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source: palm/trunk/SOURCE/lpm_collision_kernels_mod.f90 @ 1850

Last change on this file since 1850 was 1850, checked in by maronga, 8 years ago
added _mod string to several filenames to meet the naming convection for modules
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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	! Module renamed
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_collision_kernels_mod.f90 1850 2016-04-08 13:29:27Z maronga $
27	!
28	! 1822 2016-04-07 07:49:42Z hoffmann
29	! PALM kernel has been deleted.
30	! Bugfix in the calculation of the turbulent enhancement factor of the
31	! collection efficiency.
32	!
33	! Unused variables removed.
34	!
35	! 1776 2016-03-02 17:54:58Z hoffmann
36	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
37	!
38	! 1682 2015-10-07 23:56:08Z knoop
39	! Code annotations made doxygen readable
40	!
41	! 1519 2015-01-08 10:20:42Z hoffmann
42	! Bugfix: Using the new particle structure, particles are not sorted by size.
43	! Hence, computation of collision efficiencies must ensure that the ratio of
44	! two colliding droplets is < 1.
45	!
46	! 1359 2014-04-11 17:15:14Z hoffmann
47	! New particle structure integrated.
48	! Kind definition added to all floating point numbers.
49	!
50	! 1346 2014-03-27 13:18:20Z heinze
51	! Bugfix: REAL constants provided with KIND-attribute especially in call of
52	! intrinsic function like MAX, MIN, SIGN
53	!
54	! 1322 2014-03-20 16:38:49Z raasch
55	! REAL constants defined as wp_kind
56	!
57	! 1320 2014-03-20 08:40:49Z
58	! ONLY-attribute added to USE-statements,
59	! kind-parameters added to all INTEGER and REAL declaration statements,
60	! kinds are defined in new module kinds,
61	! revision history before 2012 removed,
62	! comment fields (!:) to be used for variable explanations added to
63	! all variable declaration statements
64	!
65	! 1092 2013-02-02 11:24:22Z raasch
66	! unused variables removed
67	!
68	! 1071 2012-11-29 16:54:55Z franke
69	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
70	!
71	! 1036 2012-10-22 13:43:42Z raasch
72	! code put under GPL (PALM 3.9)
73	!
74	! 1007 2012-09-19 14:30:36Z franke
75	! converted all units to SI units and replaced some parameters by corresponding
76	! PALM parameters
77	! Bugfix: factor in calculation of enhancement factor for collision efficencies
78	! changed from 10. to 1.0
79	!
80	! 849 2012-03-15 10:35:09Z raasch
81	! routine collision_efficiency_rogers added (moved from former advec_particles
82	! to here)
83	!
84	! 835 2012-02-22 11:21:19Z raasch $
85	! Bugfix: array diss can be used only in case of Wang kernel
86	!
87	! 828 2012-02-21 12:00:36Z raasch
88	! code has been completely reformatted, routine colker renamed
89	! recalculate_kernel,
90	! routine init_kernels added, radius is now communicated to the collision
91	! routines by array radclass
92	!
93	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
94	!
95	! 825 2012-02-19 03:03:44Z raasch
96	! routine renamed from wang_kernel to lpm_collision_kernels,
97	! turbulence_effects on collision replaced by wang_kernel
98	!
99	! 790 2011-11-29 03:11:20Z raasch
100	! initial revision
101	!
102	! Description:
103	! ------------
104	!> This module calculates collision efficiencies either due to pure gravitational
105	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
106	!> including the effects of turbulence (Wang kernel, see Wang and
107	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
108	!> New J. Phys., 10, 075016). The original code has been
109	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
110	!> here.
111	!------------------------------------------------------------------------------!
112	MODULE lpm_collision_kernels_mod
113
114
115	USE constants, &
116	ONLY: pi
117
118	USE kinds
119
120	USE particle_attributes, &
121	ONLY: collision_kernel, dissipation_classes, particles, &
122	radius_classes
123
124	USE pegrid
125
126
127	IMPLICIT NONE
128
129	PRIVATE
130
131	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
132	recalculate_kernel
133
134	REAL(wp) :: epsilon !<
135	REAL(wp) :: rclass_lbound !<
136	REAL(wp) :: rclass_ubound !<
137	REAL(wp) :: urms !<
138
139	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
140	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
141	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
142
143	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
144	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
145	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
146	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
147	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
148
149	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
150
151	SAVE
152
153	!
