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source: palm/trunk/SOURCE/lpm_advec.f90 @ 3197

Last change on this file since 3197 was 3189, checked in by Giersch, 6 years ago
Interpolation to particle position revised, indent revised, bugfix in calculation of the x/y indices for current particle position
Property svn:keywords set to `Id`
File size: 55.6 KB

Rev	Line
[1682]	1	!> @file lpm_advec.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	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	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[849]	20	! Current revisions:
	21	! ------------------
[2701]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_advec.f90 3189 2018-08-06 13:18:55Z knoop $
[3189]	27	! Bugfix: Index of the array dzw has to be k+1 during the interpolation.
	28	! Otherwise k=0 causes an abortion because dzw is allocated from 1 to nzt+1
	29	!
	30	! 3065 2018-06-12 07:03:02Z Giersch
[3065]	31	! dz values were replaced by dzw or dz(1) to allow for right vertical stretching
	32	!
	33	! 2969 2018-04-13 11:55:09Z thiele
[2969]	34	! Bugfix in Interpolation indices.
	35	!
	36	! 2886 2018-03-14 11:51:53Z thiele
[2886]	37	! Bugfix in passive particle SGS Model:
	38	! Sometimes the added SGS velocities would lead to a violation of the CFL
	39	! criterion for single particles. For this a check was added after the
	40	! calculation of SGS velocities.
	41	!
	42	! 2718 2018-01-02 08:49:38Z maronga
[2716]	43	! Corrected "Former revisions" section
	44	!
	45	! 2701 2017-12-15 15:40:50Z suehring
	46	! Changes from last commit documented
	47	!
	48	! 2698 2017-12-14 18:46:24Z suehring
[2698]	49	! Particle interpolations at walls in case of SGS velocities revised and not
	50	! required parts are removed. (responsible Philipp Thiele)
[2716]	51	! Bugfix in get_topography_top_index
[2698]	52	!
[2716]	53	! 2696 2017-12-14 17:12:51Z kanani
	54	! Change in file header (GPL part)
	55	!
	56	! 2630 2017-11-20 12:58:20Z schwenkel
[2629]	57	! Removed indices ilog and jlog which are no longer needed since particle box
	58	! locations are identical to scalar boxes and topography.
	59	!
[2630]	60	! 2628 2017-11-20 12:40:38Z raasch
[2610]	61	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
	62	!
	63	! 2606 2017-11-10 10:36:31Z schwenkel
[2606]	64	! Changed particle box locations: center of particle box now coincides
	65	! with scalar grid point of same index.
	66	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
	67	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
	68	! lpm_sort -> lpm_sort_timeloop_done
	69	!
	70	! 2417 2017-09-06 15:22:27Z suehring
[2417]	71	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
	72	! particle loop runs from start_index up to end_index instead from 1 to
	73	! number_of_particles. This way, it is possible to skip unnecessary
	74	! computations for particles that already completed the LES timestep.
	75	!
	76	! 2318 2017-07-20 17:27:44Z suehring
[2318]	77	! Get topography top index via Function call
	78	!
	79	! 2317 2017-07-20 17:27:19Z suehring
[1930]	80	!
[2233]	81	! 2232 2017-05-30 17:47:52Z suehring
	82	! Adjustments to new topography and surface concept
	83	!
[2101]	84	! 2100 2017-01-05 16:40:16Z suehring
	85	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
	86	! at the begin of simulations and/or in non-turbulent regions.
	87	!
[2001]	88	! 2000 2016-08-20 18:09:15Z knoop
	89	! Forced header and separation lines into 80 columns
	90	!
[1937]	91	! 1936 2016-06-13 13:37:44Z suehring
	92	! Formatting adjustments
	93	!
[1930]	94	! 1929 2016-06-09 16:25:25Z suehring
[1929]	95	! Put stochastic equation in an extra subroutine.
	96	! Set flag for stochastic equation to communicate whether a particle is near
	97	! topography. This case, memory and drift term are disabled in the Weil equation.
[1889]	98	!
[1929]	99	! Enable vertical logarithmic interpolation also above topography. This case,
	100	! set a lower limit for the friction velocity, as it can become very small
[1930]	101	! in narrow street canyons, leading to too large particle speeds.
[1823]	102	!
[1889]	103	! 1888 2016-04-21 12:20:49Z suehring
	104	! Bugfix concerning logarithmic interpolation of particle speed
	105	!
[1823]	106	! 1822 2016-04-07 07:49:42Z hoffmann
[1822]	107	! Random velocity fluctuations for particles added. Terminal fall velocity
	108	! for droplets is calculated from a parameterization (which is better than
	109	! the previous, physically correct calculation, which demands a very short
	110	! time step that is not used in the model).
	111	!
	112	! Unused variables deleted.
[1321]	113	!
[1692]	114	! 1691 2015-10-26 16:17:44Z maronga
	115	! Renamed prandtl_layer to constant_flux_layer.
	116	!
[1686]	117	! 1685 2015-10-08 07:32:13Z raasch
	118	! TKE check for negative values (so far, only zero value was checked)
	119	! offset_ocean_nzt_m1 removed
	120	!
[1683]	121	! 1682 2015-10-07 23:56:08Z knoop
	122	! Code annotations made doxygen readable
	123	!
[1584]	124	! 1583 2015-04-15 12:16:27Z suehring
	125	! Bugfix: particle advection within Prandtl-layer in case of Galilei
	126	! transformation.
	127	!
[1370]	128	! 1369 2014-04-24 05:57:38Z raasch
	129	! usage of module interfaces removed
	130	!
[1360]	131	! 1359 2014-04-11 17:15:14Z hoffmann
	132	! New particle structure integrated.
