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source: palm/trunk/SOURCE/lpm_collision_kernels_mod.f90 @ 1858

Last change on this file since 1858 was 1858, checked in by hoffmann, 8 years ago
Interpolation of collision kernels adjusted to more reasonable values
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1	!> @file lpm_collision_kernels_mod.f90
2	!--------------------------------------------------------------------------------!
3	! This file is part of PALM.
4	!
5	! PALM is free software: you can redistribute it and/or modify it under the terms
6	! of the GNU General Public License as published by the Free Software Foundation,
7	! either version 3 of the License, or (at your option) any later version.
8	!
9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
12	!
13	! You should have received a copy of the GNU General Public License along with
14	! PALM. If not, see <http://www.gnu.org/licenses/>.
15	!
16	! Copyright 1997-2016 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	! Interpolation of collision kernels adjusted to more reasonable values.
22	! Reformatting of the code.
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_collision_kernels_mod.f90 1858 2016-04-13 13:12:11Z hoffmann $
27	!
28	! 1850 2016-04-08 13:29:27Z maronga
29	! Module renamed
30	!
31	! 1822 2016-04-07 07:49:42Z hoffmann
32	! PALM kernel has been deleted.
33	! Bugfix in the calculation of the turbulent enhancement factor of the
34	! collection efficiency.
35	!
36	! Unused variables removed.
37	!
38	! 1776 2016-03-02 17:54:58Z hoffmann
39	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
40	!
41	! 1682 2015-10-07 23:56:08Z knoop
42	! Code annotations made doxygen readable
43	!
44	! 1519 2015-01-08 10:20:42Z hoffmann
45	! Bugfix: Using the new particle structure, particles are not sorted by size.
46	! Hence, computation of collision efficiencies must ensure that the ratio of
47	! two colliding droplets is < 1.
48	!
49	! 1359 2014-04-11 17:15:14Z hoffmann
50	! New particle structure integrated.
51	! Kind definition added to all floating point numbers.
52	!
53	! 1346 2014-03-27 13:18:20Z heinze
54	! Bugfix: REAL constants provided with KIND-attribute especially in call of
55	! intrinsic function like MAX, MIN, SIGN
56	!
57	! 1322 2014-03-20 16:38:49Z raasch
58	! REAL constants defined as wp_kind
59	!
60	! 1320 2014-03-20 08:40:49Z
61	! ONLY-attribute added to USE-statements,
62	! kind-parameters added to all INTEGER and REAL declaration statements,
63	! kinds are defined in new module kinds,
64	! revision history before 2012 removed,
65	! comment fields (!:) to be used for variable explanations added to
66	! all variable declaration statements
67	!
68	! 1092 2013-02-02 11:24:22Z raasch
69	! unused variables removed
70	!
71	! 1071 2012-11-29 16:54:55Z franke
72	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
73	!
74	! 1036 2012-10-22 13:43:42Z raasch
75	! code put under GPL (PALM 3.9)
76	!
77	! 1007 2012-09-19 14:30:36Z franke
78	! converted all units to SI units and replaced some parameters by corresponding
79	! PALM parameters
80	! Bugfix: factor in calculation of enhancement factor for collision efficencies
81	! changed from 10. to 1.0
82	!
83	! 849 2012-03-15 10:35:09Z raasch
84	! routine collision_efficiency_rogers added (moved from former advec_particles
85	! to here)
86	!
87	! 835 2012-02-22 11:21:19Z raasch $
88	! Bugfix: array diss can be used only in case of Wang kernel
89	!
90	! 828 2012-02-21 12:00:36Z raasch
91	! code has been completely reformatted, routine colker renamed
92	! recalculate_kernel,
93	! routine init_kernels added, radius is now communicated to the collision
94	! routines by array radclass
95	!
96	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
97	!
98	! 825 2012-02-19 03:03:44Z raasch
99	! routine renamed from wang_kernel to lpm_collision_kernels,
100	! turbulence_effects on collision replaced by wang_kernel
101	!
102	! 790 2011-11-29 03:11:20Z raasch
103	! initial revision
104	!
105	! Description:
106	! ------------
107	!> This module calculates collision efficiencies either due to pure gravitational
108	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
109	!> including the effects of turbulence (Wang kernel, see Wang and
110	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
111	!> New J. Phys., 10, 075016). The original code has been
112	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
113	!> here.
114	!------------------------------------------------------------------------------!
