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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1121

Last change on this file since 1121 was 1037, checked in by raasch, 12 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	!
	17	! Copyright 1997-2012 Leibniz University Hannover
	18	!--------------------------------------------------------------------------------!
	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
	22	!
[1017]	23	!
[1]	24	! Former revisions:
	25	! -----------------
[3]	26	! $Id: diffusion_v.f90 1037 2012-10-22 14:10:22Z raasch $
[39]	27	!
[1037]	28	! 1036 2012-10-22 13:43:42Z raasch
	29	! code put under GPL (PALM 3.9)
	30	!
[1017]	31	! 1015 2012-09-27 09:23:24Z raasch
	32	! accelerator version (*_acc) added
	33	!
[1002]	34	! 1001 2012-09-13 14:08:46Z raasch
	35	! arrays comunicated by module instead of parameter list
	36	!
[979]	37	! 978 2012-08-09 08:28:32Z fricke
	38	! outflow damping layer removed
	39	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	40	!
[668]	41	! 667 2010-12-23 12:06:00Z suehring/gryschka
	42	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
	43	!
[392]	44	! 366 2009-08-25 08:06:27Z raasch
	45	! bc_lr replaced by bc_lr_cyc
	46	!
[110]	47	! 106 2007-08-16 14:30:26Z raasch
	48	! Momentumflux at top (vswst) included as boundary condition,
	49	! j loop is starting from nysv (needed for non-cyclic boundary conditions)
	50	!
[77]	51	! 75 2007-03-22 09:54:05Z raasch
	52	! Wall functions now include diabatic conditions, call of routine wall_fluxes,
	53	! z0 removed from argument list, vynp eliminated
	54	!
[39]	55	! 20 2007-02-26 00:12:32Z raasch
	56	! Bugfix: ddzw dimensioned 1:nzt"+1"
	57	!
[3]	58	! RCS Log replace by Id keyword, revision history cleaned up
	59	!
[1]	60	! Revision 1.15 2006/02/23 10:36:00 raasch
	61	! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner
	62	! or nzb_diff_v, respectively, in vertical diffusion,
	63	! wall functions added for north and south walls, +z0 in argument list,
	64	! terms containing w(k-1,..) are removed from the Prandtl-layer equation
	65	! because they cause errors at the edges of topography
	66	! WARNING: loops containing the MAX function are still not properly vectorized!
	67	!
	68	! Revision 1.1 1997/09/12 06:24:01 raasch
	69	! Initial revision
	70	!
	71	!
	72	! Description:
	73	! ------------
	74	! Diffusion term of the v-component
	75	!------------------------------------------------------------------------------!
	76
[56]	77	USE wall_fluxes_mod
	78
[1]	79	PRIVATE
[1015]	80	PUBLIC diffusion_v, diffusion_v_acc
[1]	81
	82	INTERFACE diffusion_v
	83	MODULE PROCEDURE diffusion_v
	84	MODULE PROCEDURE diffusion_v_ij
	85	END INTERFACE diffusion_v
	86
[1015]	87	INTERFACE diffusion_v_acc
	88	MODULE PROCEDURE diffusion_v_acc
	89	END INTERFACE diffusion_v_acc
	90
[1]	91	CONTAINS
	92
	93
	94	!------------------------------------------------------------------------------!
	95	! Call for all grid points
	96	!------------------------------------------------------------------------------!
[1001]	97	SUBROUTINE diffusion_v
[1]	98
[1001]	99	USE arrays_3d
[1]	100	USE control_parameters
	101	USE grid_variables
	102	USE indices
	103
	104	IMPLICIT NONE
	105
	106	INTEGER :: i, j, k
[978]	107	REAL :: kmxm, kmxp, kmzm, kmzp
[1001]	108
[75]	109	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
[1]	110
[56]	111	!
	112	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	113	!-- if neccessary
	114	IF ( topography /= 'flat' ) THEN
[75]	115	CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
[56]	116	nzb_v_outer, wall_v )
	117	ENDIF
	118
[1]	119	DO i = nxl, nxr
[106]	120	DO j = nysv, nyn
[1]	121	!
	122	!-- Compute horizontal diffusion
	123	DO k = nzb_v_outer(j,i)+1, nzt
	124	!
