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source: palm/trunk/SOURCE/diffusion_u.f90 @ 2202

Last change on this file since 2202 was 2119, checked in by raasch, 8 years ago
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[1873]	1	!> @file diffusion_u.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_u.f90 2119 2017-01-17 16:51:50Z kanani $
	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	!
[1692]	46	! 1691 2015-10-26 16:17:44Z maronga
	47	! Formatting corrections.
	48	!
[1683]	49	! 1682 2015-10-07 23:56:08Z knoop
	50	! Code annotations made doxygen readable
	51	!
[1341]	52	! 1340 2014-03-25 19:45:13Z kanani
	53	! REAL constants defined as wp-kind
	54	!
[1321]	55	! 1320 2014-03-20 08:40:49Z raasch
[1320]	56	! ONLY-attribute added to USE-statements,
	57	! kind-parameters added to all INTEGER and REAL declaration statements,
	58	! kinds are defined in new module kinds,
	59	! revision history before 2012 removed,
	60	! comment fields (!:) to be used for variable explanations added to
	61	! all variable declaration statements
[1321]	62	!
[1258]	63	! 1257 2013-11-08 15:18:40Z raasch
	64	! openacc loop and loop vector clauses removed, declare create moved after
	65	! the FORTRAN declaration statement
	66	!
[1132]	67	! 1128 2013-04-12 06:19:32Z raasch
	68	! loop index bounds in accelerator version replaced by i_left, i_right, j_south,
	69	! j_north
	70	!
[1037]	71	! 1036 2012-10-22 13:43:42Z raasch
	72	! code put under GPL (PALM 3.9)
	73	!
[1017]	74	! 1015 2012-09-27 09:23:24Z raasch
	75	! accelerator version (*_acc) added
	76	!
[1002]	77	! 1001 2012-09-13 14:08:46Z raasch
	78	! arrays comunicated by module instead of parameter list
	79	!
[979]	80	! 978 2012-08-09 08:28:32Z fricke
	81	! outflow damping layer removed
	82	! kmym_x/_y and kmyp_x/_y change to kmym and kmyp
	83	!
[1]	84	! Revision 1.1 1997/09/12 06:23:51 raasch
	85	! Initial revision
	86	!
	87	!
	88	! Description:
	89	! ------------
[1682]	90	!> Diffusion term of the u-component
	91	!> @todo additional damping (needed for non-cyclic bc) causes bad vectorization
	92	!> and slows down the speed on NEC about 5-10%
[1]	93	!------------------------------------------------------------------------------!
[1682]	94	MODULE diffusion_u_mod
	95
[1]	96
[56]	97	USE wall_fluxes_mod
	98
[1]	99	PRIVATE
[2118]	100	PUBLIC diffusion_u
[1]	101
	102	INTERFACE diffusion_u
	103	MODULE PROCEDURE diffusion_u
	104	MODULE PROCEDURE diffusion_u_ij
	105	END INTERFACE diffusion_u
	106
	107	CONTAINS
	108
	109
	110	!------------------------------------------------------------------------------!
[1682]	111	! Description:
	112	! ------------
	113	!> Call for all grid points
[1]	114	!------------------------------------------------------------------------------!
[1001]	115	SUBROUTINE diffusion_u
[1]	116
[1320]	117	USE arrays_3d, &
[2037]	118	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, &
	119	drho_air, rho_air_zw
[1320]	120
	121	USE control_parameters, &
	122	ONLY: constant_top_momentumflux, topography, use_surface_fluxes, &
	123	use_top_fluxes
	124
	125	USE grid_variables, &
	126	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	127
	128	USE indices, &
	129	ONLY: nxl, nxlu, nxr, nyn, nys, nzb, nzb_diff_u, nzb_u_inner, &
	130	nzb_u_outer, nzt, nzt_diff
	131
	132	USE kinds
[1]	133
	134	IMPLICIT NONE
	135
[1682]	136	INTEGER(iwp) :: i !<
	137	INTEGER(iwp) :: j !<
	138	INTEGER(iwp) :: k !<
	139	REAL(wp) :: kmym !<
	140	REAL(wp) :: kmyp !<
	141	REAL(wp) :: kmzm !<
	142	REAL(wp) :: kmzp !<
[1001]	143
[1682]	144	REAL(wp), DIMENSION(nzb:nzt+1,nys:nyn,nxl:nxr) :: usvs !<
[1]	145
[56]	146	!