	133	! Kind definition added to all floating point numbers.
	134	!
[1323]	135	! 1322 2014-03-20 16:38:49Z raasch
	136	! REAL constants defined as wp_kind
	137	!
[1321]	138	! 1320 2014-03-20 08:40:49Z raasch
[1320]	139	! ONLY-attribute added to USE-statements,
	140	! kind-parameters added to all INTEGER and REAL declaration statements,
	141	! kinds are defined in new module kinds,
	142	! revision history before 2012 removed,
	143	! comment fields (!:) to be used for variable explanations added to
	144	! all variable declaration statements
[849]	145	!
[1315]	146	! 1314 2014-03-14 18:25:17Z suehring
	147	! Vertical logarithmic interpolation of horizontal particle speed for particles
	148	! between roughness height and first vertical grid level.
	149	!
[1037]	150	! 1036 2012-10-22 13:43:42Z raasch
	151	! code put under GPL (PALM 3.9)
	152	!
[850]	153	! 849 2012-03-15 10:35:09Z raasch
	154	! initial revision (former part of advec_particles)
[849]	155	!
[850]	156	!
[849]	157	! Description:
	158	! ------------
[1682]	159	!> Calculation of new particle positions due to advection using a simple Euler
	160	!> scheme. Particles may feel inertia effects. SGS transport can be included
	161	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
[849]	162	!------------------------------------------------------------------------------!
[1682]	163	SUBROUTINE lpm_advec (ip,jp,kp)
	164
[849]	165
[1320]	166	USE arrays_3d, &
[3065]	167	ONLY: de_dx, de_dy, de_dz, diss, dzw, e, km, u, v, w, zu, zw
[849]	168
[1359]	169	USE cpulog
	170
	171	USE pegrid
	172
[1320]	173	USE control_parameters, &
[1691]	174	ONLY: atmos_ocean_sign, cloud_droplets, constant_flux_layer, dt_3d, &
[1822]	175	dt_3d_reached_l, dz, g, kappa, topography, u_gtrans, v_gtrans
[849]	176
[1320]	177	USE grid_variables, &
	178	ONLY: ddx, dx, ddy, dy
	179
	180	USE indices, &
[2698]	181	ONLY: nzb, nzt, wall_flags_0
[1320]	182
	183	USE kinds
	184
	185	USE particle_attributes, &
[1822]	186	ONLY: block_offset, c_0, dt_min_part, grid_particles, &
[1359]	187	iran_part, log_z_z0, number_of_particles, number_of_sublayers, &
[1929]	188	particles, particle_groups, offset_ocean_nzt, sgs_wf_part, &
	189	use_sgs_for_particles, vertical_particle_advection, z0_av_global
[1320]	190
	191	USE statistics, &
	192	ONLY: hom
[849]	193
[2232]	194	USE surface_mod, &
[2698]	195	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
[2232]	196
[1320]	197	IMPLICIT NONE
[849]	198
[2698]	199	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
	200
[1929]	201	INTEGER(iwp) :: agp !< loop variable
	202	INTEGER(iwp) :: gp_outside_of_building(1:8) !< number of grid points used for particle interpolation in case of topography
	203	INTEGER(iwp) :: i !< index variable along x
	204	INTEGER(iwp) :: ip !< index variable along x
	205	INTEGER(iwp) :: j !< index variable along y
	206	INTEGER(iwp) :: jp !< index variable along y
	207	INTEGER(iwp) :: k !< index variable along z
[2232]	208	INTEGER(iwp) :: k_wall !< vertical index of topography top
[1929]	209	INTEGER(iwp) :: kp !< index variable along z
	210	INTEGER(iwp) :: kw !< index variable along z
	211	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
	212	INTEGER(iwp) :: nb !< block number particles are sorted in
	213	INTEGER(iwp) :: num_gp !< number of adjacent grid points inside topography
[2232]	214	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
[849]	215
[1929]	216	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
	217	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
[1359]	218
[1929]	219	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
	220	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
	221	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
	222	REAL(wp) :: d_sum !< dummy argument for horizontal particle interpolation in case of topography
	223	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
	224	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
	225	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
	226	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
	227	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
	228	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
	229	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
	230	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
	231	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
	232	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
[1822]	233	REAL(wp) :: diameter !< diamter of droplet
[1929]	234	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
	235	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
	236	REAL(wp) :: dt_particle_m !< previous particle time step
[2886]	237	REAL(wp) :: dz_temp !<
[1929]	238	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
	239	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
	240	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
[1682]	241	REAL(wp) :: exp_arg !<
	242	REAL(wp) :: exp_term !<
[1929]	243	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
	244	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
	245	REAL(wp) :: location(1:30,1:3) !< wall locations
	246	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
[1682]	247	REAL(wp) :: random_gauss !<
[1822]	248	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
	249	REAL(wp) :: rg1 !< Gaussian distributed random number
	250	REAL(wp) :: rg2 !< Gaussian distributed random number
	251	REAL(wp) :: rg3 !< Gaussian distributed random number
	252	REAL(wp) :: sigma !< velocity standard deviation
[1929]	253	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
	254	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
	255	REAL(wp) :: us_int !< friction velocity at particle grid box
[2232]	256	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
[1929]	257	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
	258	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
[2232]	259	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
[1682]	260	REAL(wp) :: vv_int !<
[1929]	261	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
	262	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
[1822]	263	REAL(wp) :: w_s !< terminal velocity of droplets
[1929]	264	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
	265	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
	266	REAL(wp) :: z_p !< surface layer height (0.5 dz)
[849]	267
[1822]	268	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
	269	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
	270	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
	271	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
	272	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
	273	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
	274
[1929]	275	REAL(wp), DIMENSION(1:30) :: d_gp_pl !< dummy argument for particle interpolation scheme in case of topography
	276	REAL(wp), DIMENSION(1:30) :: de_dxi !< horizontal TKE gradient along x at adjacent wall
	277	REAL(wp), DIMENSION(1:30) :: de_dyi !< horizontal TKE gradient along y at adjacent wall
	278	REAL(wp), DIMENSION(1:30) :: de_dzi !< horizontal TKE gradient along z at adjacent wall
	279	REAL(wp), DIMENSION(1:30) :: dissi !< dissipation at adjacent wall
	280	REAL(wp), DIMENSION(1:30) :: ei !< TKE at adjacent wall
[849]	281
[2886]	282	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
	283	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !<
	284	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
	285	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
	286	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
	287	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
	288	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
	289	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
	290	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
	291	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
	292	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
	293	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !<
	294	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !<
	295	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !<
	296	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
	297	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
	298	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
	299	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
	300	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
	301	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
[1359]	302
[1929]	303	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
[1359]	304
	305	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
	306
[1314]	307	!
