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source: palm/trunk/SOURCE/lpm_advec.f90 @ 2809

Last change on this file since 2809 was 2718, checked in by maronga, 7 years ago
deleting of deprecated files; headers updated where needed
Property svn:keywords set to `Id`
File size: 52.1 KB

Rev	Line
[1682]	1	!> @file lpm_advec.f90
[2000]	2	!------------------------------------------------------------------------------!
[2696]	3	! This file is part of the PALM model system.
[1036]	4	!
[2000]	5	! PALM is free software: you can redistribute it and/or modify it under the
	6	! terms of the GNU General Public License as published by the Free Software
	7	! Foundation, either version 3 of the License, or (at your option) any later
	8	! version.
[1036]	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[2718]	17	! Copyright 1997-2018 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[849]	20	! Current revisions:
	21	! ------------------
[2701]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_advec.f90 2718 2018-01-02 08:49:38Z schwenkel $
[2716]	27	! Corrected "Former revisions" section
	28	!
	29	! 2701 2017-12-15 15:40:50Z suehring
	30	! Changes from last commit documented
	31	!
	32	! 2698 2017-12-14 18:46:24Z suehring
[2698]	33	! Particle interpolations at walls in case of SGS velocities revised and not
	34	! required parts are removed. (responsible Philipp Thiele)
[2716]	35	! Bugfix in get_topography_top_index
[2698]	36	!
[2716]	37	! 2696 2017-12-14 17:12:51Z kanani
	38	! Change in file header (GPL part)
	39	!
	40	! 2630 2017-11-20 12:58:20Z schwenkel
[2629]	41	! Removed indices ilog and jlog which are no longer needed since particle box
	42	! locations are identical to scalar boxes and topography.
	43	!
[2630]	44	! 2628 2017-11-20 12:40:38Z raasch
[2610]	45	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
	46	!
	47	! 2606 2017-11-10 10:36:31Z schwenkel
[2606]	48	! Changed particle box locations: center of particle box now coincides
	49	! with scalar grid point of same index.
	50	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
	51	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
	52	! lpm_sort -> lpm_sort_timeloop_done
	53	!
	54	! 2417 2017-09-06 15:22:27Z suehring
[2417]	55	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
	56	! particle loop runs from start_index up to end_index instead from 1 to
	57	! number_of_particles. This way, it is possible to skip unnecessary
	58	! computations for particles that already completed the LES timestep.
	59	!
	60	! 2318 2017-07-20 17:27:44Z suehring
[2318]	61	! Get topography top index via Function call
	62	!
	63	! 2317 2017-07-20 17:27:19Z suehring
[1930]	64	!
[2233]	65	! 2232 2017-05-30 17:47:52Z suehring
	66	! Adjustments to new topography and surface concept
	67	!
[2101]	68	! 2100 2017-01-05 16:40:16Z suehring
	69	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
	70	! at the begin of simulations and/or in non-turbulent regions.
	71	!
[2001]	72	! 2000 2016-08-20 18:09:15Z knoop
	73	! Forced header and separation lines into 80 columns
	74	!
[1937]	75	! 1936 2016-06-13 13:37:44Z suehring
	76	! Formatting adjustments
	77	!
[1930]	78	! 1929 2016-06-09 16:25:25Z suehring
[1929]	79	! Put stochastic equation in an extra subroutine.
	80	! Set flag for stochastic equation to communicate whether a particle is near
	81	! topography. This case, memory and drift term are disabled in the Weil equation.
[1889]	82	!
[1929]	83	! Enable vertical logarithmic interpolation also above topography. This case,
	84	! set a lower limit for the friction velocity, as it can become very small
[1930]	85	! in narrow street canyons, leading to too large particle speeds.
[1823]	86	!
[1889]	87	! 1888 2016-04-21 12:20:49Z suehring
	88	! Bugfix concerning logarithmic interpolation of particle speed
	89	!
[1823]	90	! 1822 2016-04-07 07:49:42Z hoffmann
[1822]	91	! Random velocity fluctuations for particles added. Terminal fall velocity
	92	! for droplets is calculated from a parameterization (which is better than
	93	! the previous, physically correct calculation, which demands a very short
	94	! time step that is not used in the model).
	95	!
	96	! Unused variables deleted.
[1321]	97	!
[1692]	98	! 1691 2015-10-26 16:17:44Z maronga
	99	! Renamed prandtl_layer to constant_flux_layer.
	100	!
[1686]	101	! 1685 2015-10-08 07:32:13Z raasch
	102	! TKE check for negative values (so far, only zero value was checked)
	103	! offset_ocean_nzt_m1 removed
	104	!
[1683]	105	! 1682 2015-10-07 23:56:08Z knoop
	106	! Code annotations made doxygen readable
	107	!
[1584]	108	! 1583 2015-04-15 12:16:27Z suehring
	109	! Bugfix: particle advection within Prandtl-layer in case of Galilei
	110	! transformation.
	111	!
[1370]	112	! 1369 2014-04-24 05:57:38Z raasch
	113	! usage of module interfaces removed
	114	!
[1360]	115	! 1359 2014-04-11 17:15:14Z hoffmann
	116	! New particle structure integrated.
	117	! Kind definition added to all floating point numbers.
	118	!
[1323]	119	! 1322 2014-03-20 16:38:49Z raasch
	120	! REAL constants defined as wp_kind
	121	!