	147	!-- First calculate horizontal momentum flux u'v' at vertical walls,
	148	!-- if neccessary
	149	IF ( topography /= 'flat' ) THEN
[1320]	150	CALL wall_fluxes( usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp, nzb_u_inner, &
[56]	151	nzb_u_outer, wall_u )
	152	ENDIF
	153
[106]	154	DO i = nxlu, nxr
[1001]	155	DO j = nys, nyn
[1]	156	!
	157	!-- Compute horizontal diffusion
	158	DO k = nzb_u_outer(j,i)+1, nzt
	159	!
	160	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	161	kmyp = 0.25_wp * &
[978]	162	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	163	kmym = 0.25_wp * &
[978]	164	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	165
[1320]	166	tend(k,j,i) = tend(k,j,i) &
[1340]	167	& + 2.0_wp * ( &
[1320]	168	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	169	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	170	& ) * ddx2 &
[1320]	171	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	172	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	173	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	174	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	175	& ) * ddy
	176	ENDDO
	177
	178	!
	179	!-- Wall functions at the north and south walls, respectively
[1340]	180	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	181
[1]	182	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	183	kmyp = 0.25_wp * &
[978]	184	( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
[1340]	185	kmym = 0.25_wp * &
[978]	186	( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	187
	188	tend(k,j,i) = tend(k,j,i) &
[1340]	189	+ 2.0_wp * ( &
[1]	190	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	191	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	192	) * ddx2 &
[1]	193	+ ( fyp(j,i) * ( &
[978]	194	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	195	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	196	) &
	197	- fym(j,i) * ( &
[978]	198	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	199	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	200	) &
[56]	201	+ wall_u(j,i) * usvs(k,j,i) &
[1]	202	) * ddy
	203	ENDDO
	204	ENDIF
	205
	206	!
	207	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	208	!-- index k starts at nzb_u_inner+2.
[102]	209	DO k = nzb_diff_u(j,i), nzt_diff
[1]	210	!
	211	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	212	kmzp = 0.25_wp * &
[1]	213	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1340]	214	kmzm = 0.25_wp * &
[1]	215	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	216
[1320]	217	tend(k,j,i) = tend(k,j,i) &
	218	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	219	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
[2037]	220	& ) * rho_air_zw(k) &
[1320]	221	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	222	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
[2037]	223	& ) * rho_air_zw(k-1) &
	224	& ) * ddzw(k) * drho_air(k)
[1]	225	ENDDO
	226
	227	!
	228	!-- Vertical diffusion at the first grid point above the surface,
	229	!-- if the momentum flux at the bottom is given by the Prandtl law or
	230	!-- if it is prescribed by the user.
	231	!-- Difference quotient of the momentum flux is not formed over half
	232	!-- of the grid spacing (2.0*ddzw(k)) any more, since the comparison
[1320]	233	!-- with other (LES) models showed that the values of the momentum
[1]	234	!-- flux becomes too large in this case.
	235	!-- The term containing w(k-1,..) (see above equation) is removed here
	236	!-- because the vertical velocity is assumed to be zero at the surface.
	237	IF ( use_surface_fluxes ) THEN
	238	k = nzb_u_inner(j,i)+1
	239	!
	240	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	241	kmzp = 0.25_wp * &
[1]	242	( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	243
[1320]	244	tend(k,j,i) = tend(k,j,i) &
[2037]	245	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	246	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	247	& ) * rho_air_zw(k) &
	248	& - ( -usws(j,i) ) &
	249	& ) * ddzw(k) * drho_air(k)
[1]	250	ENDIF
	251
[102]	252	!
