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source: palm/trunk/SOURCE/lpm_droplet_condensation.f90 @ 1433

Last change on this file since 1433 was 1360, checked in by hoffmann, 11 years ago
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[1359]	1	SUBROUTINE lpm_droplet_condensation (ip,jp,kp)
[849]	2
[1036]	3	!--------------------------------------------------------------------------------!
	4	! This file is part of PALM.
	5	!
	6	! PALM is free software: you can redistribute it and/or modify it under the terms
	7	! of the GNU General Public License as published by the Free Software Foundation,
	8	! either version 3 of the License, or (at your option) any later version.
	9	!
	10	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	11	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	12	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	13	!
	14	! You should have received a copy of the GNU General Public License along with
	15	! PALM. If not, see <http://www.gnu.org/licenses/>.
	16	!
[1310]	17	! Copyright 1997-2014 Leibniz Universitaet Hannover
[1036]	18	!--------------------------------------------------------------------------------!
	19	!
[849]	20	! Current revisions:
	21	! ------------------
[1360]	22	!
	23	!
[1321]	24	! Former revisions:
	25	! -----------------
	26	! $Id: lpm_droplet_condensation.f90 1360 2014-04-11 17:20:32Z keck $
	27	!
[1360]	28	! 1359 2014-04-11 17:15:14Z hoffmann
	29	! New particle structure integrated.
	30	! Kind definition added to all floating point numbers.
	31	!
[1347]	32	! 1346 2014-03-27 13:18:20Z heinze
	33	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	34	! intrinsic function like MAX, MIN, SIGN
	35	!
[1323]	36	! 1322 2014-03-20 16:38:49Z raasch
	37	! REAL constants defined as wp-kind
	38	!
[1321]	39	! 1320 2014-03-20 08:40:49Z raasch
[1320]	40	! ONLY-attribute added to USE-statements,
	41	! kind-parameters added to all INTEGER and REAL declaration statements,
	42	! kinds are defined in new module kinds,
	43	! comment fields (!:) to be used for variable explanations added to
	44	! all variable declaration statements
[1072]	45	!
[1319]	46	! 1318 2014-03-17 13:35:16Z raasch
	47	! module interfaces removed
	48	!
[1093]	49	! 1092 2013-02-02 11:24:22Z raasch
	50	! unused variables removed
	51	!
[1072]	52	! 1071 2012-11-29 16:54:55Z franke
[1071]	53	! Ventilation effect for evaporation of large droplets included
	54	! Check for unreasonable results included in calculation of Rosenbrock method
	55	! since physically unlikely results were observed and for the same
	56	! reason the first internal time step in Rosenbrock method should be < 1.0E02 in
	57	! case of evaporation
	58	! Unnecessary calculation of ql_int removed
	59	! Unnecessary calculations in Rosenbrock method (d2rdt2, drdt_m, dt_ros_last)
	60	! removed
	61	! Bugfix: factor in calculation of surface tension changed from 0.00155 to
	62	! 0.000155
[849]	63	!
[1037]	64	! 1036 2012-10-22 13:43:42Z raasch
	65	! code put under GPL (PALM 3.9)
	66	!
[850]	67	! 849 2012-03-15 10:35:09Z raasch
	68	! initial revision (former part of advec_particles)
[849]	69	!
[850]	70	!
[849]	71	! Description:
	72	! ------------
	73	! Calculates change in droplet radius by condensation/evaporation, using
	74	! either an analytic formula or by numerically integrating the radius growth
	75	! equation including curvature and solution effects using Rosenbrocks method
	76	! (see Numerical recipes in FORTRAN, 2nd edition, p. 731).
	77	! The analytical formula and growth equation follow those given in
	78	! Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103).
	79	!------------------------------------------------------------------------------!