	308	!-- Determine height of Prandtl layer and distance between Prandtl-layer
	309	!-- height and horizontal mean roughness height, which are required for
	310	!-- vertical logarithmic interpolation of horizontal particle speeds
	311	!-- (for particles below first vertical grid level).
	312	z_p = zu(nzb+1) - zw(nzb)
[1359]	313	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
[849]	314
[1359]	315	start_index = grid_particles(kp,jp,ip)%start_index
	316	end_index = grid_particles(kp,jp,ip)%end_index
[849]	317
[1359]	318	xv = particles(1:number_of_particles)%x
	319	yv = particles(1:number_of_particles)%y
	320	zv = particles(1:number_of_particles)%z
[849]	321
[1359]	322	DO nb = 0, 7
[2606]	323	!
	324	!-- Interpolate u velocity-component
[1359]	325	i = ip
	326	j = jp + block_offset(nb)%j_off
	327	k = kp + block_offset(nb)%k_off
[2606]	328
[1359]	329	DO n = start_index(nb), end_index(nb)
[1314]	330	!
[1359]	331	!-- Interpolation of the u velocity component onto particle position.
	332	!-- Particles are interpolation bi-linearly in the horizontal and a
	333	!-- linearly in the vertical. An exception is made for particles below
	334	!-- the first vertical grid level in case of a prandtl layer. In this
	335	!-- case the horizontal particle velocity components are determined using
	336	!-- Monin-Obukhov relations (if branch).
	337	!-- First, check if particle is located below first vertical grid level
[2232]	338	!-- above topography (Prandtl-layer height)
	339	!-- Determine vertical index of topography top
[2698]	340	k_wall = get_topography_top_index_ji( jp, ip, 's' )
[1929]	341
[2232]	342	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
[1314]	343	!
[1359]	344	!-- Resolved-scale horizontal particle velocity is zero below z0.
[2232]	345	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1359]	346	u_int(n) = 0.0_wp
	347	ELSE
[1314]	348	!
[1359]	349	!-- Determine the sublayer. Further used as index.
[2232]	350	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	351	* REAL( number_of_sublayers, KIND=wp ) &
[1359]	352	* d_z_p_z0
[1314]	353	!
[1359]	354	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	355	!-- interpolate linearly between precalculated logarithm.
[1929]	356	log_z_z0_int = log_z_z0(INT(height_p)) &
[1359]	357	+ ( height_p - INT(height_p) ) &
	358	* ( log_z_z0(INT(height_p)+1) &
	359	- log_z_z0(INT(height_p)) &
	360	)
[1314]	361	!
[2232]	362	!-- Get friction velocity and momentum flux from new surface data
	363	!-- types.
[2628]	364	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	365	surf_def_h(0)%end_index(jp,ip) ) THEN
	366	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	367	!-- Limit friction velocity. In narrow canyons or holes the
	368	!-- friction velocity can become very small, resulting in a too
	369	!-- large particle speed.
	370	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
	371	usws_int = surf_def_h(0)%usws(surf_start)
[2628]	372	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	373	surf_lsm_h%end_index(jp,ip) ) THEN
	374	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	375	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
	376	usws_int = surf_lsm_h%usws(surf_start)
[2628]	377	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	378	surf_usm_h%end_index(jp,ip) ) THEN
	379	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	380	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
	381	usws_int = surf_usm_h%usws(surf_start)
	382	ENDIF
	383
[1929]	384	!
[1359]	385	!-- Neutral solution is applied for all situations, e.g. also for
	386	!-- unstable and stable situations. Even though this is not exact
	387	!-- this saves a lot of CPU time since several calls of intrinsic
	388	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	389	!-- as sensitivity studies revealed no significant effect of
	390	!-- using the neutral solution also for un/stable situations.
[2232]	391	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	392	* log_z_z0_int - u_gtrans
	393
[1359]	394	ENDIF
	395	!
	396	!-- Particle above the first grid level. Bi-linear interpolation in the
	397	!-- horizontal and linear interpolation in the vertical direction.
[1314]	398	ELSE
	399
[2969]	400	x = xv(n) - i * dx
	401	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	402	aa = x2 + y2
	403	bb = ( dx - x )2 + y2
	404	cc = x2 + ( dy - y )2
	405	dd = ( dx - x )2 + ( dy - y )2
	406	gg = aa + bb + cc + dd
[1314]	407
[1359]	408	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
	409	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
	410	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[1314]	411
[1359]	412	IF ( k == nzt ) THEN
	413	u_int(n) = u_int_l
	414	ELSE
	415	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
	416	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
	417	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[3189]	418	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	419	( u_int_u - u_int_l )
	420	ENDIF
[1929]	421
[1314]	422	ENDIF
	423
[1359]	424	ENDDO
[2606]	425	!