	253	!-- Vertical diffusion at the first gridpoint below the top boundary,
	254	!-- if the momentum flux at the top is prescribed by the user
[103]	255	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	256	k = nzt
	257	!
	258	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	259	kmzm = 0.25_wp * &
[102]	260	( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
	261
[1320]	262	tend(k,j,i) = tend(k,j,i) &
[2037]	263	& + ( ( -uswst(j,i) ) &
	264	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	265	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	266	& ) * rho_air_zw(k-1) &
	267	& ) * ddzw(k) * drho_air(k)
[102]	268	ENDIF
	269
[1]	270	ENDDO
	271	ENDDO
	272
	273	END SUBROUTINE diffusion_u
	274
	275
	276	!------------------------------------------------------------------------------!
[1682]	277	! Description:
	278	! ------------
	279	!> Call for grid point i,j
[1]	280	!------------------------------------------------------------------------------!
[1001]	281	SUBROUTINE diffusion_u_ij( i, j )
[1]	282
[1320]	283	USE arrays_3d, &
[2037]	284	ONLY: ddzu, ddzw, km, tend, u, usws, uswst, v, w, &
	285	drho_air, rho_air_zw
[1320]	286
	287	USE control_parameters, &
	288	ONLY: constant_top_momentumflux, use_surface_fluxes, use_top_fluxes
	289
	290	USE grid_variables, &
	291	ONLY: ddx, ddx2, ddy, fym, fyp, wall_u
	292
	293	USE indices, &
	294	ONLY: nzb, nzb_diff_u, nzb_u_inner, nzb_u_outer, nzt, nzt_diff
	295
	296	USE kinds
[1]	297
	298	IMPLICIT NONE
	299
[1682]	300	INTEGER(iwp) :: i !<
	301	INTEGER(iwp) :: j !<
	302	INTEGER(iwp) :: k !<
	303	REAL(wp) :: kmym !<
	304	REAL(wp) :: kmyp !<
	305	REAL(wp) :: kmzm !<
	306	REAL(wp) :: kmzp !<
[1]	307
[1682]	308	REAL(wp), DIMENSION(nzb:nzt+1) :: usvs !<
[1001]	309
[1]	310	!
	311	!-- Compute horizontal diffusion
	312	DO k = nzb_u_outer(j,i)+1, nzt
	313	!
	314	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	315	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	316	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	317
[1320]	318	tend(k,j,i) = tend(k,j,i) &
[1340]	319	& + 2.0_wp * ( &
[1320]	320	& km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	321	& - km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	322	& ) * ddx2 &
[1320]	323	& + ( kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	324	& + kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
	325	& - kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	326	& - kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	327	& ) * ddy
	328	ENDDO
	329
	330	!
	331	!-- Wall functions at the north and south walls, respectively
[1691]	332	IF ( wall_u(j,i) /= 0.0_wp ) THEN
[51]	333
	334	!
	335	!-- Calculate the horizontal momentum flux u'v'
[1320]	336	CALL wall_fluxes( i, j, nzb_u_inner(j,i)+1, nzb_u_outer(j,i), &
	337	usvs, 1.0_wp, 0.0_wp, 0.0_wp, 0.0_wp )
[51]	338
[1]	339	DO k = nzb_u_inner(j,i)+1, nzb_u_outer(j,i)
[1340]	340	kmyp = 0.25_wp * ( km(k,j,i)+km(k,j+1,i)+km(k,j,i-1)+km(k,j+1,i-1) )
	341	kmym = 0.25_wp * ( km(k,j,i)+km(k,j-1,i)+km(k,j,i-1)+km(k,j-1,i-1) )
[1]	342
	343	tend(k,j,i) = tend(k,j,i) &
[1340]	344	+ 2.0_wp * ( &
[1]	345	km(k,j,i) * ( u(k,j,i+1) - u(k,j,i) ) &
	346	- km(k,j,i-1) * ( u(k,j,i) - u(k,j,i-1) ) &
[1340]	347	) * ddx2 &
[1]	348	+ ( fyp(j,i) * ( &
[978]	349	kmyp * ( u(k,j+1,i) - u(k,j,i) ) * ddy &
	350	+ kmyp * ( v(k,j+1,i) - v(k,j+1,i-1) ) * ddx &
[1]	351	) &
	352	- fym(j,i) * ( &
[978]	353	kmym * ( u(k,j,i) - u(k,j-1,i) ) * ddy &
	354	+ kmym * ( v(k,j,i) - v(k,j,i-1) ) * ddx &
[1]	355	) &
[51]	356	+ wall_u(j,i) * usvs(k) &
[1]	357	) * ddy
	358	ENDDO
	359	ENDIF
	360
	361	!