[1321]	122	! 1320 2014-03-20 08:40:49Z raasch
[1320]	123	! ONLY-attribute added to USE-statements,
	124	! kind-parameters added to all INTEGER and REAL declaration statements,
	125	! kinds are defined in new module kinds,
	126	! revision history before 2012 removed,
	127	! comment fields (!:) to be used for variable explanations added to
	128	! all variable declaration statements
[849]	129	!
[1315]	130	! 1314 2014-03-14 18:25:17Z suehring
	131	! Vertical logarithmic interpolation of horizontal particle speed for particles
	132	! between roughness height and first vertical grid level.
	133	!
[1037]	134	! 1036 2012-10-22 13:43:42Z raasch
	135	! code put under GPL (PALM 3.9)
	136	!
[850]	137	! 849 2012-03-15 10:35:09Z raasch
	138	! initial revision (former part of advec_particles)
[849]	139	!
[850]	140	!
[849]	141	! Description:
	142	! ------------
[1682]	143	!> Calculation of new particle positions due to advection using a simple Euler
	144	!> scheme. Particles may feel inertia effects. SGS transport can be included
	145	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
[849]	146	!------------------------------------------------------------------------------!
[1682]	147	SUBROUTINE lpm_advec (ip,jp,kp)
	148
[849]	149
[1320]	150	USE arrays_3d, &
[2232]	151	ONLY: de_dx, de_dy, de_dz, diss, e, km, u, v, w, zu, zw
[849]	152
[1359]	153	USE cpulog
	154
	155	USE pegrid
	156
[1320]	157	USE control_parameters, &
[1691]	158	ONLY: atmos_ocean_sign, cloud_droplets, constant_flux_layer, dt_3d, &
[1822]	159	dt_3d_reached_l, dz, g, kappa, topography, u_gtrans, v_gtrans
[849]	160
[1320]	161	USE grid_variables, &
	162	ONLY: ddx, dx, ddy, dy
	163
	164	USE indices, &
[2698]	165	ONLY: nzb, nzt, wall_flags_0
[1320]	166
	167	USE kinds
	168
	169	USE particle_attributes, &
[1822]	170	ONLY: block_offset, c_0, dt_min_part, grid_particles, &
[1359]	171	iran_part, log_z_z0, number_of_particles, number_of_sublayers, &
[1929]	172	particles, particle_groups, offset_ocean_nzt, sgs_wf_part, &
	173	use_sgs_for_particles, vertical_particle_advection, z0_av_global
[1320]	174
	175	USE statistics, &
	176	ONLY: hom
[849]	177
[2232]	178	USE surface_mod, &
[2698]	179	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
[2232]	180
[1320]	181	IMPLICIT NONE
[849]	182
[2698]	183	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
	184
[1929]	185	INTEGER(iwp) :: agp !< loop variable
	186	INTEGER(iwp) :: gp_outside_of_building(1:8) !< number of grid points used for particle interpolation in case of topography
	187	INTEGER(iwp) :: i !< index variable along x
	188	INTEGER(iwp) :: ip !< index variable along x
	189	INTEGER(iwp) :: j !< index variable along y
	190	INTEGER(iwp) :: jp !< index variable along y
	191	INTEGER(iwp) :: k !< index variable along z
[2232]	192	INTEGER(iwp) :: k_wall !< vertical index of topography top
[1929]	193	INTEGER(iwp) :: kp !< index variable along z
	194	INTEGER(iwp) :: kw !< index variable along z
	195	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
	196	INTEGER(iwp) :: nb !< block number particles are sorted in
	197	INTEGER(iwp) :: num_gp !< number of adjacent grid points inside topography
[2232]	198	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
[849]	199
[1929]	200	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
	201	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
[1359]	202
[1929]	203	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
	204	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
	205	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
	206	REAL(wp) :: d_sum !< dummy argument for horizontal particle interpolation in case of topography
	207	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
	208	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
	209	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
	210	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
	211	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
	212	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
	213	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
	214	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
	215	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
	216	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
[1822]	217	REAL(wp) :: diameter !< diamter of droplet
[1929]	218	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
	219	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
	220	REAL(wp) :: dt_gap !< remaining time until particle time integration reaches LES time
	221	REAL(wp) :: dt_particle_m !< previous particle time step
	222	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
	223	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
	224	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
[1682]	225	REAL(wp) :: exp_arg !<
	226	REAL(wp) :: exp_term !<
[1929]	227	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
	228	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
[1822]	229	REAL(wp) :: lagr_timescale !< Lagrangian timescale
[1929]	230	REAL(wp) :: location(1:30,1:3) !< wall locations
	231	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
[1682]	232	REAL(wp) :: random_gauss !<
[1822]	233	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
	234	REAL(wp) :: rg1 !< Gaussian distributed random number
	235	REAL(wp) :: rg2 !< Gaussian distributed random number
	236	REAL(wp) :: rg3 !< Gaussian distributed random number
	237	REAL(wp) :: sigma !< velocity standard deviation
[1929]	238	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
	239	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
	240	REAL(wp) :: us_int !< friction velocity at particle grid box
[2232]	241	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
[1929]	242	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
	243	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
[2232]	244	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
[1682]	245	REAL(wp) :: vv_int !<
[1929]	246	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
	247	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
[1822]	248	REAL(wp) :: w_s !< terminal velocity of droplets
[1929]	249	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
	250	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
	251	REAL(wp) :: z_p !< surface layer height (0.5 dz)
[849]	252
[1822]	253	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
	254	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
	255	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
	256	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
	257	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
	258	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
	259
[1929]	260	REAL(wp), DIMENSION(1:30) :: d_gp_pl !< dummy argument for particle interpolation scheme in case of topography
	261	REAL(wp), DIMENSION(1:30) :: de_dxi !< horizontal TKE gradient along x at adjacent wall
	262	REAL(wp), DIMENSION(1:30) :: de_dyi !< horizontal TKE gradient along y at adjacent wall
	263	REAL(wp), DIMENSION(1:30) :: de_dzi !< horizontal TKE gradient along z at adjacent wall
	264	REAL(wp), DIMENSION(1:30) :: dissi !< dissipation at adjacent wall
	265	REAL(wp), DIMENSION(1:30) :: ei !< TKE at adjacent wall
[849]	266
[1929]	267	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
[1682]	268	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !<
[1929]	269	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
	270	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
	271	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
	272	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
	273	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
	274	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
	275	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
	276	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
	277	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
	278	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
	279	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
	280	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
	281	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
[1359]	282
[1929]	283	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
[1359]	284
	285	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
	286
[1314]	287	!