	426	!-- Same procedure for interpolation of the v velocity-component
[1359]	427	i = ip + block_offset(nb)%i_off
	428	j = jp
	429	k = kp + block_offset(nb)%k_off
[2606]	430
[1359]	431	DO n = start_index(nb), end_index(nb)
[1685]	432
[2232]	433	!
	434	!-- Determine vertical index of topography top
[2698]	435	k_wall = get_topography_top_index_ji( jp,ip, 's' )
[849]	436
[2232]	437	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
	438	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1314]	439	!
[1359]	440	!-- Resolved-scale horizontal particle velocity is zero below z0.
	441	v_int(n) = 0.0_wp
	442	ELSE
	443	!
[1929]	444	!-- Determine the sublayer. Further used as index. Please note,
	445	!-- logarithmus can not be reused from above, as in in case of
	446	!-- topography particle on u-grid can be above surface-layer height,
	447	!-- whereas it can be below on v-grid.
[2232]	448	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	449	* REAL( number_of_sublayers, KIND=wp ) &
[1929]	450	* d_z_p_z0
	451	!
	452	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	453	!-- interpolate linearly between precalculated logarithm.
	454	log_z_z0_int = log_z_z0(INT(height_p)) &
	455	+ ( height_p - INT(height_p) ) &
	456	* ( log_z_z0(INT(height_p)+1) &
	457	- log_z_z0(INT(height_p)) &
	458	)
	459	!
[2232]	460	!-- Get friction velocity and momentum flux from new surface data
	461	!-- types.
[2628]	462	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	463	surf_def_h(0)%end_index(jp,ip) ) THEN
	464	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	465	!-- Limit friction velocity. In narrow canyons or holes the
	466	!-- friction velocity can become very small, resulting in a too
	467	!-- large particle speed.
	468	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
[2610]	469	vsws_int = surf_def_h(0)%vsws(surf_start)
[2628]	470	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	471	surf_lsm_h%end_index(jp,ip) ) THEN
	472	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	473	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
[2610]	474	vsws_int = surf_lsm_h%vsws(surf_start)
[2628]	475	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	476	surf_usm_h%end_index(jp,ip) ) THEN
	477	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	478	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
[2610]	479	vsws_int = surf_usm_h%vsws(surf_start)
[2232]	480	ENDIF
[1929]	481	!
[1359]	482	!-- Neutral solution is applied for all situations, e.g. also for
	483	!-- unstable and stable situations. Even though this is not exact
	484	!-- this saves a lot of CPU time since several calls of intrinsic
	485	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	486	!-- as sensitivity studies revealed no significant effect of
	487	!-- using the neutral solution also for un/stable situations.
[2232]	488	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	489	* log_z_z0_int - v_gtrans
[1314]	490
[1359]	491	ENDIF
[1929]	492
[1359]	493	ELSE
[2969]	494	x = xv(n) + ( 0.5_wp - i ) * dx
	495	y = yv(n) - j * dy
[1359]	496	aa = x2 + y2
	497	bb = ( dx - x )2 + y2
	498	cc = x2 + ( dy - y )2
	499	dd = ( dx - x )2 + ( dy - y )2
	500	gg = aa + bb + cc + dd
[1314]	501
[1359]	502	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
	503	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
	504	) / ( 3.0_wp * gg ) - v_gtrans
[1314]	505
[1359]	506	IF ( k == nzt ) THEN
	507	v_int(n) = v_int_l
	508	ELSE
	509	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
	510	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
	511	) / ( 3.0_wp * gg ) - v_gtrans
[3189]	512	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	513	( v_int_u - v_int_l )
	514	ENDIF
[1929]	515
[1314]	516	ENDIF
	517
[1359]	518	ENDDO
[2606]	519	!
	520	!-- Same procedure for interpolation of the w velocity-component
[1359]	521	i = ip + block_offset(nb)%i_off
	522	j = jp + block_offset(nb)%j_off
[1929]	523	k = kp - 1
[2606]	524
[1359]	525	DO n = start_index(nb), end_index(nb)
[849]	526
[1359]	527	IF ( vertical_particle_advection(particles(n)%group) ) THEN
[849]	528
[2969]	529	x = xv(n) + ( 0.5_wp - i ) * dx
	530	y = yv(n) + ( 0.5_wp - j ) * dy
[849]	531	aa = x2 + y2
	532	bb = ( dx - x )2 + y2
	533	cc = x2 + ( dy - y )2
	534	dd = ( dx - x )2 + ( dy - y )2
	535	gg = aa + bb + cc + dd
	536
[1359]	537	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
	538	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
	539	) / ( 3.0_wp * gg )
[849]	540
[1359]	541	IF ( k == nzt ) THEN
	542	w_int(n) = w_int_l
[849]	543	ELSE
[1359]	544	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
	545	( gg-bb ) * w(k+1,j,i+1) + &
	546	( gg-cc ) * w(k+1,j+1,i) + &
	547	( gg-dd ) * w(k+1,j+1,i+1) &
	548	) / ( 3.0_wp * gg )
[3189]	549	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
[1359]	550	( w_int_u - w_int_l )
[849]	551	ENDIF
	552
[1359]	553	ELSE
[849]	554
[1359]	555	w_int(n) = 0.0_wp
[849]	556
[1359]	557	ENDIF
	558
	559	ENDDO
	560
	561	ENDDO
	562
	563	!-- Interpolate and calculate quantities needed for calculating the SGS
	564	!-- velocities
[1822]	565	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[2698]	566
	567	DO nb = 0,7
	568
	569	subbox_at_wall = .FALSE.
