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source: palm/trunk/SOURCE/diffusion_v.f90 @ 2198

Last change on this file since 2198 was 2119, checked in by raasch, 8 years ago
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[1873]	1	!> @file diffusion_v.f90
[2000]	2	!------------------------------------------------------------------------------!
[1036]	3	! This file is part of PALM.
	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	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	!
[2101]	17	! Copyright 1997-2017 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[484]	20	! Current revisions:
[1]	21	! -----------------
[1341]	22	!
[2119]	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: diffusion_v.f90 2119 2017-01-17 16:51:50Z raasch $
	27	!
[2119]	28	! 2118 2017-01-17 16:38:49Z raasch
	29	! OpenACC version of subroutine removed
	30	!
[2038]	31	! 2037 2016-10-26 11:15:40Z knoop
	32	! Anelastic approximation implemented
	33	!
[2001]	34	! 2000 2016-08-20 18:09:15Z knoop
	35	! Forced header and separation lines into 80 columns
	36	!
[1874]	37	! 1873 2016-04-18 14:50:06Z maronga
	38	! Module renamed (removed _mod)
	39	!
[1851]	40	! 1850 2016-04-08 13:29:27Z maronga
	41	! Module renamed
	42	!
[1741]	43	! 1740 2016-01-13 08:19:40Z raasch
	44	! unnecessary calculations of kmzm and kmzp in wall bounded parts removed
	45	!
[1683]	46	! 1682 2015-10-07 23:56:08Z knoop
	47	! Code annotations made doxygen readable
	48	!
[1341]	49	! 1340 2014-03-25 19:45:13Z kanani
	50	! REAL constants defined as wp-kind
	51	!
[1321]	52	! 1320 2014-03-20 08:40:49Z raasch
[1320]	53	! ONLY-attribute added to USE-statements,
	54	! kind-parameters added to all INTEGER and REAL declaration statements,
	55	! kinds are defined in new module kinds,
	56	! revision history before 2012 removed,
	57	! comment fields (!:) to be used for variable explanations added to
	58	! all variable declaration statements
[1321]	59	!
[1258]	60	! 1257 2013-11-08 15:18:40Z raasch
	61	! openacc loop and loop vector clauses removed, declare create moved after
	62	! the FORTRAN declaration statement
	63	!
[1132]	64	! 1128 2013-04-12 06:19:32Z raasch
	65	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	66	! j_north
	67	!
[1037]	68	! 1036 2012-10-22 13:43:42Z raasch
	69	! code put under GPL (PALM 3.9)
	70	!
[1017]	71	! 1015 2012-09-27 09:23:24Z raasch
	72	! accelerator version (*_acc) added
	73	!
[1002]	74	! 1001 2012-09-13 14:08:46Z raasch
	75	! arrays comunicated by module instead of parameter list
	76	!
[979]	77	! 978 2012-08-09 08:28:32Z fricke
	78	! outflow damping layer removed
	79	! kmxm_x/_y and kmxp_x/_y change to kmxm and kmxp
	80	!
[1]	81	! Revision 1.1 1997/09/12 06:24:01 raasch
	82	! Initial revision
	83	!
	84	!
	85	! Description:
	86	! ------------
[1682]	87	!> Diffusion term of the v-component
[1]	88	!------------------------------------------------------------------------------!
[1682]	89	MODULE diffusion_v_mod
	90
[1]	91
[56]	92	USE wall_fluxes_mod
	93
[1]	94	PRIVATE
[2118]	95	PUBLIC diffusion_v
[1]	96
	97	INTERFACE diffusion_v
	98	MODULE PROCEDURE diffusion_v
	99	MODULE PROCEDURE diffusion_v_ij
	100	END INTERFACE diffusion_v
	101
	102	CONTAINS
	103
	104
	105	!------------------------------------------------------------------------------!
[1682]	106	! Description:
	107	! ------------
	108	!> Call for all grid points
[1]	109	!------------------------------------------------------------------------------!