	288	!-- Determine height of Prandtl layer and distance between Prandtl-layer
	289	!-- height and horizontal mean roughness height, which are required for
	290	!-- vertical logarithmic interpolation of horizontal particle speeds
	291	!-- (for particles below first vertical grid level).
	292	z_p = zu(nzb+1) - zw(nzb)
[1359]	293	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
[849]	294
[1359]	295	start_index = grid_particles(kp,jp,ip)%start_index
	296	end_index = grid_particles(kp,jp,ip)%end_index
[849]	297
[1359]	298	xv = particles(1:number_of_particles)%x
	299	yv = particles(1:number_of_particles)%y
	300	zv = particles(1:number_of_particles)%z
[849]	301
[1359]	302	DO nb = 0, 7
[2606]	303	!
	304	!-- Interpolate u velocity-component
[1359]	305	i = ip
	306	j = jp + block_offset(nb)%j_off
	307	k = kp + block_offset(nb)%k_off
[2606]	308
[1359]	309	DO n = start_index(nb), end_index(nb)
[1314]	310	!
[1359]	311	!-- Interpolation of the u velocity component onto particle position.
	312	!-- Particles are interpolation bi-linearly in the horizontal and a
	313	!-- linearly in the vertical. An exception is made for particles below
	314	!-- the first vertical grid level in case of a prandtl layer. In this
	315	!-- case the horizontal particle velocity components are determined using
	316	!-- Monin-Obukhov relations (if branch).
	317	!-- First, check if particle is located below first vertical grid level
[2232]	318	!-- above topography (Prandtl-layer height)
	319	!-- Determine vertical index of topography top
[2698]	320	k_wall = get_topography_top_index_ji( jp, ip, 's' )
[1929]	321
[2232]	322	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
[1314]	323	!
[1359]	324	!-- Resolved-scale horizontal particle velocity is zero below z0.
[2232]	325	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1359]	326	u_int(n) = 0.0_wp
	327	ELSE
[1314]	328	!
[1359]	329	!-- Determine the sublayer. Further used as index.
[2232]	330	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	331	* REAL( number_of_sublayers, KIND=wp ) &
[1359]	332	* d_z_p_z0
[1314]	333	!
[1359]	334	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	335	!-- interpolate linearly between precalculated logarithm.
[1929]	336	log_z_z0_int = log_z_z0(INT(height_p)) &
[1359]	337	+ ( height_p - INT(height_p) ) &
	338	* ( log_z_z0(INT(height_p)+1) &
	339	- log_z_z0(INT(height_p)) &
	340	)
[1314]	341	!
[2232]	342	!-- Get friction velocity and momentum flux from new surface data
	343	!-- types.
[2628]	344	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	345	surf_def_h(0)%end_index(jp,ip) ) THEN
	346	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	347	!-- Limit friction velocity. In narrow canyons or holes the
	348	!-- friction velocity can become very small, resulting in a too
	349	!-- large particle speed.
	350	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
	351	usws_int = surf_def_h(0)%usws(surf_start)
[2628]	352	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	353	surf_lsm_h%end_index(jp,ip) ) THEN
	354	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	355	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
	356	usws_int = surf_lsm_h%usws(surf_start)
[2628]	357	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	358	surf_usm_h%end_index(jp,ip) ) THEN
	359	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	360	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
	361	usws_int = surf_usm_h%usws(surf_start)
	362	ENDIF
	363
[1929]	364	!
[1359]	365	!-- Neutral solution is applied for all situations, e.g. also for
	366	!-- unstable and stable situations. Even though this is not exact
	367	!-- this saves a lot of CPU time since several calls of intrinsic
	368	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	369	!-- as sensitivity studies revealed no significant effect of
	370	!-- using the neutral solution also for un/stable situations.
[2232]	371	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	372	* log_z_z0_int - u_gtrans
	373
[1359]	374	ENDIF
	375	!
	376	!-- Particle above the first grid level. Bi-linear interpolation in the
	377	!-- horizontal and linear interpolation in the vertical direction.
