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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 3552

Last change on this file since 3552 was 3274, checked in by knoop, 6 years ago
Modularization of all bulk cloud physics code components
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1	!> @file lpm_collision_kernels.f90
2	!------------------------------------------------------------------------------!
3	! This file is part of the PALM model system.
4	!
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.
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	!
17	! Copyright 1997-2018 Leibniz Universitaet Hannover
18	!------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_collision_kernels.f90 3274 2018-09-24 15:42:55Z suehring $
27	! Modularization of all bulk cloud physics code components
28	!
29	! 2718 2018-01-02 08:49:38Z maronga
30	! Corrected "Former revisions" section
31	!
32	! 2696 2017-12-14 17:12:51Z kanani
33	! Change in file header (GPL part)
34	!
35	! 2101 2017-01-05 16:42:31Z suehring
36	!
37	! 2000 2016-08-20 18:09:15Z knoop
38	! Forced header and separation lines into 80 columns
39	!
40	! 1880 2016-04-20 09:36:50Z hoffmann
41	! Bugfix: The index of the larger particle has to be chosen for interpolation.
42	!
43	! 1873 2016-04-18 14:50:06Z maronga
44	! Module renamed (removed _mod)
45	!
46	! 1858 2016-04-13 13:12:11Z hoffmann
47	! Interpolation of collision kernels adjusted to more reasonable values.
48	! Reformatting of the code.
49	!
50	! 1850 2016-04-08 13:29:27Z maronga
51	! Module renamed
52	!
53	! 1822 2016-04-07 07:49:42Z hoffmann
54	! PALM kernel has been deleted.
55	! Bugfix in the calculation of the turbulent enhancement factor of the
56	! collection efficiency.
57	!
58	! Unused variables removed.
59	!
60	! 1776 2016-03-02 17:54:58Z hoffmann
61	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
62	!
63	! 1682 2015-10-07 23:56:08Z knoop
64	! Code annotations made doxygen readable
65	!
66	! 1519 2015-01-08 10:20:42Z hoffmann
67	! Bugfix: Using the new particle structure, particles are not sorted by size.
68	! Hence, computation of collision efficiencies must ensure that the ratio of
69	! two colliding droplets is < 1.
70	!
71	! 1359 2014-04-11 17:15:14Z hoffmann
72	! New particle structure integrated.
73	! Kind definition added to all floating point numbers.
74	!
75	! 1346 2014-03-27 13:18:20Z heinze
76	! Bugfix: REAL constants provided with KIND-attribute especially in call of
77	! intrinsic function like MAX, MIN, SIGN
78	!
79	! 1322 2014-03-20 16:38:49Z raasch
80	! REAL constants defined as wp_kind
81	!
82	! 1320 2014-03-20 08:40:49Z
83	! ONLY-attribute added to USE-statements,
84	! kind-parameters added to all INTEGER and REAL declaration statements,
85	! kinds are defined in new module kinds,
86	! revision history before 2012 removed,
87	! comment fields (!:) to be used for variable explanations added to
88	! all variable declaration statements
89	!
90	! 1092 2013-02-02 11:24:22Z raasch
91	! unused variables removed
92	!
93	! 1071 2012-11-29 16:54:55Z franke
94	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
95	!
96	! 1036 2012-10-22 13:43:42Z raasch
97	! code put under GPL (PALM 3.9)
98	!
99	! 1007 2012-09-19 14:30:36Z franke
100	! converted all units to SI units and replaced some parameters by corresponding
101	! PALM parameters
102	! Bugfix: factor in calculation of enhancement factor for collision efficencies
103	! changed from 10. to 1.0
104	!
105	! 849 2012-03-15 10:35:09Z raasch
106	! routine collision_efficiency_rogers added (moved from former advec_particles
107	! to here)
108	!
109	! 835 2012-02-22 11:21:19Z raasch $
110	! Bugfix: array diss can be used only in case of Wang kernel
111	!