[1001]	110	SUBROUTINE diffusion_v
[1]	111
[1320]	112	USE arrays_3d, &
[2037]	113	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, &
	114	drho_air, rho_air_zw
[1320]	115
	116	USE control_parameters, &
	117	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	118	use_top_fluxes
	119
	120	USE grid_variables, &
	121	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	122
	123	USE indices, &
	124	ONLY: nxl, nxr, nyn, nys, nysv, nzb, nzb_diff_v, nzb_v_inner, &
	125	nzb_v_outer, nzt, nzt_diff
	126
	127	USE kinds
[1]	128
	129	IMPLICIT NONE
	130
[1682]	131	INTEGER(iwp) :: i !<
	132	INTEGER(iwp) :: j !<
	133	INTEGER(iwp) :: k !<
	134	REAL(wp) :: kmxm !<
	135	REAL(wp) :: kmxp !<
	136	REAL(wp) :: kmzm !<
	137	REAL(wp) :: kmzp !<
[1001]	138
[1682]	139	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: vsus !<
[1]	140
[56]	141	!
	142	!-- First calculate horizontal momentum flux v'u' at vertical walls,
	143	!-- if neccessary
	144	IF ( topography /= 'flat' ) THEN
[1320]	145	CALL wall_fluxes( vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp, nzb_v_inner, &
[56]	146	nzb_v_outer, wall_v )
	147	ENDIF
	148
[1]	149	DO i = nxl, nxr
[106]	150	DO j = nysv, nyn
[1]	151	!
	152	!-- Compute horizontal diffusion
	153	DO k = nzb_v_outer(j,i)+1, nzt
	154	!
	155	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	156	kmxp = 0.25_wp * &
[978]	157	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	158	kmxm = 0.25_wp * &
[978]	159	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	160
[1320]	161	tend(k,j,i) = tend(k,j,i) &
	162	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	163	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	164	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	165	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	166	& ) * ddx &
[1340]	167	& + 2.0_wp * ( &
[1320]	168	& km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	169	& - km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	170	& ) * ddy2
[1]	171	ENDDO
	172
	173	!
	174	!-- Wall functions at the left and right walls, respectively
[1340]	175	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	176
[1]	177	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	178	kmxp = 0.25_wp * &
[978]	179	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	180	kmxm = 0.25_wp * &
[978]	181	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
	182
[1]	183	tend(k,j,i) = tend(k,j,i) &
[1340]	184	+ 2.0_wp * ( &
[1]	185	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	186	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	187	) * ddy2 &
[1]	188	+ ( fxp(j,i) * ( &
[978]	189	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	190	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	191	) &
	192	- fxm(j,i) * ( &
[978]	193	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	194	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	195	) &
[56]	196	+ wall_v(j,i) * vsus(k,j,i) &
[1]	197	) * ddx
	198	ENDDO
	199	ENDIF
	200
	201	!
	202	!-- Compute vertical diffusion. In case of simulating a Prandtl
	203	!-- layer, index k starts at nzb_v_inner+2.
[102]	204	DO k = nzb_diff_v(j,i), nzt_diff
[1]	205	!
	206	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	207	kmzp = 0.25_wp * &
[1]	208	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1340]	209	kmzm = 0.25_wp * &
[1]	210	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	211
[1320]	212	tend(k,j,i) = tend(k,j,i) &
	213	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	214	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2037]	215	& ) * rho_air_zw(k) &
[1320]	216	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	217	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2037]	218	& ) * rho_air_zw(k-1) &
	219	& ) * ddzw(k) * drho_air(k)
[1]	220	ENDDO
	221
	222	!
	223	!-- Vertical diffusion at the first grid point above the surface,
	224	!-- if the momentum flux at the bottom is given by the Prandtl law
	225	!-- or if it is prescribed by the user.
	226	!-- Difference quotient of the momentum flux is not formed over
	227	!-- half of the grid spacing (2.0*ddzw(k)) any more, since the
[1320]	228	!-- comparison with other (LES) models showed that the values of
[1]	229	!-- the momentum flux becomes too large in this case.