[1314]	378	ELSE
	379
[1359]	380	x = xv(n) + ( 0.5_wp - i ) * dx
	381	y = yv(n) - j * dy
	382	aa = x2 + y2
	383	bb = ( dx - x )2 + y2
	384	cc = x2 + ( dy - y )2
	385	dd = ( dx - x )2 + ( dy - y )2
	386	gg = aa + bb + cc + dd
[1314]	387
[1359]	388	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
	389	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
	390	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[1314]	391
[1359]	392	IF ( k == nzt ) THEN
	393	u_int(n) = u_int_l
	394	ELSE
	395	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
	396	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
	397	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
	398	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dz * &
	399	( u_int_u - u_int_l )
	400	ENDIF
[1929]	401
[1314]	402	ENDIF
	403
[1359]	404	ENDDO
[2606]	405	!
	406	!-- Same procedure for interpolation of the v velocity-component
[1359]	407	i = ip + block_offset(nb)%i_off
	408	j = jp
	409	k = kp + block_offset(nb)%k_off
[2606]	410
[1359]	411	DO n = start_index(nb), end_index(nb)
[1685]	412
[2232]	413	!
	414	!-- Determine vertical index of topography top
[2698]	415	k_wall = get_topography_top_index_ji( jp,ip, 's' )
[849]	416
[2232]	417	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
	418	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1314]	419	!
[1359]	420	!-- Resolved-scale horizontal particle velocity is zero below z0.
	421	v_int(n) = 0.0_wp
	422	ELSE
	423	!
[1929]	424	!-- Determine the sublayer. Further used as index. Please note,
	425	!-- logarithmus can not be reused from above, as in in case of
	426	!-- topography particle on u-grid can be above surface-layer height,
	427	!-- whereas it can be below on v-grid.
[2232]	428	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	429	* REAL( number_of_sublayers, KIND=wp ) &
[1929]	430	* d_z_p_z0
	431	!
	432	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	433	!-- interpolate linearly between precalculated logarithm.
	434	log_z_z0_int = log_z_z0(INT(height_p)) &
	435	+ ( height_p - INT(height_p) ) &
	436	* ( log_z_z0(INT(height_p)+1) &
	437	- log_z_z0(INT(height_p)) &
	438	)
	439	!
[2232]	440	!-- Get friction velocity and momentum flux from new surface data
	441	!-- types.
[2628]	442	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	443	surf_def_h(0)%end_index(jp,ip) ) THEN
	444	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	445	!-- Limit friction velocity. In narrow canyons or holes the
	446	!-- friction velocity can become very small, resulting in a too
	447	!-- large particle speed.
	448	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
[2610]	449	vsws_int = surf_def_h(0)%vsws(surf_start)
[2628]	450	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	451	surf_lsm_h%end_index(jp,ip) ) THEN
	452	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	453	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
[2610]	454	vsws_int = surf_lsm_h%vsws(surf_start)
[2628]	455	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	456	surf_usm_h%end_index(jp,ip) ) THEN
	457	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	458	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
[2610]	459	vsws_int = surf_usm_h%vsws(surf_start)
[2232]	460	ENDIF
[1929]	461	!
[1359]	462	!-- Neutral solution is applied for all situations, e.g. also for
	463	!-- unstable and stable situations. Even though this is not exact
	464	!-- this saves a lot of CPU time since several calls of intrinsic
	465	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	466	!-- as sensitivity studies revealed no significant effect of
	467	!-- using the neutral solution also for un/stable situations.
[2232]	468	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	469	* log_z_z0_int - v_gtrans
[1314]	470
[1359]	471	ENDIF
[1929]	472
[1359]	473	ELSE
	474	x = xv(n) - i * dx
	475	y = yv(n) + ( 0.5_wp - j ) * dy
	476	aa = x2 + y2
	477	bb = ( dx - x )2 + y2
	478	cc = x2 + ( dy - y )2
	479	dd = ( dx - x )2 + ( dy - y )2
	480	gg = aa + bb + cc + dd
[1314]	481
[1359]	482	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
	483	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
	484	) / ( 3.0_wp * gg ) - v_gtrans
[1314]	485
[1359]	486	IF ( k == nzt ) THEN
	487	v_int(n) = v_int_l
	488	ELSE
	489	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
	490	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
	491	) / ( 3.0_wp * gg ) - v_gtrans
	492	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dz * &
	493	( v_int_u - v_int_l )
	494	ENDIF
[1929]	495
[1314]	496	ENDIF
	497
[1359]	498	ENDDO
[2606]	499	!
	500	!-- Same procedure for interpolation of the w velocity-component
[1359]	501	i = ip + block_offset(nb)%i_off
	502	j = jp + block_offset(nb)%j_off
[1929]	503	k = kp - 1
[2606]	504
[1359]	505	DO n = start_index(nb), end_index(nb)
[849]	506
[1359]	507	IF ( vertical_particle_advection(particles(n)%group) ) THEN
[849]	508
[1359]	509	x = xv(n) - i * dx
	510	y = yv(n) - j * dy
[849]	511	aa = x2 + y2
	512	bb = ( dx - x )2 + y2
	513	cc = x2 + ( dy - y )2
	514	dd = ( dx - x )2 + ( dy - y )2
	515	gg = aa + bb + cc + dd
	516
[1359]	517	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
	518	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
	519	) / ( 3.0_wp * gg )
[849]	520
[1359]	521	IF ( k == nzt ) THEN
	522	w_int(n) = w_int_l
[849]	523	ELSE
[1359]	524	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
	525	( gg-bb ) * w(k+1,j,i+1) + &
	526	( gg-cc ) * w(k+1,j+1,i) + &
	527	( gg-dd ) * w(k+1,j+1,i+1) &
	528	) / ( 3.0_wp * gg )
	529	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dz * &
	530	( w_int_u - w_int_l )
[849]	531	ENDIF
	532
[1359]	533	ELSE
[849]	534
[1359]	535	w_int(n) = 0.0_wp
[849]	536
[1359]	537	ENDIF
	538
	539	ENDDO
	540
	541	ENDDO
	542
	543	!-- Interpolate and calculate quantities needed for calculating the SGS
	544	!-- velocities
[1822]	545	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[2698]	546
	547	DO nb = 0,7
	548
	549	subbox_at_wall = .FALSE.