112	! 828 2012-02-21 12:00:36Z raasch
113	! code has been completely reformatted, routine colker renamed
114	! recalculate_kernel,
115	! routine init_kernels added, radius is now communicated to the collision
116	! routines by array radclass
117	!
118	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
119	!
120	! 825 2012-02-19 03:03:44Z raasch
121	! routine renamed from wang_kernel to lpm_collision_kernels,
122	! turbulence_effects on collision replaced by wang_kernel
123	!
124	! 790 2011-11-29 03:11:20Z raasch
125	! initial revision
126	!
127	! Description:
128	! ------------
129	!> This module calculates collision efficiencies either due to pure gravitational
130	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
131	!> including the effects of turbulence (Wang kernel, see Wang and
132	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
133	!> New J. Phys., 10, 075016). The original code has been
134	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
135	!> here.
136	!------------------------------------------------------------------------------!
137	MODULE lpm_collision_kernels_mod
138
139
140	USE basic_constants_and_equations_mod, &
141	ONLY: g, pi
142
143	USE kinds
144
145	USE particle_attributes, &
146	ONLY: collision_kernel, dissipation_classes, particles, &
147	radius_classes
148
149	USE pegrid
150
151
152	IMPLICIT NONE
153
154	PRIVATE
155
156	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
157	recalculate_kernel
158
159	REAL(wp) :: epsilon !<
160	REAL(wp) :: rclass_lbound !<
161	REAL(wp) :: rclass_ubound !<
162	REAL(wp) :: urms !<
163
164	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
165	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
166	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
167
168	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
169	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
170	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
171	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
172	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
173
174	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
175
176	SAVE
177
178	!
179	!-- Public interfaces
180	INTERFACE init_kernels
181	MODULE PROCEDURE init_kernels
182	END INTERFACE init_kernels
183
184	INTERFACE recalculate_kernel
185	MODULE PROCEDURE recalculate_kernel
186	END INTERFACE recalculate_kernel
187
188
189	CONTAINS
190
191
192	!------------------------------------------------------------------------------!
193	! Description:
194	! ------------
195	!> Initialization of the collision efficiency matrix with fixed radius and
196	!> dissipation classes, calculated at simulation start only.
197	!------------------------------------------------------------------------------!
198
199	SUBROUTINE init_kernels
200
201	IMPLICIT NONE
202
203	INTEGER(iwp) :: i !<
204	INTEGER(iwp) :: j !<
205	INTEGER(iwp) :: k !<
206
207
208	!
209	!-- Calculate collision efficiencies for fixed radius- and dissipation
210	!-- classes
211	IF ( collision_kernel(6:9) == 'fast' ) THEN
212
213	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
214	0:dissipation_classes), epsclass(1:dissipation_classes), &
215	radclass(1:radius_classes) )
216
217	!
218	!-- Calculate the radius class bounds with logarithmic distances
219	!-- in the interval [1.0E-6, 1000.0E-6] m
220	rclass_lbound = LOG( 1.0E-6_wp )
221	rclass_ubound = LOG( 1000.0E-6_wp )
222	radclass(1) = EXP( rclass_lbound )
223	DO i = 2, radius_classes
224	radclass(i) = EXP( rclass_lbound + &
225	( rclass_ubound - rclass_lbound ) * &
226	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
227	ENDDO
228
229	!
230	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
231	DO i = 1, dissipation_classes
232	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
233	ENDDO
234	!
235	!-- Calculate collision efficiencies of the Wang/ayala kernel
236	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
237	ecf(1:radius_classes,1:radius_classes), &
238	gck(1:radius_classes,1:radius_classes), &
239	winf(1:radius_classes) )
240
241	DO k = 1, dissipation_classes
242
243	epsilon = epsclass(k)
244	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
245
246	CALL turbsd
247	CALL turb_enhance_eff
248	CALL effic
249
250	DO j = 1, radius_classes
251	DO i = 1, radius_classes
252	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
253	ENDDO
254	ENDDO
255
256	ENDDO
257
258	!