	80
[1320]	81	USE arrays_3d, &
	82	ONLY: hyp, pt, q, ql_c, ql_v, zu
[849]	83
[1320]	84	USE cloud_parameters, &
	85	ONLY: bfactor, curvature_solution_effects, diff_coeff_l, &
	86	eps_ros, l_d_rv, l_v, rho_l, r_v, thermal_conductivity_l
[849]	87
[1320]	88	USE constants, &
	89	ONLY: pi
[849]	90
[1320]	91	USE control_parameters, &
	92	ONLY: atmos_ocean_sign, dt_3d, dz, message_string, &
	93	molecular_viscosity, rho_surface
	94	USE cpulog, &
	95	ONLY: cpu_log, log_point_s
[849]	96
[1320]	97	USE grid_variables, &
	98	ONLY: dx, ddx, dy, ddy
[1071]	99
[1320]	100	USE lpm_collision_kernels_mod, &
	101	ONLY: rclass_lbound, rclass_ubound
[849]	102
[1320]	103	USE kinds
	104
	105	USE particle_attributes, &
[1359]	106	ONLY: block_offset, grid_particles, hall_kernel, number_of_particles, &
	107	offset_ocean_nzt, offset_ocean_nzt_m1, particles, &
	108	radius_classes, use_kernel_tables, wang_kernel
[1320]	109
	110
	111	IMPLICIT NONE
	112
	113	INTEGER(iwp) :: i !:
[1359]	114	INTEGER(iwp) :: ip !:
[1320]	115	INTEGER(iwp) :: internal_timestep_count !:
	116	INTEGER(iwp) :: j !:
[1359]	117	INTEGER(iwp) :: jp !:
[1320]	118	INTEGER(iwp) :: jtry !:
	119	INTEGER(iwp) :: k !:
[1359]	120	INTEGER(iwp) :: kp !:
[1320]	121	INTEGER(iwp) :: n !:
[1359]	122	INTEGER(iwp) :: nb !:
[1320]	123	INTEGER(iwp) :: ros_count !:
	124
[1359]	125	INTEGER(iwp), PARAMETER :: maxtry = 40 !:
[1320]	126
[1359]	127	INTEGER(iwp), DIMENSION(0:7) :: end_index !:
	128	INTEGER(iwp), DIMENSION(0:7) :: start_index !:
[1320]	129
[1359]	130	LOGICAL :: repeat !:
	131
	132	LOGICAL, DIMENSION(number_of_particles) :: flag_1 !:
	133
[1320]	134	REAL(wp) :: aa !:
	135	REAL(wp) :: afactor !:
	136	REAL(wp) :: arg !:
	137	REAL(wp) :: bb !:
	138	REAL(wp) :: cc !:
	139	REAL(wp) :: dd !:
	140	REAL(wp) :: ddenom !:
	141	REAL(wp) :: delta_r !:
	142	REAL(wp) :: drdt !:
	143	REAL(wp) :: drdt_ini !:
	144	REAL(wp) :: dt_ros !:
	145	REAL(wp) :: dt_ros_next !:
	146	REAL(wp) :: dt_ros_sum !:
	147	REAL(wp) :: dt_ros_sum_ini !:
	148	REAL(wp) :: d2rdtdr !:
	149	REAL(wp) :: errmax !:
	150	REAL(wp) :: err_ros !:
	151	REAL(wp) :: g1 !:
	152	REAL(wp) :: g2 !:
	153	REAL(wp) :: g3 !:
	154	REAL(wp) :: g4 !:
	155	REAL(wp) :: gg !:
	156	REAL(wp) :: pt_int !:
	157	REAL(wp) :: pt_int_l !:
	158	REAL(wp) :: pt_int_u !:
	159	REAL(wp) :: q_int !:
	160	REAL(wp) :: q_int_l !:
	161	REAL(wp) :: q_int_u !:
	162	REAL(wp) :: r_ros !:
	163	REAL(wp) :: r_ros_ini !:
	164	REAL(wp) :: sigma !:
	165	REAL(wp) :: x !:
	166	REAL(wp) :: y !:
	167	REAL(wp) :: re_p !:
