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source: palm/trunk/SOURCE/lpm_advec.f90 @ 3454

Last change on this file since 3454 was 3274, checked in by knoop, 6 years ago
Modularization of all bulk cloud physics code components
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1	!> @file lpm_advec.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
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.
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	!
17	! Copyright 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! ------------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_advec.f90 3274 2018-09-24 15:42:55Z schwenkel $
27	! Modularization of all bulk cloud physics code components
28	!
29	! 3241 2018-09-12 15:02:00Z raasch
30	! unused variables removed
31	!
32	! 3207 2018-08-27 12:55:33Z schwenkel
33	! Minor bugfix for sgs-velocities in case of cloud droplets
34	!
35	! 3189 2018-08-06 13:18:55Z raasch
36	! Bugfix: Index of the array dzw has to be k+1 during the interpolation.
37	! Otherwise k=0 causes an abortion because dzw is allocated from 1 to nzt+1
38	!
39	! 3065 2018-06-12 07:03:02Z Giersch
40	! dz values were replaced by dzw or dz(1) to allow for right vertical stretching
41	!
42	! 2969 2018-04-13 11:55:09Z thiele
43	! Bugfix in Interpolation indices.
44	!
45	! 2886 2018-03-14 11:51:53Z thiele
46	! Bugfix in passive particle SGS Model:
47	! Sometimes the added SGS velocities would lead to a violation of the CFL
48	! criterion for single particles. For this a check was added after the
49	! calculation of SGS velocities.
50	!
51	! 2718 2018-01-02 08:49:38Z maronga
52	! Corrected "Former revisions" section
53	!
54	! 2701 2017-12-15 15:40:50Z suehring
55	! Changes from last commit documented
56	!
57	! 2698 2017-12-14 18:46:24Z suehring
58	! Particle interpolations at walls in case of SGS velocities revised and not
59	! required parts are removed. (responsible Philipp Thiele)
60	! Bugfix in get_topography_top_index
61	!
62	! 2696 2017-12-14 17:12:51Z kanani
63	! Change in file header (GPL part)
64	!
65	! 2630 2017-11-20 12:58:20Z schwenkel
66	! Removed indices ilog and jlog which are no longer needed since particle box
67	! locations are identical to scalar boxes and topography.
68	!
69	! 2628 2017-11-20 12:40:38Z raasch
70	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
71	!
72	! 2606 2017-11-10 10:36:31Z schwenkel
73	! Changed particle box locations: center of particle box now coincides
74	! with scalar grid point of same index.
75	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
76	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
77	! lpm_sort -> lpm_sort_timeloop_done
78	!
79	! 2417 2017-09-06 15:22:27Z suehring
80	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
81	! particle loop runs from start_index up to end_index instead from 1 to
82	! number_of_particles. This way, it is possible to skip unnecessary
83	! computations for particles that already completed the LES timestep.
84	!
85	! 2318 2017-07-20 17:27:44Z suehring
86	! Get topography top index via Function call
87	!
88	! 2317 2017-07-20 17:27:19Z suehring
89	!
90	! 2232 2017-05-30 17:47:52Z suehring
91	! Adjustments to new topography and surface concept
92	!
93	! 2100 2017-01-05 16:40:16Z suehring
94	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
95	! at the begin of simulations and/or in non-turbulent regions.
96	!
97	! 2000 2016-08-20 18:09:15Z knoop
98	! Forced header and separation lines into 80 columns
99	!
100	! 1936 2016-06-13 13:37:44Z suehring
101	! Formatting adjustments
102	!
103	! 1929 2016-06-09 16:25:25Z suehring
104	! Put stochastic equation in an extra subroutine.
105	! Set flag for stochastic equation to communicate whether a particle is near
106	! topography. This case, memory and drift term are disabled in the Weil equation.
107	!
108	! Enable vertical logarithmic interpolation also above topography. This case,
109	! set a lower limit for the friction velocity, as it can become very small
110	! in narrow street canyons, leading to too large particle speeds.
111	!
112	! 1888 2016-04-21 12:20:49Z suehring
113	! Bugfix concerning logarithmic interpolation of particle speed
114	!