154	!-- Public interfaces
155	INTERFACE init_kernels
156	MODULE PROCEDURE init_kernels
157	END INTERFACE init_kernels
158
159	INTERFACE recalculate_kernel
160	MODULE PROCEDURE recalculate_kernel
161	END INTERFACE recalculate_kernel
162
163
164	CONTAINS
165
166
167	!------------------------------------------------------------------------------!
168	! Description:
169	! ------------
170	!> Initialization of the collision efficiency matrix with fixed radius and
171	!> dissipation classes, calculated at simulation start only.
172	!------------------------------------------------------------------------------!
173
174	SUBROUTINE init_kernels
175
176	IMPLICIT NONE
177
178	INTEGER(iwp) :: i !<
179	INTEGER(iwp) :: j !<
180	INTEGER(iwp) :: k !<
181
182
183	!
184	!-- Calculate collision efficiencies for fixed radius- and dissipation
185	!-- classes
186	IF ( collision_kernel(6:9) == 'fast' ) THEN
187
188	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
189	0:dissipation_classes), epsclass(1:dissipation_classes), &
190	radclass(1:radius_classes) )
191
192	!
193	!-- Calculate the radius class bounds with logarithmic distances
194	!-- in the interval [1.0E-6, 2.0E-4] m
195	rclass_lbound = LOG( 1.0E-6_wp )
196	rclass_ubound = LOG( 2.0E-4_wp )
197	radclass(1) = EXP( rclass_lbound )
198	DO i = 2, radius_classes
199	radclass(i) = EXP( rclass_lbound + &
200	( rclass_ubound - rclass_lbound ) * &
201	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
202	ENDDO
203
204	!
205	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
206	DO i = 1, dissipation_classes
207	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
208	ENDDO
209	!
210	!-- Calculate collision efficiencies of the Wang/ayala kernel
211	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
212	ecf(1:radius_classes,1:radius_classes), &
213	gck(1:radius_classes,1:radius_classes), &
214	winf(1:radius_classes) )
215
216	DO k = 1, dissipation_classes
217
218	epsilon = epsclass(k)
219	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
220
221	CALL turbsd
222	CALL turb_enhance_eff
223	CALL effic
224
225	DO j = 1, radius_classes
226	DO i = 1, radius_classes
227	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
228	ENDDO
229	ENDDO
230
231	ENDDO
232
233	!
234	!-- Calculate collision efficiencies of the Hall kernel
235	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
236	hwratio(1:radius_classes,1:radius_classes) )
237
238	CALL fallg
239	CALL effic
240
241	DO j = 1, radius_classes
242	DO i = 1, radius_classes
243	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
244	* ec(i,j) * ABS( winf(j) - winf(i) )
245	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
246	ENDDO
247	ENDDO
248
249	!
250	!-- Test output of efficiencies
251	IF ( j == -1 ) THEN
252
253	PRINT, '** Hall kernel'
254	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
255	i = 1,radius_classes )
256	DO j = 1, radius_classes
257	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
258	( hkernel(i,j), i = 1,radius_classes )
259	ENDDO
260
261	DO k = 1, dissipation_classes
262	DO i = 1, radius_classes
263	DO j = 1, radius_classes
264	IF ( hkernel(i,j) == 0.0_wp ) THEN
265	hwratio(i,j) = 9999999.9_wp
266	ELSE
267	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
268	ENDIF
269	ENDDO
270	ENDDO
271
272	PRINT, '** epsilon = ', epsclass(k)
273	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
274	i = 1,radius_classes )
275	DO j = 1, radius_classes
276	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
277	( hwratio(i,j), i = 1,radius_classes )
278	ENDDO
279	ENDDO
280
281	ENDIF
282
283	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
284
285	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
286	THEN
287	!
288	!-- Initial settings for Hall- and Wang-Kernel
289	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
290	ENDIF
291
292	END SUBROUTINE init_kernels
293
294
295	!------------------------------------------------------------------------------!
296	! Description:
297	! ------------
298	!> Calculation of collision kernels during each timestep and for each grid box
299	!------------------------------------------------------------------------------!