	570	!
	571	!-- In case of topography check if subbox is adjacent to a wall
	572	IF ( .NOT. topography == 'flat' ) THEN
	573	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
	574	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
	575	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
	576	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
	577	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
	578	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
	579	THEN
	580	subbox_at_wall = .TRUE.
	581	ENDIF
	582	ENDIF
	583	IF ( subbox_at_wall ) THEN
	584	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
	585	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
	586	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
	587	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
	588	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
	589	!
	590	!-- Set flag for stochastic equation.
	591	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
	592	ELSE
[1359]	593	i = ip + block_offset(nb)%i_off
	594	j = jp + block_offset(nb)%j_off
	595	k = kp + block_offset(nb)%k_off
	596
	597	DO n = start_index(nb), end_index(nb)
[849]	598	!
[1359]	599	!-- Interpolate TKE
[2969]	600	x = xv(n) + ( 0.5_wp - i ) * dx
	601	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	602	aa = x2 + y2
	603	bb = ( dx - x )2 + y2
	604	cc = x2 + ( dy - y )2
	605	dd = ( dx - x )2 + ( dy - y )2
	606	gg = aa + bb + cc + dd
[849]	607
[1359]	608	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
	609	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
	610	) / ( 3.0_wp * gg )
	611
	612	IF ( k+1 == nzt+1 ) THEN
	613	e_int(n) = e_int_l
	614	ELSE
	615	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
	616	( gg - bb ) * e(k+1,j,i+1) + &
	617	( gg - cc ) * e(k+1,j+1,i) + &
	618	( gg - dd ) * e(k+1,j+1,i+1) &
	619	) / ( 3.0_wp * gg )
[3189]	620	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	621	( e_int_u - e_int_l )
	622	ENDIF
[849]	623	!
[1685]	624	!-- Needed to avoid NaN particle velocities (this might not be
	625	!-- required any more)
	626	IF ( e_int(n) <= 0.0_wp ) THEN
[1359]	627	e_int(n) = 1.0E-20_wp
	628	ENDIF
	629	!
	630	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
	631	!-- all position variables from above (TKE))
	632	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
	633	( gg - bb ) * de_dx(k,j,i+1) + &
	634	( gg - cc ) * de_dx(k,j+1,i) + &
	635	( gg - dd ) * de_dx(k,j+1,i+1) &
	636	) / ( 3.0_wp * gg )
[849]	637
	638	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
[1359]	639	de_dx_int(n) = de_dx_int_l
[849]	640	ELSE
[1359]	641	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
	642	( gg - bb ) * de_dx(k+1,j,i+1) + &
	643	( gg - cc ) * de_dx(k+1,j+1,i) + &
	644	( gg - dd ) * de_dx(k+1,j+1,i+1) &
	645	) / ( 3.0_wp * gg )
[3189]	646	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	647	( de_dx_int_u - de_dx_int_l )
[849]	648	ENDIF
[1359]	649	!
	650	!-- Interpolate the TKE gradient along y
	651	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
	652	( gg - bb ) * de_dy(k,j,i+1) + &
	653	( gg - cc ) * de_dy(k,j+1,i) + &
	654	( gg - dd ) * de_dy(k,j+1,i+1) &
	655	) / ( 3.0_wp * gg )
	656	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	657	de_dy_int(n) = de_dy_int_l
	658	ELSE
	659	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
[2698]	660	( gg - bb ) * de_dy(k+1,j,i+1) + &
	661	( gg - cc ) * de_dy(k+1,j+1,i) + &
	662	( gg - dd ) * de_dy(k+1,j+1,i+1) &
[1359]	663	) / ( 3.0_wp * gg )
[3189]	664	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	665	( de_dy_int_u - de_dy_int_l )
[1359]	666	ENDIF
[849]	667
	668	!
[1359]	669	!-- Interpolate the TKE gradient along z
[3065]	670	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
[1359]	671	de_dz_int(n) = 0.0_wp
	672	ELSE
	673	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
	674	( gg - bb ) * de_dz(k,j,i+1) + &
	675	( gg - cc ) * de_dz(k,j+1,i) + &
	676	( gg - dd ) * de_dz(k,j+1,i+1) &
	677	) / ( 3.0_wp * gg )
[849]	678
[1359]	679	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	680	de_dz_int(n) = de_dz_int_l
	681	ELSE
	682	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
	683	( gg - bb ) * de_dz(k+1,j,i+1) + &
	684	( gg - cc ) * de_dz(k+1,j+1,i) + &
	685	( gg - dd ) * de_dz(k+1,j+1,i+1) &
	686	) / ( 3.0_wp * gg )
[3189]	687	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	688	( de_dz_int_u - de_dz_int_l )
	689	ENDIF
	690	ENDIF
[849]	691
[1359]	692	!
	693	!-- Interpolate the dissipation of TKE
	694	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
	695	( gg - bb ) * diss(k,j,i+1) + &
	696	( gg - cc ) * diss(k,j+1,i) + &
	697	( gg - dd ) * diss(k,j+1,i+1) &
[2698]	698	) / ( 3.0_wp * gg )
[849]	699
[1359]	700	IF ( k == nzt ) THEN
	701	diss_int(n) = diss_int_l
	702	ELSE
	703	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
	704	( gg - bb ) * diss(k+1,j,i+1) + &
	705	( gg - cc ) * diss(k+1,j+1,i) + &
	706	( gg - dd ) * diss(k+1,j+1,i+1) &
	707	) / ( 3.0_wp * gg )
[3189]	708	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	709	( diss_int_u - diss_int_l )
[1359]	710	ENDIF
	711
[1929]	712	!
	713	!-- Set flag for stochastic equation.
