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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1727

Last change on this file since 1727 was 1683, checked in by knoop, 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	!
[1683]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: diffusion_v.f90 1683 2015-10-07 23:57:51Z knoop $
	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) )
[1340]	222	kmzm = 0.25_wp * &
[1]	223	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	224
[1320]	225	tend(k,j,i) = tend(k,j,i) &
	226	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	227	& ) * ddzw(k) &
	228	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	229	& + vsws(j,i) &
[1]	230	& ) * ddzw(k)
	231	ENDIF
	232
[102]	233	!
	234	!-- Vertical diffusion at the first gridpoint below the top boundary,
	235	!-- if the momentum flux at the top is prescribed by the user
[103]	236	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	237	k = nzt
	238	!
	239	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	240	kmzp = 0.25_wp * &
[102]	241	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	242	kmzm = 0.25_wp * &
[102]	243	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	244
[1320]	245	tend(k,j,i) = tend(k,j,i) &
	246	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	247	& ) * ddzw(k) &
	248	& + ( -vswst(j,i) &
	249	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[102]	250	& ) * ddzw(k)
	251	ENDIF
	252
[1]	253	ENDDO
	254	ENDDO
	255
	256	END SUBROUTINE diffusion_v
	257
	258
	259	!------------------------------------------------------------------------------!
[1682]	260	! Description:
	261	! ------------
	262	!> Call for all grid points - accelerator version
[1015]	263	!------------------------------------------------------------------------------!
	264	SUBROUTINE diffusion_v_acc
	265
[1320]	266	USE arrays_3d, &
	267	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	268
	269	USE control_parameters, &
	270	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	271	use_top_fluxes
	272
	273	USE grid_variables, &
	274	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	275
	276	USE indices, &
	277	ONLY: i_left, i_right, j_north, j_south, nxl, nxr, nyn, nys, nzb, &
	278	nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	279
	280	USE kinds
[1015]	281
	282	IMPLICIT NONE
	283
[1682]	284	INTEGER(iwp) :: i !<
	285	INTEGER(iwp) :: j !<
	286	INTEGER(iwp) :: k !<
	287	REAL(wp) :: kmxm !<
	288	REAL(wp) :: kmxp !<
	289	REAL(wp) :: kmzm !<
	290	REAL(wp) :: kmzp !<
[1015]	291
[1682]	292	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1015]	293	!$acc declare create ( vsus )
	294
	295	!
	296	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	297	!-- if neccessary
	298	IF ( topography /= 'flat' ) THEN
[1320]	299	CALL wall_fluxes_acc( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, &
	300	nzb_v_inner, nzb_v_outer, wall_v )
[1015]	301	ENDIF
	302
[1320]	303	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	304	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
[1015]	305	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
[1128]	306	DO i = i_left, i_right
	307	DO j = j_south, j_north
[1015]	308	!
	309	!-- Compute horizontal diffusion
	310	DO k = 1, nzt
	311	IF ( k > nzb_v_outer(j,i) ) THEN
	312	!
	313	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	314	kmxp = 0.25_wp * &
[1015]	315	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	316	kmxm = 0.25_wp * &
[1015]	317	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	318
	319	tend(k,j,i) = tend(k,j,i) &
	320	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	321	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	322	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	323	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	324	& ) * ddx &
[1340]	325	& + 2.0_wp * ( &
[1015]	326	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	327	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	328	& ) * ddy2
[1015]	329	ENDIF
	330	ENDDO
	331
	332	!
	333	!-- Wall functions at the left and right walls, respectively
	334	DO k = 1, nzt
[1320]	335	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
[1340]	336	wall_v(j,i) /= 0.0_wp ) THEN
[1015]	337
[1340]	338	kmxp = 0.25_wp * &
[1015]	339	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	340	kmxm = 0.25_wp * &
[1015]	341	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	342
	343	tend(k,j,i) = tend(k,j,i) &
[1340]	344	+ 2.0_wp * ( &
[1015]	345	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	346	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	347	) * ddy2 &
[1015]	348	+ ( fxp(j,i) * ( &
	349	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	350	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	351	) &
	352	- fxm(j,i) * ( &
	353	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	354	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	355	) &
	356	+ wall_v(j,i) * vsus(k,j,i) &
	357	) * ddx
	358	ENDIF
	359	ENDDO
	360
	361	!
	362	!-- Compute vertical diffusion. In case of simulating a Prandtl
	363	!-- layer, index k starts at nzb_v_inner+2.
	364	DO k = 1, nzt_diff
	365	IF ( k >= nzb_diff_v(j,i) ) THEN
	366	!
	367	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	368	kmzp = 0.25_wp * &
[1015]	369	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	370	kmzm = 0.25_wp * &
[1015]	371	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	372
	373	tend(k,j,i) = tend(k,j,i) &
	374	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	375	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	376	& ) &
	377	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	378	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	379	& ) &
	380	& ) * ddzw(k)
	381	ENDIF
	382	ENDDO
	383
	384	ENDDO
	385	ENDDO
	386
	387	!
	388	!-- Vertical diffusion at the first grid point above the surface,
	389	!-- if the momentum flux at the bottom is given by the Prandtl law
	390	!-- or if it is prescribed by the user.
	391	!-- Difference quotient of the momentum flux is not formed over
	392	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	393	!-- comparison with other (LES) models showed that the values of
[1015]	394	!-- the momentum flux becomes too large in this case.