	550	!
	551	!-- In case of topography check if subbox is adjacent to a wall
	552	IF ( .NOT. topography == 'flat' ) THEN
	553	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
	554	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
	555	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
	556	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
	557	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
	558	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
	559	THEN
	560	subbox_at_wall = .TRUE.
	561	ENDIF
	562	ENDIF
	563	IF ( subbox_at_wall ) THEN
	564	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
	565	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
	566	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
	567	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
	568	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
	569	!
	570	!-- Set flag for stochastic equation.
	571	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
	572	ELSE
[1359]	573	i = ip + block_offset(nb)%i_off
	574	j = jp + block_offset(nb)%j_off
	575	k = kp + block_offset(nb)%k_off
	576
	577	DO n = start_index(nb), end_index(nb)
[849]	578	!
[1359]	579	!-- Interpolate TKE
	580	x = xv(n) - i * dx
	581	y = yv(n) - j * dy
	582	aa = x2 + y2
	583	bb = ( dx - x )2 + y2
	584	cc = x2 + ( dy - y )2
	585	dd = ( dx - x )2 + ( dy - y )2
	586	gg = aa + bb + cc + dd
[849]	587
[1359]	588	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
	589	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
	590	) / ( 3.0_wp * gg )
	591
	592	IF ( k+1 == nzt+1 ) THEN
	593	e_int(n) = e_int_l
	594	ELSE
	595	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
	596	( gg - bb ) * e(k+1,j,i+1) + &
	597	( gg - cc ) * e(k+1,j+1,i) + &
	598	( gg - dd ) * e(k+1,j+1,i+1) &
	599	) / ( 3.0_wp * gg )
	600	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dz * &
	601	( e_int_u - e_int_l )
	602	ENDIF
[849]	603	!
[1685]	604	!-- Needed to avoid NaN particle velocities (this might not be
	605	!-- required any more)
	606	IF ( e_int(n) <= 0.0_wp ) THEN
[1359]	607	e_int(n) = 1.0E-20_wp
	608	ENDIF
	609	!
	610	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
	611	!-- all position variables from above (TKE))
	612	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
	613	( gg - bb ) * de_dx(k,j,i+1) + &
	614	( gg - cc ) * de_dx(k,j+1,i) + &
	615	( gg - dd ) * de_dx(k,j+1,i+1) &
	616	) / ( 3.0_wp * gg )
[849]	617
	618	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
[1359]	619	de_dx_int(n) = de_dx_int_l
[849]	620	ELSE
[1359]	621	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
	622	( gg - bb ) * de_dx(k+1,j,i+1) + &
	623	( gg - cc ) * de_dx(k+1,j+1,i) + &
	624	( gg - dd ) * de_dx(k+1,j+1,i+1) &
	625	) / ( 3.0_wp * gg )
	626	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dz * &
	627	( de_dx_int_u - de_dx_int_l )
[849]	628	ENDIF
[1359]	629	!
	630	!-- Interpolate the TKE gradient along y
	631	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
	632	( gg - bb ) * de_dy(k,j,i+1) + &
	633	( gg - cc ) * de_dy(k,j+1,i) + &
	634	( gg - dd ) * de_dy(k,j+1,i+1) &
	635	) / ( 3.0_wp * gg )
	636	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	637	de_dy_int(n) = de_dy_int_l
	638	ELSE
	639	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
[2698]	640	( gg - bb ) * de_dy(k+1,j,i+1) + &
	641	( gg - cc ) * de_dy(k+1,j+1,i) + &
	642	( gg - dd ) * de_dy(k+1,j+1,i+1) &
[1359]	643	) / ( 3.0_wp * gg )
[2698]	644	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dz * &
	645	( de_dy_int_u - de_dy_int_l )
[1359]	646	ENDIF
[849]	647
	648	!
[1359]	649	!-- Interpolate the TKE gradient along z
	650	IF ( zv(n) < 0.5_wp * dz ) THEN
	651	de_dz_int(n) = 0.0_wp
	652	ELSE
	653	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
	654	( gg - bb ) * de_dz(k,j,i+1) + &
	655	( gg - cc ) * de_dz(k,j+1,i) + &
	656	( gg - dd ) * de_dz(k,j+1,i+1) &
	657	) / ( 3.0_wp * gg )
[849]	658
[1359]	659	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	660	de_dz_int(n) = de_dz_int_l
	661	ELSE
	662	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
	663	( gg - bb ) * de_dz(k+1,j,i+1) + &
	664	( gg - cc ) * de_dz(k+1,j+1,i) + &
	665	( gg - dd ) * de_dz(k+1,j+1,i+1) &
	666	) / ( 3.0_wp * gg )
	667	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dz * &
	668	( de_dz_int_u - de_dz_int_l )
	669	ENDIF
	670	ENDIF
[849]	671
[1359]	672	!