	714	term_1_2(n) = 1.0_wp
[1359]	715	ENDDO
[2698]	716	ENDIF
	717	ENDDO
[1359]	718
	719	DO nb = 0,7
	720	i = ip + block_offset(nb)%i_off
	721	j = jp + block_offset(nb)%j_off
	722	k = kp + block_offset(nb)%k_off
[849]	723
[1359]	724	DO n = start_index(nb), end_index(nb)
[849]	725	!
[1359]	726	!-- Vertical interpolation of the horizontally averaged SGS TKE and
	727	!-- resolved-scale velocity variances and use the interpolated values
	728	!-- to calculate the coefficient fs, which is a measure of the ratio
	729	!-- of the subgrid-scale turbulent kinetic energy to the total amount
	730	!-- of turbulent kinetic energy.
	731	IF ( k == 0 ) THEN
	732	e_mean_int = hom(0,1,8,0)
	733	ELSE
	734	e_mean_int = hom(k,1,8,0) + &
	735	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
	736	( zu(k+1) - zu(k) ) * &
	737	( zv(n) - zu(k) )
	738	ENDIF
[849]	739
[1685]	740	kw = kp - 1
[849]	741
[1359]	742	IF ( k == 0 ) THEN
	743	aa = hom(k+1,1,30,0) * ( zv(n) / &
	744	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	745	bb = hom(k+1,1,31,0) * ( zv(n) / &
	746	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	747	cc = hom(kw+1,1,32,0) * ( zv(n) / &
	748	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
	749	ELSE
	750	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
	751	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	752	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
	753	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	754	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
	755	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
	756	ENDIF
[849]	757
[1359]	758	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
	759	!
	760	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
	761	!-- an educated guess for the given case.
	762	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
	763	fs_int(n) = 1.0_wp
	764	ELSE
	765	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
	766	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
	767	ENDIF
[849]	768
[1359]	769	ENDDO
	770	ENDDO
[849]	771
[2417]	772	DO nb = 0, 7
	773	DO n = start_index(nb), end_index(nb)
	774	rg(n,1) = random_gauss( iran_part, 5.0_wp )
	775	rg(n,2) = random_gauss( iran_part, 5.0_wp )
	776	rg(n,3) = random_gauss( iran_part, 5.0_wp )
	777	ENDDO
	778	ENDDO
[1359]	779
[2417]	780	DO nb = 0, 7
	781	DO n = start_index(nb), end_index(nb)
[1359]	782
[849]	783	!
[2417]	784	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
[2886]	785	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
[2417]	786	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
[849]	787
	788	!
[2417]	789	!-- Calculate the next particle timestep. dt_gap is the time needed to
	790	!-- complete the current LES timestep.
[2886]	791	dt_gap(n) = dt_3d - particles(n)%dt_sum
	792	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
	793	particles(n)%aux1 = lagr_timescale(n)
	794	particles(n)%aux2 = dt_gap(n)
[849]	795	!
[2417]	796	!-- The particle timestep should not be too small in order to prevent
	797	!-- the number of particle timesteps of getting too large
[2886]	798	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap(n) ) THEN
[2417]	799	dt_particle(n) = dt_min_part
	800	ENDIF
[2886]	801	rvar1_temp(n) = particles(n)%rvar1
	802	rvar2_temp(n) = particles(n)%rvar2
	803	rvar3_temp(n) = particles(n)%rvar3
[849]	804	!
[2417]	805	!-- Calculate the SGS velocity components
	806	IF ( particles(n)%age == 0.0_wp ) THEN
[849]	807	!
[2417]	808	!-- For new particles the SGS components are derived from the SGS
	809	!-- TKE. Limit the Gaussian random number to the interval
	810	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
	811	!-- from becoming unrealistically large.
[2886]	812	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	813	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
	814	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	815	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
	816	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	817	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
[849]	818
[2417]	819	ELSE
[849]	820	!
[2417]	821	!-- Restriction of the size of the new timestep: compared to the
	822	!-- previous timestep the increase must not exceed 200%. First,
	823	!-- check if age > age_m, in order to prevent that particles get zero
	824	!-- timestep.
	825	dt_particle_m = MERGE( dt_particle(n), &
	826	particles(n)%age - particles(n)%age_m, &
	827	particles(n)%age - particles(n)%age_m < &
	828	1E-8_wp )
	829	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
	830	dt_particle(n) = 2.0_wp * dt_particle_m
	831	ENDIF
[849]	832
[2417]	833	!-- For old particles the SGS components are correlated with the
	834	!-- values from the previous timestep. Random numbers have also to
	835	!-- be limited (see above).
	836	!-- As negative values for the subgrid TKE are not allowed, the
	837	!-- change of the subgrid TKE with time cannot be smaller than
	838	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
	839	!-- value for the change of TKE
	840	de_dt_min = - e_int(n) / dt_particle(n)
[849]	841
[2417]	842	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
[849]	843
[2417]	844	IF ( de_dt < de_dt_min ) THEN
	845	de_dt = de_dt_min
	846	ENDIF
[849]	847
[2886]	848	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
[2417]	849	de_dx_int(n), de_dt, diss_int(n), &
	850	dt_particle(n), rg(n,1), term_1_2(n) )
[849]	851
[2886]	852	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
[2417]	853	de_dy_int(n), de_dt, diss_int(n), &
	854	dt_particle(n), rg(n,2), term_1_2(n) )
[849]	855
[2886]	856	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
[2417]	857	de_dz_int(n), de_dt, diss_int(n), &
	858	dt_particle(n), rg(n,3), term_1_2(n) )
[849]	859
[2417]	860	ENDIF
[849]	861
[2886]	862	ENDDO
	863	ENDDO
	864	!
