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source: palm/trunk/SOURCE/lpm_advec.f90 @ 3768

Last change on this file since 3768 was 3655, checked in by knoop, 5 years ago
Bugfix: made "unit" and "found" intend INOUT in module interface subroutines + automatic copyright update
Property svn:keywords set to `Id`
File size: 55.5 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	!
[3655]	17	! Copyright 1997-2019 Leibniz Universitaet Hannover
[2000]	18	!------------------------------------------------------------------------------!
[1036]	19	!
[849]	20	! Current revisions:
	21	! ------------------
[2701]	22	!
	23	!
	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_advec.f90 3655 2019-01-07 16:51:22Z raasch $
[3562]	27	! variables documented
	28	!
	29	! 3274 2018-09-24 15:42:55Z knoop
[3274]	30	! Modularization of all bulk cloud physics code components
	31	!
	32	! 3241 2018-09-12 15:02:00Z raasch
[3241]	33	! unused variables removed
	34	!
	35	! 3207 2018-08-27 12:55:33Z schwenkel
[3207]	36	! Minor bugfix for sgs-velocities in case of cloud droplets
	37	!
	38	! 3189 2018-08-06 13:18:55Z raasch
[3189]	39	! Bugfix: Index of the array dzw has to be k+1 during the interpolation.
	40	! Otherwise k=0 causes an abortion because dzw is allocated from 1 to nzt+1
	41	!
	42	! 3065 2018-06-12 07:03:02Z Giersch
[3065]	43	! dz values were replaced by dzw or dz(1) to allow for right vertical stretching
	44	!
	45	! 2969 2018-04-13 11:55:09Z thiele
[2969]	46	! Bugfix in Interpolation indices.
	47	!
	48	! 2886 2018-03-14 11:51:53Z thiele
[2886]	49	! Bugfix in passive particle SGS Model:
	50	! Sometimes the added SGS velocities would lead to a violation of the CFL
	51	! criterion for single particles. For this a check was added after the
	52	! calculation of SGS velocities.
	53	!
	54	! 2718 2018-01-02 08:49:38Z maronga
[2716]	55	! Corrected "Former revisions" section
	56	!
	57	! 2701 2017-12-15 15:40:50Z suehring
	58	! Changes from last commit documented
	59	!
	60	! 2698 2017-12-14 18:46:24Z suehring
[2698]	61	! Particle interpolations at walls in case of SGS velocities revised and not
	62	! required parts are removed. (responsible Philipp Thiele)
[2716]	63	! Bugfix in get_topography_top_index
[2698]	64	!
[2716]	65	! 2696 2017-12-14 17:12:51Z kanani
	66	! Change in file header (GPL part)
	67	!
	68	! 2630 2017-11-20 12:58:20Z schwenkel
[2629]	69	! Removed indices ilog and jlog which are no longer needed since particle box
	70	! locations are identical to scalar boxes and topography.
	71	!
[2630]	72	! 2628 2017-11-20 12:40:38Z raasch
[2610]	73	! bugfix in logarithmic interpolation of v-component (usws was used by mistake)
	74	!
	75	! 2606 2017-11-10 10:36:31Z schwenkel
[2606]	76	! Changed particle box locations: center of particle box now coincides
	77	! with scalar grid point of same index.
	78	! Renamed module and subroutines: lpm_pack_arrays_mod -> lpm_pack_and_sort_mod
	79	! lpm_pack_all_arrays -> lpm_sort_in_subboxes, lpm_pack_arrays -> lpm_pack
	80	! lpm_sort -> lpm_sort_timeloop_done
	81	!
	82	! 2417 2017-09-06 15:22:27Z suehring
[2417]	83	! Particle loops adapted for sub-box structure, i.e. for each sub-box the
	84	! particle loop runs from start_index up to end_index instead from 1 to
	85	! number_of_particles. This way, it is possible to skip unnecessary
	86	! computations for particles that already completed the LES timestep.
	87	!
	88	! 2318 2017-07-20 17:27:44Z suehring
[2318]	89	! Get topography top index via Function call
	90	!
	91	! 2317 2017-07-20 17:27:19Z suehring
[1930]	92	!
[2233]	93	! 2232 2017-05-30 17:47:52Z suehring
	94	! Adjustments to new topography and surface concept
	95	!
[2101]	96	! 2100 2017-01-05 16:40:16Z suehring
	97	! Prevent extremely large SGS-velocities in regions where TKE is zero, e.g.
	98	! at the begin of simulations and/or in non-turbulent regions.
	99	!
[2001]	100	! 2000 2016-08-20 18:09:15Z knoop
	101	! Forced header and separation lines into 80 columns
	102	!
[1937]	103	! 1936 2016-06-13 13:37:44Z suehring
	104	! Formatting adjustments
	105	!
[1930]	106	! 1929 2016-06-09 16:25:25Z suehring
[1929]	107	! Put stochastic equation in an extra subroutine.
	108	! Set flag for stochastic equation to communicate whether a particle is near
	109	! topography. This case, memory and drift term are disabled in the Weil equation.
[1889]	110	!
[1929]	111	! Enable vertical logarithmic interpolation also above topography. This case,
	112	! set a lower limit for the friction velocity, as it can become very small
[1930]	113	! in narrow street canyons, leading to too large particle speeds.
[1823]	114	!
[1889]	115	! 1888 2016-04-21 12:20:49Z suehring
	116	! Bugfix concerning logarithmic interpolation of particle speed
	117	!
[1823]	118	! 1822 2016-04-07 07:49:42Z hoffmann
[1822]	119	! Random velocity fluctuations for particles added. Terminal fall velocity
	120	! for droplets is calculated from a parameterization (which is better than
	121	! the previous, physically correct calculation, which demands a very short
	122	! time step that is not used in the model).
	123	!
	124	! Unused variables deleted.
[1321]	125	!
[1692]	126	! 1691 2015-10-26 16:17:44Z maronga
	127	! Renamed prandtl_layer to constant_flux_layer.
	128	!
[1686]	129	! 1685 2015-10-08 07:32:13Z raasch
	130	! TKE check for negative values (so far, only zero value was checked)
	131	! offset_ocean_nzt_m1 removed
	132	!
[1683]	133	! 1682 2015-10-07 23:56:08Z knoop
	134	! Code annotations made doxygen readable
	135	!
[1584]	136	! 1583 2015-04-15 12:16:27Z suehring
	137	! Bugfix: particle advection within Prandtl-layer in case of Galilei
	138	! transformation.
	139	!
[1370]	140	! 1369 2014-04-24 05:57:38Z raasch
	141	! usage of module interfaces removed
	142	!
[1360]	143	! 1359 2014-04-11 17:15:14Z hoffmann
	144	! New particle structure integrated.
	145	! Kind definition added to all floating point numbers.
	146	!
[1323]	147	! 1322 2014-03-20 16:38:49Z raasch
	148	! REAL constants defined as wp_kind
	149	!
[1321]	150	! 1320 2014-03-20 08:40:49Z raasch
[1320]	151	! ONLY-attribute added to USE-statements,
	152	! kind-parameters added to all INTEGER and REAL declaration statements,
	153	! kinds are defined in new module kinds,
	154	! revision history before 2012 removed,
	155	! comment fields (!:) to be used for variable explanations added to
	156	! all variable declaration statements
[849]	157	!
[1315]	158	! 1314 2014-03-14 18:25:17Z suehring
	159	! Vertical logarithmic interpolation of horizontal particle speed for particles
	160	! between roughness height and first vertical grid level.
	161	!
[1037]	162	! 1036 2012-10-22 13:43:42Z raasch
	163	! code put under GPL (PALM 3.9)
	164	!
