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source: palm/trunk/SOURCE/lpm_advec.f90 @ 2912

Last change on this file since 2912 was 2886, checked in by thiele, 7 years ago
Bugfix in passive particle SGS Model
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File size: 55.1 KB

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

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