259	!-- Calculate collision efficiencies of the Hall kernel
260	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
261	hwratio(1:radius_classes,1:radius_classes) )
262
263	CALL fallg
264	CALL effic
265
266	DO j = 1, radius_classes
267	DO i = 1, radius_classes
268	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
269	* ec(i,j) * ABS( winf(j) - winf(i) )
270	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
271	ENDDO
272	ENDDO
273
274	!
275	!-- Test output of efficiencies
276	IF ( j == -1 ) THEN
277
278	PRINT, '** Hall kernel'
279	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
280	i = 1,radius_classes )
281	DO j = 1, radius_classes
282	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
283	( hkernel(i,j), i = 1,radius_classes )
284	ENDDO
285
286	DO k = 1, dissipation_classes
287	DO i = 1, radius_classes
288	DO j = 1, radius_classes
289	IF ( hkernel(i,j) == 0.0_wp ) THEN
290	hwratio(i,j) = 9999999.9_wp
291	ELSE
292	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
293	ENDIF
294	ENDDO
295	ENDDO
296
297	PRINT, '** epsilon = ', epsclass(k)
298	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
299	i = 1,radius_classes )
300	DO j = 1, radius_classes
301	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
302	( hwratio(i,j), i = 1,radius_classes )
303	ENDDO
304	ENDDO
305
306	ENDIF
307
308	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
309
310	ENDIF
311
312	END SUBROUTINE init_kernels
313
314
315	!------------------------------------------------------------------------------!
316	! Description:
317	! ------------
318	!> Calculation of collision kernels during each timestep and for each grid box
319	!------------------------------------------------------------------------------!
320	SUBROUTINE recalculate_kernel( i1, j1, k1 )
321
322	USE arrays_3d, &
323	ONLY: diss
324
325	USE particle_attributes, &
326	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
327
328	IMPLICIT NONE
329
330	INTEGER(iwp) :: i !<
331	INTEGER(iwp) :: i1 !<
332	INTEGER(iwp) :: j !<
333	INTEGER(iwp) :: j1 !<
334	INTEGER(iwp) :: k1 !<
335
336
337	number_of_particles = prt_count(k1,j1,i1)
338	radius_classes = number_of_particles ! necessary to use the same
339	! subroutines as for
340	! precalculated kernels
341
342	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
343	radclass(1:number_of_particles), winf(1:number_of_particles) )
344
345	!
346	!-- Store particle radii on the radclass array
347	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
348
349	IF ( wang_kernel ) THEN
350	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
351	ELSE
352	epsilon = 0.0_wp
353	ENDIF
354	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
355
356	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
357	!
358	!-- Call routines to calculate efficiencies for the Wang kernel
359	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
360	ecf(1:number_of_particles,1:number_of_particles) )
361
362	CALL turbsd
363	CALL turb_enhance_eff
364	CALL effic
365
366	DO j = 1, number_of_particles
367	DO i = 1, number_of_particles
368	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
369	ENDDO
370	ENDDO
371
372	DEALLOCATE( gck, ecf )
373
374	ELSE
375	!
376	!-- Call routines to calculate efficiencies for the Hall kernel
377	CALL fallg
378	CALL effic
379
380	DO j = 1, number_of_particles
381	DO i = 1, number_of_particles
382	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
383	* ec(i,j) * ABS( winf(j) - winf(i) )
384	ENDDO
385	ENDDO
386
387	ENDIF
388
389	DEALLOCATE( ec, radclass, winf )
390
391	END SUBROUTINE recalculate_kernel
392
393
394	!------------------------------------------------------------------------------!
395	! Description:
396	! ------------
397	!> Calculation of effects of turbulence on the geometric collision kernel
398	!> (by including the droplets' average radial relative velocities and their
399	!> radial distribution function) following the analytic model by Aayala et al.
400	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
401	!> page 37ff.
402	!>
403	!> Input parameters, which need to be replaced by PALM parameters:
404	!> water density, air density
405	!------------------------------------------------------------------------------!