[850]	165	! 849 2012-03-15 10:35:09Z raasch
	166	! initial revision (former part of advec_particles)
[849]	167	!
[850]	168	!
[849]	169	! Description:
	170	! ------------
[1682]	171	!> Calculation of new particle positions due to advection using a simple Euler
	172	!> scheme. Particles may feel inertia effects. SGS transport can be included
	173	!> using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887).
[849]	174	!------------------------------------------------------------------------------!
[1682]	175	SUBROUTINE lpm_advec (ip,jp,kp)
	176
[849]	177
[1320]	178	USE arrays_3d, &
[3065]	179	ONLY: de_dx, de_dy, de_dz, diss, dzw, e, km, u, v, w, zu, zw
[849]	180
[3274]	181	USE basic_constants_and_equations_mod, &
	182	ONLY: g, kappa
	183
[1359]	184	USE cpulog
	185
	186	USE pegrid
	187
[1320]	188	USE control_parameters, &
[3241]	189	ONLY: cloud_droplets, constant_flux_layer, dt_3d, dt_3d_reached_l, &
[3274]	190	dz, topography, u_gtrans, v_gtrans
[849]	191
[1320]	192	USE grid_variables, &
[3241]	193	ONLY: dx, dy
[1320]	194
	195	USE indices, &
[2698]	196	ONLY: nzb, nzt, wall_flags_0
[1320]	197
	198	USE kinds
	199
	200	USE particle_attributes, &
[3241]	201	ONLY: block_offset, c_0, dt_min_part, grid_particles, iran_part, &
	202	log_z_z0, number_of_particles, number_of_sublayers, &
	203	particles, particle_groups, sgs_wf_part, &
[1929]	204	use_sgs_for_particles, vertical_particle_advection, z0_av_global
[1320]	205
	206	USE statistics, &
	207	ONLY: hom
[849]	208
[2232]	209	USE surface_mod, &
[2698]	210	ONLY: get_topography_top_index_ji, surf_def_h, surf_lsm_h, surf_usm_h
[2232]	211
[1320]	212	IMPLICIT NONE
[849]	213
[2698]	214	LOGICAL :: subbox_at_wall !< flag to see if the current subgridbox is adjacent to a wall
	215
[1929]	216	INTEGER(iwp) :: i !< index variable along x
	217	INTEGER(iwp) :: ip !< index variable along x
	218	INTEGER(iwp) :: j !< index variable along y
	219	INTEGER(iwp) :: jp !< index variable along y
	220	INTEGER(iwp) :: k !< index variable along z
[2232]	221	INTEGER(iwp) :: k_wall !< vertical index of topography top
[1929]	222	INTEGER(iwp) :: kp !< index variable along z
	223	INTEGER(iwp) :: kw !< index variable along z
	224	INTEGER(iwp) :: n !< loop variable over all particles in a grid box
	225	INTEGER(iwp) :: nb !< block number particles are sorted in
[2232]	226	INTEGER(iwp) :: surf_start !< Index on surface data-type for current grid box
[849]	227
[1929]	228	INTEGER(iwp), DIMENSION(0:7) :: start_index !< start particle index for current block
	229	INTEGER(iwp), DIMENSION(0:7) :: end_index !< start particle index for current block
[1359]	230
[1929]	231	REAL(wp) :: aa !< dummy argument for horizontal particle interpolation
	232	REAL(wp) :: bb !< dummy argument for horizontal particle interpolation
	233	REAL(wp) :: cc !< dummy argument for horizontal particle interpolation
	234	REAL(wp) :: d_z_p_z0 !< inverse of interpolation length for logarithmic interpolation
	235	REAL(wp) :: dd !< dummy argument for horizontal particle interpolation
	236	REAL(wp) :: de_dx_int_l !< x/y-interpolated TKE gradient (x) at particle position at lower vertical level
	237	REAL(wp) :: de_dx_int_u !< x/y-interpolated TKE gradient (x) at particle position at upper vertical level
	238	REAL(wp) :: de_dy_int_l !< x/y-interpolated TKE gradient (y) at particle position at lower vertical level
	239	REAL(wp) :: de_dy_int_u !< x/y-interpolated TKE gradient (y) at particle position at upper vertical level
	240	REAL(wp) :: de_dt !< temporal derivative of TKE experienced by the particle
	241	REAL(wp) :: de_dt_min !< lower level for temporal TKE derivative
	242	REAL(wp) :: de_dz_int_l !< x/y-interpolated TKE gradient (z) at particle position at lower vertical level
	243	REAL(wp) :: de_dz_int_u !< x/y-interpolated TKE gradient (z) at particle position at upper vertical level
[1822]	244	REAL(wp) :: diameter !< diamter of droplet
[1929]	245	REAL(wp) :: diss_int_l !< x/y-interpolated dissipation at particle position at lower vertical level
	246	REAL(wp) :: diss_int_u !< x/y-interpolated dissipation at particle position at upper vertical level
	247	REAL(wp) :: dt_particle_m !< previous particle time step
[3562]	248	REAL(wp) :: dz_temp !< dummy for the vertical grid spacing
[1929]	249	REAL(wp) :: e_int_l !< x/y-interpolated TKE at particle position at lower vertical level
	250	REAL(wp) :: e_int_u !< x/y-interpolated TKE at particle position at upper vertical level
	251	REAL(wp) :: e_mean_int !< horizontal mean TKE at particle height
[3562]	252	REAL(wp) :: exp_arg !< argument in the exponent - particle radius
	253	REAL(wp) :: exp_term !< exponent term
[1929]	254	REAL(wp) :: gg !< dummy argument for horizontal particle interpolation
	255	REAL(wp) :: height_p !< dummy argument for logarithmic interpolation
	256	REAL(wp) :: log_z_z0_int !< logarithmus used for surface_layer interpolation
[3562]	257	REAL(wp) :: random_gauss !< Gaussian-distributed random number used for SGS particle advection
[1822]	258	REAL(wp) :: RL !< Lagrangian autocorrelation coefficient
	259	REAL(wp) :: rg1 !< Gaussian distributed random number
	260	REAL(wp) :: rg2 !< Gaussian distributed random number
	261	REAL(wp) :: rg3 !< Gaussian distributed random number
	262	REAL(wp) :: sigma !< velocity standard deviation
[1929]	263	REAL(wp) :: u_int_l !< x/y-interpolated u-component at particle position at lower vertical level
	264	REAL(wp) :: u_int_u !< x/y-interpolated u-component at particle position at upper vertical level
	265	REAL(wp) :: us_int !< friction velocity at particle grid box
[2232]	266	REAL(wp) :: usws_int !< surface momentum flux (u component) at particle grid box
[1929]	267	REAL(wp) :: v_int_l !< x/y-interpolated v-component at particle position at lower vertical level
	268	REAL(wp) :: v_int_u !< x/y-interpolated v-component at particle position at upper vertical level
[2232]	269	REAL(wp) :: vsws_int !< surface momentum flux (u component) at particle grid box
[3562]	270	REAL(wp) :: vv_int !< dummy to compute interpolated mean SGS TKE, used to scale SGS advection
[1929]	271	REAL(wp) :: w_int_l !< x/y-interpolated w-component at particle position at lower vertical level
	272	REAL(wp) :: w_int_u !< x/y-interpolated w-component at particle position at upper vertical level
[1822]	273	REAL(wp) :: w_s !< terminal velocity of droplets
[1929]	274	REAL(wp) :: x !< dummy argument for horizontal particle interpolation
	275	REAL(wp) :: y !< dummy argument for horizontal particle interpolation
	276	REAL(wp) :: z_p !< surface layer height (0.5 dz)
[849]	277
[1822]	278	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter for fall velocity
	279	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter for fall velocity
	280	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter for fall velocity
	281	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter for fall velocity
	282	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter for fall velocity
	283	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< separation diameter
	284
[2886]	285	REAL(wp), DIMENSION(number_of_particles) :: term_1_2 !< flag to communicate whether a particle is near topography or not