115	MODULE lpm_collision_kernels_mod
116
117
118	USE constants, &
119	ONLY: pi
120
121	USE kinds
122
123	USE particle_attributes, &
124	ONLY: collision_kernel, dissipation_classes, particles, &
125	radius_classes
126
127	USE pegrid
128
129
130	IMPLICIT NONE
131
132	PRIVATE
133
134	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
135	recalculate_kernel
136
137	REAL(wp) :: epsilon !<
138	REAL(wp) :: rclass_lbound !<
139	REAL(wp) :: rclass_ubound !<
140	REAL(wp) :: urms !<
141
142	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
143	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
144	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
145
146	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
147	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
148	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
149	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
150	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
151
152	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
153
154	SAVE
155
156	!
157	!-- Public interfaces
158	INTERFACE init_kernels
159	MODULE PROCEDURE init_kernels
160	END INTERFACE init_kernels
161
162	INTERFACE recalculate_kernel
163	MODULE PROCEDURE recalculate_kernel
164	END INTERFACE recalculate_kernel
165
166
167	CONTAINS
168
169
170	!------------------------------------------------------------------------------!
171	! Description:
172	! ------------
173	!> Initialization of the collision efficiency matrix with fixed radius and
174	!> dissipation classes, calculated at simulation start only.
175	!------------------------------------------------------------------------------!
176
177	SUBROUTINE init_kernels
178
179	IMPLICIT NONE
180
181	INTEGER(iwp) :: i !<
182	INTEGER(iwp) :: j !<
183	INTEGER(iwp) :: k !<
184
185
186	!
187	!-- Calculate collision efficiencies for fixed radius- and dissipation
188	!-- classes
189	IF ( collision_kernel(6:9) == 'fast' ) THEN
190
191	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
192	0:dissipation_classes), epsclass(1:dissipation_classes), &
193	radclass(1:radius_classes) )
194
195	!
196	!-- Calculate the radius class bounds with logarithmic distances
197	!-- in the interval [1.0E-6, 1000.0E-6] m
198	rclass_lbound = LOG( 1.0E-6_wp )
199	rclass_ubound = LOG( 1000.0E-6_wp )
200	radclass(1) = EXP( rclass_lbound )
201	DO i = 2, radius_classes
202	radclass(i) = EXP( rclass_lbound + &
203	( rclass_ubound - rclass_lbound ) * &
204	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
205	ENDDO
206
207	!
208	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
209	DO i = 1, dissipation_classes
210	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
211	ENDDO
212	!
213	!-- Calculate collision efficiencies of the Wang/ayala kernel
214	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
215	ecf(1:radius_classes,1:radius_classes), &
216	gck(1:radius_classes,1:radius_classes), &
217	winf(1:radius_classes) )
218
219	DO k = 1, dissipation_classes
220
221	epsilon = epsclass(k)
222	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
223
224	CALL turbsd
225	CALL turb_enhance_eff
226	CALL effic
227
228	DO j = 1, radius_classes
229	DO i = 1, radius_classes
230	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
231	ENDDO
232	ENDDO
233
234	ENDDO
235
236	!
237	!-- Calculate collision efficiencies of the Hall kernel
238	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
239	hwratio(1:radius_classes,1:radius_classes) )
240
241	CALL fallg
242	CALL effic
243
244	DO j = 1, radius_classes
245	DO i = 1, radius_classes
246	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
247	* ec(i,j) * ABS( winf(j) - winf(i) )
248	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
249	ENDDO
250	ENDDO
251
252	!
253	!-- Test output of efficiencies
254	IF ( j == -1 ) THEN
255
256	PRINT, '** Hall kernel'
257	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
258	i = 1,radius_classes )
259	DO j = 1, radius_classes
260	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
261	( hkernel(i,j), i = 1,radius_classes )
262	ENDDO
263
264	DO k = 1, dissipation_classes
265	DO i = 1, radius_classes
266	DO j = 1, radius_classes
267	IF ( hkernel(i,j) == 0.0_wp ) THEN
268	hwratio(i,j) = 9999999.9_wp
269	ELSE
270	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
271	ENDIF
272	ENDDO
273	ENDDO
274
275	PRINT, '** epsilon = ', epsclass(k)
276	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
277	i = 1,radius_classes )
278	DO j = 1, radius_classes
279	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
280	( hwratio(i,j), i = 1,radius_classes )
281	ENDDO
282	ENDDO
283
284	ENDIF
285
286	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
287
288	ENDIF
289
290	END SUBROUTINE init_kernels
291
292
293	!------------------------------------------------------------------------------!