406	SUBROUTINE turbsd
407
408	USE control_parameters, &
409	ONLY: molecular_viscosity
410
411	USE particle_attributes, &
412	ONLY: radius_classes
413
414	IMPLICIT NONE
415
416	INTEGER(iwp) :: i !<
417	INTEGER(iwp) :: j !<
418
419	REAL(wp) :: ao !<
420	REAL(wp) :: ao_gr !<
421	REAL(wp) :: bbb !<
422	REAL(wp) :: be !<
423	REAL(wp) :: b1 !<
424	REAL(wp) :: b2 !<
425	REAL(wp) :: ccc !<
426	REAL(wp) :: c1 !<
427	REAL(wp) :: c1_gr !<
428	REAL(wp) :: c2 !<
429	REAL(wp) :: d1 !<
430	REAL(wp) :: d2 !<
431	REAL(wp) :: eta !<
432	REAL(wp) :: e1 !<
433	REAL(wp) :: e2 !<
434	REAL(wp) :: fao_gr !<
435	REAL(wp) :: fr !<
436	REAL(wp) :: grfin !<
437	REAL(wp) :: lambda !<
438	REAL(wp) :: lambda_re !<
439	REAL(wp) :: lf !<
440	REAL(wp) :: rc !<
441	REAL(wp) :: rrp !<
442	REAL(wp) :: sst !<
443	REAL(wp) :: tauk !<
444	REAL(wp) :: tl !<
445	REAL(wp) :: t2 !<
446	REAL(wp) :: tt !<
447	REAL(wp) :: t1 !<
448	REAL(wp) :: vk !<
449	REAL(wp) :: vrms1xy !<
450	REAL(wp) :: vrms2xy !<
451	REAL(wp) :: v1 !<
452	REAL(wp) :: v1v2xy !<
453	REAL(wp) :: v1xysq !<
454	REAL(wp) :: v2 !<
455	REAL(wp) :: v2xysq !<
456	REAL(wp) :: wrfin !<
457	REAL(wp) :: wrgrav2 !<
458	REAL(wp) :: wrtur2xy !<
459	REAL(wp) :: xx !<
460	REAL(wp) :: yy !<
461	REAL(wp) :: z !<
462
463	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
464	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
465
466	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
467	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
468	tl = urms**2 / epsilon
469	lf = 0.5_wp * urms**3 / epsilon
470	tauk = SQRT( molecular_viscosity / epsilon )
471	eta = ( molecular_viscosity3 / epsilon )0.25_wp
472	vk = eta / tauk
473
474	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
475	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
476
477	!
478	!-- Get terminal velocity of droplets
479	CALL fallg
480
481	DO i = 1, radius_classes
482	tau(i) = winf(i) / g ! inertial time scale
483	st(i) = tau(i) / tauk ! Stokes number
484	ENDDO
485
486	!
487	!-- Calculate average radial relative velocity at contact (wrfin)
488	z = tt / tl
489	be = SQRT( 2.0_wp ) * lambda / lf
490	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
491	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
492	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
493	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
494	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
495	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
496	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
497	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
498	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
499	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
500
501	DO i = 1, radius_classes
502
503	v1 = winf(i)
504	t1 = tau(i)
505
506	DO j = 1, i
507	rrp = radclass(i) + radclass(j)
508	v2 = winf(j)
509	t2 = tau(j)
510
511	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
512	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
513	v1xysq = v1xysq * urms**2 / t1
514	vrms1xy = SQRT( v1xysq )
515
516	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
517	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
518	v2xysq = v2xysq * urms**2 / t2
519	vrms2xy = SQRT( v2xysq )
520
521	IF ( winf(i) >= winf(j) ) THEN
522	v1 = winf(i)
523	t1 = tau(i)
524	v2 = winf(j)
525	t2 = tau(j)
526	ELSE
527	v1 = winf(j)
528	t1 = tau(j)
529	v2 = winf(i)
530	t2 = tau(i)
531	ENDIF
532
533	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
534	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
535	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
536	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
537	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
538	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
539	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
540	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
541	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
542	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
543
544	!