[3562]	286	REAL(wp), DIMENSION(number_of_particles) :: dens_ratio !< ratio between the density of the fluid and the density of the particles
[2886]	287	REAL(wp), DIMENSION(number_of_particles) :: de_dx_int !< horizontal TKE gradient along x at particle position
	288	REAL(wp), DIMENSION(number_of_particles) :: de_dy_int !< horizontal TKE gradient along y at particle position
	289	REAL(wp), DIMENSION(number_of_particles) :: de_dz_int !< horizontal TKE gradient along z at particle position
	290	REAL(wp), DIMENSION(number_of_particles) :: diss_int !< dissipation at particle position
	291	REAL(wp), DIMENSION(number_of_particles) :: dt_gap !< remaining time until particle time integration reaches LES time
	292	REAL(wp), DIMENSION(number_of_particles) :: dt_particle !< particle time step
	293	REAL(wp), DIMENSION(number_of_particles) :: e_int !< TKE at particle position
	294	REAL(wp), DIMENSION(number_of_particles) :: fs_int !< weighting factor for subgrid-scale particle speed
	295	REAL(wp), DIMENSION(number_of_particles) :: lagr_timescale !< Lagrangian timescale
[3562]	296	REAL(wp), DIMENSION(number_of_particles) :: rvar1_temp !< SGS particle velocity - u-component
	297	REAL(wp), DIMENSION(number_of_particles) :: rvar2_temp !< SGS particle velocity - v-component
	298	REAL(wp), DIMENSION(number_of_particles) :: rvar3_temp !< SGS particle velocity - w-component
[2886]	299	REAL(wp), DIMENSION(number_of_particles) :: u_int !< u-component of particle speed
	300	REAL(wp), DIMENSION(number_of_particles) :: v_int !< v-component of particle speed
	301	REAL(wp), DIMENSION(number_of_particles) :: w_int !< w-component of particle speed
	302	REAL(wp), DIMENSION(number_of_particles) :: xv !< x-position
	303	REAL(wp), DIMENSION(number_of_particles) :: yv !< y-position
	304	REAL(wp), DIMENSION(number_of_particles) :: zv !< z-position
[1359]	305
[1929]	306	REAL(wp), DIMENSION(number_of_particles, 3) :: rg !< vector of Gaussian distributed random numbers
[1359]	307
	308	CALL cpu_log( log_point_s(44), 'lpm_advec', 'continue' )
	309
[1314]	310	!
	311	!-- Determine height of Prandtl layer and distance between Prandtl-layer
	312	!-- height and horizontal mean roughness height, which are required for
	313	!-- vertical logarithmic interpolation of horizontal particle speeds
	314	!-- (for particles below first vertical grid level).
	315	z_p = zu(nzb+1) - zw(nzb)
[1359]	316	d_z_p_z0 = 1.0_wp / ( z_p - z0_av_global )
[849]	317
[1359]	318	start_index = grid_particles(kp,jp,ip)%start_index
	319	end_index = grid_particles(kp,jp,ip)%end_index
[849]	320
[1359]	321	xv = particles(1:number_of_particles)%x
	322	yv = particles(1:number_of_particles)%y
	323	zv = particles(1:number_of_particles)%z
[849]	324
[1359]	325	DO nb = 0, 7
[2606]	326	!
	327	!-- Interpolate u velocity-component
[1359]	328	i = ip
	329	j = jp + block_offset(nb)%j_off
	330	k = kp + block_offset(nb)%k_off
[2606]	331
[1359]	332	DO n = start_index(nb), end_index(nb)
[1314]	333	!
[1359]	334	!-- Interpolation of the u velocity component onto particle position.
	335	!-- Particles are interpolation bi-linearly in the horizontal and a
	336	!-- linearly in the vertical. An exception is made for particles below
	337	!-- the first vertical grid level in case of a prandtl layer. In this
	338	!-- case the horizontal particle velocity components are determined using
	339	!-- Monin-Obukhov relations (if branch).
	340	!-- First, check if particle is located below first vertical grid level
[2232]	341	!-- above topography (Prandtl-layer height)
	342	!-- Determine vertical index of topography top
[2698]	343	k_wall = get_topography_top_index_ji( jp, ip, 's' )
[1929]	344
[2232]	345	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
[1314]	346	!
[1359]	347	!-- Resolved-scale horizontal particle velocity is zero below z0.
[2232]	348	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1359]	349	u_int(n) = 0.0_wp
	350	ELSE
[1314]	351	!
[1359]	352	!-- Determine the sublayer. Further used as index.
[2232]	353	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	354	* REAL( number_of_sublayers, KIND=wp ) &
[1359]	355	* d_z_p_z0
[1314]	356	!
[1359]	357	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	358	!-- interpolate linearly between precalculated logarithm.
[1929]	359	log_z_z0_int = log_z_z0(INT(height_p)) &
[1359]	360	+ ( height_p - INT(height_p) ) &
	361	* ( log_z_z0(INT(height_p)+1) &
	362	- log_z_z0(INT(height_p)) &
	363	)
[1314]	364	!
[2232]	365	!-- Get friction velocity and momentum flux from new surface data
	366	!-- types.
[2628]	367	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	368	surf_def_h(0)%end_index(jp,ip) ) THEN
	369	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	370	!-- Limit friction velocity. In narrow canyons or holes the
	371	!-- friction velocity can become very small, resulting in a too
	372	!-- large particle speed.
	373	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
	374	usws_int = surf_def_h(0)%usws(surf_start)
[2628]	375	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	376	surf_lsm_h%end_index(jp,ip) ) THEN
	377	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	378	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
	379	usws_int = surf_lsm_h%usws(surf_start)
[2628]	380	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	381	surf_usm_h%end_index(jp,ip) ) THEN
	382	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	383	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
	384	usws_int = surf_usm_h%usws(surf_start)
	385	ENDIF
	386
[1929]	387	!
[1359]	388	!-- Neutral solution is applied for all situations, e.g. also for
	389	!-- unstable and stable situations. Even though this is not exact
	390	!-- this saves a lot of CPU time since several calls of intrinsic
	391	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	392	!-- as sensitivity studies revealed no significant effect of
	393	!-- using the neutral solution also for un/stable situations.
[2232]	394	u_int(n) = -usws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	395	* log_z_z0_int - u_gtrans
	396
[1359]	397	ENDIF
	398	!
	399	!-- Particle above the first grid level. Bi-linear interpolation in the
	400	!-- horizontal and linear interpolation in the vertical direction.
[1314]	401	ELSE
	402
[2969]	403	x = xv(n) - i * dx
	404	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	405	aa = x2 + y2
	406	bb = ( dx - x )2 + y2
	407	cc = x2 + ( dy - y )2
	408	dd = ( dx - x )2 + ( dy - y )2
	409	gg = aa + bb + cc + dd
[1314]	410
[1359]	411	u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) &
	412	+ ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * &
	413	u(k,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[1314]	414
[1359]	415	IF ( k == nzt ) THEN
	416	u_int(n) = u_int_l
	417	ELSE
	418	u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) &
	419	+ ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * &
	420	u(k+1,j+1,i+1) ) / ( 3.0_wp * gg ) - u_gtrans
[3189]	421	u_int(n) = u_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	422	( u_int_u - u_int_l )
	423	ENDIF
[1929]	424
[1314]	425	ENDIF
	426
[1359]	427	ENDDO
[2606]	428	!