	168
[849]	169	!-- Parameters for Rosenbrock method
[1359]	170	REAL(wp), PARAMETER :: a21 = 2.0_wp !:
	171	REAL(wp), PARAMETER :: a31 = 48.0_wp / 25.0_wp !:
	172	REAL(wp), PARAMETER :: a32 = 6.0_wp / 25.0_wp !:
	173	REAL(wp), PARAMETER :: b1 = 19.0_wp / 9.0_wp !:
	174	REAL(wp), PARAMETER :: b2 = 0.5_wp !:
	175	REAL(wp), PARAMETER :: b3 = 25.0_wp / 108.0_wp !:
	176	REAL(wp), PARAMETER :: b4 = 125.0_wp / 108.0_wp !:
	177	REAL(wp), PARAMETER :: c21 = -8.0_wp !:
	178	REAL(wp), PARAMETER :: c31 = 372.0_wp / 25.0_wp !:
	179	REAL(wp), PARAMETER :: c32 = 12.0_wp / 5.0_wp !:
	180	REAL(wp), PARAMETER :: c41 = -112.0_wp / 125.0_wp !:
	181	REAL(wp), PARAMETER :: c42 = -54.0_wp / 125.0_wp !:
	182	REAL(wp), PARAMETER :: c43 = -2.0_wp / 5.0_wp !:
	183	REAL(wp), PARAMETER :: errcon = 0.1296_wp !:
	184	REAL(wp), PARAMETER :: e1 = 17.0_wp / 54.0_wp !:
	185	REAL(wp), PARAMETER :: e2 = 7.0_wp / 36.0_wp !:
	186	REAL(wp), PARAMETER :: e3 = 0.0_wp !:
	187	REAL(wp), PARAMETER :: e4 = 125.0_wp / 108.0_wp !:
	188	REAL(wp), PARAMETER :: gam = 0.5_wp !:
	189	REAL(wp), PARAMETER :: grow = 1.5_wp !:
	190	REAL(wp), PARAMETER :: pgrow = -0.25_wp !:
	191	REAL(wp), PARAMETER :: pshrnk = -1.0_wp /3.0_wp !:
	192	REAL(wp), PARAMETER :: shrnk = 0.5_wp !:
[849]	193
[1359]	194	REAL(wp), DIMENSION(number_of_particles) :: afactor_v !:
	195	REAL(wp), DIMENSION(number_of_particles) :: diff_coeff_v !:
	196	REAL(wp), DIMENSION(number_of_particles) :: e_s !:
	197	REAL(wp), DIMENSION(number_of_particles) :: e_a !:
	198	REAL(wp), DIMENSION(number_of_particles) :: new_r !:
	199	REAL(wp), DIMENSION(number_of_particles) :: p_int !:
	200	REAL(wp), DIMENSION(number_of_particles) :: thermal_conductivity_v !:
	201	REAL(wp), DIMENSION(number_of_particles) :: t_int !:
	202	REAL(wp), DIMENSION(number_of_particles) :: xv !:
	203	REAL(wp), DIMENSION(number_of_particles) :: yv !:
	204	REAL(wp), DIMENSION(number_of_particles) :: zv !:
[849]	205
[1320]	206
[849]	207	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' )
	208
[1359]	209	start_index = grid_particles(kp,jp,ip)%start_index
	210	end_index = grid_particles(kp,jp,ip)%end_index
	211
	212	xv = particles(1:number_of_particles)%x
	213	yv = particles(1:number_of_particles)%y
	214	zv = particles(1:number_of_particles)%z
	215
	216	DO nb = 0,7
	217
	218	i = ip + block_offset(nb)%i_off
	219	j = jp + block_offset(nb)%j_off
	220	k = kp + block_offset(nb)%k_off
	221
	222	DO n = start_index(nb), end_index(nb)
[849]	223	!
	224	!-- Interpolate temperature and humidity.
