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source: palm/trunk/SOURCE/diffusion_v.f90 @ 1015

Last change on this file since 1015 was 1015, checked in by raasch, 12 years ago
Starting with changes required for GPU optimization. OpenACC statements for using NVIDIA GPUs added. Adjustment of mixing length to the Prandtl mixing length at first grid point above ground removed. mask array is set zero for ghost boundaries
Property svn:keywords set to `Id`
File size: 23.4 KB

Rev	Line
[1]	1	MODULE diffusion_v_mod
	2
	3	!------------------------------------------------------------------------------!
[484]	4	! Current revisions:
[1]	5	! -----------------
[1015]	6	! accelerator version (*_acc) added
[1]	7	!
	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: diffusion_v.f90 1015 2012-09-27 09:23:24Z raasch $
[39]	11	!
[1002]	12	! 1001 2012-09-13 14:08:46Z raasch
	13	! arrays comunicated by module instead of parameter list
	14	!
[979]	15	! 978 2012-08-09 08:28:32Z fricke
	16	! outflow damping layer removed
	17	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	18	!
[668]	19	! 667 2010-12-23 12:06:00Z suehring/gryschka
	20	! nxl-1, nxr+1, nys-1, nyn+1 replaced by nxlg, nxrg, nysg, nyng
	21	!
[392]	22	! 366 2009-08-25 08:06:27Z raasch
	23	! bc_lr replaced by bc_lr_cyc
	24	!
[110]	25	! 106 2007-08-16 14:30:26Z raasch
	26	! Momentumflux at top (vswst) included as boundary condition,
	27	! j loop is starting from nysv (needed for non-cyclic boundary conditions)
	28	!
[77]	29	! 75 2007-03-22 09:54:05Z raasch
	30	! Wall functions now include diabatic conditions, call of routine wall_fluxes,
	31	! z0 removed from argument list, vynp eliminated
	32	!
[39]	33	! 20 2007-02-26 00:12:32Z raasch
	34	! Bugfix: ddzw dimensioned 1:nzt"+1"
	35	!
[3]	36	! RCS Log replace by Id keyword, revision history cleaned up
	37	!
[1]	38	! Revision 1.15 2006/02/23 10:36:00 raasch
	39	! nzb_2d replaced by nzb_v_outer in horizontal diffusion and by nzb_v_inner
	40	! or nzb_diff_v, respectively, in vertical diffusion,
	41	! wall functions added for north and south walls, +z0 in argument list,
	42	! terms containing w(k-1,..) are removed from the Prandtl-layer equation
	43	! because they cause errors at the edges of topography
	44	! WARNING: loops containing the MAX function are still not properly vectorized!
	45	!
	46	! Revision 1.1 1997/09/12 06:24:01 raasch
	47	! Initial revision
	48	!
	49	!
	50	! Description:
	51	! ------------
	52	! Diffusion term of the v-component
	53	!------------------------------------------------------------------------------!
	54
[56]	55	USE wall_fluxes_mod
	56
[1]	57	PRIVATE
[1015]	58	PUBLIC diffusion_v, diffusion_v_acc
[1]	59
	60	INTERFACE diffusion_v
	61	MODULE PROCEDURE diffusion_v
	62	MODULE PROCEDURE diffusion_v_ij
	63	END INTERFACE diffusion_v
	64
[1015]	65	INTERFACE diffusion_v_acc
	66	MODULE PROCEDURE diffusion_v_acc
	67	END INTERFACE diffusion_v_acc
	68
[1]	69	CONTAINS
	70
	71
	72	!------------------------------------------------------------------------------!
	73	! Call for all grid points
	74	!------------------------------------------------------------------------------!
[1001]	75	SUBROUTINE diffusion_v
[1]	76
[1001]	77	USE arrays_3d
[1]	78	USE control_parameters
	79	USE grid_variables
	80	USE indices
	81
	82	IMPLICIT NONE
	83
	84	INTEGER :: i, j, k
[978]	85	REAL :: kmxm, kmxp, kmzm, kmzp
[1001]	86
[75]	87	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
[1]	88
[56]	89	!
	90	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	91	!-- if neccessary
	92	IF ( topography /= 'flat' ) THEN
[75]	93	CALL wall_fluxes( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
[56]	94	nzb_v_outer, wall_v )
	95	ENDIF
	96
[1]	97	DO i = nxl, nxr
[106]	98	DO j = nysv, nyn
[1]	99	!
	100	!-- Compute horizontal diffusion
	101	DO k = nzb_v_outer(j,i)+1, nzt
	102	!