	230	!-- The term containing w(k-1,..) (see above equation) is removed here
	231	!-- because the vertical velocity is assumed to be zero at the surface.
	232	IF ( use_surface_fluxes ) THEN
	233	k = nzb_v_inner(j,i)+1
	234	!
	235	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	236	kmzp = 0.25_wp * &
[1]	237	( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	238
[1320]	239	tend(k,j,i) = tend(k,j,i) &
[2037]	240	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	241	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	242	& ) * rho_air_zw(k) &
	243	& - ( -vsws(j,i) ) &
	244	& ) * ddzw(k) * drho_air(k)
[1]	245	ENDIF
	246
[102]	247	!
	248	!-- Vertical diffusion at the first gridpoint below the top boundary,
	249	!-- if the momentum flux at the top is prescribed by the user
[103]	250	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	251	k = nzt
	252	!
	253	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	254	kmzm = 0.25_wp * &
[102]	255	( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
	256
[1320]	257	tend(k,j,i) = tend(k,j,i) &
[2037]	258	& + ( ( -vswst(j,i) ) &
	259	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	260	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	261	& ) * rho_air_zw(k-1) &
	262	& ) * ddzw(k) * drho_air(k)
[102]	263	ENDIF
	264
[1]	265	ENDDO
	266	ENDDO
	267
	268	END SUBROUTINE diffusion_v
	269
	270
	271	!------------------------------------------------------------------------------!
[1682]	272	! Description:
	273	! ------------
	274	!> Call for grid point i,j
[1]	275	!------------------------------------------------------------------------------!
[1001]	276	SUBROUTINE diffusion_v_ij( i, j )
[1]	277
[1320]	278	USE arrays_3d, &
[2037]	279	ONLY: ddzu, ddzw, km, tend, u, v, vsws, vswst, w, &
	280	drho_air, rho_air_zw
[1320]	281
	282	USE control_parameters, &
	283	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	284
	285	USE grid_variables, &
	286	ONLY: ddx, ddy, ddy2, fxm, fxp, wall_v
	287
	288	USE indices, &
	289	ONLY: nzb, nzb_diff_v, nzb_v_inner, nzb_v_outer, nzt, nzt_diff
	290
	291	USE kinds
[1]	292
	293	IMPLICIT NONE
	294
[1682]	295	INTEGER(iwp) :: i !<
	296	INTEGER(iwp) :: j !<
	297	INTEGER(iwp) :: k !<
	298	REAL(wp) :: kmxm !<
	299	REAL(wp) :: kmxp !<
	300	REAL(wp) :: kmzm !<
	301	REAL(wp) :: kmzp !<
[1]	302
[1682]	303	REAL(wp), DIMENSION(nzb:nzt+1) :: vsus !<
[1001]	304
[1]	305	!
	306	!-- Compute horizontal diffusion
	307	DO k = nzb_v_outer(j,i)+1, nzt
	308	!
	309	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	310	kmxp = 0.25_wp * ( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
	311	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]	312
[1320]	313	tend(k,j,i) = tend(k,j,i) &
	314	& + ( kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	315	& + kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
	316	& - kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	317	& - kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	318	& ) * ddx &
[1340]	319	& + 2.0_wp * ( &
[1320]	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) ) &
[1340]	322	& ) * ddy2
[1]	323	ENDDO
	324
	325	!
	326	!-- Wall functions at the left and right walls, respectively
[1340]	327	IF ( wall_v(j,i) /= 0.0_wp ) THEN
[51]	328
	329	!