[1359]	225	x = xv(n) - i * dx
	226	y = yv(n) - j * dy
	227	aa = x2 + y2
	228	bb = ( dx - x )2 + y2
	229	cc = x2 + ( dy - y )2
	230	dd = ( dx - x )2 + ( dy - y )2
	231	gg = aa + bb + cc + dd
[849]	232
[1359]	233	pt_int_l = ( ( gg - aa ) * pt(k,j,i) + ( gg - bb ) * pt(k,j,i+1) &
	234	+ ( gg - cc ) * pt(k,j+1,i) + ( gg - dd ) * pt(k,j+1,i+1) &
	235	) / ( 3.0_wp * gg )
[849]	236
[1359]	237	pt_int_u = ( ( gg-aa ) * pt(k+1,j,i) + ( gg-bb ) * pt(k+1,j,i+1) &
	238	+ ( gg-cc ) * pt(k+1,j+1,i) + ( gg-dd ) * pt(k+1,j+1,i+1) &
	239	) / ( 3.0_wp * gg )
[849]	240
[1359]	241	pt_int = pt_int_l + ( particles(n)%z - zu(k) ) / dz * &
	242	( pt_int_u - pt_int_l )
[849]	243
[1359]	244	q_int_l = ( ( gg - aa ) * q(k,j,i) + ( gg - bb ) * q(k,j,i+1) &
	245	+ ( gg - cc ) * q(k,j+1,i) + ( gg - dd ) * q(k,j+1,i+1) &
	246	) / ( 3.0_wp * gg )
[849]	247
[1359]	248	q_int_u = ( ( gg-aa ) * q(k+1,j,i) + ( gg-bb ) * q(k+1,j,i+1) &
	249	+ ( gg-cc ) * q(k+1,j+1,i) + ( gg-dd ) * q(k+1,j+1,i+1) &
	250	) / ( 3.0_wp * gg )
[849]	251
[1359]	252	q_int = q_int_l + ( zv(n) - zu(k) ) / dz * &
	253	( q_int_u - q_int_l )
[849]	254
	255	!
[1359]	256	!-- Calculate real temperature and saturation vapor pressure
	257	p_int(n) = hyp(k) + ( particles(n)%z - zu(k) ) / dz * &
	258	( hyp(k+1)-hyp(k) )
	259	t_int(n) = pt_int * ( p_int(n) / 100000.0_wp )**0.286_wp
[849]	260
[1359]	261	e_s(n) = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / &
	262	t_int(n) ) )
[849]	263
	264	!
[1359]	265	!-- Current vapor pressure
	266	e_a(n) = q_int * p_int(n) / ( 0.378_wp * q_int + 0.622_wp )
[849]	267
[1359]	268	ENDDO
	269	ENDDO
	270
	271	new_r = 0.0_wp
	272	flag_1 = .false.
	273
	274	DO n = 1, number_of_particles
[849]	275	!
	276	!-- Change in radius by condensation/evaporation
[1359]	277	IF ( particles(n)%radius >= 4.0E-5_wp .AND. &
	278	e_a(n)/e_s(n) < 1.0_wp ) THEN
[849]	279	!
[1359]	280	!-- Approximation for large radii, where curvature and solution effects
	281	!-- can be neglected but ventilation effect has to be included in case of
	282	!-- evaporation.
	283	!-- First calculate the droplet's Reynolds number
	284	re_p = 2.0_wp * particles(n)%radius * ABS( particles(n)%speed_z ) / &
	285	molecular_viscosity
[1071]	286	!
[1359]	287	!-- Ventilation coefficient (Rogers and Yau, 1989):
	288	IF ( re_p > 2.5_wp ) THEN
	289	afactor_v(n) = 0.78_wp + 0.28_wp * SQRT( re_p )
[1071]	290	ELSE
[1359]	291	afactor_v(n) = 1.0_wp + 0.09_wp * re_p
[1071]	292	ENDIF
[1359]	293	flag_1(n) = .TRUE.
	294	ELSEIF ( particles(n)%radius >= 1.0E-6_wp .OR. &
[1071]	295	.NOT. curvature_solution_effects ) THEN
	296	!
[1359]	297	!-- Approximation for larger radii in case that curvature and solution
	298	!-- effects are neglected and ventilation effects does not play a role
	299	afactor_v(n) = 1.0_wp
	300	flag_1(n) = .TRUE.
[849]	301	ENDIF
[1359]	302	ENDDO
[849]	303
[1359]	304	DO n = 1, number_of_particles
[849]	305	!