115	! 1822 2016-04-07 07:49:42Z hoffmann
116	! Random velocity fluctuations for particles added. Terminal fall velocity
117	! for droplets is calculated from a parameterization (which is better than
118	! the previous, physically correct calculation, which demands a very short
119	! time step that is not used in the model).
120	!
121	! Unused variables deleted.
122	!
123	! 1691 2015-10-26 16:17:44Z maronga
124	! Renamed prandtl_layer to constant_flux_layer.
125	!
126	! 1685 2015-10-08 07:32:13Z raasch
127	! TKE check for negative values (so far, only zero value was checked)
128	! offset_ocean_nzt_m1 removed
129	!
130	! 1682 2015-10-07 23:56:08Z knoop
131	! Code annotations made doxygen readable
132	!
133	! 1583 2015-04-15 12:16:27Z suehring
134	! Bugfix: particle advection within Prandtl-layer in case of Galilei
135	! transformation.
136	!
137	! 1369 2014-04-24 05:57:38Z raasch
138	! usage of module interfaces removed
139	!
140	! 1359 2014-04-11 17:15:14Z hoffmann
141	! New particle structure integrated.
142	! Kind definition added to all floating point numbers.
143	!
144	! 1322 2014-03-20 16:38:49Z raasch
145	! REAL constants defined as wp_kind
146	!
147	! 1320 2014-03-20 08:40:49Z raasch
148	! ONLY-attribute added to USE-statements,
149	! kind-parameters added to all INTEGER and REAL declaration statements,
150	! kinds are defined in new module kinds,
151	! revision history before 2012 removed,
152	! comment fields (!:) to be used for variable explanations added to
153	! all variable declaration statements
154	!
155	! 1314 2014-03-14 18:25:17Z suehring
156	! Vertical logarithmic interpolation of horizontal particle speed for particles
157	! between roughness height and first vertical grid level.
158	!
159	! 1036 2012-10-22 13:43:42Z raasch
160	! code put under GPL (PALM 3.9)
161	!
162	! 849 2012-03-15 10:35:09Z raasch
163	! initial revision (former part of advec_particles)
164	!
165	!
166	! Description:
167	! ------------
168	!> Calculation of new particle positions due to advection using a simple Euler
169	!> scheme. Particles may feel inertia effects. SGS transport can be included
170	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
171	!------------------------------------------------------------------------------!
172	SUBROUTINE lpm_advec (ip,jp,kp)
173
174
175	USE arrays_3d, &
176	ONLY: de_dx, de_dy, de_dz, diss, dzw, e, km, u, v, w, zu, zw
177
178	USE basic_constants_and_equations_mod, &
179	ONLY: g, kappa
180
181	USE cpulog
182
183	USE pegrid
184
185	USE control_parameters, &
186	ONLY: cloud_droplets, constant_flux_layer, dt_3d, dt_3d_reached_l, &
187	dz, topography, u_gtrans, v_gtrans
188
189	USE grid_variables, &
190	ONLY: dx, dy
191
192	USE indices, &
193	ONLY: nzb, nzt, wall_flags_0
194
195	USE kinds
196
197	USE particle_attributes, &
198	ONLY: block_offset, c_0, dt_min_part, grid_particles, iran_part, &
199	log_z_z0, number_of_particles, number_of_sublayers, &
200	particles, particle_groups, sgs_wf_part, &
201	use_sgs_for_particles, vertical_particle_advection, z0_av_global
202
203	USE statistics, &
204	ONLY: hom
205
206	USE surface_mod, &
207	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
208
209	IMPLICIT NONE
210
211	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
212
213	INTEGER(iwp) :: i !< index variable along x
214	INTEGER(iwp) :: ip !< index variable along x
215	INTEGER(iwp) :: j !< index variable along y
216	INTEGER(iwp) :: jp !< index variable along y
217	INTEGER(iwp) :: k !< index variable along z
218	INTEGER(iwp) :: k_wall !< vertical index of topography top
219	INTEGER(iwp) :: kp !< index variable along z
220	INTEGER(iwp) :: kw !< index variable along z
221	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
222	INTEGER(iwp) :: nb !< block number particles are sorted in
223	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
224
225	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
226	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
227
228	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
229	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
230	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
231	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
232	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
233	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
234	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
235	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
236	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
237	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
238	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
239	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
240	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
241	REAL(wp) :: diameter !< diamter of droplet
242	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
243	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
244	REAL(wp) :: dt_particle_m !< previous particle time step
245	REAL(wp) :: dz_temp !<
246	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
