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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1203

Last change on this file since 1203 was 1132, checked in by raasch, 12 years ago
r1028 documented
Property svn:keywords set to `Id`
File size: 24.4 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	!
	17	! Copyright 1997-2012 Leibniz University Hannover
	18	!--------------------------------------------------------------------------------!
	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
	22	!
[1132]	23	!
[1]	24	! Former revisions:
	25	! -----------------
[3]	26	! $Id: diffusion_v.f90 1132 2013-04-12 14:35:30Z witha $
[39]	27	!
[1132]	28	! 1128 2013-04-12 06:19:32Z raasch
	29	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	30	! j_north
	31	!
[1037]	32	! 1036 2012-10-22 13:43:42Z raasch
	33	! code put under GPL (PALM 3.9)
	34	!
[1017]	35	! 1015 2012-09-27 09:23:24Z raasch
	36	! accelerator version (*_acc) added
	37	!
[1002]	38	! 1001 2012-09-13 14:08:46Z raasch
	39	! arrays comunicated by module instead of parameter list
	40	!
[979]	41	! 978 2012-08-09 08:28:32Z fricke
	42	! outflow damping layer removed
	43	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	44	!
[668]	45	! 667 2010-12-23 12:06:00Z suehring/gryschka
	46	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
	47	!
[392]	48	! 366 2009-08-25 08:06:27Z raasch
	49	! bc_lr replaced by bc_lr_cyc
	50	!
[110]	51	! 106 2007-08-16 14:30:26Z raasch
	52	! Momentumflux at top (vswst) included as boundary condition,
	53	! j loop is starting from nysv (needed for non-cyclic boundary conditions)
	54	!
[77]	55	! 75 2007-03-22 09:54:05Z raasch
	56	! Wall functions now include diabatic conditions, call of routine wall_fluxes,
	57	! z0 removed from argument list, vynp eliminated
	58	!
[39]	59	! 20 2007-02-26 00:12:32Z raasch
	60	! Bugfix: ddzw dimensioned 1:nzt"+1"
	61	!
[3]	62	! RCS Log replace by Id keyword, revision history cleaned up
	63	!
[1]	64	! Revision 1.15 2006/02/23 10:36:00 raasch
	65	! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner
	66	! or nzb_diff_v, respectively, in vertical diffusion,
	67	! wall functions added for north and south walls, +z0 in argument list,
	68	! terms containing w(k-1,..) are removed from the Prandtl-layer equation
	69	! because they cause errors at the edges of topography
	70	! WARNING: loops containing the MAX function are still not properly vectorized!
	71	!
	72	! Revision 1.1 1997/09/12 06:24:01 raasch
	73	! Initial revision
	74	!
	75	!
	76	! Description:
	77	! ------------
	78	! Diffusion term of the v-component
	79	!------------------------------------------------------------------------------!
	80
[56]	81	USE wall_fluxes_mod
	82
[1]	83	PRIVATE
[1015]	84	PUBLIC diffusion_v, diffusion_v_acc
[1]	85
	86	INTERFACE diffusion_v
	87	MODULE PROCEDURE diffusion_v
	88	MODULE PROCEDURE diffusion_v_ij
	89	END INTERFACE diffusion_v
	90
[1015]	91	INTERFACE diffusion_v_acc
	92	MODULE PROCEDURE diffusion_v_acc
	93	END INTERFACE diffusion_v_acc
	94
[1]	95	CONTAINS
	96
	97
	98	!------------------------------------------------------------------------------!
	99	! Call for all grid points
	100	!------------------------------------------------------------------------------!
[1001]	101	SUBROUTINE diffusion_v
[1]	102
[1001]	103	USE arrays_3d
[1]	104	USE control_parameters
	105	USE grid_variables
	106	USE indices
	107
	108	IMPLICIT NONE
	109
	110	INTEGER :: i, j, k
[978]	111	REAL :: kmxm, kmxp, kmzm, kmzp
[1001]	112
[75]	113	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
[1]	114
[56]	115	!
	116	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	117	!-- if neccessary
	118	IF ( topography /= 'flat' ) THEN
[75]	119	CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
[56]	120	nzb_v_outer, wall_v )
	121	ENDIF
	122
[1]	123	DO i = nxl, nxr
[106]	124	DO j = nysv, nyn
[1]	125	!