	429	!-- Same procedure for interpolation of the v velocity-component
[1359]	430	i = ip + block_offset(nb)%i_off
	431	j = jp
	432	k = kp + block_offset(nb)%k_off
[2606]	433
[1359]	434	DO n = start_index(nb), end_index(nb)
[1685]	435
[2232]	436	!
	437	!-- Determine vertical index of topography top
[2698]	438	k_wall = get_topography_top_index_ji( jp,ip, 's' )
[849]	439
[2232]	440	IF ( constant_flux_layer .AND. zv(n) - zw(k_wall) < z_p ) THEN
	441	IF ( zv(n) - zw(k_wall) < z0_av_global ) THEN
[1314]	442	!
[1359]	443	!-- Resolved-scale horizontal particle velocity is zero below z0.
	444	v_int(n) = 0.0_wp
	445	ELSE
	446	!
[1929]	447	!-- Determine the sublayer. Further used as index. Please note,
	448	!-- logarithmus can not be reused from above, as in in case of
	449	!-- topography particle on u-grid can be above surface-layer height,
	450	!-- whereas it can be below on v-grid.
[2232]	451	height_p = ( zv(n) - zw(k_wall) - z0_av_global ) &
[1936]	452	* REAL( number_of_sublayers, KIND=wp ) &
[1929]	453	* d_z_p_z0
	454	!
	455	!-- Calculate LOG(z/z0) for exact particle height. Therefore,
	456	!-- interpolate linearly between precalculated logarithm.
	457	log_z_z0_int = log_z_z0(INT(height_p)) &
	458	+ ( height_p - INT(height_p) ) &
	459	* ( log_z_z0(INT(height_p)+1) &
	460	- log_z_z0(INT(height_p)) &
	461	)
	462	!
[2232]	463	!-- Get friction velocity and momentum flux from new surface data
	464	!-- types.
[2628]	465	IF ( surf_def_h(0)%start_index(jp,ip) <= &
	466	surf_def_h(0)%end_index(jp,ip) ) THEN
	467	surf_start = surf_def_h(0)%start_index(jp,ip)
[2232]	468	!-- Limit friction velocity. In narrow canyons or holes the
	469	!-- friction velocity can become very small, resulting in a too
	470	!-- large particle speed.
	471	us_int = MAX( surf_def_h(0)%us(surf_start), 0.01_wp )
[2610]	472	vsws_int = surf_def_h(0)%vsws(surf_start)
[2628]	473	ELSEIF ( surf_lsm_h%start_index(jp,ip) <= &
	474	surf_lsm_h%end_index(jp,ip) ) THEN
	475	surf_start = surf_lsm_h%start_index(jp,ip)
[2232]	476	us_int = MAX( surf_lsm_h%us(surf_start), 0.01_wp )
[2610]	477	vsws_int = surf_lsm_h%vsws(surf_start)
[2628]	478	ELSEIF ( surf_usm_h%start_index(jp,ip) <= &
	479	surf_usm_h%end_index(jp,ip) ) THEN
	480	surf_start = surf_usm_h%start_index(jp,ip)
[2232]	481	us_int = MAX( surf_usm_h%us(surf_start), 0.01_wp )
[2610]	482	vsws_int = surf_usm_h%vsws(surf_start)
[2232]	483	ENDIF
[1929]	484	!
[1359]	485	!-- Neutral solution is applied for all situations, e.g. also for
	486	!-- unstable and stable situations. Even though this is not exact
	487	!-- this saves a lot of CPU time since several calls of intrinsic
	488	!-- FORTRAN procedures (LOG, ATAN) are avoided, This is justified
	489	!-- as sensitivity studies revealed no significant effect of
	490	!-- using the neutral solution also for un/stable situations.
[2232]	491	v_int(n) = -vsws_int / ( us_int * kappa + 1E-10_wp ) &
[1929]	492	* log_z_z0_int - v_gtrans
[1314]	493
[1359]	494	ENDIF
[1929]	495
[1359]	496	ELSE
[2969]	497	x = xv(n) + ( 0.5_wp - i ) * dx
	498	y = yv(n) - j * dy
[1359]	499	aa = x2 + y2
	500	bb = ( dx - x )2 + y2
	501	cc = x2 + ( dy - y )2
	502	dd = ( dx - x )2 + ( dy - y )2
	503	gg = aa + bb + cc + dd
[1314]	504
[1359]	505	v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) &
	506	+ ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) &
	507	) / ( 3.0_wp * gg ) - v_gtrans
[1314]	508
[1359]	509	IF ( k == nzt ) THEN
	510	v_int(n) = v_int_l
	511	ELSE
	512	v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) &
	513	+ ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) &
	514	) / ( 3.0_wp * gg ) - v_gtrans
[3189]	515	v_int(n) = v_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	516	( v_int_u - v_int_l )
	517	ENDIF
[1929]	518
[1314]	519	ENDIF
	520
[1359]	521	ENDDO
[2606]	522	!
	523	!-- Same procedure for interpolation of the w velocity-component
[1359]	524	i = ip + block_offset(nb)%i_off
	525	j = jp + block_offset(nb)%j_off
[1929]	526	k = kp - 1
[2606]	527
[1359]	528	DO n = start_index(nb), end_index(nb)
[849]	529
[1359]	530	IF ( vertical_particle_advection(particles(n)%group) ) THEN
[849]	531
[2969]	532	x = xv(n) + ( 0.5_wp - i ) * dx
	533	y = yv(n) + ( 0.5_wp - j ) * dy
[849]	534	aa = x2 + y2
	535	bb = ( dx - x )2 + y2
	536	cc = x2 + ( dy - y )2
	537	dd = ( dx - x )2 + ( dy - y )2
	538	gg = aa + bb + cc + dd
	539
[1359]	540	w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) &
	541	+ ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) &
	542	) / ( 3.0_wp * gg )
[849]	543
[1359]	544	IF ( k == nzt ) THEN
	545	w_int(n) = w_int_l
[849]	546	ELSE
[1359]	547	w_int_u = ( ( gg-aa ) * w(k+1,j,i) + &
	548	( gg-bb ) * w(k+1,j,i+1) + &
	549	( gg-cc ) * w(k+1,j+1,i) + &
	550	( gg-dd ) * w(k+1,j+1,i+1) &
	551	) / ( 3.0_wp * gg )
[3189]	552	w_int(n) = w_int_l + ( zv(n) - zw(k) ) / dzw(k+1) * &
[1359]	553	( w_int_u - w_int_l )
[849]	554	ENDIF
	555
[1359]	556	ELSE
[849]	557
[1359]	558	w_int(n) = 0.0_wp
[849]	559
[1359]	560	ENDIF
	561
	562	ENDDO
	563
	564	ENDDO
	565
	566	!-- Interpolate and calculate quantities needed for calculating the SGS
	567	!-- velocities
[1822]	568	IF ( use_sgs_for_particles .AND. .NOT. cloud_droplets ) THEN
[2698]	569
	570	DO nb = 0,7
	571
	572	subbox_at_wall = .FALSE.
	573	!