294	! Description:
295	! ------------
296	!> Calculation of collision kernels during each timestep and for each grid box
297	!------------------------------------------------------------------------------!
298	SUBROUTINE recalculate_kernel( i1, j1, k1 )
299
300	USE arrays_3d, &
301	ONLY: diss
302
303	USE particle_attributes, &
304	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
305
306	IMPLICIT NONE
307
308	INTEGER(iwp) :: i !<
309	INTEGER(iwp) :: i1 !<
310	INTEGER(iwp) :: j !<
311	INTEGER(iwp) :: j1 !<
312	INTEGER(iwp) :: k1 !<
313
314
315	number_of_particles = prt_count(k1,j1,i1)
316	radius_classes = number_of_particles ! necessary to use the same
317	! subroutines as for
318	! precalculated kernels
319
320	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
321	radclass(1:number_of_particles), winf(1:number_of_particles) )
322
323	!
324	!-- Store particle radii on the radclass array
325	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
326
327	IF ( wang_kernel ) THEN
328	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
329	ELSE
330	epsilon = 0.0_wp
331	ENDIF
332	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
333
334	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
335	!
336	!-- Call routines to calculate efficiencies for the Wang kernel
337	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
338	ecf(1:number_of_particles,1:number_of_particles) )
339
340	CALL turbsd
341	CALL turb_enhance_eff
342	CALL effic
343
344	DO j = 1, number_of_particles
345	DO i = 1, number_of_particles
346	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
347	ENDDO
348	ENDDO
349
350	DEALLOCATE( gck, ecf )
351
352	ELSE
353	!
354	!-- Call routines to calculate efficiencies for the Hall kernel
355	CALL fallg
356	CALL effic
357
358	DO j = 1, number_of_particles
359	DO i = 1, number_of_particles
360	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
361	* ec(i,j) * ABS( winf(j) - winf(i) )
362	ENDDO
363	ENDDO
364
365	ENDIF
366
367	DEALLOCATE( ec, radclass, winf )
368
369	END SUBROUTINE recalculate_kernel
370
371
372	!------------------------------------------------------------------------------!
373	! Description:
374	! ------------
375	!> Calculation of effects of turbulence on the geometric collision kernel
376	!> (by including the droplets' average radial relative velocities and their
377	!> radial distribution function) following the analytic model by Aayala et al.
378	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
379	!> page 37ff.
380	!>
381	!> Input parameters, which need to be replaced by PALM parameters:
382	!> water density, air density
383	!------------------------------------------------------------------------------!
384	SUBROUTINE turbsd
385
386	USE control_parameters, &
387	ONLY: g, molecular_viscosity
388
389	USE particle_attributes, &
390	ONLY: radius_classes
391
392	IMPLICIT NONE
393
394	INTEGER(iwp) :: i !<
395	INTEGER(iwp) :: j !<
396
397	REAL(wp) :: ao !<
398	REAL(wp) :: ao_gr !<
399	REAL(wp) :: bbb !<
400	REAL(wp) :: be !<
401	REAL(wp) :: b1 !<
402	REAL(wp) :: b2 !<
403	REAL(wp) :: ccc !<
404	REAL(wp) :: c1 !<
405	REAL(wp) :: c1_gr !<
406	REAL(wp) :: c2 !<
407	REAL(wp) :: d1 !<
408	REAL(wp) :: d2 !<
409	REAL(wp) :: eta !<
410	REAL(wp) :: e1 !<
411	REAL(wp) :: e2 !<
412	REAL(wp) :: fao_gr !<
413	REAL(wp) :: fr !<
414	REAL(wp) :: grfin !<
415	REAL(wp) :: lambda !<
416	REAL(wp) :: lambda_re !<
417	REAL(wp) :: lf !<
418	REAL(wp) :: rc !<
419	REAL(wp) :: rrp !<
420	REAL(wp) :: sst !<
421	REAL(wp) :: tauk !<
422	REAL(wp) :: tl !<
423	REAL(wp) :: t2 !<
424	REAL(wp) :: tt !<
425	REAL(wp) :: t1 !<
426	REAL(wp) :: vk !<
427	REAL(wp) :: vrms1xy !<
428	REAL(wp) :: vrms2xy !<
429	REAL(wp) :: v1 !<
430	REAL(wp) :: v1v2xy !<
431	REAL(wp) :: v1xysq !<
432	REAL(wp) :: v2 !<
433	REAL(wp) :: v2xysq !<
434	REAL(wp) :: wrfin !<
435	REAL(wp) :: wrgrav2 !<
436	REAL(wp) :: wrtur2xy !<
437	REAL(wp) :: xx !<
438	REAL(wp) :: yy !<
439	REAL(wp) :: z !<
440
441	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
442	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
443
444	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
445	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
446	tl = urms**2 / epsilon
447	lf = 0.5_wp * urms**3 / epsilon
448	tauk = SQRT( molecular_viscosity / epsilon )
449	eta = ( molecular_viscosity3 / epsilon )0.25_wp
450	vk = eta / tauk
451
452	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
453	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
454
455	!