	125	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	126	kmxp = 0.25 * &
	127	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	128	kmxm = 0.25 * &
	129	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	130
	131	tend(k,j,i) = tend(k,j,i) &
[978]	132	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	133	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	134	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	135	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	136	& ) * ddx &
	137	& + 2.0 * ( &
	138	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	139	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	140	& ) * ddy2
	141	ENDDO
	142
	143	!
	144	!-- Wall functions at the left and right walls, respectively
	145	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	146
[1]	147	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	148	kmxp = 0.25 * &
	149	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	150	kmxm = 0.25 * &
	151	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	152
[1]	153	tend(k,j,i) = tend(k,j,i) &
	154	+ 2.0 * ( &
	155	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	156	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	157	) * ddy2 &
	158	+ ( fxp(j,i) * ( &
[978]	159	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	160	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	161	) &
	162	- fxm(j,i) * ( &
[978]	163	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	164	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	165	) &
[56]	166	+ wall_v(j,i) * vsus(k,j,i) &
[1]	167	) * ddx
	168	ENDDO
	169	ENDIF
	170
	171	!
	172	!-- Compute vertical diffusion. In case of simulating a Prandtl
	173	!-- layer, index k starts at nzb_v_inner+2.
[102]	174	DO k = nzb_diff_v(j,i), nzt_diff
[1]	175	!
	176	!-- Interpolate eddy diffusivities on staggered gridpoints
	177	kmzp = 0.25 * &
	178	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	179	kmzm = 0.25 * &
	180	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	181
	182	tend(k,j,i) = tend(k,j,i) &
	183	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	184	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	185	& ) &
	186	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	187	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	188	& ) &
	189	& ) * ddzw(k)
	190	ENDDO
	191
	192	!
	193	!-- Vertical diffusion at the first grid point above the surface,
	194	!-- if the momentum flux at the bottom is given by the Prandtl law
	195	!-- or if it is prescribed by the user.
	196	!-- Difference quotient of the momentum flux is not formed over
	197	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	198	!-- comparison with other (LES) modell showed that the values of
	199	!-- the momentum flux becomes too large in this case.
	200	!-- The term containing w(k-1,..) (see above equation) is removed here
	201	!-- because the vertical velocity is assumed to be zero at the surface.
	202	IF ( use_surface_fluxes ) THEN
	203	k = nzb_v_inner(j,i)+1
	204	!
	205	!-- Interpolate eddy diffusivities on staggered gridpoints
	206	kmzp = 0.25 * &
	207	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	208	kmzm = 0.25 * &
	209	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	210
	211	tend(k,j,i) = tend(k,j,i) &
	212	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	213	& ) * ddzw(k) &
[102]	214	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	215	& + vsws(j,i) &
	216	& ) * ddzw(k)
	217	ENDIF
	218
[102]	219	!
	220	!-- Vertical diffusion at the first gridpoint below the top boundary,
	221	!-- if the momentum flux at the top is prescribed by the user
[103]	222	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	223	k = nzt
	224	!
	225	!-- Interpolate eddy diffusivities on staggered gridpoints
	226	kmzp = 0.25 * &
	227	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	228	kmzm = 0.25 * &
	229	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	230
	231	tend(k,j,i) = tend(k,j,i) &
	232	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	233	& ) * ddzw(k) &
	234	& + ( -vswst(j,i) &
	235	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	236	& ) * ddzw(k)
	237	ENDIF
	238
[1]	239	ENDDO
	240	ENDDO
	241
	242	END SUBROUTINE diffusion_v
	243
	244
	245	!------------------------------------------------------------------------------!
[1015]	246	! Call for all grid points - accelerator version
	247	!------------------------------------------------------------------------------!
	248	SUBROUTINE diffusion_v_acc
	249
	250	USE arrays_3d
	251	USE control_parameters
	252	USE grid_variables
	253	USE indices
	254
	255	IMPLICIT NONE
	256
	257	INTEGER :: i, j, k
	258	REAL :: kmxm, kmxp, kmzm, kmzp
	259
	260	!$acc declare create ( vsus )
	261	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
	262
	263	!
	264	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	265	!-- if neccessary
	266	IF ( topography /= 'flat' ) THEN
	267	CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
	268	nzb_v_outer, wall_v )
	269	ENDIF
	270
	271	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	272	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
	273	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
	274	!$acc loop
	275	DO i = nxl, nxr
	276	DO j = nysv, nyn
	277	!