	574	!-- In case of topography check if subbox is adjacent to a wall
	575	IF ( .NOT. topography == 'flat' ) THEN
	576	i = ip + MERGE( -1_iwp , 1_iwp, BTEST( nb, 2 ) )
	577	j = jp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 1 ) )
	578	k = kp + MERGE( -1_iwp , 1_iwp, BTEST( nb, 0 ) )
	579	IF ( .NOT. BTEST(wall_flags_0(k, jp, ip), 0) .OR. &
	580	.NOT. BTEST(wall_flags_0(kp, j, ip), 0) .OR. &
	581	.NOT. BTEST(wall_flags_0(kp, jp, i ), 0) ) &
	582	THEN
	583	subbox_at_wall = .TRUE.
	584	ENDIF
	585	ENDIF
	586	IF ( subbox_at_wall ) THEN
	587	e_int(start_index(nb):end_index(nb)) = e(kp,jp,ip)
	588	diss_int(start_index(nb):end_index(nb)) = diss(kp,jp,ip)
	589	de_dx_int(start_index(nb):end_index(nb)) = de_dx(kp,jp,ip)
	590	de_dy_int(start_index(nb):end_index(nb)) = de_dy(kp,jp,ip)
	591	de_dz_int(start_index(nb):end_index(nb)) = de_dz(kp,jp,ip)
	592	!
	593	!-- Set flag for stochastic equation.
	594	term_1_2(start_index(nb):end_index(nb)) = 0.0_wp
	595	ELSE
[1359]	596	i = ip + block_offset(nb)%i_off
	597	j = jp + block_offset(nb)%j_off
	598	k = kp + block_offset(nb)%k_off
	599
	600	DO n = start_index(nb), end_index(nb)
[849]	601	!
[1359]	602	!-- Interpolate TKE
[2969]	603	x = xv(n) + ( 0.5_wp - i ) * dx
	604	y = yv(n) + ( 0.5_wp - j ) * dy
[1359]	605	aa = x2 + y2
	606	bb = ( dx - x )2 + y2
	607	cc = x2 + ( dy - y )2
	608	dd = ( dx - x )2 + ( dy - y )2
	609	gg = aa + bb + cc + dd
[849]	610
[1359]	611	e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) &
	612	+ ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) &
	613	) / ( 3.0_wp * gg )
	614
	615	IF ( k+1 == nzt+1 ) THEN
	616	e_int(n) = e_int_l
	617	ELSE
	618	e_int_u = ( ( gg - aa ) * e(k+1,j,i) + &
	619	( gg - bb ) * e(k+1,j,i+1) + &
	620	( gg - cc ) * e(k+1,j+1,i) + &
	621	( gg - dd ) * e(k+1,j+1,i+1) &
	622	) / ( 3.0_wp * gg )
[3189]	623	e_int(n) = e_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	624	( e_int_u - e_int_l )
	625	ENDIF
[849]	626	!
[1685]	627	!-- Needed to avoid NaN particle velocities (this might not be
	628	!-- required any more)
	629	IF ( e_int(n) <= 0.0_wp ) THEN
[1359]	630	e_int(n) = 1.0E-20_wp
	631	ENDIF
	632	!
	633	!-- Interpolate the TKE gradient along x (adopt incides i,j,k and
	634	!-- all position variables from above (TKE))
	635	de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + &
	636	( gg - bb ) * de_dx(k,j,i+1) + &
	637	( gg - cc ) * de_dx(k,j+1,i) + &
	638	( gg - dd ) * de_dx(k,j+1,i+1) &
	639	) / ( 3.0_wp * gg )
[849]	640
	641	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
[1359]	642	de_dx_int(n) = de_dx_int_l
[849]	643	ELSE
[1359]	644	de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + &
	645	( gg - bb ) * de_dx(k+1,j,i+1) + &
	646	( gg - cc ) * de_dx(k+1,j+1,i) + &
	647	( gg - dd ) * de_dx(k+1,j+1,i+1) &
	648	) / ( 3.0_wp * gg )
[3189]	649	de_dx_int(n) = de_dx_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	650	( de_dx_int_u - de_dx_int_l )
[849]	651	ENDIF
[1359]	652	!
	653	!-- Interpolate the TKE gradient along y
	654	de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + &
	655	( gg - bb ) * de_dy(k,j,i+1) + &
	656	( gg - cc ) * de_dy(k,j+1,i) + &
	657	( gg - dd ) * de_dy(k,j+1,i+1) &
	658	) / ( 3.0_wp * gg )
	659	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	660	de_dy_int(n) = de_dy_int_l
	661	ELSE
	662	de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + &
[2698]	663	( gg - bb ) * de_dy(k+1,j,i+1) + &
	664	( gg - cc ) * de_dy(k+1,j+1,i) + &
	665	( gg - dd ) * de_dy(k+1,j+1,i+1) &
[1359]	666	) / ( 3.0_wp * gg )
[3189]	667	de_dy_int(n) = de_dy_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	668	( de_dy_int_u - de_dy_int_l )
[1359]	669	ENDIF
[849]	670
	671	!
[1359]	672	!-- Interpolate the TKE gradient along z
[3065]	673	IF ( zv(n) < 0.5_wp * dz(1) ) THEN
[1359]	674	de_dz_int(n) = 0.0_wp
	675	ELSE
	676	de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + &
	677	( gg - bb ) * de_dz(k,j,i+1) + &
	678	( gg - cc ) * de_dz(k,j+1,i) + &
	679	( gg - dd ) * de_dz(k,j+1,i+1) &
	680	) / ( 3.0_wp * gg )
[849]	681
[1359]	682	IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN
	683	de_dz_int(n) = de_dz_int_l
	684	ELSE
	685	de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + &
	686	( gg - bb ) * de_dz(k+1,j,i+1) + &
	687	( gg - cc ) * de_dz(k+1,j+1,i) + &
	688	( gg - dd ) * de_dz(k+1,j+1,i+1) &
	689	) / ( 3.0_wp * gg )
[3189]	690	de_dz_int(n) = de_dz_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[1359]	691	( de_dz_int_u - de_dz_int_l )
	692	ENDIF
	693	ENDIF
[849]	694
[1359]	695	!
	696	!-- Interpolate the dissipation of TKE
	697	diss_int_l = ( ( gg - aa ) * diss(k,j,i) + &
	698	( gg - bb ) * diss(k,j,i+1) + &
	699	( gg - cc ) * diss(k,j+1,i) + &
	700	( gg - dd ) * diss(k,j+1,i+1) &
[2698]	701	) / ( 3.0_wp * gg )
[849]	702
[1359]	703	IF ( k == nzt ) THEN
	704	diss_int(n) = diss_int_l
	705	ELSE
	706	diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + &
	707	( gg - bb ) * diss(k+1,j,i+1) + &
	708	( gg - cc ) * diss(k+1,j+1,i) + &
	709	( gg - dd ) * diss(k+1,j+1,i+1) &
	710	) / ( 3.0_wp * gg )
[3189]	711	diss_int(n) = diss_int_l + ( zv(n) - zu(k) ) / dzw(k+1) * &
[2698]	712	( diss_int_u - diss_int_l )
[1359]	713	ENDIF
	714
[1929]	715	!
	716	!-- Set flag for stochastic equation.
	717	term_1_2(n) = 1.0_wp
[1359]	718	ENDDO
[2698]	719	ENDIF
	720	ENDDO
[1359]	721
	722	DO nb = 0,7
	723	i = ip + block_offset(nb)%i_off
	724	j = jp + block_offset(nb)%j_off
	725	k = kp + block_offset(nb)%k_off
[849]	726
[1359]	727	DO n = start_index(nb), end_index(nb)
[849]	728	!