[1359]	306	!-- Thermal conductivity for water (from Rogers and Yau, Table 7.1),
	307	!-- diffusivity for water vapor (after Hall und Pruppacher, 1976)
	308	thermal_conductivity_v(n) = 7.94048E-05_wp * t_int(n) + 0.00227011_wp
	309	diff_coeff_v(n) = 0.211E-4_wp * &
	310	( t_int(n) / 273.15_wp )*1.94_wp ( 101325.0_wp / p_int(n))
	311
	312	IF(flag_1(n)) then
	313	arg = particles(n)%radius*2 + 2.0_wp dt_3d * afactor_v(n) * &
	314	( e_a(n) / e_s(n) - 1.0_wp ) / &
	315	( ( l_d_rv / t_int(n) - 1.0_wp ) * l_v * rho_l / t_int(n) / &
	316	thermal_conductivity_v(n) + &
	317	rho_l * r_v * t_int(n) / diff_coeff_v(n) / e_s(n) )
	318
	319	arg = MAX( arg, 1.0E-16_wp )
	320	new_r(n) = SQRT( arg )
	321	ENDIF
	322	ENDDO
	323
	324	DO n = 1, number_of_particles
	325	IF ( curvature_solution_effects .AND. &
	326	( ( particles(n)%radius < 1.0E-6_wp ) .OR. &
	327	( new_r(n) < 1.0E-6_wp ) ) ) THEN
	328	!
[849]	329	!-- Curvature and solutions effects are included in growth equation.
	330	!-- Change in Radius is calculated with 4th-order Rosenbrock method
	331	!-- for stiff o.d.e's with monitoring local truncation error to adjust
	332	!-- stepsize (see Numerical recipes in FORTRAN, 2nd edition, p. 731).
	333	!-- For larger radii the simple analytic method (see ELSE) gives
	334	!-- almost the same results.
[1071]	335
	336	ros_count = 0
	337	repeat = .TRUE.
[849]	338	!
[1071]	339	!-- Carry out the Rosenbrock algorithm. In case of unreasonable results
	340	!-- the switch "repeat" will be set true and the algorithm will be carried
	341	!-- out again with the internal time step set to its initial (small) value.
[1359]	342	!-- Unreasonable results may occur if the external conditions, especially
	343	!-- the supersaturation, has significantly changed compared to the last
	344	!-- PALM timestep.
[1071]	345	DO WHILE ( repeat )
[849]	346
[1071]	347	repeat = .FALSE.
	348	!
[1359]	349	!-- Surface tension (Straka, 2009):
	350	sigma = 0.0761_wp - 0.000155_wp * ( t_int(n) - 273.15_wp )
[849]	351
[1071]	352	r_ros = particles(n)%radius
[1359]	353	dt_ros_sum = 0.0_wp ! internal integrated time (s)
[1071]	354	internal_timestep_count = 0
[849]	355
[1359]	356	ddenom = 1.0_wp / ( rho_l * r_v * t_int(n) / ( e_s(n) * &
	357	diff_coeff_v(n) ) + ( l_v / &
	358	( r_v * t_int(n) ) - 1.0_wp ) * &
	359	rho_l * l_v / ( thermal_conductivity_v(n) * &
	360	t_int(n) ) &
	361	)
[1071]	362
[1359]	363	afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int(n) )
[1071]	364
[849]	365	!
[1071]	366	!-- Take internal time step values from the end of last PALM time step
	367	dt_ros_next = particles(n)%rvar1
	368
[849]	369	!
[1071]	370	!-- Internal time step should not be > 1.0E-2 in case of evaporation
	371	!-- because larger values may lead to secondary solutions which are
	372	!-- physically unlikely
[1359]	373	IF ( dt_ros_next > 1.0E-2_wp .AND. e_a(n)/e_s(n) < 1.0_wp ) THEN
	374	dt_ros_next = 1.0E-3_wp
[1071]	375	ENDIF
[849]	376	!
[1071]	377	!-- If calculation of Rosenbrock method is repeated due to unreasonalble
	378	!-- results during previous try the initial internal time step has to be
	379	!-- reduced
	380	IF ( ros_count > 1 ) THEN
[1359]	381	dt_ros_next = dt_ros_next - ( 0.2_wp * dt_ros_next )
[1071]	382	ELSEIF ( ros_count > 5 ) THEN
[849]	383	!
[1071]	384	!-- Prevent creation of infinite loop
	385	message_string = 'ros_count > 5 in Rosenbrock method'
	386	CALL message( 'lpm_droplet_condensation', 'PA0018', 2, 2, &
	387	0, 6, 0 )
	388	ENDIF
	389
[849]	390	!