247	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
248	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
249	REAL(wp) :: exp_arg !<
250	REAL(wp) :: exp_term !<
251	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
252	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
253	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
254	REAL(wp) :: random_gauss !<
255	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
256	REAL(wp) :: rg1 !< Gaussian distributed random number
257	REAL(wp) :: rg2 !< Gaussian distributed random number
258	REAL(wp) :: rg3 !< Gaussian distributed random number
259	REAL(wp) :: sigma !< velocity standard deviation
260	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
261	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
262	REAL(wp) :: us_int !< friction velocity at particle grid box
263	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
264	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
265	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
266	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
267	REAL(wp) :: vv_int !<
268	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
269	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
270	REAL(wp) :: w_s !< terminal velocity of droplets
271	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
272	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
273	REAL(wp) :: z_p !< surface layer height (0.5 dz)
274
275	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
276	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
277	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
278	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
279	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
280	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
281
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
302
303	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
304
305	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
306
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)
313	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
314
315	start_index = grid_particles(kp,jp,ip)%start_index
316	end_index = grid_particles(kp,jp,ip)%end_index
317
318	xv = particles(1:number_of_particles)%x
319	yv = particles(1:number_of_particles)%y
320	zv = particles(1:number_of_particles)%z
321
322	DO nb = 0, 7
323	!
324	!-- Interpolate u velocity-component
325	i = ip
326	j = jp + block_offset(nb)%j_off
327	k = kp + block_offset(nb)%k_off
328
329	DO n = start_index(nb), end_index(nb)
330	!
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
338	!-- above topography (Prandtl-layer height)
339	!-- Determine vertical index of topography top
340	k_wall = get_topography_top_index_ji( jp, ip, 's' )
341
342	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
343	!
344	!-- Resolved-scale horizontal particle velocity is zero below z0.
345	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
346	u_int(n) = 0.0_wp
347	ELSE
348	!
349	!-- Determine the sublayer. Further used as index.
350	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
351	* REAL( number_of_sublayers, KIND=wp ) &
352	* d_z_p_z0
353	!
354	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
355	!-- interpolate linearly between precalculated logarithm.
356	log_z_z0_int = log_z_z0(INT(height_p)) &
357	+ ( height_p - INT(height_p) ) &
358	* ( log_z_z0(INT(height_p)+1) &
359	- log_z_z0(INT(height_p)) &
360	)
361	!
362	!-- Get friction velocity and momentum flux from new surface data
363	!-- types.
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)
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)
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)
375	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
376	usws_int = surf_lsm_h%usws(surf_start)
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)
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
384	!
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.
391	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
392	* log_z_z0_int - u_gtrans
393
394	ENDIF
395	!
396	!-- Particle above the first grid level. Bi-linear interpolation in the
397	!-- horizontal and linear interpolation in the vertical direction.
398	ELSE
399
400	x = xv(n) - i * dx
401	y = yv(n) + ( 0.5_wp - j ) * dy
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
407
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
411
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
418	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
419	( u_int_u - u_int_l )
420	ENDIF
421
422	ENDIF
423
424	ENDDO
425	!
426	!-- Same procedure for interpolation of the v velocity-component
427	i = ip + block_offset(nb)%i_off
428	j = jp
429	k = kp + block_offset(nb)%k_off
430
431	DO n = start_index(nb), end_index(nb)
432
433	!
434	!-- Determine vertical index of topography top
435	k_wall = get_topography_top_index_ji( jp,ip, 's' )
436
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
439	!
440	!-- Resolved-scale horizontal particle velocity is zero below z0.
441	v_int(n) = 0.0_wp
442	ELSE
443	!