[1359]	729	!-- Vertical interpolation of the horizontally averaged SGS TKE and
	730	!-- resolved-scale velocity variances and use the interpolated values
	731	!-- to calculate the coefficient fs, which is a measure of the ratio
	732	!-- of the subgrid-scale turbulent kinetic energy to the total amount
	733	!-- of turbulent kinetic energy.
	734	IF ( k == 0 ) THEN
	735	e_mean_int = hom(0,1,8,0)
	736	ELSE
	737	e_mean_int = hom(k,1,8,0) + &
	738	( hom(k+1,1,8,0) - hom(k,1,8,0) ) / &
	739	( zu(k+1) - zu(k) ) * &
	740	( zv(n) - zu(k) )
	741	ENDIF
[849]	742
[1685]	743	kw = kp - 1
[849]	744
[1359]	745	IF ( k == 0 ) THEN
	746	aa = hom(k+1,1,30,0) * ( zv(n) / &
	747	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	748	bb = hom(k+1,1,31,0) * ( zv(n) / &
	749	( 0.5_wp * ( zu(k+1) - zu(k) ) ) )
	750	cc = hom(kw+1,1,32,0) * ( zv(n) / &
	751	( 1.0_wp * ( zw(kw+1) - zw(kw) ) ) )
	752	ELSE
	753	aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * &
	754	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	755	bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * &
	756	( ( zv(n) - zu(k) ) / ( zu(k+1) - zu(k) ) )
	757	cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) * &
	758	( ( zv(n) - zw(kw) ) / ( zw(kw+1)-zw(kw) ) )
	759	ENDIF
[849]	760
[1359]	761	vv_int = ( 1.0_wp / 3.0_wp ) * ( aa + bb + cc )
	762	!
	763	!-- Needed to avoid NaN particle velocities. The value of 1.0 is just
	764	!-- an educated guess for the given case.
	765	IF ( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int == 0.0_wp ) THEN
	766	fs_int(n) = 1.0_wp
	767	ELSE
	768	fs_int(n) = ( 2.0_wp / 3.0_wp ) * e_mean_int / &
	769	( vv_int + ( 2.0_wp / 3.0_wp ) * e_mean_int )
	770	ENDIF
[849]	771
[1359]	772	ENDDO
	773	ENDDO
[849]	774
[2417]	775	DO nb = 0, 7
	776	DO n = start_index(nb), end_index(nb)
	777	rg(n,1) = random_gauss( iran_part, 5.0_wp )
	778	rg(n,2) = random_gauss( iran_part, 5.0_wp )
	779	rg(n,3) = random_gauss( iran_part, 5.0_wp )
	780	ENDDO
	781	ENDDO
[1359]	782
[2417]	783	DO nb = 0, 7
	784	DO n = start_index(nb), end_index(nb)
[1359]	785
[849]	786	!
[2417]	787	!-- Calculate the Lagrangian timescale according to Weil et al. (2004).
[2886]	788	lagr_timescale(n) = ( 4.0_wp * e_int(n) + 1E-20_wp ) / &
[2417]	789	( 3.0_wp * fs_int(n) * c_0 * diss_int(n) + 1E-20_wp )
[849]	790
	791	!
[2417]	792	!-- Calculate the next particle timestep. dt_gap is the time needed to
	793	!-- complete the current LES timestep.
[2886]	794	dt_gap(n) = dt_3d - particles(n)%dt_sum
	795	dt_particle(n) = MIN( dt_3d, 0.025_wp * lagr_timescale(n), dt_gap(n) )
	796	particles(n)%aux1 = lagr_timescale(n)
	797	particles(n)%aux2 = dt_gap(n)
[849]	798	!
[2417]	799	!-- The particle timestep should not be too small in order to prevent
	800	!-- the number of particle timesteps of getting too large
[2886]	801	IF ( dt_particle(n) < dt_min_part .AND. dt_min_part < dt_gap(n) ) THEN
[2417]	802	dt_particle(n) = dt_min_part
	803	ENDIF
[2886]	804	rvar1_temp(n) = particles(n)%rvar1
	805	rvar2_temp(n) = particles(n)%rvar2
	806	rvar3_temp(n) = particles(n)%rvar3
[849]	807	!
[2417]	808	!-- Calculate the SGS velocity components
	809	IF ( particles(n)%age == 0.0_wp ) THEN
[849]	810	!
[2417]	811	!-- For new particles the SGS components are derived from the SGS
	812	!-- TKE. Limit the Gaussian random number to the interval
	813	!-- [-5.0sigma, 5.0sigma] in order to prevent the SGS velocities
	814	!-- from becoming unrealistically large.
[2886]	815	rvar1_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	816	+ 1E-20_wp ) * ( rg(n,1) - 1.0_wp )
	817	rvar2_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	818	+ 1E-20_wp ) * ( rg(n,2) - 1.0_wp )
	819	rvar3_temp(n) = SQRT( 2.0_wp * sgs_wf_part * e_int(n) &
	820	+ 1E-20_wp ) * ( rg(n,3) - 1.0_wp )
[849]	821
[2417]	822	ELSE
[849]	823	!
[2417]	824	!-- Restriction of the size of the new timestep: compared to the
	825	!-- previous timestep the increase must not exceed 200%. First,
	826	!-- check if age > age_m, in order to prevent that particles get zero
	827	!-- timestep.
	828	dt_particle_m = MERGE( dt_particle(n), &
	829	particles(n)%age - particles(n)%age_m, &
	830	particles(n)%age - particles(n)%age_m < &
	831	1E-8_wp )
	832	IF ( dt_particle(n) > 2.0_wp * dt_particle_m ) THEN
	833	dt_particle(n) = 2.0_wp * dt_particle_m
	834	ENDIF
[849]	835
[2417]	836	!-- For old particles the SGS components are correlated with the
	837	!-- values from the previous timestep. Random numbers have also to
	838	!-- be limited (see above).
	839	!-- As negative values for the subgrid TKE are not allowed, the
	840	!-- change of the subgrid TKE with time cannot be smaller than
	841	!-- -e_int(n)/dt_particle. This value is used as a lower boundary
	842	!-- value for the change of TKE
	843	de_dt_min = - e_int(n) / dt_particle(n)
[849]	844
[2417]	845	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
[849]	846
[2417]	847	IF ( de_dt < de_dt_min ) THEN
	848	de_dt = de_dt_min
	849	ENDIF
[849]	850
[2886]	851	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
[2417]	852	de_dx_int(n), de_dt, diss_int(n), &
	853	dt_particle(n), rg(n,1), term_1_2(n) )
[849]	854
[2886]	855	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
[2417]	856	de_dy_int(n), de_dt, diss_int(n), &
	857	dt_particle(n), rg(n,2), term_1_2(n) )
[849]	858
[2886]	859	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
[2417]	860	de_dz_int(n), de_dt, diss_int(n), &
	861	dt_particle(n), rg(n,3), term_1_2(n) )
[849]	862
[2417]	863	ENDIF
[849]	864
[2886]	865	ENDDO
	866	ENDDO
	867	!
	868	!-- Check if the added SGS velocities result in a violation of the CFL-
	869	!-- criterion. If yes choose a smaller timestep based on the new velocities
	870	!-- and calculate SGS velocities again
	871	dz_temp = zw(kp)-zw(kp-1)
	872
	873	DO nb = 0, 7
	874	DO n = start_index(nb), end_index(nb)
	875	IF ( .NOT. particles(n)%age == 0.0_wp .AND. &
	876	(ABS( u_int(n) + rvar1_temp(n) ) > (dx/dt_particle(n)) .OR. &
	877	ABS( v_int(n) + rvar2_temp(n) ) > (dy/dt_particle(n)) .OR. &
	878	ABS( w_int(n) + rvar3_temp(n) ) > (dz_temp/dt_particle(n)))) THEN
	879
	880	dt_particle(n) = 0.9_wp * MIN( &
	881	( dx / ABS( u_int(n) + rvar1_temp(n) ) ), &
	882	( dy / ABS( v_int(n) + rvar2_temp(n) ) ), &
	883	( dz_temp / ABS( w_int(n) + rvar3_temp(n) ) ) )
	884
	885	!