	362	!-- Compute vertical diffusion. In case of simulating a Prandtl layer,
	363	!-- index k starts at nzb_u_inner+2.
[102]	364	DO k = nzb_diff_u(j,i), nzt_diff
[1]	365	!
	366	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	367	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
	368	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
[1]	369
[1320]	370	tend(k,j,i) = tend(k,j,i) &
	371	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	372	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
[2037]	373	& ) * rho_air_zw(k) &
[1320]	374	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	375	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
[2037]	376	& ) * rho_air_zw(k-1) &
	377	& ) * ddzw(k) * drho_air(k)
[1]	378	ENDDO
	379
	380	!
	381	!-- Vertical diffusion at the first grid point above the surface, if the
	382	!-- momentum flux at the bottom is given by the Prandtl law or if it is
	383	!-- prescribed by the user.
	384	!-- Difference quotient of the momentum flux is not formed over half of
	385	!-- the grid spacing (2.0*ddzw(k)) any more, since the comparison with
[1320]	386	!-- other (LES) models showed that the values of the momentum flux becomes
[1]	387	!-- too large in this case.
	388	!-- The term containing w(k-1,..) (see above equation) is removed here
	389	!-- because the vertical velocity is assumed to be zero at the surface.
	390	IF ( use_surface_fluxes ) THEN
	391	k = nzb_u_inner(j,i)+1
	392	!
	393	!-- Interpolate eddy diffusivities on staggered gridpoints
[1340]	394	kmzp = 0.25_wp * ( km(k,j,i)+km(k+1,j,i)+km(k,j,i-1)+km(k+1,j,i-1) )
[1]	395
[1320]	396	tend(k,j,i) = tend(k,j,i) &
[2037]	397	& + ( kmzp * ( ( u(k+1,j,i) - u(k,j,i) ) * ddzu(k+1) &
	398	& + ( w(k,j,i) - w(k,j,i-1) ) * ddx &
	399	& ) * rho_air_zw(k) &
	400	& - ( -usws(j,i) ) &
	401	& ) * ddzw(k) * drho_air(k)
[1]	402	ENDIF
	403
[102]	404	!
	405	!-- Vertical diffusion at the first gridpoint below the top boundary,
	406	!-- if the momentum flux at the top is prescribed by the user
[103]	407	IF ( use_top_fluxes .AND. constant_top_momentumflux ) THEN
[102]	408	k = nzt
	409	!
	410	!-- Interpolate eddy diffusivities on staggered gridpoints
[2037]	411	kmzm = 0.25_wp * ( km(k,j,i)+km(k-1,j,i)+km(k,j,i-1)+km(k-1,j,i-1) )
[102]	412
[1320]	413	tend(k,j,i) = tend(k,j,i) &
[2037]	414	& + ( ( -uswst(j,i) ) &
	415	& - kmzm * ( ( u(k,j,i) - u(k-1,j,i) ) * ddzu(k) &
	416	& + ( w(k-1,j,i) - w(k-1,j,i-1) ) * ddx &
	417	& ) * rho_air_zw(k-1) &
	418	& ) * ddzw(k) * drho_air(k)
[102]	419	ENDIF
	420
[1]	421	END SUBROUTINE diffusion_u_ij
	422
	423	END MODULE diffusion_u_mod

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