	865	!-- Check if the added SGS velocities result in a violation of the CFL-
	866	!-- criterion. If yes choose a smaller timestep based on the new velocities
	867	!-- and calculate SGS velocities again
	868	dz_temp = zw(kp)-zw(kp-1)
	869
	870	DO nb = 0, 7
	871	DO n = start_index(nb), end_index(nb)
	872	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
	873	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
	874	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
	875	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
	876
	877	dt_particle(n) = 0.9_wp * MIN( &
	878	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
	879	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
	880	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
	881
	882	!
	883	!-- Reset temporary SGS velocites to "current" ones
	884	rvar1_temp(n) = particles(n)%rvar1
	885	rvar2_temp(n) = particles(n)%rvar2
	886	rvar3_temp(n) = particles(n)%rvar3
	887
	888	de_dt_min = - e_int(n) / dt_particle(n)
	889
	890	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
	891
	892	IF ( de_dt < de_dt_min ) THEN
	893	de_dt = de_dt_min
	894	ENDIF
	895
	896	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
	897	de_dx_int(n), de_dt, diss_int(n), &
	898	dt_particle(n), rg(n,1), term_1_2(n) )
	899
	900	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
	901	de_dy_int(n), de_dt, diss_int(n), &
	902	dt_particle(n), rg(n,2), term_1_2(n) )
	903
	904	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
	905	de_dz_int(n), de_dt, diss_int(n), &
	906	dt_particle(n), rg(n,3), term_1_2(n) )
	907	ENDIF
	908
	909	!
	910	!-- Update particle velocites
	911	particles(n)%rvar1 = rvar1_temp(n)
	912	particles(n)%rvar2 = rvar2_temp(n)
	913	particles(n)%rvar3 = rvar3_temp(n)
[2417]	914	u_int(n) = u_int(n) + particles(n)%rvar1
	915	v_int(n) = v_int(n) + particles(n)%rvar2
	916	w_int(n) = w_int(n) + particles(n)%rvar3
[849]	917	!
[2417]	918	!-- Store the SGS TKE of the current timelevel which is needed for
	919	!-- for calculating the SGS particle velocities at the next timestep
	920	particles(n)%e_m = e_int(n)
	921	ENDDO
[1359]	922	ENDDO
[2886]	923
[1359]	924	ELSE
[849]	925	!
[1359]	926	!-- If no SGS velocities are used, only the particle timestep has to
	927	!-- be set
	928	dt_particle = dt_3d
[849]	929
[1359]	930	ENDIF
[849]	931
[1359]	932	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
[849]	933
[1359]	934	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
[2417]	935	DO nb = 0, 7
	936	DO n = start_index(nb), end_index(nb)
[1359]	937
[849]	938	!
[2417]	939	!-- Particle advection
	940	IF ( dens_ratio(n) == 0.0_wp ) THEN
[849]	941	!
[2417]	942	!-- Pure passive transport (without particle inertia)
	943	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
	944	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
	945	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
[849]	946
[2417]	947	particles(n)%speed_x = u_int(n)
	948	particles(n)%speed_y = v_int(n)
	949	particles(n)%speed_z = w_int(n)
[849]	950
[2417]	951	ELSE
[849]	952	!
[2417]	953	!-- Transport of particles with inertia
	954	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
	955	dt_particle(n)
	956	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
	957	dt_particle(n)
	958	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
	959	dt_particle(n)
[849]	960
	961	!
[2417]	962	!-- Update of the particle velocity
	963	IF ( cloud_droplets ) THEN
	964	!
	965	!-- Terminal velocity is computed for vertical direction (Rogers et
	966	!-- al., 1993, J. Appl. Meteorol.)
	967	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	968	IF ( diameter <= d0_rog ) THEN
	969	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	970	ELSE
	971	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	972	ENDIF
	973
	974	!
	975	!-- If selected, add random velocities following Soelch and Kaercher
	976	!-- (2010, Q. J. R. Meteorol. Soc.)
	977	IF ( use_sgs_for_particles ) THEN
[2886]	978	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	979	RL = EXP( -1.0_wp * dt_3d / lagr_timescale(n) )
[2417]	980	sigma = SQRT( e(kp,jp,ip) )
	981
	982	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	983	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	984	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	985
	986	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	987	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	988	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	989	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	990	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	991	SQRT( 1.0_wp - RL*2 ) sigma * rg3
	992
	993	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	994	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	995	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
	996	ELSE
	997	particles(n)%speed_x = u_int(n)
	998	particles(n)%speed_y = v_int(n)
	999	particles(n)%speed_z = w_int(n) - w_s
	1000	ENDIF
	1001
	1002	ELSE
	1003
	1004	IF ( use_sgs_for_particles ) THEN
	1005	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1006	exp_term = EXP( -exp_arg * dt_particle(n) )
	1007	ELSE
	1008	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1009	exp_term = particle_groups(particles(n)%group)%exp_term
	1010	ENDIF
	1011	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
	1012	u_int(n) * ( 1.0_wp - exp_term )
	1013	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
	1014	v_int(n) * ( 1.0_wp - exp_term )
	1015	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1016	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
	1017	g / exp_arg ) * ( 1.0_wp - exp_term )
	1018	ENDIF
	1019
	1020	ENDIF
	1021	ENDDO
	1022	ENDDO
	1023
	1024	ELSE
	1025
	1026	DO nb = 0, 7
	1027	DO n = start_index(nb), end_index(nb)
	1028	!
	1029	!-- Transport of particles with inertia
	1030	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
	1031	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
	1032	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
	1033	!
[1359]	1034	!-- Update of the particle velocity
	1035	IF ( cloud_droplets ) THEN
[1822]	1036	!