	886	!-- Reset temporary SGS velocites to "current" ones
	887	rvar1_temp(n) = particles(n)%rvar1
	888	rvar2_temp(n) = particles(n)%rvar2
	889	rvar3_temp(n) = particles(n)%rvar3
	890
	891	de_dt_min = - e_int(n) / dt_particle(n)
	892
	893	de_dt = ( e_int(n) - particles(n)%e_m ) / dt_particle_m
	894
	895	IF ( de_dt < de_dt_min ) THEN
	896	de_dt = de_dt_min
	897	ENDIF
	898
	899	CALL weil_stochastic_eq(rvar1_temp(n), fs_int(n), e_int(n),&
	900	de_dx_int(n), de_dt, diss_int(n), &
	901	dt_particle(n), rg(n,1), term_1_2(n) )
	902
	903	CALL weil_stochastic_eq(rvar2_temp(n), fs_int(n), e_int(n),&
	904	de_dy_int(n), de_dt, diss_int(n), &
	905	dt_particle(n), rg(n,2), term_1_2(n) )
	906
	907	CALL weil_stochastic_eq(rvar3_temp(n), fs_int(n), e_int(n),&
	908	de_dz_int(n), de_dt, diss_int(n), &
	909	dt_particle(n), rg(n,3), term_1_2(n) )
	910	ENDIF
	911
	912	!
	913	!-- Update particle velocites
	914	particles(n)%rvar1 = rvar1_temp(n)
	915	particles(n)%rvar2 = rvar2_temp(n)
	916	particles(n)%rvar3 = rvar3_temp(n)
[2417]	917	u_int(n) = u_int(n) + particles(n)%rvar1
	918	v_int(n) = v_int(n) + particles(n)%rvar2
	919	w_int(n) = w_int(n) + particles(n)%rvar3
[849]	920	!
[2417]	921	!-- Store the SGS TKE of the current timelevel which is needed for
	922	!-- for calculating the SGS particle velocities at the next timestep
	923	particles(n)%e_m = e_int(n)
	924	ENDDO
[1359]	925	ENDDO
[2886]	926
[1359]	927	ELSE
[849]	928	!
[1359]	929	!-- If no SGS velocities are used, only the particle timestep has to
	930	!-- be set
	931	dt_particle = dt_3d
[849]	932
[1359]	933	ENDIF
[849]	934
[1359]	935	dens_ratio = particle_groups(particles(1:number_of_particles)%group)%density_ratio
[849]	936
[1359]	937	IF ( ANY( dens_ratio == 0.0_wp ) ) THEN
[2417]	938	DO nb = 0, 7
	939	DO n = start_index(nb), end_index(nb)
[1359]	940
[849]	941	!
[2417]	942	!-- Particle advection
	943	IF ( dens_ratio(n) == 0.0_wp ) THEN
[849]	944	!
[2417]	945	!-- Pure passive transport (without particle inertia)
	946	particles(n)%x = xv(n) + u_int(n) * dt_particle(n)
	947	particles(n)%y = yv(n) + v_int(n) * dt_particle(n)
	948	particles(n)%z = zv(n) + w_int(n) * dt_particle(n)
[849]	949
[2417]	950	particles(n)%speed_x = u_int(n)
	951	particles(n)%speed_y = v_int(n)
	952	particles(n)%speed_z = w_int(n)
[849]	953
[2417]	954	ELSE
[849]	955	!
[2417]	956	!-- Transport of particles with inertia
	957	particles(n)%x = particles(n)%x + particles(n)%speed_x * &
	958	dt_particle(n)
	959	particles(n)%y = particles(n)%y + particles(n)%speed_y * &
	960	dt_particle(n)
	961	particles(n)%z = particles(n)%z + particles(n)%speed_z * &
	962	dt_particle(n)
[849]	963
	964	!
[2417]	965	!-- Update of the particle velocity
	966	IF ( cloud_droplets ) THEN
	967	!
	968	!-- Terminal velocity is computed for vertical direction (Rogers et
	969	!-- al., 1993, J. Appl. Meteorol.)
	970	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	971	IF ( diameter <= d0_rog ) THEN
	972	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	973	ELSE
	974	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	975	ENDIF
	976
	977	!
	978	!-- If selected, add random velocities following Soelch and Kaercher
	979	!-- (2010, Q. J. R. Meteorol. Soc.)
	980	IF ( use_sgs_for_particles ) THEN
[2886]	981	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
[3207]	982	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
	983	1.0E-20_wp ) )
[2417]	984	sigma = SQRT( e(kp,jp,ip) )
	985
	986	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	987	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	988	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	989
	990	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	991	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	992	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	993	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	994	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	995	SQRT( 1.0_wp - RL*2 ) sigma * rg3
	996
	997	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	998	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	999	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
	1000	ELSE
	1001	particles(n)%speed_x = u_int(n)
	1002	particles(n)%speed_y = v_int(n)
	1003	particles(n)%speed_z = w_int(n) - w_s
	1004	ENDIF
	1005
	1006	ELSE
	1007
	1008	IF ( use_sgs_for_particles ) THEN
	1009	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1010	exp_term = EXP( -exp_arg * dt_particle(n) )
	1011	ELSE
	1012	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1013	exp_term = particle_groups(particles(n)%group)%exp_term
	1014	ENDIF
	1015	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
	1016	u_int(n) * ( 1.0_wp - exp_term )
	1017	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
	1018	v_int(n) * ( 1.0_wp - exp_term )
	1019	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1020	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * &
	1021	g / exp_arg ) * ( 1.0_wp - exp_term )
	1022	ENDIF
	1023
	1024	ENDIF
	1025	ENDDO
	1026	ENDDO
	1027
	1028	ELSE
	1029
	1030	DO nb = 0, 7
	1031	DO n = start_index(nb), end_index(nb)
	1032	!
	1033	!-- Transport of particles with inertia
	1034	particles(n)%x = xv(n) + particles(n)%speed_x * dt_particle(n)
	1035	particles(n)%y = yv(n) + particles(n)%speed_y * dt_particle(n)
	1036	particles(n)%z = zv(n) + particles(n)%speed_z * dt_particle(n)
	1037	!
[1359]	1038	!-- Update of the particle velocity
	1039	IF ( cloud_droplets ) THEN
[1822]	1040	!
[2417]	1041	!-- Terminal velocity is computed for vertical direction (Rogers et al.,
	1042	!-- 1993, J. Appl. Meteorol.)
[1822]	1043	diameter = particles(n)%radius * 2000.0_wp !diameter in mm
	1044	IF ( diameter <= d0_rog ) THEN
	1045	w_s = k_cap_rog * diameter * ( 1.0_wp - EXP( -k_low_rog * diameter ) )
	1046	ELSE
	1047	w_s = a_rog - b_rog * EXP( -c_rog * diameter )
	1048	ENDIF
[1359]	1049
[1822]	1050	!
	1051	!-- If selected, add random velocities following Soelch and Kaercher
	1052	!-- (2010, Q. J. R. Meteorol. Soc.)