	126	!-- Compute horizontal diffusion
	127	DO k = nzb_v_outer(j,i)+1, nzt
	128	!
	129	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	130	kmxp = 0.25 * &
	131	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	132	kmxm = 0.25 * &
	133	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	134
	135	tend(k,j,i) = tend(k,j,i) &
[978]	136	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	137	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	138	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	139	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	140	& ) * ddx &
	141	& + 2.0 * ( &
	142	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	143	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	144	& ) * ddy2
	145	ENDDO
	146
	147	!
	148	!-- Wall functions at the left and right walls, respectively
	149	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	150
[1]	151	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	152	kmxp = 0.25 * &
	153	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	154	kmxm = 0.25 * &
	155	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	156
[1]	157	tend(k,j,i) = tend(k,j,i) &
	158	+ 2.0 * ( &
	159	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	160	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	161	) * ddy2 &
	162	+ ( fxp(j,i) * ( &
[978]	163	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	164	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	165	) &
	166	- fxm(j,i) * ( &
[978]	167	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	168	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	169	) &
[56]	170	+ wall_v(j,i) * vsus(k,j,i) &
[1]	171	) * ddx
	172	ENDDO
	173	ENDIF
	174
	175	!
	176	!-- Compute vertical diffusion. In case of simulating a Prandtl
	177	!-- layer, index k starts at nzb_v_inner+2.
[102]	178	DO k = nzb_diff_v(j,i), nzt_diff
[1]	179	!
	180	!-- Interpolate eddy diffusivities on staggered gridpoints
	181	kmzp = 0.25 * &
	182	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	183	kmzm = 0.25 * &
	184	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	185
	186	tend(k,j,i) = tend(k,j,i) &
	187	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	188	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	189	& ) &
	190	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	191	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	192	& ) &
	193	& ) * ddzw(k)
	194	ENDDO
	195
	196	!
	197	!-- Vertical diffusion at the first grid point above the surface,
	198	!-- if the momentum flux at the bottom is given by the Prandtl law
	199	!-- or if it is prescribed by the user.
	200	!-- Difference quotient of the momentum flux is not formed over
	201	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	202	!-- comparison with other (LES) modell showed that the values of
	203	!-- the momentum flux becomes too large in this case.
	204	!-- The term containing w(k-1,..) (see above equation) is removed here
	205	!-- because the vertical velocity is assumed to be zero at the surface.
	206	IF ( use_surface_fluxes ) THEN
	207	k = nzb_v_inner(j,i)+1
	208	!
	209	!-- Interpolate eddy diffusivities on staggered gridpoints
	210	kmzp = 0.25 * &
	211	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	212	kmzm = 0.25 * &
	213	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	214
	215	tend(k,j,i) = tend(k,j,i) &
	216	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	217	& ) * ddzw(k) &
[102]	218	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	219	& + vsws(j,i) &
	220	& ) * ddzw(k)
	221	ENDIF
	222
[102]	223	!
	224	!-- Vertical diffusion at the first gridpoint below the top boundary,
	225	!-- if the momentum flux at the top is prescribed by the user
[103]	226	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	227	k = nzt
	228	!
	229	!-- Interpolate eddy diffusivities on staggered gridpoints
	230	kmzp = 0.25 * &
	231	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	232	kmzm = 0.25 * &
	233	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	234
	235	tend(k,j,i) = tend(k,j,i) &
	236	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	237	& ) * ddzw(k) &
	238	& + ( -vswst(j,i) &
	239	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	240	& ) * ddzw(k)
	241	ENDIF
	242
[1]	243	ENDDO
	244	ENDDO
	245
	246	END SUBROUTINE diffusion_v
	247
	248
	249	!------------------------------------------------------------------------------!
[1015]	250	! Call for all grid points - accelerator version
	251	!------------------------------------------------------------------------------!
	252	SUBROUTINE diffusion_v_acc
	253
	254	USE arrays_3d
	255	USE control_parameters
	256	USE grid_variables
	257	USE indices
	258
	259	IMPLICIT NONE
	260
	261	INTEGER :: i, j, k
	262	REAL :: kmxm, kmxp, kmzm, kmzp
	263
	264	!$acc declare create ( vsus )
	265	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
	266
	267	!
	268	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	269	!-- if neccessary
	270	IF ( topography /= 'flat' ) THEN
	271	CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
	272	nzb_v_outer, wall_v )
	273	ENDIF
	274
	275	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	276	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
	277	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
	278	!$acc loop
[1128]	279	DO i = i_left, i_right
	280	DO j = j_south, j_north
[1015]	281	!
