + vsws(j,i) &
[1]	221	& ) * ddzw(k)
	222	ENDIF
	223
[102]	224	!
	225	!-- Vertical diffusion at the first gridpoint below the top boundary,
	226	!-- if the momentum flux at the top is prescribed by the user
[103]	227	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	228	k = nzt
	229	!
	230	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	231	kmzp = 0.25 * &
[102]	232	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1320]	233	kmzm = 0.25 * &
[102]	234	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	235
[1320]	236	tend(k,j,i) = tend(k,j,i) &
	237	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	238	& ) * ddzw(k) &
	239	& + ( -vswst(j,i) &
	240	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	241	& ) * ddzw(k)
	242	ENDIF
	243
[1]	244	ENDDO
	245	ENDDO
	246
	247	END SUBROUTINE diffusion_v
	248
	249
	250	!------------------------------------------------------------------------------!
[1015]	251	! Call for all grid points - accelerator version
	252	!------------------------------------------------------------------------------!
	253	SUBROUTINE diffusion_v_acc
	254
[1320]	255	USE arrays_3d, &
	256	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	257
	258	USE control_parameters, &
	259	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	260	use_top_fluxes
	261
	262	USE grid_variables, &
	263	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	264
	265	USE indices, &
	266	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	267	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	268
	269	USE kinds
[1015]	270
	271	IMPLICIT NONE
	272
[1320]	273	INTEGER(iwp) :: i !:
	274	INTEGER(iwp) :: j !:
	275	INTEGER(iwp) :: k !:
	276	REAL(wp) :: kmxm !:
	277	REAL(wp) :: kmxp !:
	278	REAL(wp) :: kmzm !:
	279	REAL(wp) :: kmzp !:
[1015]	280
[1320]	281	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !:
[1015]	282	!$acc declare create ( vsus )
	283
	284	!
	285	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	286	!-- if neccessary
	287	IF ( topography /= 'flat' ) THEN
[1320]	288	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	289	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	290	ENDIF
	291
[1320]	292	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	293	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	294	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	295	DO i = i_left, i_right
	296	DO j = j_south, j_north
[1015]	297	!
	298	!-- Compute horizontal diffusion
	299	DO k = 1, nzt
	300	IF ( k > nzb_v_outer(j,i) ) THEN
	301	!
	302	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	303	kmxp = 0.25 * &
[1015]	304	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1320]	305	kmxm = 0.25 * &
[1015]	306	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	307
	308	tend(k,j,i) = tend(k,j,i) &
	309	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	310	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	311	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	312	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	313	& ) * ddx &
	314	& + 2.0 * ( &
	315	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	316	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	317	& ) * ddy2
	318	ENDIF
	319	ENDDO
	320
	321	!
	322	!-- Wall functions at the left and right walls, respectively
	323	DO k = 1, nzt
[1320]	324	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1015]	325	wall_v(j,i) /= 0.0 ) THEN
	326
[1320]	327	kmxp = 0.25 * &
[1015]	328	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1320]	329	kmxm = 0.25 * &
[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	+ 2.0 * ( &
	334	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	335	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	336	) * ddy2 &
	337	+ ( fxp(j,i) * ( &
	338	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	339	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	340	) &
	341	- fxm(j,i) * ( &
	342	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	343	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	344	) &
	345	+ wall_v(j,i) * vsus(k,j,i) &
	346	) * ddx
	347	ENDIF
	348	ENDDO
	349
	350	!
	351	!-- Compute vertical diffusion. In case of simulating a Prandtl
	352	!-- layer, index k starts at nzb_v_inner+2.
	353	DO k = 1, nzt_diff
	354	IF ( k >= nzb_diff_v(j,i) ) THEN
	355	!
	356	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	357	kmzp = 0.25 * &
[1015]	358	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1320]	359	kmzm = 0.25 * &
[1015]	360	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	361
	362	tend(k,j,i) = tend(k,j,i) &
	363	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	364	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	365	& ) &
	366	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	367	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	368	& ) &
	369	& ) * ddzw(k)
	370	ENDIF
	371	ENDDO
	372
	373	ENDDO
	374	ENDDO
	375
	376	!
	377	!-- Vertical diffusion at the first grid point above the surface,
	378	!-- if the momentum flux at the bottom is given by the Prandtl law
	379	!-- or if it is prescribed by the user.
	380	!-- Difference quotient of the momentum flux is not formed over
	381	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	382	!-- comparison with other (LES) models showed that the values of
[1015]	383	!-- the momentum flux becomes too large in this case.
	384	!-- The term containing w(k-1,..) (see above equation) is removed here
	385	!-- because the vertical velocity is assumed to be zero at the surface.
	386	IF ( use_surface_fluxes ) THEN
	387
[1128]	388	DO i = i_left, i_right
	389	DO j = j_south, j_north
[1015]	390
	391	k = nzb_v_inner(j,i)+1
	392	!
	393	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	394	kmzp = 0.25 * &
[1015]	395	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1320]	396	kmzm = 0.25 * &
[1015]	397	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	398
[1320]	399	tend(k,j,i) = tend(k,j,i) &
	400	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	401	& ) * ddzw(k) &
	402	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	403	& + vsws(j,i) &
[1015]	404	& ) * ddzw(k)
	405	ENDDO
	406	ENDDO
	407
	408	ENDIF
	409
	410	!