	278	!-- Compute horizontal diffusion
	279	!$acc loop vector(32)
	280	DO k = 1, nzt
	281	IF ( k > nzb_v_outer(j,i) ) THEN
	282	!
	283	!-- Interpolate eddy diffusivities on staggered gridpoints
	284	kmxp = 0.25 * &
	285	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	286	kmxm = 0.25 * &
	287	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	288
	289	tend(k,j,i) = tend(k,j,i) &
	290	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	291	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	292	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	293	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	294	& ) * ddx &
	295	& + 2.0 * ( &
	296	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	297	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	298	& ) * ddy2
	299	ENDIF
	300	ENDDO
	301
	302	!
	303	!-- Wall functions at the left and right walls, respectively
	304	!$acc loop vector(32)
	305	DO k = 1, nzt
	306	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
	307	wall_v(j,i) /= 0.0 ) THEN
	308
	309	kmxp = 0.25 * &
	310	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	311	kmxm = 0.25 * &
	312	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	313
	314	tend(k,j,i) = tend(k,j,i) &
	315	+ 2.0 * ( &
	316	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	317	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	318	) * ddy2 &
	319	+ ( fxp(j,i) * ( &
	320	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	321	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	322	) &
	323	- fxm(j,i) * ( &
	324	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	325	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	326	) &
	327	+ wall_v(j,i) * vsus(k,j,i) &
	328	) * ddx
	329	ENDIF
	330	ENDDO
	331
	332	!
	333	!-- Compute vertical diffusion. In case of simulating a Prandtl
	334	!-- layer, index k starts at nzb_v_inner+2.
	335	!$acc loop vector(32)
	336	DO k = 1, nzt_diff
	337	IF ( k >= nzb_diff_v(j,i) ) THEN
	338	!
	339	!-- Interpolate eddy diffusivities on staggered gridpoints
	340	kmzp = 0.25 * &
	341	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	342	kmzm = 0.25 * &
	343	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	344
	345	tend(k,j,i) = tend(k,j,i) &
	346	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	347	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	348	& ) &
	349	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	350	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	351	& ) &
	352	& ) * ddzw(k)
	353	ENDIF
	354	ENDDO
	355
	356	ENDDO
	357	ENDDO
	358
	359	!
	360	!-- Vertical diffusion at the first grid point above the surface,
	361	!-- if the momentum flux at the bottom is given by the Prandtl law
	362	!-- or if it is prescribed by the user.
	363	!-- Difference quotient of the momentum flux is not formed over
	364	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	365	!-- comparison with other (LES) modell showed that the values of
	366	!-- the momentum flux becomes too large in this case.
	367	!-- The term containing w(k-1,..) (see above equation) is removed here
	368	!-- because the vertical velocity is assumed to be zero at the surface.
	369	IF ( use_surface_fluxes ) THEN
	370
	371	!$acc loop
	372	DO i = nxl, nxr
	373	!$acc loop vector(32)
	374	DO j = nysv, nyn
	375
	376	k = nzb_v_inner(j,i)+1
	377	!
	378	!-- Interpolate eddy diffusivities on staggered gridpoints
	379	kmzp = 0.25 * &
	380	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	381	kmzm = 0.25 * &
	382	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	383
	384	tend(k,j,i) = tend(k,j,i) &
	385	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	386	& ) * ddzw(k) &
	387	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	388	& + vsws(j,i) &
	389	& ) * ddzw(k)
	390	ENDDO
	391	ENDDO
	392
	393	ENDIF
	394
	395	!
	396	!-- Vertical diffusion at the first gridpoint below the top boundary,
	397	!-- if the momentum flux at the top is prescribed by the user
	398	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	399
	400	k = nzt
	401
	402	!$acc loop
	403	DO i = nxl, nxr
	404	!$acc loop vector(32)
	405	DO j = nysv, nyn
	406
	407	!