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.
448	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
449	* REAL( number_of_sublayers, KIND=wp ) &
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	!
460	!-- Get friction velocity and momentum flux from new surface data
461	!-- types.
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)
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 )
469	vsws_int = surf_def_h(0)%vsws(surf_start)
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)
473	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
474	vsws_int = surf_lsm_h%vsws(surf_start)
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)
478	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
479	vsws_int = surf_usm_h%vsws(surf_start)
480	ENDIF
481	!
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.
488	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
489	* log_z_z0_int - v_gtrans
490
491	ENDIF
492
493	ELSE
494	x = xv(n) + ( 0.5_wp - i ) * dx
495	y = yv(n) - j * dy
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
501
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
505
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
512	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
513	( v_int_u - v_int_l )
514	ENDIF
515
516	ENDIF
517
518	ENDDO
519	!
520	!-- Same procedure for interpolation of the w velocity-component
521	i = ip + block_offset(nb)%i_off
522	j = jp + block_offset(nb)%j_off
523	k = kp - 1
524
525	DO n = start_index(nb), end_index(nb)
526
527	IF ( vertical_particle_advection(particles(n)%group) ) THEN
528
529	x = xv(n) + ( 0.5_wp - i ) * dx
530	y = yv(n) + ( 0.5_wp - j ) * dy
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
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 )
540
541	IF ( k == nzt ) THEN
542	w_int(n) = w_int_l
543	ELSE
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 )
549	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
550	( w_int_u - w_int_l )
551	ENDIF
552
553	ELSE
554
555	w_int(n) = 0.0_wp
556
557	ENDIF
558
559	ENDDO
560
561	ENDDO
562
563	!-- Interpolate and calculate quantities needed for calculating the SGS
564	!-- velocities
565	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
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
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)
598	!
599	!-- Interpolate TKE
600	x = xv(n) + ( 0.5_wp - i ) * dx
601	y = yv(n) + ( 0.5_wp - j ) * dy
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
607
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 )
620	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
621	( e_int_u - e_int_l )
622	ENDIF
623	!
624	!-- Needed to avoid NaN particle velocities (this might not be
625	!-- required any more)
626	IF ( e_int(n) <= 0.0_wp ) THEN
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 )
637
638	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
639	de_dx_int(n) = de_dx_int_l
640	ELSE
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 )
646	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
647	( de_dx_int_u - de_dx_int_l )
648	ENDIF
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) + &
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) &
663	) / ( 3.0_wp * gg )
664	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
665	( de_dy_int_u - de_dy_int_l )
666	ENDIF
667
668	!
669	!-- Interpolate the TKE gradient along z
670	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
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 )
678
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 )
687	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
688	( de_dz_int_u - de_dz_int_l )
689	ENDIF
690	ENDIF
691
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) &
698	) / ( 3.0_wp * gg )
699
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 )
708	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
709	( diss_int_u - diss_int_l )
710	ENDIF
711
712	!
713	!-- Set flag for stochastic equation.
714	term_1_2(n) = 1.0_wp
715	ENDDO
716	ENDIF
717	ENDDO
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
723
724	DO n = start_index(nb), end_index(nb)
725	!
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
739
740	kw = kp - 1
741
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
757
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
768
769	ENDDO
770	ENDDO
771
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
779
780	DO nb = 0, 7
781	DO n = start_index(nb), end_index(nb)
782
783	!
784	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
785	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
786	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
787
788	!
789	!-- Calculate the next particle timestep. dt_gap is the time needed to
790	!-- complete the current LES timestep.
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)
795	!
796	!-- The particle timestep should not be too small in order to prevent
797	!-- the number of particle timesteps of getting too large
798	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap(n) ) THEN
799	dt_particle(n) = dt_min_part
800	ENDIF
801	rvar1_temp(n) = particles(n)%rvar1
802	rvar2_temp(n) = particles(n)%rvar2
803	rvar3_temp(n) = particles(n)%rvar3
804	!
805	!-- Calculate the SGS velocity components
806	IF ( particles(n)%age == 0.0_wp ) THEN
807	!
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.