456	!-- Get terminal velocity of droplets
457	CALL fallg
458
459	DO i = 1, radius_classes
460	tau(i) = winf(i) / g ! inertial time scale
461	st(i) = tau(i) / tauk ! Stokes number
462	ENDDO
463
464	!
465	!-- Calculate average radial relative velocity at contact (wrfin)
466	z = tt / tl
467	be = SQRT( 2.0_wp ) * lambda / lf
468	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
469	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
470	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
471	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
472	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
473	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
474	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
475	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
476	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
477	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
478
479	DO i = 1, radius_classes
480
481	v1 = winf(i)
482	t1 = tau(i)
483
484	DO j = 1, i
485	rrp = radclass(i) + radclass(j)
486	v2 = winf(j)
487	t2 = tau(j)
488
489	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
490	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
491	v1xysq = v1xysq * urms**2 / t1
492	vrms1xy = SQRT( v1xysq )
493
494	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
495	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
496	v2xysq = v2xysq * urms**2 / t2
497	vrms2xy = SQRT( v2xysq )
498
499	IF ( winf(i) >= winf(j) ) THEN
500	v1 = winf(i)
501	t1 = tau(i)
502	v2 = winf(j)
503	t2 = tau(j)
504	ELSE
505	v1 = winf(j)
506	t1 = tau(j)
507	v2 = winf(i)
508	t2 = tau(i)
509	ENDIF
510
511	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
512	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
513	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
514	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
515	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
516	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
517	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
518	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
519	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
520	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
521
522	!
523	!-- Calculate radial distribution function (grfin)
524	IF ( st(j) > st(i) ) THEN
525	sst = st(j)
526	ELSE
527	sst = st(i)
528	ENDIF
529
530	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
531	sst*2 + 5.3406_wp sst
532	IF ( xx < 0.0_wp ) xx = 0.0_wp
533	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
534
535	c1_gr = xx / ( g / vk * tauk )**yy
536
537	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
538	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
539	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
540
541	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
542	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
543
544	!
545	!-- Calculate general collection kernel (without the consideration of
546	!-- collection efficiencies)
547	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
548	gck(j,i) = gck(i,j)
549
550	ENDDO
551	ENDDO
552
553	END SUBROUTINE turbsd
554
555	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
556	!
557	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
558	!-- effects on the collision kernel
559	IMPLICIT NONE
560
561	REAL(wp) :: a !<
562	REAL(wp) :: aa1 !<
563	REAL(wp) :: b !<
564	REAL(wp) :: tau0 !<
565	REAL(wp) :: vsett !<
566
567	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
568	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
569
570	END FUNCTION phi_w
571
572	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
573	!
574	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
575	!-- effects on the collision kernel
576	IMPLICIT NONE
577
578	REAL(wp) :: a !<
579	REAL(wp) :: aa1 !<
580	REAL(wp) :: aa2 !<
581	REAL(wp) :: aa3 !<
582	REAL(wp) :: aa4 !<
583	REAL(wp) :: aa5 !<
584	REAL(wp) :: aa6 !<
585	REAL(wp) :: b !<
586	REAL(wp) :: tau1 !<
587	REAL(wp) :: tau2 !<
588	REAL(wp) :: vsett1 !<
589	REAL(wp) :: vsett2 !<
590
591	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
592	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
593	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
594	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
595	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
596	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
597	vsett1 / vsett2
598	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
599	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
600	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
601	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
602
603	END FUNCTION zhi
604
605
606	!------------------------------------------------------------------------------!
607	! Description:
608	! ------------
609	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
610	!> Meteorol.)
611	!------------------------------------------------------------------------------!