	673	!-- Interpolate the dissipation of TKE
	674	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
	675	( gg - bb ) * diss(k,j,i+1) + &
	676	( gg - cc ) * diss(k,j+1,i) + &
	677	( gg - dd ) * diss(k,j+1,i+1) &
[2698]	678	) / ( 3.0_wp * gg )
[849]	679
[1359]	680	IF ( k == nzt ) THEN
	681	diss_int(n) = diss_int_l
	682	ELSE
	683	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
	684	( gg - bb ) * diss(k+1,j,i+1) + &
	685	( gg - cc ) * diss(k+1,j+1,i) + &
	686	( gg - dd ) * diss(k+1,j+1,i+1) &
	687	) / ( 3.0_wp * gg )
	688	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dz * &
[2698]	689	( diss_int_u - diss_int_l )
[1359]	690	ENDIF
	691
[1929]	692	!
	693	!-- Set flag for stochastic equation.
	694	term_1_2(n) = 1.0_wp
[1359]	695	ENDDO
[2698]	696	ENDIF
	697	ENDDO
[1359]	698
	699	DO nb = 0,7
	700	i = ip + block_offset(nb)%i_off
	701	j = jp + block_offset(nb)%j_off
	702	k = kp + block_offset(nb)%k_off
[849]	703
[1359]	704	DO n = start_index(nb), end_index(nb)
[849]	705	!
[1359]	706	!-- Vertical interpolation of the horizontally averaged SGS TKE and
	707	!-- resolved-scale velocity variances and use the interpolated values
	708	!-- to calculate the coefficient fs, which is a measure of the ratio
	709	!-- of the subgrid-scale turbulent kinetic energy to the total amount
	710	!-- of turbulent kinetic energy.
	711	IF ( k == 0 ) THEN
	712	e_mean_int = hom(0,1,8,0)
	713	ELSE
	714	e_mean_int = hom(k,1,8,0) + &
	715	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
	716	( zu(k+1) - zu(k) ) * &
	717	( zv(n) - zu(k) )
	718	ENDIF
[849]	719
[1685]	720	kw = kp - 1
[849]	721
[1359]	722	IF ( k == 0 ) THEN
	723	aa = hom(k+1,1,30,0) * ( zv(n) / &
	724	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	725	bb = hom(k+1,1,31,0) * ( zv(n) / &
	726	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	727	cc = hom(kw+1,1,32,0) * ( zv(n) / &
	728	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
	729	ELSE
	730	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
	731	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	732	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
	733	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	734	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
	735	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
	736	ENDIF
[849]	737
[1359]	738	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
	739	!
	740	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
	741	!-- an educated guess for the given case.
	742	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
	743	fs_int(n) = 1.0_wp
	744	ELSE
	745	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
	746	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
	747	ENDIF
[849]	748
[1359]	749	ENDDO
	750	ENDDO
[849]	751
[2417]	752	DO nb = 0, 7
	753	DO n = start_index(nb), end_index(nb)
	754	rg(n,1) = random_gauss( iran_part, 5.0_wp )
	755	rg(n,2) = random_gauss( iran_part, 5.0_wp )
	756	rg(n,3) = random_gauss( iran_part, 5.0_wp )
	757	ENDDO
	758	ENDDO
[1359]	759
[2417]	760	DO nb = 0, 7
	761	DO n = start_index(nb), end_index(nb)
[1359]	762
[849]	763	!
[2417]	764	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
	765	lagr_timescale = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
	766	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
[849]	767
	768	!
[2417]	769	!-- Calculate the next particle timestep. dt_gap is the time needed to
	770	!-- complete the current LES timestep.
	771	dt_gap = dt_3d - particles(n)%dt_sum
	772	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale, dt_gap )
[849]	773
	774	!
[2417]	775	!-- The particle timestep should not be too small in order to prevent
	776	!-- the number of particle timesteps of getting too large
	777	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap ) THEN
	778	dt_particle(n) = dt_min_part
	779	ENDIF
[849]	780
	781	!
[2417]	782	!-- Calculate the SGS velocity components
	783	IF ( particles(n)%age == 0.0_wp ) THEN
[849]	784	!
[2417]	785	!-- For new particles the SGS components are derived from the SGS
	786	!-- TKE. Limit the Gaussian random number to the interval
	787	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
	788	!-- from becoming unrealistically large.
	789	particles(n)%rvar1 = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	790	+ 1E-20_wp ) * &
	791	( rg(n,1) - 1.0_wp )
	792	particles(n)%rvar2 = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	793	+ 1E-20_wp ) * &
	794	( rg(n,2) - 1.0_wp )
	795	particles(n)%rvar3 = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	796	+ 1E-20_wp ) * &
	797	( rg(n,3) - 1.0_wp )
[849]	798
[2417]	799	ELSE
[849]	800	!
[2417]	801	!-- Restriction of the size of the new timestep: compared to the
	802	!-- previous timestep the increase must not exceed 200%. First,
	803	!-- check if age > age_m, in order to prevent that particles get zero
	804	!-- timestep.