300	SUBROUTINE recalculate_kernel( i1, j1, k1 )
301
302	USE arrays_3d, &
303	ONLY: diss
304
305	USE particle_attributes, &
306	ONLY: prt_count, radius_classes, wang_kernel
307
308	IMPLICIT NONE
309
310	INTEGER(iwp) :: i !<
311	INTEGER(iwp) :: i1 !<
312	INTEGER(iwp) :: j !<
313	INTEGER(iwp) :: j1 !<
314	INTEGER(iwp) :: k1 !<
315	INTEGER(iwp) :: pend !<
316	INTEGER(iwp) :: pstart !<
317
318
319	pstart = 1
320	pend = prt_count(k1,j1,i1)
321	radius_classes = prt_count(k1,j1,i1)
322
323	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
324	radclass(1:radius_classes), winf(1:radius_classes) )
325
326	!
327	!-- Store particle radii on the radclass array
328	radclass(1:radius_classes) = particles(pstart:pend)%radius
329
330	IF ( wang_kernel ) THEN
331	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
332	ELSE
333	epsilon = 0.0_wp
334	ENDIF
335	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
336
337	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
338	!
339	!-- Call routines to calculate efficiencies for the Wang kernel
340	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
341	ecf(1:radius_classes,1:radius_classes) )
342
343	CALL turbsd
344	CALL turb_enhance_eff
345	CALL effic
346
347	DO j = 1, radius_classes
348	DO i = 1, radius_classes
349	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
350	ENDDO
351	ENDDO
352
353	DEALLOCATE( gck, ecf )
354
355	ELSE
356	!
357	!-- Call routines to calculate efficiencies for the Hall kernel
358	CALL fallg
359	CALL effic
360
361	DO j = 1, radius_classes
362	DO i = 1, radius_classes
363	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
364	( radclass(j) + radclass(i) )**2 &
365	* ec(i,j) * ABS( winf(j) - winf(i) )
366	ENDDO
367	ENDDO
368
369	ENDIF
370
371	DEALLOCATE( ec, radclass, winf )
372
373	END SUBROUTINE recalculate_kernel
374
375
376	!------------------------------------------------------------------------------!
377	! Description:
378	! ------------
379	!> Calculation of effects of turbulence on the geometric collision kernel
380	!> (by including the droplets' average radial relative velocities and their
381	!> radial distribution function) following the analytic model by Aayala et al.
382	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
383	!> page 37ff.
384	!>
385	!> Input parameters, which need to be replaced by PALM parameters:
386	!> water density, air density
387	!------------------------------------------------------------------------------!
388	SUBROUTINE turbsd
389
390	USE control_parameters, &
391	ONLY: g, molecular_viscosity
392
393	USE particle_attributes, &
394	ONLY: radius_classes
395
396	IMPLICIT NONE
397
398	INTEGER(iwp) :: i !<
399	INTEGER(iwp) :: j !<
400
401	REAL(wp) :: ao !<
402	REAL(wp) :: ao_gr !<
403	REAL(wp) :: bbb !<
404	REAL(wp) :: be !<
405	REAL(wp) :: b1 !<
406	REAL(wp) :: b2 !<
407	REAL(wp) :: ccc !<
408	REAL(wp) :: c1 !<
409	REAL(wp) :: c1_gr !<
410	REAL(wp) :: c2 !<
411	REAL(wp) :: d1 !<
412	REAL(wp) :: d2 !<
413	REAL(wp) :: eta !<
414	REAL(wp) :: e1 !<
415	REAL(wp) :: e2 !<
416	REAL(wp) :: fao_gr !<
417	REAL(wp) :: fr !<
418	REAL(wp) :: grfin !<
419	REAL(wp) :: lambda !<
420	REAL(wp) :: lambda_re !<
421	REAL(wp) :: lf !<
422	REAL(wp) :: rc !<
423	REAL(wp) :: rrp !<
424	REAL(wp) :: sst !<
425	REAL(wp) :: tauk !<
426	REAL(wp) :: tl !<
427	REAL(wp) :: t2 !<
428	REAL(wp) :: tt !<
429	REAL(wp) :: t1 !<
430	REAL(wp) :: vk !<
431	REAL(wp) :: vrms1xy !<
432	REAL(wp) :: vrms2xy !<
433	REAL(wp) :: v1 !<
434	REAL(wp) :: v1v2xy !<
435	REAL(wp) :: v1xysq !<
436	REAL(wp) :: v2 !<
437	REAL(wp) :: v2xysq !<
438	REAL(wp) :: wrfin !<
439	REAL(wp) :: wrgrav2 !<
440	REAL(wp) :: wrtur2xy !<
441	REAL(wp) :: xx !<
442	REAL(wp) :: yy !<
443	REAL(wp) :: z !<
444
445	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
446	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
447
448	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
449	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
450	tl = urms**2 / epsilon
451	lf = 0.5_wp * urms**3 / epsilon
452	tauk = SQRT( molecular_viscosity / epsilon )
453	eta = ( molecular_viscosity3 / epsilon )0.25_wp
454	vk = eta / tauk
455
456	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
457	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
458
459	!