612	SUBROUTINE fallg
613
614	USE particle_attributes, &
615	ONLY: radius_classes
616
617	IMPLICIT NONE
618
619	INTEGER(iwp) :: j !<
620
621	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
622	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
623	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
624	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
625	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
626	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
627
628	REAL(wp) :: diameter !< droplet diameter in mm
629
630
631	DO j = 1, radius_classes
632
633	diameter = radclass(j) * 2000.0_wp
634
635	IF ( diameter <= d0_rog ) THEN
636	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
637	EXP( -k_low_rog * diameter ) )
638	ELSE
639	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
640	ENDIF
641
642	ENDDO
643
644	END SUBROUTINE fallg
645
646
647	!------------------------------------------------------------------------------!
648	! Description:
649	! ------------
650	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
651	!------------------------------------------------------------------------------!
652	SUBROUTINE effic
653
654	USE particle_attributes, &
655	ONLY: radius_classes
656
657	IMPLICIT NONE
658
659	INTEGER(iwp) :: i !<
660	INTEGER(iwp) :: iq !<
661	INTEGER(iwp) :: ir !<
662	INTEGER(iwp) :: j !<
663	INTEGER(iwp) :: k !<
664
665	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
666
667	LOGICAL, SAVE :: first = .TRUE. !<
668
669	REAL(wp) :: ek !<
670	REAL(wp) :: particle_radius !<
671	REAL(wp) :: pp !<
672	REAL(wp) :: qq !<
673	REAL(wp) :: rq !<
674
675	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
676
677	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
678
679	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
680
681	!
682	!-- Initial assignment of constants
683	IF ( first ) THEN
684
685	first = .FALSE.
686	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
687	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
688	150.0_wp, 200.0_wp, 300.0_wp /)
689
690	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
691	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
692	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
693	0.90_wp, 0.95_wp, 1.00_wp /)
694
695	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
696	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
697	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
698	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
699	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
700	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
701	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
702	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
703	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
704	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
705	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
706	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
707	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
708	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
709	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
710	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
711	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
712	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
713	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
714	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
715	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
716	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
717	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
718	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
719	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
720	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
721	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
722	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
723	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
724	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
725	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
726	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
727	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
728	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
729	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
730	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
731	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
732	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
733	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
734	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
735	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
736	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
737	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
738	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
739	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
740	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
741	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
742	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
743	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
744	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
745	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
746	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
747	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
748	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
749	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
750	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
751	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
752	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
753	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
754	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
755	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
756	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
757	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
758	ENDIF
759
760	!
761	!-- Calculate the radius class index of particles with respect to array r
762	!-- Radius has to be in microns
763	ALLOCATE( ira(1:radius_classes) )
764	DO j = 1, radius_classes
765	particle_radius = radclass(j) * 1.0E6_wp
766	DO k = 1, 15
767	IF ( particle_radius < r0(k) ) THEN
768	ira(j) = k
769	EXIT
770	ENDIF
771	ENDDO
772	IF ( particle_radius >= r0(15) ) ira(j) = 16
773	ENDDO
774
775	!
776	!-- Two-dimensional linear interpolation of the collision efficiency.
777	!-- Radius has to be in microns
778	DO j = 1, radius_classes
779	DO i = 1, j
780
781	ir = ira(j)
782	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
783	iq = INT( rq * 20 ) + 1
784	iq = MAX( iq , 2)
785
786	IF ( ir < 16 ) THEN
787	IF ( ir >= 2 ) THEN
788	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
789	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
790	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
791	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
792	* ecoll(ir-1,iq-1) &
793	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
794	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
795	+ pp * qq * ecoll(ir,iq)
796	ELSE
797	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
798	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
799	ENDIF
800	ELSE
801	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
802	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
803	ec(j,i) = MIN( ek, 1.0_wp )
804	ENDIF
805
806	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
807
808	ec(i,j) = ec(j,i)
809
810	ENDDO
811	ENDDO
812
813	DEALLOCATE( ira )
814
815	END SUBROUTINE effic
816
817
818	!------------------------------------------------------------------------------!
819	! Description:
820	! ------------
821	!> Interpolation of turbulent enhancement factor for collision efficencies
822	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
823	!------------------------------------------------------------------------------!