	805	dt_particle_m = MERGE( dt_particle(n), &
	806	particles(n)%age - particles(n)%age_m, &
	807	particles(n)%age - particles(n)%age_m < &
	808	1E-8_wp )
	809	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
	810	dt_particle(n) = 2.0_wp * dt_particle_m
	811	ENDIF
[849]	812
	813	!
[2417]	814	!-- For old particles the SGS components are correlated with the
	815	!-- values from the previous timestep. Random numbers have also to
	816	!-- be limited (see above).
	817	!-- As negative values for the subgrid TKE are not allowed, the
	818	!-- change of the subgrid TKE with time cannot be smaller than
	819	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
	820	!-- value for the change of TKE
	821	de_dt_min = - e_int(n) / dt_particle(n)
[849]	822
[2417]	823	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
[849]	824
[2417]	825	IF ( de_dt < de_dt_min ) THEN
	826	de_dt = de_dt_min
	827	ENDIF
[849]	828
[2417]	829	CALL weil_stochastic_eq(particles(n)%rvar1, fs_int(n), e_int(n),&
	830	de_dx_int(n), de_dt, diss_int(n), &
	831	dt_particle(n), rg(n,1), term_1_2(n) )
[849]	832
[2417]	833	CALL weil_stochastic_eq(particles(n)%rvar2, fs_int(n), e_int(n),&
	834	de_dy_int(n), de_dt, diss_int(n), &
	835	dt_particle(n), rg(n,2), term_1_2(n) )
[849]	836
[2417]	837	CALL weil_stochastic_eq(particles(n)%rvar3, fs_int(n), e_int(n),&
	838	de_dz_int(n), de_dt, diss_int(n), &
	839	dt_particle(n), rg(n,3), term_1_2(n) )
[849]	840
[2417]	841	ENDIF
[849]	842
[2417]	843	u_int(n) = u_int(n) + particles(n)%rvar1
	844	v_int(n) = v_int(n) + particles(n)%rvar2
	845	w_int(n) = w_int(n) + particles(n)%rvar3
[849]	846	!
[2417]	847	!-- Store the SGS TKE of the current timelevel which is needed for
	848	!-- for calculating the SGS particle velocities at the next timestep
	849	particles(n)%e_m = e_int(n)
	850	ENDDO
[1359]	851	ENDDO
[849]	852
[1359]	853	ELSE
[849]	854	!
[1359]	855	!-- If no SGS velocities are used, only the particle timestep has to
	856	!-- be set
	857	dt_particle = dt_3d
[849]	858
[1359]	859	ENDIF
[849]	860
[1359]	861	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
[849]	862
[1359]	863	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
[2417]	864	DO nb = 0, 7
	865	DO n = start_index(nb), end_index(nb)
[1359]	866
[849]	867	!
[2417]	868	!-- Particle advection
	869	IF ( dens_ratio(n) == 0.0_wp ) THEN
[849]	870	!
[2417]	871	!-- Pure passive transport (without particle inertia)
	872	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
	873	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
	874	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
[849]	875
[2417]	876	particles(n)%speed_x = u_int(n)
	877	particles(n)%speed_y = v_int(n)
	878	particles(n)%speed_z = w_int(n)
[849]	879
[2417]	880	ELSE
[849]	881	!
[2417]	882	!-- Transport of particles with inertia
	883	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
	884	dt_particle(n)
	885	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
	886	dt_particle(n)
	887	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
	888	dt_particle(n)
[849]	889
	890	!
[2417]	891	!-- Update of the particle velocity
	892	IF ( cloud_droplets ) THEN
	893	!
	894	!-- Terminal velocity is computed for vertical direction (Rogers et
	895	!-- al., 1993, J. Appl. Meteorol.)
	896	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	897	IF ( diameter <= d0_rog ) THEN
	898	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	899	ELSE
	900	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	901	ENDIF
	902
	903	!
	904	!-- If selected, add random velocities following Soelch and Kaercher
	905	!-- (2010, Q. J. R. Meteorol. Soc.)
	906	IF ( use_sgs_for_particles ) THEN
	907	lagr_timescale = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	908	RL = EXP( -1.0_wp * dt_3d / lagr_timescale )
	909	sigma = SQRT( e(kp,jp,ip) )
	910
	911	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	912	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	913	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	914
	915	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	916	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	917	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	918	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	919	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	920	SQRT( 1.0_wp - RL*2 ) sigma * rg3
	921
	922	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	923	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	924	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
	925	ELSE
	926	particles(n)%speed_x = u_int(n)
	927	particles(n)%speed_y = v_int(n)
	928	particles(n)%speed_z = w_int(n) - w_s
	929	ENDIF
	930
	931	ELSE
	932
	933	IF ( use_sgs_for_particles ) THEN
	934	exp_arg = particle_groups(particles(n)%group)%exp_arg
	935	exp_term = EXP( -exp_arg * dt_particle(n) )
	936	ELSE
	937	exp_arg = particle_groups(particles(n)%group)%exp_arg
	938	exp_term = particle_groups(particles(n)%group)%exp_term
	939	ENDIF
	940	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
	941	u_int(n) * ( 1.0_wp - exp_term )
	942	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
	943	v_int(n) * ( 1.0_wp - exp_term )
	944	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	945	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
	946	g / exp_arg ) * ( 1.0_wp - exp_term )
	947	ENDIF
	948
	949	ENDIF
	950	ENDDO
	951	ENDDO
	952
	953	ELSE
	954
	955	DO nb = 0, 7
	956	DO n = start_index(nb), end_index(nb)
	957	!