	1053	IF ( use_sgs_for_particles ) THEN
[2886]	1054	lagr_timescale(n) = km(kp,jp,ip) / MAX( e(kp,jp,ip), 1.0E-20_wp )
[3207]	1055	RL = EXP( -1.0_wp * dt_3d / MAX( lagr_timescale(n), &
	1056	1.0E-20_wp ) )
[2417]	1057	sigma = SQRT( e(kp,jp,ip) )
[1822]	1058
[2417]	1059	rg1 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1060	rg2 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
	1061	rg3 = random_gauss( iran_part, 5.0_wp ) - 1.0_wp
[1822]	1062
[2417]	1063	particles(n)%rvar1 = RL * particles(n)%rvar1 + &
	1064	SQRT( 1.0_wp - RL*2 ) sigma * rg1
	1065	particles(n)%rvar2 = RL * particles(n)%rvar2 + &
	1066	SQRT( 1.0_wp - RL*2 ) sigma * rg2
	1067	particles(n)%rvar3 = RL * particles(n)%rvar3 + &
	1068	SQRT( 1.0_wp - RL*2 ) sigma * rg3
[1822]	1069
[2417]	1070	particles(n)%speed_x = u_int(n) + particles(n)%rvar1
	1071	particles(n)%speed_y = v_int(n) + particles(n)%rvar2
	1072	particles(n)%speed_z = w_int(n) + particles(n)%rvar3 - w_s
[1822]	1073	ELSE
[2417]	1074	particles(n)%speed_x = u_int(n)
	1075	particles(n)%speed_y = v_int(n)
	1076	particles(n)%speed_z = w_int(n) - w_s
[1822]	1077	ENDIF
	1078
[1359]	1079	ELSE
[1822]	1080
	1081	IF ( use_sgs_for_particles ) THEN
	1082	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1083	exp_term = EXP( -exp_arg * dt_particle(n) )
	1084	ELSE
	1085	exp_arg = particle_groups(particles(n)%group)%exp_arg
	1086	exp_term = particle_groups(particles(n)%group)%exp_term
	1087	ENDIF
[2417]	1088	particles(n)%speed_x = particles(n)%speed_x * exp_term + &
[1822]	1089	u_int(n) * ( 1.0_wp - exp_term )
[2417]	1090	particles(n)%speed_y = particles(n)%speed_y * exp_term + &
[1822]	1091	v_int(n) * ( 1.0_wp - exp_term )
[2417]	1092	particles(n)%speed_z = particles(n)%speed_z * exp_term + &
	1093	( w_int(n) - ( 1.0_wp - dens_ratio(n) ) * g / &
	1094	exp_arg ) * ( 1.0_wp - exp_term )
[1359]	1095	ENDIF
[2417]	1096	ENDDO
[1359]	1097	ENDDO
	1098
[2417]	1099	ENDIF
[1359]	1100
	1101	!
[2417]	1102	!-- Store the old age of the particle ( needed to prevent that a
	1103	!-- particle crosses several PEs during one timestep, and for the
	1104	!-- evaluation of the subgrid particle velocity fluctuations )
	1105	particles(1:number_of_particles)%age_m = particles(1:number_of_particles)%age
	1106
	1107	DO nb = 0, 7
	1108	DO n = start_index(nb), end_index(nb)
[1822]	1109	!
[2417]	1110	!-- Increment the particle age and the total time that the particle
	1111	!-- has advanced within the particle timestep procedure
	1112	particles(n)%age = particles(n)%age + dt_particle(n)
	1113	particles(n)%dt_sum = particles(n)%dt_sum + dt_particle(n)
[1359]	1114
[1822]	1115	!
[2417]	1116	!-- Check whether there is still a particle that has not yet completed
	1117	!-- the total LES timestep
	1118	IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8_wp ) THEN
	1119	dt_3d_reached_l = .FALSE.
[849]	1120	ENDIF
[1822]	1121
[1359]	1122	ENDDO
[849]	1123	ENDDO
	1124
[1359]	1125	CALL cpu_log( log_point_s(44), 'lpm_advec', 'pause' )
[849]	1126
[1929]	1127
[849]	1128	END SUBROUTINE lpm_advec
[1929]	1129
	1130	! Description:
	1131	! ------------
	1132	!> Calculation of subgrid-scale particle speed using the stochastic model
	1133	!> of Weil et al. (2004, JAS, 61, 2877-2887).
	1134	!------------------------------------------------------------------------------!
	1135	SUBROUTINE weil_stochastic_eq( v_sgs, fs_n, e_n, dedxi_n, dedt_n, diss_n, &
	1136	dt_n, rg_n, fac )
	1137
	1138	USE kinds
	1139
	1140	USE particle_attributes, &
	1141	ONLY: c_0, sgs_wf_part
	1142
	1143	IMPLICIT NONE
	1144
	1145	REAL(wp) :: a1 !< dummy argument
	1146	REAL(wp) :: dedt_n !< time derivative of TKE at particle position
	1147	REAL(wp) :: dedxi_n !< horizontal derivative of TKE at particle position
	1148	REAL(wp) :: diss_n !< dissipation at particle position
	1149	REAL(wp) :: dt_n !< particle timestep
	1150	REAL(wp) :: e_n !< TKE at particle position
	1151	REAL(wp) :: fac !< flag to identify adjacent topography
	1152	REAL(wp) :: fs_n !< weighting factor to prevent that subgrid-scale particle speed becomes too large
	1153	REAL(wp) :: rg_n !< random number
	1154	REAL(wp) :: term1 !< memory term
	1155	REAL(wp) :: term2 !< drift correction term
	1156	REAL(wp) :: term3 !< random term
	1157	REAL(wp) :: v_sgs !< subgrid-scale velocity component
	1158
[2100]	1159	!-- At first, limit TKE to a small non-zero number, in order to prevent
	1160	!-- the occurrence of extremely large SGS-velocities in case TKE is zero,
	1161	!-- (could occur at the simulation begin).
	1162	e_n = MAX( e_n, 1E-20_wp )
[1929]	1163	!
	1164	!-- Please note, terms 1 and 2 (drift and memory term, respectively) are
	1165	!-- multiplied by a flag to switch of both terms near topography.
	1166	!-- This is necessary, as both terms may cause a subgrid-scale velocity build up
	1167	!-- if particles are trapped in regions with very small TKE, e.g. in narrow street
	1168	!-- canyons resolved by only a few grid points. Hence, term 1 and term 2 are
	1169	!-- disabled if one of the adjacent grid points belongs to topography.
	1170	!-- Moreover, in this case, the previous subgrid-scale component is also set
	1171	!-- to zero.
	1172
	1173	a1 = fs_n * c_0 * diss_n
	1174	!
	1175	!-- Memory term
	1176	term1 = - a1 * v_sgs * dt_n / ( 4.0_wp * sgs_wf_part * e_n + 1E-20_wp ) &
	1177	* fac
	1178	!
	1179	!-- Drift correction term
	1180	term2 = ( ( dedt_n * v_sgs / e_n ) + dedxi_n ) * 0.5_wp * dt_n &
	1181	* fac
	1182	!
	1183	!-- Random term
[3241]	1184	term3 = SQRT( MAX( a1, 1E-20_wp ) ) * ( rg_n - 1.0_wp ) * SQRT( dt_n )
[1929]	1185	!
	1186	!-- In cese one of the adjacent grid-boxes belongs to topograhy, the previous
	1187	!-- subgrid-scale velocity component is set to zero, in order to prevent a
	1188	!-- velocity build-up.
	1189	!-- This case, set also previous subgrid-scale component to zero.
	1190	v_sgs = v_sgs * fac + term1 + term2 + term3
	1191
	1192	END SUBROUTINE weil_stochastic_eq

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