	103	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	104	kmxp = 0.25 * &
	105	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	106	kmxm = 0.25 * &
	107	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	108
	109	tend(k,j,i) = tend(k,j,i) &
[978]	110	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	111	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	112	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	113	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	114	& ) * ddx &
	115	& + 2.0 * ( &
	116	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	117	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	118	& ) * ddy2
	119	ENDDO
	120
	121	!
	122	!-- Wall functions at the left and right walls, respectively
	123	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	124
[1]	125	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[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) )
	130
[1]	131	tend(k,j,i) = tend(k,j,i) &
	132	+ 2.0 * ( &
	133	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	134	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	135	) * ddy2 &
	136	+ ( fxp(j,i) * ( &
[978]	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 &
[1]	139	) &
	140	- fxm(j,i) * ( &
[978]	141	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	142	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	143	) &
[56]	144	+ wall_v(j,i) * vsus(k,j,i) &
[1]	145	) * ddx
	146	ENDDO
	147	ENDIF
	148
	149	!
	150	!-- Compute vertical diffusion. In case of simulating a Prandtl
	151	!-- layer, index k starts at nzb_v_inner+2.
[102]	152	DO k = nzb_diff_v(j,i), nzt_diff
[1]	153	!
	154	!-- Interpolate eddy diffusivities on staggered gridpoints
	155	kmzp = 0.25 * &
	156	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	157	kmzm = 0.25 * &
	158	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	159
	160	tend(k,j,i) = tend(k,j,i) &
	161	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	162	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	163	& ) &
	164	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	165	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	166	& ) &
	167	& ) * ddzw(k)
	168	ENDDO
	169
	170	!
	171	!-- Vertical diffusion at the first grid point above the surface,
	172	!-- if the momentum flux at the bottom is given by the Prandtl law
	173	!-- or if it is prescribed by the user.
	174	!-- Difference quotient of the momentum flux is not formed over
	175	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	176	!-- comparison with other (LES) modell showed that the values of
	177	!-- the momentum flux becomes too large in this case.
	178	!-- The term containing w(k-1,..) (see above equation) is removed here
	179	!-- because the vertical velocity is assumed to be zero at the surface.
	180	IF ( use_surface_fluxes ) THEN
	181	k = nzb_v_inner(j,i)+1
	182	!
	183	!-- Interpolate eddy diffusivities on staggered gridpoints
	184	kmzp = 0.25 * &
	185	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	186	kmzm = 0.25 * &
	187	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	188
	189	tend(k,j,i) = tend(k,j,i) &
	190	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	191	& ) * ddzw(k) &
[102]	192	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	193	& + vsws(j,i) &
	194	& ) * ddzw(k)
	195	ENDIF
	196
[102]	197	!
	198	!-- Vertical diffusion at the first gridpoint below the top boundary,
	199	!-- if the momentum flux at the top is prescribed by the user
[103]	200	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	201	k = nzt
	202	!
	203	!-- Interpolate eddy diffusivities on staggered gridpoints
	204	kmzp = 0.25 * &
	205	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	206	kmzm = 0.25 * &
	207	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	208
	209	tend(k,j,i) = tend(k,j,i) &
	210	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	211	& ) * ddzw(k) &
	212	& + ( -vswst(j,i) &
	213	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	214	& ) * ddzw(k)
	215	ENDIF
	216
[1]	217	ENDDO
	218	ENDDO
	219
	220	END SUBROUTINE diffusion_v
	221
	222
	223	!------------------------------------------------------------------------------!
[1015]	224	! Call for all grid points - accelerator version
	225	!------------------------------------------------------------------------------!
	226	SUBROUTINE diffusion_v_acc
	227
	228	USE arrays_3d
	229	USE control_parameters
	230	USE grid_variables
	231	USE indices
	232
	233	IMPLICIT NONE
	234
	235	INTEGER :: i, j, k
	236	REAL :: kmxm, kmxp, kmzm, kmzp
	237
	238	!$acc declare create ( vsus )
	239	REAL, DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus
	240
	241	!
	242	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	243	!-- if neccessary
	244	IF ( topography /= 'flat' ) THEN
	245	CALL wall_fluxes_acc( vsus, 0.0, 1.0, 0.0, 0.0, nzb_v_inner, &
	246	nzb_v_outer, wall_v )
	247	ENDIF
	248
	249	!$acc kernels present ( u, v, w, km, tend, vsws, vswst ) &
	250	!$acc present ( ddzu, ddzw, fxm, fxp, wall_v ) &
	251	!$acc present ( nzb_v_inner, nzb_v_outer, nzb_diff_v )
	252	!$acc loop
	253	DO i = nxl, nxr
	254	DO j = nysv, nyn
	255	!