	282	!-- Compute horizontal diffusion
	283	!$acc loop vector(32)
	284	DO k = 1, nzt
	285	IF ( k > nzb_v_outer(j,i) ) THEN
	286	!
	287	!-- Interpolate eddy diffusivities on staggered gridpoints
	288	kmxp = 0.25 * &
	289	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	290	kmxm = 0.25 * &
	291	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	292
	293	tend(k,j,i) = tend(k,j,i) &
	294	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	295	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	296	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	297	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	298	& ) * ddx &
	299	& + 2.0 * ( &
	300	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	301	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	302	& ) * ddy2
	303	ENDIF
	304	ENDDO
	305
	306	!
	307	!-- Wall functions at the left and right walls, respectively
	308	!$acc loop vector(32)
	309	DO k = 1, nzt
	310	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
	311	wall_v(j,i) /= 0.0 ) THEN
	312
	313	kmxp = 0.25 * &
	314	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	315	kmxm = 0.25 * &
	316	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	317
	318	tend(k,j,i) = tend(k,j,i) &
	319	+ 2.0 * ( &
	320	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	321	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	322	) * ddy2 &
	323	+ ( fxp(j,i) * ( &
	324	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	325	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	326	) &
	327	- fxm(j,i) * ( &
	328	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	329	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	330	) &
	331	+ wall_v(j,i) * vsus(k,j,i) &
	332	) * ddx
	333	ENDIF
	334	ENDDO
	335
	336	!
	337	!-- Compute vertical diffusion. In case of simulating a Prandtl
	338	!-- layer, index k starts at nzb_v_inner+2.
	339	!$acc loop vector(32)
	340	DO k = 1, nzt_diff
	341	IF ( k >= nzb_diff_v(j,i) ) THEN
	342	!
	343	!-- Interpolate eddy diffusivities on staggered gridpoints
	344	kmzp = 0.25 * &
	345	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	346	kmzm = 0.25 * &
	347	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	348
	349	tend(k,j,i) = tend(k,j,i) &
	350	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	351	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	352	& ) &
	353	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	354	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	355	& ) &
	356	& ) * ddzw(k)
	357	ENDIF
	358	ENDDO
	359
	360	ENDDO
	361	ENDDO
	362
	363	!
	364	!-- Vertical diffusion at the first grid point above the surface,
	365	!-- if the momentum flux at the bottom is given by the Prandtl law
	366	!-- or if it is prescribed by the user.
	367	!-- Difference quotient of the momentum flux is not formed over
	368	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	369	!-- comparison with other (LES) modell showed that the values of
	370	!-- the momentum flux becomes too large in this case.
	371	!-- The term containing w(k-1,..) (see above equation) is removed here
	372	!-- because the vertical velocity is assumed to be zero at the surface.
	373	IF ( use_surface_fluxes ) THEN
	374
	375	!$acc loop
[1128]	376	DO i = i_left, i_right
[1015]	377	!$acc loop vector(32)
[1128]	378	DO j = j_south, j_north
[1015]	379
	380	k = nzb_v_inner(j,i)+1
	381	!
	382	!-- Interpolate eddy diffusivities on staggered gridpoints
	383	kmzp = 0.25 * &
	384	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	385	kmzm = 0.25 * &
	386	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	387
	388	tend(k,j,i) = tend(k,j,i) &
	389	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	390	& ) * ddzw(k) &
	391	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	392	& + vsws(j,i) &
	393	& ) * ddzw(k)
	394	ENDDO
	395	ENDDO
	396
	397	ENDIF
	398
	399	!
	400	!-- Vertical diffusion at the first gridpoint below the top boundary,
	401	!-- if the momentum flux at the top is prescribed by the user
	402	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	403
	404	k = nzt
	405
	406	!$acc loop
[1128]	407	DO i = i_left, i_right
[1015]	408	!$acc loop vector(32)
[1128]	409	DO j = j_south, j_north
[1015]	410
	411	!