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 )
818
819	ELSE
820	!
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
832
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)
841
842	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
843
844	IF ( de_dt < de_dt_min ) THEN
845	de_dt = de_dt_min
846	ENDIF
847
848	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
849	de_dx_int(n), de_dt, diss_int(n), &
850	dt_particle(n), rg(n,1), term_1_2(n) )
851
852	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
853	de_dy_int(n), de_dt, diss_int(n), &
854	dt_particle(n), rg(n,2), term_1_2(n) )
855
856	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
857	de_dz_int(n), de_dt, diss_int(n), &
858	dt_particle(n), rg(n,3), term_1_2(n) )
859
860	ENDIF
861
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)
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
917	!
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
922	ENDDO
923
924	ELSE
925	!
926	!-- If no SGS velocities are used, only the particle timestep has to
927	!-- be set
928	dt_particle = dt_3d
929
930	ENDIF
931
932	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
933
934	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
935	DO nb = 0, 7
936	DO n = start_index(nb), end_index(nb)
937
938	!
939	!-- Particle advection
940	IF ( dens_ratio(n) == 0.0_wp ) THEN
941	!
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)
946
947	particles(n)%speed_x = u_int(n)
948	particles(n)%speed_y = v_int(n)
949	particles(n)%speed_z = w_int(n)
950
951	ELSE
952	!
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)
960
961	!
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
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 / MAX( lagr_timescale(n), &
980	1.0E-20_wp ) )
981	sigma = SQRT( e(kp,jp,ip) )
982
983	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
984	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
985	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
986
987	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
988	SQRT( 1.0_wp - RL*2 ) sigma * rg1
989	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
990	SQRT( 1.0_wp - RL*2 ) sigma * rg2
991	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
992	SQRT( 1.0_wp - RL*2 ) sigma * rg3
993
994	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
995	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
996	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
997	ELSE
998	particles(n)%speed_x = u_int(n)
999	particles(n)%speed_y = v_int(n)
1000	particles(n)%speed_z = w_int(n) - w_s
1001	ENDIF
1002
1003	ELSE
1004
1005	IF ( use_sgs_for_particles ) THEN
1006	exp_arg = particle_groups(particles(n)%group)%exp_arg
1007	exp_term = EXP( -exp_arg * dt_particle(n) )
1008	ELSE
1009	exp_arg = particle_groups(particles(n)%group)%exp_arg
1010	exp_term = particle_groups(particles(n)%group)%exp_term
1011	ENDIF
1012	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
1013	u_int(n) * ( 1.0_wp - exp_term )
1014	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
1015	v_int(n) * ( 1.0_wp - exp_term )
1016	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
1017	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
1018	g / exp_arg ) * ( 1.0_wp - exp_term )
1019	ENDIF
1020
1021	ENDIF
1022	ENDDO
1023	ENDDO
1024
1025	ELSE
1026
1027	DO nb = 0, 7
1028	DO n = start_index(nb), end_index(nb)
1029	!
1030	!-- Transport of particles with inertia
1031	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
1032	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
1033	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
1034	!
1035	!-- Update of the particle velocity
1036	IF ( cloud_droplets ) THEN
1037	!
1038	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
1039	!-- 1993, J. Appl. Meteorol.)
1040	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
1041	IF ( diameter <= d0_rog ) THEN
1042	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
1043	ELSE
1044	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
1045	ENDIF
1046
1047	!
1048	!-- If selected, add random velocities following Soelch and Kaercher
1049	!-- (2010, Q. J. R. Meteorol. Soc.)