	256	!-- Compute horizontal diffusion
	257	!$acc loop vector(32)
	258	DO k = 1, nzt
	259	IF ( k > nzb_v_outer(j,i) ) THEN
	260	!
	261	!-- Interpolate eddy diffusivities on staggered gridpoints
	262	kmxp = 0.25 * &
	263	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	264	kmxm = 0.25 * &
	265	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	266
	267	tend(k,j,i) = tend(k,j,i) &
	268	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	269	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	270	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	271	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	272	& ) * ddx &
	273	& + 2.0 * ( &
	274	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	275	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	276	& ) * ddy2
	277	ENDIF
	278	ENDDO
	279
	280	!
	281	!-- Wall functions at the left and right walls, respectively
	282	!$acc loop vector(32)
	283	DO k = 1, nzt
	284	IF( k > nzb_v_inner(j,i) .AND. k <= nzb_v_outer(j,i) .AND. &
	285	wall_v(j,i) /= 0.0 ) THEN
	286
	287	kmxp = 0.25 * &
	288	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	289	kmxm = 0.25 * &
	290	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	291
	292	tend(k,j,i) = tend(k,j,i) &
	293	+ 2.0 * ( &
	294	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	295	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	296	) * ddy2 &
	297	+ ( fxp(j,i) * ( &
	298	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	299	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	300	) &
	301	- fxm(j,i) * ( &
	302	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	303	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	304	) &
	305	+ wall_v(j,i) * vsus(k,j,i) &
	306	) * ddx
	307	ENDIF
	308	ENDDO
	309
	310	!
	311	!-- Compute vertical diffusion. In case of simulating a Prandtl
	312	!-- layer, index k starts at nzb_v_inner+2.
	313	!$acc loop vector(32)
	314	DO k = 1, nzt_diff
	315	IF ( k >= nzb_diff_v(j,i) ) THEN
	316	!
	317	!-- Interpolate eddy diffusivities on staggered gridpoints
	318	kmzp = 0.25 * &
	319	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	320	kmzm = 0.25 * &
	321	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	322
	323	tend(k,j,i) = tend(k,j,i) &
	324	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1)&
	325	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	326	& ) &
	327	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k)&
	328	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	329	& ) &
	330	& ) * ddzw(k)
	331	ENDIF
	332	ENDDO
	333
	334	ENDDO
	335	ENDDO
	336
	337	!
	338	!-- Vertical diffusion at the first grid point above the surface,
	339	!-- if the momentum flux at the bottom is given by the Prandtl law
	340	!-- or if it is prescribed by the user.
	341	!-- Difference quotient of the momentum flux is not formed over
	342	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
	343	!-- comparison with other (LES) modell showed that the values of
	344	!-- the momentum flux becomes too large in this case.
	345	!-- The term containing w(k-1,..) (see above equation) is removed here
	346	!-- because the vertical velocity is assumed to be zero at the surface.
	347	IF ( use_surface_fluxes ) THEN
	348
	349	!$acc loop
	350	DO i = nxl, nxr
	351	!$acc loop vector(32)
	352	DO j = nysv, nyn
	353
	354	k = nzb_v_inner(j,i)+1
	355	!
	356	!-- Interpolate eddy diffusivities on staggered gridpoints
	357	kmzp = 0.25 * &
	358	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	359	kmzm = 0.25 * &
	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 * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	364	& ) * ddzw(k) &
	365	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	366	& + vsws(j,i) &
	367	& ) * ddzw(k)
	368	ENDDO
	369	ENDDO
	370
	371	ENDIF
	372
	373	!
	374	!-- Vertical diffusion at the first gridpoint below the top boundary,
	375	!-- if the momentum flux at the top is prescribed by the user
	376	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
	377
	378	k = nzt
	379
	380	!$acc loop
	381	DO i = nxl, nxr
	382	!$acc loop vector(32)
	383	DO j = nysv, nyn
	384
	385	!
	386	!-- Interpolate eddy diffusivities on staggered gridpoints
	387	kmzp = 0.25 * &
	388	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	389	kmzm = 0.25 * &
	390	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	391
	392	tend(k,j,i) = tend(k,j,i) &
	393	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	394	& ) * ddzw(k) &
	395	& + ( -vswst(j,i) &
	396	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	397	& ) * ddzw(k)
	398	ENDDO
	399	ENDDO
	400
	401	ENDIF
	402	!$acc end kernels
	403
	404	END SUBROUTINE diffusion_v_acc
	405
	406
	407	!------------------------------------------------------------------------------!