	411	!-- Vertical diffusion at the first gridpoint below the top boundary,
	412	!-- if the momentum flux at the top is prescribed by the user
	413	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	414
	415	k = nzt
	416
[1128]	417	DO i = i_left, i_right
	418	DO j = j_south, j_north
[1015]	419
	420	!
	421	!-- Interpolate eddy diffusivities on staggered gridpoints
[1320]	422	kmzp = 0.25 * &
[1015]	423	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1320]	424	kmzm = 0.25 * &
[1015]	425	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	426
[1320]	427	tend(k,j,i) = tend(k,j,i) &
	428	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	429	& ) * ddzw(k) &
	430	& + ( -vswst(j,i) &
	431	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[1015]	432	& ) * ddzw(k)
	433	ENDDO
	434	ENDDO
	435
	436	ENDIF
	437	!$acc end kernels
	438
	439	END SUBROUTINE diffusion_v_acc
	440
	441
	442	!------------------------------------------------------------------------------!
[1]	443	! Call for grid point i,j
	444	!------------------------------------------------------------------------------!
[1001]	445	SUBROUTINE diffusion_v_ij( i, j )
[1]	446
[1320]	447	USE arrays_3d, &
	448	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	449
	450	USE control_parameters, &
	451	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	452
	453	USE grid_variables, &
	454	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	455
	456	USE indices, &
	457	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	458
	459	USE kinds
[1]	460
	461	IMPLICIT NONE
	462
[1320]	463	INTEGER(iwp) :: i !:
	464	INTEGER(iwp) :: j !:
	465	INTEGER(iwp) :: k !:
	466	REAL(wp) :: kmxm !:
	467	REAL(wp) :: kmxp !:
	468	REAL(wp) :: kmzm !:
	469	REAL(wp) :: kmzp !:
[1]	470
[1320]	471	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !:
[1001]	472
[1]	473	!
	474	!-- Compute horizontal diffusion
	475	DO k = nzb_v_outer(j,i)+1, nzt
	476	!
	477	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	478	kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	479	kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	480
[1320]	481	tend(k,j,i) = tend(k,j,i) &
	482	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	483	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	484	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	485	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	486	& ) * ddx &
	487	& + 2.0 * ( &
	488	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	489	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1]	490	& ) * ddy2
	491	ENDDO
	492
	493	!
	494	!-- Wall functions at the left and right walls, respectively
	495	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	496
	497	!
	498	!-- Calculate the horizontal momentum flux v'u'
[1320]	499	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	500	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	501
[1]	502	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1320]	503	kmxp = 0.25 * &
[978]	504	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1320]	505	kmxm = 0.25 * &
[978]	506	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	507
	508	tend(k,j,i) = tend(k,j,i) &
	509	+ 2.0 * ( &
	510	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	511	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	512	) * ddy2 &
	513	+ ( fxp(j,i) * ( &
[978]	514	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	515	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	516	) &
	517	- fxm(j,i) * ( &
[978]	518	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	519	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	520	) &
[51]	521	+ wall_v(j,i) * vsus(k) &
[1]	522	) * ddx
	523	ENDDO
	524	ENDIF
	525
	526	!
	527	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	528	!-- index k starts at nzb_v_inner+2.
[102]	529	DO k = nzb_diff_v(j,i), nzt_diff
[1]	530	!
	531	!-- Interpolate eddy diffusivities on staggered gridpoints
	532	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	533	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	534
[1320]	535	tend(k,j,i) = tend(k,j,i) &
	536	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	537	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	538	& ) &
	539	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	540	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	541	& ) &
[1]	542	& ) * ddzw(k)
	543	ENDDO
	544
	545	!
	546	!-- Vertical diffusion at the first grid point above the surface, if the
	547	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	548	!-- prescribed by the user.
	549	!-- Difference quotient of the momentum flux is not formed over half of
	550	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	551	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	552	!-- too large in this case.
	553	!-- The term containing w(k-1,..) (see above equation) is removed here
	554	!-- because the vertical velocity is assumed to be zero at the surface.
	555	IF ( use_surface_fluxes ) THEN
	556	k = nzb_v_inner(j,i)+1
	557	!
	558	!-- Interpolate eddy diffusivities on staggered gridpoints
	559	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	560	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	561
[1320]	562	tend(k,j,i) = tend(k,j,i) &
	563	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	564	& ) * ddzw(k) &
	565	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	566	& + vsws(j,i) &
[1]	567	& ) * ddzw(k)
	568	ENDIF
	569
[102]	570	!
	571	!-- Vertical diffusion at the first gridpoint below the top boundary,
	572	!-- if the momentum flux at the top is prescribed by the user
[103]	573	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	574	k = nzt
	575	!
	576	!-- Interpolate eddy diffusivities on staggered gridpoints
	577	kmzp = 0.25 * &
	578	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	579	kmzm = 0.25 * &
	580	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	581
[1320]	582	tend(k,j,i) = tend(k,j,i) &
	583	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	584	& ) * ddzw(k) &
	585	& + ( -vswst(j,i) &
	586	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	587	& ) * ddzw(k)
	588	ENDIF
	589
[1]	590	END SUBROUTINE diffusion_v_ij
	591
[1321]	592	END MODULE diffusion_v_mod

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