	395	!-- The term containing w(k-1,..) (see above equation) is removed here
	396	!-- because the vertical velocity is assumed to be zero at the surface.
	397	IF ( use_surface_fluxes ) THEN
	398
[1128]	399	DO i = i_left, i_right
	400	DO j = j_south, j_north
[1015]	401
	402	k = nzb_v_inner(j,i)+1
	403	!
	404	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	405	kmzp = 0.25_wp * &
[1015]	406	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	407	kmzm = 0.25_wp * &
[1015]	408	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	409
[1320]	410	tend(k,j,i) = tend(k,j,i) &
	411	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	412	& ) * ddzw(k) &
	413	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	414	& + vsws(j,i) &
[1015]	415	& ) * ddzw(k)
	416	ENDDO
	417	ENDDO
	418
	419	ENDIF
	420
	421	!
	422	!-- Vertical diffusion at the first gridpoint below the top boundary,
	423	!-- if the momentum flux at the top is prescribed by the user
	424	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	425
	426	k = nzt
	427
[1128]	428	DO i = i_left, i_right
	429	DO j = j_south, j_north
[1015]	430
	431	!
	432	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	433	kmzp = 0.25_wp * &
[1015]	434	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	435	kmzm = 0.25_wp * &
[1015]	436	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	437
[1320]	438	tend(k,j,i) = tend(k,j,i) &
	439	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	440	& ) * ddzw(k) &
	441	& + ( -vswst(j,i) &
	442	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
[1015]	443	& ) * ddzw(k)
	444	ENDDO
	445	ENDDO
	446
	447	ENDIF
	448	!$acc end kernels
	449
	450	END SUBROUTINE diffusion_v_acc
	451
	452
	453	!------------------------------------------------------------------------------!
[1682]	454	! Description:
	455	! ------------
	456	!> Call for grid point i,j
[1]	457	!------------------------------------------------------------------------------!
[1001]	458	SUBROUTINE diffusion_v_ij( i, j )
[1]	459
[1320]	460	USE arrays_3d, &
	461	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w
	462
	463	USE control_parameters, &
	464	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	465
	466	USE grid_variables, &
	467	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	468
	469	USE indices, &
	470	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	471
	472	USE kinds
[1]	473
	474	IMPLICIT NONE
	475
[1682]	476	INTEGER(iwp) :: i !<
	477	INTEGER(iwp) :: j !<
	478	INTEGER(iwp) :: k !<
	479	REAL(wp) :: kmxm !<
	480	REAL(wp) :: kmxp !<
	481	REAL(wp) :: kmzm !<
	482	REAL(wp) :: kmzp !<
[1]	483
[1682]	484	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	485
[1]	486	!
	487	!-- Compute horizontal diffusion
	488	DO k = nzb_v_outer(j,i)+1, nzt
	489	!
	490	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	491	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	492	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]	493
[1320]	494	tend(k,j,i) = tend(k,j,i) &
	495	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	496	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	497	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	498	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	499	& ) * ddx &
[1340]	500	& + 2.0_wp * ( &
[1320]	501	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	502	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	503	& ) * ddy2
[1]	504	ENDDO
	505
	506	!
	507	!-- Wall functions at the left and right walls, respectively
[1340]	508	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	509
	510	!
	511	!-- Calculate the horizontal momentum flux v'u'
[1320]	512	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	513	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	514
[1]	515	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	516	kmxp = 0.25_wp * &
[978]	517	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	518	kmxm = 0.25_wp * &
[978]	519	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	520
	521	tend(k,j,i) = tend(k,j,i) &
[1340]	522	+ 2.0_wp * ( &
[1]	523	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	524	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	525	) * ddy2 &
[1]	526	+ ( fxp(j,i) * ( &
[978]	527	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	528	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	529	) &
	530	- fxm(j,i) * ( &
[978]	531	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	532	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	533	) &
[51]	534	+ wall_v(j,i) * vsus(k) &
[1]	535	) * ddx
	536	ENDDO
	537	ENDIF
	538
	539	!
	540	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	541	!-- index k starts at nzb_v_inner+2.
[102]	542	DO k = nzb_diff_v(j,i), nzt_diff
[1]	543	!
	544	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	545	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	546	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]	547
[1320]	548	tend(k,j,i) = tend(k,j,i) &
	549	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	550	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	551	& ) &
	552	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	553	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	554	& ) &
[1]	555	& ) * ddzw(k)
	556	ENDDO
	557
	558	!
	559	!-- Vertical diffusion at the first grid point above the surface, if the
	560	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	561	!-- prescribed by the user.
	562	!-- Difference quotient of the momentum flux is not formed over half of
	563	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	564	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	565	!-- too large in this case.
	566	!-- The term containing w(k-1,..) (see above equation) is removed here
	567	!-- because the vertical velocity is assumed to be zero at the surface.
	568	IF ( use_surface_fluxes ) THEN
	569	k = nzb_v_inner(j,i)+1
	570	!
	571	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	572	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	573	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]	574
[1320]	575	tend(k,j,i) = tend(k,j,i) &
	576	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	577	& ) * ddzw(k) &
	578	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	579	& + vsws(j,i) &
[1]	580	& ) * ddzw(k)
	581	ENDIF
	582
[102]	583	!
	584	!-- Vertical diffusion at the first gridpoint below the top boundary,
	585	!-- if the momentum flux at the top is prescribed by the user
[103]	586	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	587	k = nzt
	588	!
	589	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	590	kmzp = 0.25_wp * &
[102]	591	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[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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