1050	IF ( use_sgs_for_particles ) THEN
1051	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
1052	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
1053	1.0E-20_wp ) )
1054	sigma = SQRT( e(kp,jp,ip) )
1055
1056	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
1057	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
1058	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
1059
1060	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
1061	SQRT( 1.0_wp - RL*2 ) sigma * rg1
1062	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
1063	SQRT( 1.0_wp - RL*2 ) sigma * rg2
1064	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
1065	SQRT( 1.0_wp - RL*2 ) sigma * rg3
1066
1067	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
1068	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
1069	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
1070	ELSE
1071	particles(n)%speed_x = u_int(n)
1072	particles(n)%speed_y = v_int(n)
1073	particles(n)%speed_z = w_int(n) - w_s
1074	ENDIF
1075
1076	ELSE
1077
1078	IF ( use_sgs_for_particles ) THEN
1079	exp_arg = particle_groups(particles(n)%group)%exp_arg
1080	exp_term = EXP( -exp_arg * dt_particle(n) )
1081	ELSE
1082	exp_arg = particle_groups(particles(n)%group)%exp_arg
1083	exp_term = particle_groups(particles(n)%group)%exp_term
1084	ENDIF
1085	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
1086	u_int(n) * ( 1.0_wp - exp_term )
1087	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
1088	v_int(n) * ( 1.0_wp - exp_term )
1089	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
1090	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
1091	exp_arg ) * ( 1.0_wp - exp_term )
1092	ENDIF
1093	ENDDO
1094	ENDDO
1095
1096	ENDIF
1097
1098	!
1099	!-- Store the old age of the particle ( needed to prevent that a
1100	!-- particle crosses several PEs during one timestep, and for the
1101	!-- evaluation of the subgrid particle velocity fluctuations )
1102	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
1103
1104	DO nb = 0, 7
1105	DO n = start_index(nb), end_index(nb)
1106	!
1107	!-- Increment the particle age and the total time that the particle
1108	!-- has advanced within the particle timestep procedure
1109	particles(n)%age = particles(n)%age + dt_particle(n)
1110	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
1111
1112	!
1113	!-- Check whether there is still a particle that has not yet completed
1114	!-- the total LES timestep
1115	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
1116	dt_3d_reached_l = .FALSE.
1117	ENDIF
1118
1119	ENDDO
1120	ENDDO
1121
1122	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
1123
1124
1125	END SUBROUTINE lpm_advec
1126
1127	! Description:
1128	! ------------
1129	!> Calculation of subgrid-scale particle speed using the stochastic model
1130	!> of Weil et al. (2004, JAS, 61, 2877-2887).
1131	!------------------------------------------------------------------------------!
1132	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
1133	dt_n, rg_n, fac )
1134
1135	USE kinds
1136
1137	USE particle_attributes, &
1138	ONLY: c_0, sgs_wf_part
1139
1140	IMPLICIT NONE
1141
1142	REAL(wp) :: a1 !< dummy argument
1143	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
1144	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
1145	REAL(wp) :: diss_n !< dissipation at particle position
1146	REAL(wp) :: dt_n !< particle timestep
1147	REAL(wp) :: e_n !< TKE at particle position
1148	REAL(wp) :: fac !< flag to identify adjacent topography
1149	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
1150	REAL(wp) :: rg_n !< random number
1151	REAL(wp) :: term1 !< memory term
1152	REAL(wp) :: term2 !< drift correction term
1153	REAL(wp) :: term3 !< random term
1154	REAL(wp) :: v_sgs !< subgrid-scale velocity component
1155
1156	!-- At first, limit TKE to a small non-zero number, in order to prevent
1157	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
1158	!-- (could occur at the simulation begin).
1159	e_n = MAX( e_n, 1E-20_wp )
1160	!
1161	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
1162	!-- multiplied by a flag to switch of both terms near topography.
1163	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
1164	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
1165	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
1166	!-- disabled if one of the adjacent grid points belongs to topography.
1167	!-- Moreover, in this case, the previous subgrid-scale component is also set
1168	!-- to zero.
1169
1170	a1 = fs_n * c_0 * diss_n
1171	!
1172	!-- Memory term
1173	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
1174	* fac
1175	!
1176	!-- Drift correction term
1177	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
1178	* fac
1179	!
1180	!-- Random term
1181	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
1182	!
1183	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
1184	!-- subgrid-scale velocity component is set to zero, in order to prevent a
1185	!-- velocity build-up.
1186	!-- This case, set also previous subgrid-scale component to zero.
1187	v_sgs = v_sgs * fac + term1 + term2 + term3
1188
1189	END SUBROUTINE weil_stochastic_eq

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