	412	!-- Interpolate eddy diffusivities on staggered gridpoints
	413	kmzp = 0.25 * &
	414	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	415	kmzm = 0.25 * &
	416	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	417
	418	tend(k,j,i) = tend(k,j,i) &
	419	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	420	& ) * ddzw(k) &
	421	& + ( -vswst(j,i) &
	422	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	423	& ) * ddzw(k)
	424	ENDDO
	425	ENDDO
	426
	427	ENDIF
	428	!$acc end kernels
	429
	430	END SUBROUTINE diffusion_v_acc
	431
	432
	433	!------------------------------------------------------------------------------!
[1]	434	! Call for grid point i,j
	435	!------------------------------------------------------------------------------!
[1001]	436	SUBROUTINE diffusion_v_ij( i, j )
[1]	437
[1001]	438	USE arrays_3d
[1]	439	USE control_parameters
	440	USE grid_variables
	441	USE indices
	442
	443	IMPLICIT NONE
	444
	445	INTEGER :: i, j, k
[978]	446	REAL :: kmxm, kmxp, kmzm, kmzp
[1]	447
[1001]	448	REAL, DIMENSION(nzb:nzt+1) :: vsus
	449
[1]	450	!
	451	!-- Compute horizontal diffusion
	452	DO k = nzb_v_outer(j,i)+1, nzt
	453	!
	454	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	455	kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	456	kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	457
	458	tend(k,j,i) = tend(k,j,i) &
[978]	459	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	460	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	461	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	462	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	463	& ) * ddx &
	464	& + 2.0 * ( &
	465	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	466	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	467	& ) * ddy2
	468	ENDDO
	469
	470	!
	471	!-- Wall functions at the left and right walls, respectively
	472	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	473
	474	!
	475	!-- Calculate the horizontal momentum flux v'u'
	476	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	477	vsus, 0.0, 1.0, 0.0, 0.0 )
	478
[1]	479	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	480	kmxp = 0.25 * &
	481	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	482	kmxm = 0.25 * &
	483	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	484
	485	tend(k,j,i) = tend(k,j,i) &
	486	+ 2.0 * ( &
	487	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	488	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	489	) * ddy2 &
	490	+ ( fxp(j,i) * ( &
[978]	491	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	492	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	493	) &
	494	- fxm(j,i) * ( &
[978]	495	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	496	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	497	) &
[51]	498	+ wall_v(j,i) * vsus(k) &
[1]	499	) * ddx
	500	ENDDO
	501	ENDIF
	502
	503	!
	504	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	505	!-- index k starts at nzb_v_inner+2.
[102]	506	DO k = nzb_diff_v(j,i), nzt_diff
[1]	507	!
	508	!-- Interpolate eddy diffusivities on staggered gridpoints
	509	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	510	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	511
	512	tend(k,j,i) = tend(k,j,i) &
	513	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	514	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	515	& ) &
	516	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	517	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	518	& ) &
	519	& ) * ddzw(k)
	520	ENDDO
	521
	522	!
	523	!-- Vertical diffusion at the first grid point above the surface, if the
	524	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	525	!-- prescribed by the user.
	526	!-- Difference quotient of the momentum flux is not formed over half of
	527	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
	528	!-- other (LES) modell showed that the values of the momentum flux becomes
	529	!-- too large in this case.
	530	!-- The term containing w(k-1,..) (see above equation) is removed here
	531	!-- because the vertical velocity is assumed to be zero at the surface.
	532	IF ( use_surface_fluxes ) THEN
	533	k = nzb_v_inner(j,i)+1
	534	!
	535	!-- Interpolate eddy diffusivities on staggered gridpoints
	536	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	537	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	538
	539	tend(k,j,i) = tend(k,j,i) &
	540	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	541	& ) * ddzw(k) &
[102]	542	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	543	& + vsws(j,i) &
	544	& ) * ddzw(k)
	545	ENDIF
	546
[102]	547	!
	548	!-- Vertical diffusion at the first gridpoint below the top boundary,
	549	!-- if the momentum flux at the top is prescribed by the user
[103]	550	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	551	k = nzt
	552	!
	553	!-- Interpolate eddy diffusivities on staggered gridpoints
	554	kmzp = 0.25 * &
	555	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	556	kmzm = 0.25 * &
	557	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	558
	559	tend(k,j,i) = tend(k,j,i) &
	560	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	561	& ) * ddzw(k) &
	562	& + ( -vswst(j,i) &
	563	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	564	& ) * ddzw(k)
	565	ENDIF
	566
[1]	567	END SUBROUTINE diffusion_v_ij
	568
	569	END MODULE diffusion_v_mod

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