[1071]	391	!-- Internal time step must not be larger than PALM time step
	392	dt_ros = MIN( dt_ros_next, dt_3d )
	393	!
	394	!-- Integrate growth equation in time unless PALM time step is reached
	395	DO WHILE ( dt_ros_sum < dt_3d )
[849]	396
[1071]	397	internal_timestep_count = internal_timestep_count + 1
[849]	398
	399	!
[1071]	400	!-- Derivative at starting value
[1359]	401	drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - afactor / &
	402	r_ros + bfactor / r_ros**3 )
[1071]	403	drdt_ini = drdt
	404	dt_ros_sum_ini = dt_ros_sum
	405	r_ros_ini = r_ros
[849]	406
	407	!
[1071]	408	!-- Calculate radial derivative of dr/dt
[1359]	409	d2rdtdr = ddenom * ( ( 1.0_wp - e_a(n)/e_s(n) ) / r_ros**2 + &
	410	2.0_wp * afactor / r_ros**3 - &
	411	4.0_wp * bfactor / r_ros**5 )
[849]	412	!
[1071]	413	!-- Adjust stepsize unless required accuracy is reached
	414	DO jtry = 1, maxtry+1
[849]	415
[1071]	416	IF ( jtry == maxtry+1 ) THEN
	417	message_string = 'maxtry > 40 in Rosenbrock method'
[1359]	418	CALL message( 'lpm_droplet_condensation', 'PA0347', 2, &
	419	2, 0, 6, 0 )
[1071]	420	ENDIF
[849]	421
[1359]	422	aa = 1.0_wp / ( gam * dt_ros ) - d2rdtdr
[1071]	423	g1 = drdt_ini / aa
	424	r_ros = r_ros_ini + a21 * g1
[1359]	425	drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - &
	426	afactor / r_ros + &
[1071]	427	bfactor / r_ros**3 )
[849]	428
[1071]	429	g2 = ( drdt + c21 * g1 / dt_ros )&
	430	/ aa
	431	r_ros = r_ros_ini + a31 * g1 + a32 * g2
[1359]	432	drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - &
	433	afactor / r_ros + &
[1071]	434	bfactor / r_ros**3 )
[849]	435
[1071]	436	g3 = ( drdt + &
	437	( c31 * g1 + c32 * g2 ) / dt_ros ) / aa
	438	g4 = ( drdt + &
	439	( c41 * g1 + c42 * g2 + c43 * g3 ) / dt_ros ) / aa
	440	r_ros = r_ros_ini + b1 * g1 + b2 * g2 + b3 * g3 + b4 * g4
[849]	441
[1071]	442	dt_ros_sum = dt_ros_sum_ini + dt_ros
[849]	443
[1071]	444	IF ( dt_ros_sum == dt_ros_sum_ini ) THEN
	445	message_string = 'zero stepsize in Rosenbrock method'
[1359]	446	CALL message( 'lpm_droplet_condensation', 'PA0348', 2, &
	447	2, 0, 6, 0 )
[1071]	448	ENDIF
[849]	449	!
[1071]	450	!-- Calculate error
[1359]	451	err_ros = e1 * g1 + e2 * g2 + e3 * g3 + e4 * g4
	452	errmax = 0.0_wp
[1071]	453	errmax = MAX( errmax, ABS( err_ros / r_ros_ini ) ) / eps_ros
[849]	454	!
[1071]	455	!-- Leave loop if accuracy is sufficient, otherwise try again
	456	!-- with a reduced stepsize
[1359]	457	IF ( errmax <= 1.0_wp ) THEN
[1071]	458	EXIT
	459	ELSE
[1359]	460	dt_ros = SIGN( MAX( ABS( 0.9_wp * dt_ros * &
	461	errmax**pshrnk ), &
	462	shrnk * ABS( dt_ros ) ), dt_ros )
[1071]	463	ENDIF
	464
	465	ENDDO ! loop for stepsize adjustment
	466
	467	!
	468	!-- Calculate next internal time step
	469	IF ( errmax > errcon ) THEN
[1359]	470	dt_ros_next = 0.9_wp * dt_ros * errmax**pgrow
[849]	471	ELSE
[1071]	472	dt_ros_next = grow * dt_ros
[849]	473	ENDIF
	474
[1071]	475	!