460	!-- Get terminal velocity of droplets
461	CALL fallg
462
463	DO i = 1, radius_classes
464	tau(i) = winf(i) / g ! inertial time scale
465	st(i) = tau(i) / tauk ! Stokes number
466	ENDDO
467
468	!
469	!-- Calculate average radial relative velocity at contact (wrfin)
470	z = tt / tl
471	be = SQRT( 2.0_wp ) * lambda / lf
472	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
473	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
474	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
475	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
476	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
477	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
478	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
479	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
480	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
481	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
482
483	DO i = 1, radius_classes
484
485	v1 = winf(i)
486	t1 = tau(i)
487
488	DO j = 1, i
489	rrp = radclass(i) + radclass(j)
490	v2 = winf(j)
491	t2 = tau(j)
492
493	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
494	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
495	v1xysq = v1xysq * urms**2 / t1
496	vrms1xy = SQRT( v1xysq )
497
498	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
499	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
500	v2xysq = v2xysq * urms**2 / t2
501	vrms2xy = SQRT( v2xysq )
502
503	IF ( winf(i) >= winf(j) ) THEN
504	v1 = winf(i)
505	t1 = tau(i)
506	v2 = winf(j)
507	t2 = tau(j)
508	ELSE
509	v1 = winf(j)
510	t1 = tau(j)
511	v2 = winf(i)
512	t2 = tau(i)
513	ENDIF
514
515	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
516	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
517	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
518	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
519	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
520	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
521	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
522	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
523	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
524	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
525
526	!
527	!-- Calculate radial distribution function (grfin)
528	IF ( st(j) > st(i) ) THEN
529	sst = st(j)
530	ELSE
531	sst = st(i)
532	ENDIF
533
534	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
535	sst*2 + 5.3406_wp sst
536	IF ( xx < 0.0_wp ) xx = 0.0_wp
537	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
538
539	c1_gr = xx / ( g / vk * tauk )**yy
540
541	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
542	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
543	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
544
545	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
546	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
547
548	!
549	!-- Calculate general collection kernel (without the consideration of
550	!-- collection efficiencies)
551	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
552	gck(j,i) = gck(i,j)
553
554	ENDDO
555	ENDDO
556
557	END SUBROUTINE turbsd
558
559	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
560	!
561	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
562	!-- effects on the collision kernel
563	IMPLICIT NONE
564
565	REAL(wp) :: a !<
566	REAL(wp) :: aa1 !<
567	REAL(wp) :: b !<
568	REAL(wp) :: tau0 !<
569	REAL(wp) :: vsett !<
570
571	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
572	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
573
574	END FUNCTION phi_w
575
576	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
577	!
578	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
579	!-- effects on the collision kernel
580	IMPLICIT NONE
581
582	REAL(wp) :: a !<
583	REAL(wp) :: aa1 !<
584	REAL(wp) :: aa2 !<
585	REAL(wp) :: aa3 !<
586	REAL(wp) :: aa4 !<
587	REAL(wp) :: aa5 !<
588	REAL(wp) :: aa6 !<
589	REAL(wp) :: b !<
590	REAL(wp) :: tau1 !<
591	REAL(wp) :: tau2 !<
592	REAL(wp) :: vsett1 !<
593	REAL(wp) :: vsett2 !<
594
595	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
596	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
597	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
598	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
599	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
600	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
601	vsett1 / vsett2
602	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
603	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
604	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
605	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
606
607	END FUNCTION zhi
608
609
610	!------------------------------------------------------------------------------!
611	! Description:
612	! ------------
613	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
614	!> Meteorol.)
615	!------------------------------------------------------------------------------!