824	SUBROUTINE turb_enhance_eff
825
826	USE particle_attributes, &
827	ONLY: radius_classes
828
829	IMPLICIT NONE
830
831	INTEGER(iwp) :: i !<
832	INTEGER(iwp) :: iq !<
833	INTEGER(iwp) :: ir !<
834	INTEGER(iwp) :: j !<
835	INTEGER(iwp) :: k !<
836	INTEGER(iwp) :: kk !<
837
838	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
839
840	LOGICAL, SAVE :: first = .TRUE. !<
841
842	REAL(wp) :: particle_radius !<
843	REAL(wp) :: pp !<
844	REAL(wp) :: qq !<
845	REAL(wp) :: rq !<
846	REAL(wp) :: y1 !<
847	REAL(wp) :: y2 !<
848	REAL(wp) :: y3 !<
849
850	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
851	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
852
853	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
854	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
855
856	!
857	!-- Initial assignment of constants
858	IF ( first ) THEN
859
860	first = .FALSE.
861
862	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
863	100.0_wp /)
864
865	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
866	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
867	!
868	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
869	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
870	1.207_wp, 1.207_wp, 1.0_wp /)
871	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
872	1.069_wp, 1.069_wp, 1.0_wp /)
873	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
874	1.000_wp, 1.000_wp, 1.0_wp /)
875	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
876	1.025_wp, 1.025_wp, 1.0_wp /)
877	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
878	1.056_wp, 1.056_wp, 1.0_wp /)
879	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
880	1.028_wp, 1.028_wp, 1.0_wp /)
881	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
882	1.046_wp, 1.046_wp, 1.0_wp /)
883	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
884	1.029_wp, 1.029_wp, 1.0_wp /)
885	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
886	1.021_wp, 1.021_wp, 1.0_wp /)
887	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
888	1.088_wp, 1.088_wp, 1.0_wp /)
889	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
890	2.60_wp, 2.60_wp, 1.0_wp /)
891	!
892	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
893	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
894	1.445_wp, 1.445_wp, 1.0_wp /)
895	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
896	1.201_wp, 1.201_wp, 1.0_wp /)
897	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
898	1.150_wp, 1.150_wp, 1.0_wp /)
899	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
900	1.126_wp, 1.126_wp, 1.0_wp /)
901	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
902	1.092_wp, 1.092_wp, 1.0_wp /)
903	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
904	1.051_wp, 1.051_wp, 1.0_wp /)
905	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
906	1.086_wp, 1.086_wp, 1.0_wp /)
907	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
908	1.063_wp, 1.063_wp, 1.0_wp /)
909	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
910	1.100_wp, 1.100_wp, 1.0_wp /)
911	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
912	1.120_wp, 1.120_wp, 1.0_wp /)
913	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
914	26.0_wp, 26.0_wp, 1.0_wp /)
915
916	ENDIF
917
918	!
919	!-- Calculate the radius class index of particles with respect to array r0
920	!-- The droplet radius has to be given in microns.
921	ALLOCATE( ira(1:radius_classes) )
922
923	DO j = 1, radius_classes
924	particle_radius = radclass(j) * 1.0E6_wp
925	DO k = 1, 7
926	IF ( particle_radius < r0(k) ) THEN
927	ira(j) = k
928	EXIT
929	ENDIF
930	ENDDO
931	IF ( particle_radius >= r0(7) ) ira(j) = 8
932	ENDDO
933
934	!
935	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
936	!-- The droplet radius has to be given in microns.
937	DO j = 1, radius_classes
938	DO i = 1, j
939
940	ir = ira(j)
941	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
942
943	DO kk = 2, 11
944	IF ( rq <= rat(kk) ) THEN
945	iq = kk
946	EXIT
947	ENDIF
948	ENDDO
949
950	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
951
952	IF ( ir < 8 ) THEN
953	IF ( ir >= 2 ) THEN
954	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
955	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
956	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
957	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
958	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
959	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
960	pp * qq * ecoll_100(ir,iq)
961	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
962	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
963	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
964	pp * qq * ecoll_400(ir,iq)
965	ELSE
966	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
967	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
968	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
969	ENDIF
970	ELSE
971	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
972	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
973	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
974	ENDIF
975	!
976	!-- Linear interpolation of turbulent enhancement factor
977	IF ( epsilon <= 0.01_wp ) THEN
978	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
979	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
980	ELSEIF ( epsilon <= 0.06_wp ) THEN
981	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
982	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
983	ELSE
984	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
985	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
986	ENDIF
987
988	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
989
990	ecf(i,j) = ecf(j,i)
991
992	ENDDO
993	ENDDO
994
995	END SUBROUTINE turb_enhance_eff
996
997	END MODULE lpm_collision_kernels_mod

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