	330	!-- Calculate the horizontal momentum flux v'u'
[1320]	331	CALL wall_fluxes( i, j, nzb_v_inner(j,i)+1, nzb_v_outer(j,i), &
	332	vsus, 0.0_wp, 1.0_wp, 0.0_wp, 0.0_wp )
[51]	333
[1]	334	DO k = nzb_v_inner(j,i)+1, nzb_v_outer(j,i)
[1340]	335	kmxp = 0.25_wp * &
[978]	336	( km(k,j,i)+km(k,j,i+1)+km(k,j-1,i)+km(k,j-1,i+1) )
[1340]	337	kmxm = 0.25_wp * &
[978]	338	( km(k,j,i)+km(k,j,i-1)+km(k,j-1,i)+km(k,j-1,i-1) )
[1]	339
	340	tend(k,j,i) = tend(k,j,i) &
[1340]	341	+ 2.0_wp * ( &
[1]	342	km(k,j,i) * ( v(k,j+1,i) - v(k,j,i) ) &
	343	- km(k,j-1,i) * ( v(k,j,i) - v(k,j-1,i) ) &
[1340]	344	) * ddy2 &
[1]	345	+ ( fxp(j,i) * ( &
[978]	346	kmxp * ( v(k,j,i+1) - v(k,j,i) ) * ddx &
	347	+ kmxp * ( u(k,j,i+1) - u(k,j-1,i+1) ) * ddy &
[1]	348	) &
	349	- fxm(j,i) * ( &
[978]	350	kmxm * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
	351	+ kmxm * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
[1]	352	) &
[51]	353	+ wall_v(j,i) * vsus(k) &
[1]	354	) * ddx
	355	ENDDO
	356	ENDIF
	357
	358	!
	359	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	360	!-- index k starts at nzb_v_inner+2.
[102]	361	DO k = nzb_diff_v(j,i), nzt_diff
[1]	362	!
	363	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	364	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
	365	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]	366
[1320]	367	tend(k,j,i) = tend(k,j,i) &
	368	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	369	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
[2037]	370	& ) * rho_air_zw(k) &
[1320]	371	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	372	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
[2037]	373	& ) * rho_air_zw(k-1) &
	374	& ) * ddzw(k) * drho_air(k)
[1]	375	ENDDO
	376
	377	!
	378	!-- Vertical diffusion at the first grid point above the surface, if the
	379	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	380	!-- prescribed by the user.
	381	!-- Difference quotient of the momentum flux is not formed over half of
	382	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	383	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	384	!-- too large in this case.
	385	!-- The term containing w(k-1,..) (see above equation) is removed here
	386	!-- because the vertical velocity is assumed to be zero at the surface.
	387	IF ( use_surface_fluxes ) THEN
	388	k = nzb_v_inner(j,i)+1
	389	!
	390	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	391	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j-1,i)+km(k+1,j-1,i) )
[1]	392
[1320]	393	tend(k,j,i) = tend(k,j,i) &
[2037]	394	& + ( kmzp * ( ( v(k+1,j,i) - v(k,j,i) ) * ddzu(k+1) &
	395	& + ( w(k,j,i) - w(k,j-1,i) ) * ddy &
	396	& ) * rho_air_zw(k) &
	397	& - ( -vsws(j,i) ) &
	398	& ) * ddzw(k) * drho_air(k)
[1]	399	ENDIF
	400
[102]	401	!
	402	!-- Vertical diffusion at the first gridpoint below the top boundary,
	403	!-- if the momentum flux at the top is prescribed by the user
[103]	404	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	405	k = nzt
	406	!
	407	!-- Interpolate eddy diffusivities on staggered gridpoints
[2037]	408	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j-1,i)+km(k-1,j-1,i) )
[102]	409
[1320]	410	tend(k,j,i) = tend(k,j,i) &
[2037]	411	& + ( ( -vswst(j,i) ) &
	412	& - kmzm * ( ( v(k,j,i) - v(k-1,j,i) ) * ddzu(k) &
	413	& + ( w(k-1,j,i) - w(k-1,j-1,i) ) * ddy &
	414	& ) * rho_air_zw(k-1) &
	415	& ) * ddzw(k) * drho_air(k)
[102]	416	ENDIF
	417
[1]	418	END SUBROUTINE diffusion_v_ij
	419
[1321]	420	END MODULE diffusion_v_mod

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