616	SUBROUTINE fallg
617
618	USE particle_attributes, &
619	ONLY: radius_classes
620
621	IMPLICIT NONE
622
623	INTEGER(iwp) :: j !<
624
625	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
626	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
627	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
628	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
629	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
630	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
631
632	REAL(wp) :: diameter !< droplet diameter in mm
633
634
635	DO j = 1, radius_classes
636
637	diameter = radclass(j) * 2000.0_wp
638
639	IF ( diameter <= d0_rog ) THEN
640	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
641	EXP( -k_low_rog * diameter ) )
642	ELSE
643	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
644	ENDIF
645
646	ENDDO
647
648	END SUBROUTINE fallg
649
650
651	!------------------------------------------------------------------------------!
652	! Description:
653	! ------------
654	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
655	!------------------------------------------------------------------------------!
656	SUBROUTINE effic
657
658	USE particle_attributes, &
659	ONLY: radius_classes
660
661	IMPLICIT NONE
662
663	INTEGER(iwp) :: i !<
664	INTEGER(iwp) :: iq !<
665	INTEGER(iwp) :: ir !<
666	INTEGER(iwp) :: j !<
667	INTEGER(iwp) :: k !<
668
669	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
670
671	LOGICAL, SAVE :: first = .TRUE. !<
672
673	REAL(wp) :: ek !<
674	REAL(wp) :: particle_radius !<
675	REAL(wp) :: pp !<
676	REAL(wp) :: qq !<
677	REAL(wp) :: rq !<
678
679	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
680
681	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
682
683	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
684
685	!
686	!-- Initial assignment of constants
687	IF ( first ) THEN
688
689	first = .FALSE.
690	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
691	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
692	150.0_wp, 200.0_wp, 300.0_wp /)
693
694	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
695	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
696	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
697	0.90_wp, 0.95_wp, 1.00_wp /)
698
699	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
700	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
701	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
702	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
703	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
704	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
705	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
706	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
707	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
708	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
709	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
710	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
711	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
712	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
713	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
714	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
715	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
716	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
717	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
718	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
719	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
720	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
721	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
722	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
723	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
724	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
725	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
726	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
727	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
728	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
729	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
730	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
731	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
732	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
733	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
734	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
735	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
736	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
737	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
738	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
739	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
740	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
741	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
742	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
743	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
744	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
745	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
746	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
747	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
748	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
749	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
750	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
751	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
752	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
753	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
754	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
755	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
756	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
757	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
758	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
759	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
760	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
761	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
762	ENDIF
763
764	!
765	!-- Calculate the radius class index of particles with respect to array r
766	!-- Radius has to be in microns
767	ALLOCATE( ira(1:radius_classes) )
768	DO j = 1, radius_classes
769	particle_radius = radclass(j) * 1.0E6_wp
770	DO k = 1, 15
771	IF ( particle_radius < r0(k) ) THEN
772	ira(j) = k
773	EXIT
774	ENDIF
775	ENDDO
776	IF ( particle_radius >= r0(15) ) ira(j) = 16
777	ENDDO
778
779	!
780	!-- Two-dimensional linear interpolation of the collision efficiency.
781	!-- Radius has to be in microns
782	DO j = 1, radius_classes
783	DO i = 1, j
784
785	ir = ira(j)
786	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
787	iq = INT( rq * 20 ) + 1
788	iq = MAX( iq , 2)
789
790	IF ( ir < 16 ) THEN
791	IF ( ir >= 2 ) THEN
792	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
793	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
794	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
795	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
796	* ecoll(ir-1,iq-1) &
797	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
798	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
799	+ pp * qq * ecoll(ir,iq)
800	ELSE
801	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
802	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
803	ENDIF
804	ELSE
805	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
806	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
807	ec(j,i) = MIN( ek, 1.0_wp )
808	ENDIF
809
810	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
811
812	ec(i,j) = ec(j,i)
813
814	ENDDO
815	ENDDO
816
817	DEALLOCATE( ira )
818
819	END SUBROUTINE effic
820
821
822	!------------------------------------------------------------------------------!
823	! Description:
824	! ------------
825	!> Interpolation of turbulent enhancement factor for collision efficencies
826	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
827	!------------------------------------------------------------------------------!