[2417]	1037	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
	1038	!-- 1993, J. Appl. Meteorol.)
[1822]	1039	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	1040	IF ( diameter <= d0_rog ) THEN
	1041	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	1042	ELSE
	1043	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	1044	ENDIF
[1359]	1045
[1822]	1046	!
	1047	!-- If selected, add random velocities following Soelch and Kaercher
	1048	!-- (2010, Q. J. R. Meteorol. Soc.)
	1049	IF ( use_sgs_for_particles ) THEN
[2886]	1050	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	1051	RL = EXP( -1.0_wp * dt_3d / lagr_timescale(n) )
[2417]	1052	sigma = SQRT( e(kp,jp,ip) )
[1822]	1053
[2417]	1054	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1055	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1056	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
[1822]	1057
[2417]	1058	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	1059	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	1060	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	1061	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	1062	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	1063	SQRT( 1.0_wp - RL*2 ) sigma * rg3
[1822]	1064
[2417]	1065	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	1066	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	1067	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
[1822]	1068	ELSE
[2417]	1069	particles(n)%speed_x = u_int(n)
	1070	particles(n)%speed_y = v_int(n)
	1071	particles(n)%speed_z = w_int(n) - w_s
[1822]	1072	ENDIF
	1073
[1359]	1074	ELSE
[1822]	1075
	1076	IF ( use_sgs_for_particles ) THEN
	1077	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1078	exp_term = EXP( -exp_arg * dt_particle(n) )
	1079	ELSE
	1080	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1081	exp_term = particle_groups(particles(n)%group)%exp_term
	1082	ENDIF
[2417]	1083	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
[1822]	1084	u_int(n) * ( 1.0_wp - exp_term )
[2417]	1085	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
[1822]	1086	v_int(n) * ( 1.0_wp - exp_term )
[2417]	1087	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1088	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
	1089	exp_arg ) * ( 1.0_wp - exp_term )
[1359]	1090	ENDIF
[2417]	1091	ENDDO
[1359]	1092	ENDDO
	1093
[2417]	1094	ENDIF
[1359]	1095
	1096	!
[2417]	1097	!-- Store the old age of the particle ( needed to prevent that a
	1098	!-- particle crosses several PEs during one timestep, and for the
	1099	!-- evaluation of the subgrid particle velocity fluctuations )
	1100	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
	1101
	1102	DO nb = 0, 7
	1103	DO n = start_index(nb), end_index(nb)
[1822]	1104	!
[2417]	1105	!-- Increment the particle age and the total time that the particle
	1106	!-- has advanced within the particle timestep procedure
	1107	particles(n)%age = particles(n)%age + dt_particle(n)
	1108	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
[1359]	1109
[1822]	1110	!
[2417]	1111	!-- Check whether there is still a particle that has not yet completed
	1112	!-- the total LES timestep
	1113	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
	1114	dt_3d_reached_l = .FALSE.
[849]	1115	ENDIF
[1822]	1116
[1359]	1117	ENDDO
[849]	1118	ENDDO
	1119
[1359]	1120	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
[849]	1121
[1929]	1122
[849]	1123	END SUBROUTINE lpm_advec
[1929]	1124
	1125	! Description:
	1126	! ------------
	1127	!> Calculation of subgrid-scale particle speed using the stochastic model
	1128	!> of Weil et al. (2004, JAS, 61, 2877-2887).
	1129	!------------------------------------------------------------------------------!
	1130	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
	1131	dt_n, rg_n, fac )
	1132
	1133	USE kinds
	1134
	1135	USE particle_attributes, &
	1136	ONLY: c_0, sgs_wf_part
	1137
	1138	IMPLICIT NONE
	1139
	1140	REAL(wp) :: a1 !< dummy argument
	1141	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
	1142	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
	1143	REAL(wp) :: diss_n !< dissipation at particle position
	1144	REAL(wp) :: dt_n !< particle timestep
	1145	REAL(wp) :: e_n !< TKE at particle position
	1146	REAL(wp) :: fac !< flag to identify adjacent topography
	1147	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
	1148	REAL(wp) :: sgs_w !< constant (1/3)
	1149	REAL(wp) :: rg_n !< random number
	1150	REAL(wp) :: term1 !< memory term
	1151	REAL(wp) :: term2 !< drift correction term
	1152	REAL(wp) :: term3 !< random term
	1153	REAL(wp) :: v_sgs !< subgrid-scale velocity component
	1154
[2100]	1155	!-- At first, limit TKE to a small non-zero number, in order to prevent
	1156	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
	1157	!-- (could occur at the simulation begin).
	1158	e_n = MAX( e_n, 1E-20_wp )
[1929]	1159	!
	1160	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
	1161	!-- multiplied by a flag to switch of both terms near topography.
	1162	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
	1163	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
	1164	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
	1165	!-- disabled if one of the adjacent grid points belongs to topography.
	1166	!-- Moreover, in this case, the previous subgrid-scale component is also set
	1167	!-- to zero.
	1168
	1169	a1 = fs_n * c_0 * diss_n
	1170	!
	1171	!-- Memory term
	1172	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
	1173	* fac
	1174	!
	1175	!-- Drift correction term
	1176	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
	1177	* fac
	1178	!
	1179	!-- Random term
	1180	term3 = SQRT( MAX( a1, 1E-20 ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
	1181	!
	1182	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
	1183	!-- subgrid-scale velocity component is set to zero, in order to prevent a
	1184	!-- velocity build-up.
	1185	!-- This case, set also previous subgrid-scale component to zero.
	1186	v_sgs = v_sgs * fac + term1 + term2 + term3
	1187
	1188	END SUBROUTINE weil_stochastic_eq

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