	476	!-- Estimated time step is reduced if the PALM time step is exceeded
	477	IF ( ( dt_ros_next + dt_ros_sum ) >= dt_3d ) THEN
	478	dt_ros = dt_3d - dt_ros_sum
	479	ELSE
	480	dt_ros = dt_ros_next
	481	ENDIF
[849]	482
[1071]	483	ENDDO
[849]	484	!
[1071]	485	!-- Store internal time step value for next PALM step
	486	particles(n)%rvar1 = dt_ros_next
[849]	487
[1359]	488	new_r(n) = r_ros
[849]	489	!
[1071]	490	!-- Radius should not fall below 1E-8 because Rosenbrock method may
	491	!-- lead to errors otherwise
[1359]	492	new_r(n) = MAX( new_r(n), 1.0E-8_wp )
[1071]	493	!
	494	!-- Check if calculated droplet radius change is reasonable since in
	495	!-- case of droplet evaporation the Rosenbrock method may lead to
	496	!-- secondary solutions which are physically unlikely.
	497	!-- Due to the solution effect the droplets may grow for relative
[1359]	498	!-- humidities below 100%, but change of radius should not be too
	499	!-- large. In case of unreasonable droplet growth the Rosenbrock
	500	!-- method is recalculated using a smaller initial time step.
[1071]	501	!-- Limiting values are tested for droplets down to 1.0E-7
[1359]	502	IF ( new_r(n) - particles(n)%radius >= 3.0E-7_wp .AND. &
	503	e_a(n)/e_s(n) < 0.97_wp ) THEN
[1071]	504	ros_count = ros_count + 1
	505	repeat = .TRUE.
[849]	506	ENDIF
	507
[1071]	508	ENDDO ! Rosenbrock method
[849]	509
	510	ENDIF
	511
[1359]	512	delta_r = new_r(n) - particles(n)%radius
[849]	513
	514	!
	515	!-- Sum up the change in volume of liquid water for the respective grid
	516	!-- volume (this is needed later in lpm_calc_liquid_water_content for
	517	!-- calculating the release of latent heat)
[1359]	518	i = ip
	519	j = jp
	520	k = kp
[849]	521	! only exact if equidistant
	522
[1359]	523	ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * &
	524	rho_l * 1.33333333_wp * pi * &
	525	( new_r(n)3 - particles(n)%radius3 ) / &
[849]	526	( rho_surface * dx * dy * dz )
[1359]	527	IF ( ql_c(k,j,i) > 100.0_wp ) THEN
[849]	528	WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, &
	529	' ql_c=',ql_c(k,j,i), ' &part(',n,')%wf=', &
	530	particles(n)%weight_factor,' delta_r=',delta_r
	531	CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 )
	532	ENDIF
	533
	534	!
	535	!-- Change the droplet radius
[1359]	536	IF ( ( new_r(n) - particles(n)%radius ) < 0.0_wp .AND. &
	537	new_r(n) < 0.0_wp ) THEN
	538	WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, &
	539	' e_s=',e_s(n), ' e_a=',e_a(n),' t_int=',t_int(n), &
	540	' &delta_r=',delta_r, &
[849]	541	' particle_radius=',particles(n)%radius
	542	CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 )
	543	ENDIF
	544
	545	!
	546	!-- Sum up the total volume of liquid water (needed below for
	547	!-- re-calculating the weighting factors)
[1359]	548	ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r(n)**3
[849]	549
[1359]	550	particles(n)%radius = new_r(n)
[849]	551
	552	!
	553	!-- Determine radius class of the particle needed for collision
[1359]	554	IF ( ( hall_kernel .OR. wang_kernel ) .AND. use_kernel_tables ) &
[849]	555	THEN
[1359]	556	particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / &
	557	( rclass_ubound - rclass_lbound ) * &
[849]	558	radius_classes
	559	particles(n)%class = MIN( particles(n)%class, radius_classes )
	560	particles(n)%class = MAX( particles(n)%class, 1 )
	561	ENDIF
	562
	563	ENDDO
	564
	565	CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' )
	566
	567
	568	END SUBROUTINE lpm_droplet_condensation

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