	408	!-- Interpolate eddy diffusivities on staggered gridpoints
	409	kmzp = 0.25 * &
	410	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	411	kmzm = 0.25 * &
	412	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	413
	414	tend(k,j,i) = tend(k,j,i) &
	415	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	416	& ) * ddzw(k) &
	417	& + ( -vswst(j,i) &
	418	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	419	& ) * ddzw(k)
	420	ENDDO
	421	ENDDO
	422
	423	ENDIF
	424	!$acc end kernels
	425
	426	END SUBROUTINE diffusion_v_acc
	427
	428
	429	!------------------------------------------------------------------------------!
[1]	430	! Call for grid point i,j
	431	!------------------------------------------------------------------------------!
[1001]	432	SUBROUTINE diffusion_v_ij( i, j )
[1]	433
[1001]	434	USE arrays_3d
[1]	435	USE control_parameters
	436	USE grid_variables
	437	USE indices
	438
	439	IMPLICIT NONE
	440
	441	INTEGER :: i, j, k
[978]	442	REAL :: kmxm, kmxp, kmzm, kmzp
[1]	443
[1001]	444	REAL, DIMENSION(nzb:nzt+1) :: vsus
	445
[1]	446	!
	447	!-- Compute horizontal diffusion
	448	DO k = nzb_v_outer(j,i)+1, nzt
	449	!
	450	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	451	kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	452	kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	453
	454	tend(k,j,i) = tend(k,j,i) &
[978]	455	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	456	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	457	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	458	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	459	& ) * ddx &
	460	& + 2.0 * ( &
	461	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	462	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	463	& ) * ddy2
	464	ENDDO
	465
	466	!
	467	!-- Wall functions at the left and right walls, respectively
	468	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	469
	470	!
	471	!-- Calculate the horizontal momentum flux v'u'
	472	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	473	vsus, 0.0, 1.0, 0.0, 0.0 )
	474
[1]	475	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	476	kmxp = 0.25 * &
	477	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	478	kmxm = 0.25 * &
	479	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	480
	481	tend(k,j,i) = tend(k,j,i) &
	482	+ 2.0 * ( &
	483	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	484	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	485	) * ddy2 &
	486	+ ( fxp(j,i) * ( &
[978]	487	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	488	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	489	) &
	490	- fxm(j,i) * ( &
[978]	491	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	492	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	493	) &
[51]	494	+ wall_v(j,i) * vsus(k) &
[1]	495	) * ddx
	496	ENDDO
	497	ENDIF
	498
	499	!
	500	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	501	!-- index k starts at nzb_v_inner+2.
[102]	502	DO k = nzb_diff_v(j,i), nzt_diff
[1]	503	!
	504	!-- Interpolate eddy diffusivities on staggered gridpoints
	505	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	506	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	507
	508	tend(k,j,i) = tend(k,j,i) &
	509	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	510	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	511	& ) &
	512	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	513	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	514	& ) &
	515	& ) * ddzw(k)
	516	ENDDO
	517
	518	!
	519	!-- Vertical diffusion at the first grid point above the surface, if the
	520	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	521	!-- prescribed by the user.
	522	!-- Difference quotient of the momentum flux is not formed over half of
	523	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
	524	!-- other (LES) modell showed that the values of the momentum flux becomes
	525	!-- too large in this case.
	526	!-- The term containing w(k-1,..) (see above equation) is removed here
	527	!-- because the vertical velocity is assumed to be zero at the surface.
	528	IF ( use_surface_fluxes ) THEN
	529	k = nzb_v_inner(j,i)+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
	535	tend(k,j,i) = tend(k,j,i) &
	536	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	537	& ) * ddzw(k) &
[102]	538	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	539	& + vsws(j,i) &
	540	& ) * ddzw(k)
	541	ENDIF
	542
[102]	543	!
	544	!-- Vertical diffusion at the first gridpoint below the top boundary,
	545	!-- if the momentum flux at the top is prescribed by the user
[103]	546	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	547	k = nzt
	548	!
	549	!-- Interpolate eddy diffusivities on staggered gridpoints
	550	kmzp = 0.25 * &
	551	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	552	kmzm = 0.25 * &
	553	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	554
	555	tend(k,j,i) = tend(k,j,i) &
	556	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	557	& ) * ddzw(k) &
	558	& + ( -vswst(j,i) &
	559	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	560	& ) * ddzw(k)
	561	ENDIF
	562
[1]	563	END SUBROUTINE diffusion_v_ij
	564
	565	END MODULE diffusion_v_mod

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