	958	!-- Transport of particles with inertia
	959	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
	960	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
	961	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
	962	!
[1359]	963	!-- Update of the particle velocity
	964	IF ( cloud_droplets ) THEN
[1822]	965	!
[2417]	966	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
	967	!-- 1993, J. Appl. Meteorol.)
[1822]	968	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	969	IF ( diameter <= d0_rog ) THEN
	970	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	971	ELSE
	972	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	973	ENDIF
[1359]	974
[1822]	975	!
	976	!-- If selected, add random velocities following Soelch and Kaercher
	977	!-- (2010, Q. J. R. Meteorol. Soc.)
	978	IF ( use_sgs_for_particles ) THEN
[2417]	979	lagr_timescale = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
	980	RL = EXP( -1.0_wp * dt_3d / lagr_timescale )
	981	sigma = SQRT( e(kp,jp,ip) )
[1822]	982
[2417]	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
[1822]	986
[2417]	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
[1822]	993
[2417]	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
[1822]	997	ELSE
[2417]	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
[1822]	1001	ENDIF
	1002
[1359]	1003	ELSE
[1822]	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
[2417]	1012	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
[1822]	1013	u_int(n) * ( 1.0_wp - exp_term )
[2417]	1014	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
[1822]	1015	v_int(n) * ( 1.0_wp - exp_term )
[2417]	1016	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1017	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
	1018	exp_arg ) * ( 1.0_wp - exp_term )
[1359]	1019	ENDIF
[2417]	1020	ENDDO
[1359]	1021	ENDDO
	1022
[2417]	1023	ENDIF
[1359]	1024
	1025	!
[2417]	1026	!-- Store the old age of the particle ( needed to prevent that a
	1027	!-- particle crosses several PEs during one timestep, and for the
	1028	!-- evaluation of the subgrid particle velocity fluctuations )
	1029	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
	1030
	1031	DO nb = 0, 7
	1032	DO n = start_index(nb), end_index(nb)
[1822]	1033	!
[2417]	1034	!-- Increment the particle age and the total time that the particle
	1035	!-- has advanced within the particle timestep procedure
	1036	particles(n)%age = particles(n)%age + dt_particle(n)
	1037	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
[1359]	1038
[1822]	1039	!
[2417]	1040	!-- Check whether there is still a particle that has not yet completed
	1041	!-- the total LES timestep
	1042	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
	1043	dt_3d_reached_l = .FALSE.
[849]	1044	ENDIF
[1822]	1045
[1359]	1046	ENDDO
[849]	1047	ENDDO
	1048
[1359]	1049	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
[849]	1050
[1929]	1051
[849]	1052	END SUBROUTINE lpm_advec
[1929]	1053
	1054	! Description:
	1055	! ------------
	1056	!> Calculation of subgrid-scale particle speed using the stochastic model
	1057	!> of Weil et al. (2004, JAS, 61, 2877-2887).
	1058	!------------------------------------------------------------------------------!
	1059	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
	1060	dt_n, rg_n, fac )
	1061
	1062	USE kinds
	1063
	1064	USE particle_attributes, &
	1065	ONLY: c_0, sgs_wf_part
	1066
	1067	IMPLICIT NONE
	1068
	1069	REAL(wp) :: a1 !< dummy argument
	1070	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
	1071	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
	1072	REAL(wp) :: diss_n !< dissipation at particle position
	1073	REAL(wp) :: dt_n !< particle timestep
	1074	REAL(wp) :: e_n !< TKE at particle position
	1075	REAL(wp) :: fac !< flag to identify adjacent topography
	1076	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
	1077	REAL(wp) :: sgs_w !< constant (1/3)
	1078	REAL(wp) :: rg_n !< random number
	1079	REAL(wp) :: term1 !< memory term
	1080	REAL(wp) :: term2 !< drift correction term
	1081	REAL(wp) :: term3 !< random term
	1082	REAL(wp) :: v_sgs !< subgrid-scale velocity component
	1083
[2100]	1084	!-- At first, limit TKE to a small non-zero number, in order to prevent
	1085	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
	1086	!-- (could occur at the simulation begin).
	1087	e_n = MAX( e_n, 1E-20_wp )
[1929]	1088	!
	1089	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
	1090	!-- multiplied by a flag to switch of both terms near topography.
	1091	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
	1092	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
	1093	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
	1094	!-- disabled if one of the adjacent grid points belongs to topography.
	1095	!-- Moreover, in this case, the previous subgrid-scale component is also set
	1096	!-- to zero.
	1097
	1098	a1 = fs_n * c_0 * diss_n
	1099	!
	1100	!-- Memory term
	1101	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
	1102	* fac
	1103	!
	1104	!-- Drift correction term
	1105	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
	1106	* fac
	1107	!
	1108	!-- Random term
	1109	term3 = SQRT( MAX( a1, 1E-20 ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
	1110	!
	1111	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
	1112	!-- subgrid-scale velocity component is set to zero, in order to prevent a
	1113	!-- velocity build-up.
	1114	!-- This case, set also previous subgrid-scale component to zero.
	1115	v_sgs = v_sgs * fac + term1 + term2 + term3
	1116
	1117	END SUBROUTINE weil_stochastic_eq

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