828	SUBROUTINE turb_enhance_eff
829
830	USE particle_attributes, &
831	ONLY: radius_classes
832
833	IMPLICIT NONE
834
835	INTEGER(iwp) :: i !<
836	INTEGER(iwp) :: iq !<
837	INTEGER(iwp) :: ir !<
838	INTEGER(iwp) :: j !<
839	INTEGER(iwp) :: k !<
840	INTEGER(iwp) :: kk !<
841
842	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
843
844	LOGICAL, SAVE :: first = .TRUE. !<
845
846	REAL(wp) :: particle_radius !<
847	REAL(wp) :: pp !<
848	REAL(wp) :: qq !<
849	REAL(wp) :: rq !<
850	REAL(wp) :: y1 !<
851	REAL(wp) :: y2 !<
852	REAL(wp) :: y3 !<
853
854	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
855	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
856
857	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
858	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
859
860	!
861	!-- Initial assignment of constants
862	IF ( first ) THEN
863
864	first = .FALSE.
865
866	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
867	100.0_wp /)
868
869	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
870	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
871	!
872	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
873	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
874	1.207_wp, 1.207_wp, 1.0_wp /)
875	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
876	1.069_wp, 1.069_wp, 1.0_wp /)
877	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
878	1.000_wp, 1.000_wp, 1.0_wp /)
879	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
880	1.025_wp, 1.025_wp, 1.0_wp /)
881	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
882	1.056_wp, 1.056_wp, 1.0_wp /)
883	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
884	1.028_wp, 1.028_wp, 1.0_wp /)
885	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
886	1.046_wp, 1.046_wp, 1.0_wp /)
887	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
888	1.029_wp, 1.029_wp, 1.0_wp /)
889	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
890	1.021_wp, 1.021_wp, 1.0_wp /)
891	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
892	1.088_wp, 1.088_wp, 1.0_wp /)
893	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
894	2.60_wp, 2.60_wp, 1.0_wp /)
895	!
896	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
897	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
898	1.445_wp, 1.445_wp, 1.0_wp /)
899	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
900	1.201_wp, 1.201_wp, 1.0_wp /)
901	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
902	1.150_wp, 1.150_wp, 1.0_wp /)
903	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
904	1.126_wp, 1.126_wp, 1.0_wp /)
905	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
906	1.092_wp, 1.092_wp, 1.0_wp /)
907	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
908	1.051_wp, 1.051_wp, 1.0_wp /)
909	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
910	1.086_wp, 1.086_wp, 1.0_wp /)
911	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
912	1.063_wp, 1.063_wp, 1.0_wp /)
913	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
914	1.100_wp, 1.100_wp, 1.0_wp /)
915	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
916	1.120_wp, 1.120_wp, 1.0_wp /)
917	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
918	26.0_wp, 26.0_wp, 1.0_wp /)
919
920	ENDIF
921
922	!
923	!-- Calculate the radius class index of particles with respect to array r0
924	!-- The droplet radius has to be given in microns.
925	ALLOCATE( ira(1:radius_classes) )
926
927	DO j = 1, radius_classes
928	particle_radius = radclass(j) * 1.0E6_wp
929	DO k = 1, 7
930	IF ( particle_radius < r0(k) ) THEN
931	ira(j) = k
932	EXIT
933	ENDIF
934	ENDDO
935	IF ( particle_radius >= r0(7) ) ira(j) = 8
936	ENDDO
937
938	!
939	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
940	!-- The droplet radius has to be given in microns.
941	DO j = 1, radius_classes
942	DO i = 1, j
943
944	ir = ira(j)
945	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
946
947	DO kk = 2, 11
948	IF ( rq <= rat(kk) ) THEN
949	iq = kk
950	EXIT
951	ENDIF
952	ENDDO
953
954	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
955
956	IF ( ir < 8 ) THEN
957	IF ( ir >= 2 ) THEN
958	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
959	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
960	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
961	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
962	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
963	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
964	pp * qq * ecoll_100(ir,iq)
965	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
966	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
967	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
968	pp * qq * ecoll_400(ir,iq)
969	ELSE
970	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
971	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
972	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
973	ENDIF
974	ELSE
975	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
976	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
977	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
978	ENDIF
979	!
980	!-- Linear interpolation of turbulent enhancement factor
981	IF ( epsilon <= 0.01_wp ) THEN
982	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
983	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
984	ELSEIF ( epsilon <= 0.06_wp ) THEN
985	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
986	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
987	ELSE
988	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
989	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
990	ENDIF
991
992	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
993
994	ecf(i,j) = ecf(j,i)
995
996	ENDDO
997	ENDDO
998
999	END SUBROUTINE turb_enhance_eff
1000
1001	END MODULE lpm_collision_kernels_mod

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