[1]	408	! Call for grid point i,j
	409	!------------------------------------------------------------------------------!
[1001]	410	SUBROUTINE diffusion_v_ij( i, j )
[1]	411
[1001]	412	USE arrays_3d
[1]	413	USE control_parameters
	414	USE grid_variables
	415	USE indices
	416
	417	IMPLICIT NONE
	418
	419	INTEGER :: i, j, k
[978]	420	REAL :: kmxm, kmxp, kmzm, kmzp
[1]	421
[1001]	422	REAL, DIMENSION(nzb:nzt+1) :: vsus
	423
[1]	424	!
	425	!-- Compute horizontal diffusion
	426	DO k = nzb_v_outer(j,i)+1, nzt
	427	!
	428	!-- Interpolate eddy diffusivities on staggered gridpoints
[978]	429	kmxp = 0.25 * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	430	kmxm = 0.25 * ( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	431
	432	tend(k,j,i) = tend(k,j,i) &
[978]	433	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	434	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	435	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	436	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	437	& ) * ddx &
	438	& + 2.0 * ( &
	439	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	440	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
	441	& ) * ddy2
	442	ENDDO
	443
	444	!
	445	!-- Wall functions at the left and right walls, respectively
	446	IF ( wall_v(j,i) /= 0.0 ) THEN
[51]	447
	448	!
	449	!-- Calculate the horizontal momentum flux v'u'
	450	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	451	vsus, 0.0, 1.0, 0.0, 0.0 )
	452
[1]	453	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[978]	454	kmxp = 0.25 * &
	455	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	456	kmxm = 0.25 * &
	457	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	458
	459	tend(k,j,i) = tend(k,j,i) &
	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	+ ( fxp(j,i) * ( &
[978]	465	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	466	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	467	) &
	468	- fxm(j,i) * ( &
[978]	469	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	470	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	471	) &
[51]	472	+ wall_v(j,i) * vsus(k) &
[1]	473	) * ddx
	474	ENDDO
	475	ENDIF
	476
	477	!
	478	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	479	!-- index k starts at nzb_v_inner+2.
[102]	480	DO k = nzb_diff_v(j,i), nzt_diff
[1]	481	!
	482	!-- Interpolate eddy diffusivities on staggered gridpoints
	483	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	484	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	485
	486	tend(k,j,i) = tend(k,j,i) &
	487	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	488	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	489	& ) &
	490	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	491	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	492	& ) &
	493	& ) * ddzw(k)
	494	ENDDO
	495
	496	!
	497	!-- Vertical diffusion at the first grid point above the surface, if the
	498	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	499	!-- prescribed by the user.
	500	!-- Difference quotient of the momentum flux is not formed over half of
	501	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
	502	!-- other (LES) modell showed that the values of the momentum flux becomes
	503	!-- too large in this case.
	504	!-- The term containing w(k-1,..) (see above equation) is removed here
	505	!-- because the vertical velocity is assumed to be zero at the surface.
	506	IF ( use_surface_fluxes ) THEN
	507	k = nzb_v_inner(j,i)+1
	508	!
	509	!-- Interpolate eddy diffusivities on staggered gridpoints
	510	kmzp = 0.25 * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	511	kmzm = 0.25 * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	512
	513	tend(k,j,i) = tend(k,j,i) &
	514	& + ( kmzp * ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	515	& ) * ddzw(k) &
[102]	516	& + ( kmzp * ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
[1]	517	& + vsws(j,i) &
	518	& ) * ddzw(k)
	519	ENDIF
	520
[102]	521	!
	522	!-- Vertical diffusion at the first gridpoint below the top boundary,
	523	!-- if the momentum flux at the top is prescribed by the user
[103]	524	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	525	k = nzt
	526	!
	527	!-- Interpolate eddy diffusivities on staggered gridpoints
	528	kmzp = 0.25 * &
	529	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	530	kmzm = 0.25 * &
	531	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	532
	533	tend(k,j,i) = tend(k,j,i) &
	534	& - ( kmzm * ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	535	& ) * ddzw(k) &
	536	& + ( -vswst(j,i) &
	537	& - kmzm * ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	538	& ) * ddzw(k)
	539	ENDIF
	540
[1]	541	END SUBROUTINE diffusion_v_ij
	542
	543	END MODULE diffusion_v_mod

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