545	!-- Calculate radial distribution function (grfin)
546	IF ( st(j) > st(i) ) THEN
547	sst = st(j)
548	ELSE
549	sst = st(i)
550	ENDIF
551
552	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
553	sst*2 + 5.3406_wp sst
554	IF ( xx < 0.0_wp ) xx = 0.0_wp
555	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
556
557	c1_gr = xx / ( g / vk * tauk )**yy
558
559	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
560	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
561	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
562
563	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
564	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
565
566	!
567	!-- Calculate general collection kernel (without the consideration of
568	!-- collection efficiencies)
569	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
570	gck(j,i) = gck(i,j)
571
572	ENDDO
573	ENDDO
574
575	END SUBROUTINE turbsd
576
577	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
578	!
579	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
580	!-- effects on the collision kernel
581	IMPLICIT NONE
582
583	REAL(wp) :: a !<
584	REAL(wp) :: aa1 !<
585	REAL(wp) :: b !<
586	REAL(wp) :: tau0 !<
587	REAL(wp) :: vsett !<
588
589	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
590	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
591
592	END FUNCTION phi_w
593
594	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
595	!
596	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
597	!-- effects on the collision kernel
598	IMPLICIT NONE
599
600	REAL(wp) :: a !<
601	REAL(wp) :: aa1 !<
602	REAL(wp) :: aa2 !<
603	REAL(wp) :: aa3 !<
604	REAL(wp) :: aa4 !<
605	REAL(wp) :: aa5 !<
606	REAL(wp) :: aa6 !<
607	REAL(wp) :: b !<
608	REAL(wp) :: tau1 !<
609	REAL(wp) :: tau2 !<
610	REAL(wp) :: vsett1 !<
611	REAL(wp) :: vsett2 !<
612
613	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
614	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
615	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
616	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
617	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
618	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
619	vsett1 / vsett2
620	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
621	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
622	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
623	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
624
625	END FUNCTION zhi
626
627
628	!------------------------------------------------------------------------------!
629	! Description:
630	! ------------
631	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
632	!> Meteorol.)
633	!------------------------------------------------------------------------------!
634	SUBROUTINE fallg
635
636	USE particle_attributes, &
637	ONLY: radius_classes
638
639	IMPLICIT NONE
640
641	INTEGER(iwp) :: j !<
642
643	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
644	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
645	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
646	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
647	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
648	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
649
650	REAL(wp) :: diameter !< droplet diameter in mm
651
652
653	DO j = 1, radius_classes
654
655	diameter = radclass(j) * 2000.0_wp
656
657	IF ( diameter <= d0_rog ) THEN
658	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
659	EXP( -k_low_rog * diameter ) )
660	ELSE
661	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
662	ENDIF
663
664	ENDDO
665
666	END SUBROUTINE fallg
667
668
669	!------------------------------------------------------------------------------!
670	! Description:
671	! ------------
672	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
673	!------------------------------------------------------------------------------!
674	SUBROUTINE effic
675
676	USE particle_attributes, &
677	ONLY: radius_classes
678
679	IMPLICIT NONE
680
681	INTEGER(iwp) :: i !<
682	INTEGER(iwp) :: iq !<
683	INTEGER(iwp) :: ir !<
684	INTEGER(iwp) :: j !<
685	INTEGER(iwp) :: k !<
686
687	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
688
689	LOGICAL, SAVE :: first = .TRUE. !<
690
691	REAL(wp) :: ek !<
692	REAL(wp) :: particle_radius !<
693	REAL(wp) :: pp !<
694	REAL(wp) :: qq !<
695	REAL(wp) :: rq !<
696
697	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
698
699	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
700
701	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
702
703	!
704	!-- Initial assignment of constants
705	IF ( first ) THEN
706
707	first = .FALSE.
708	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
709	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
710	150.0_wp, 200.0_wp, 300.0_wp /)
711
712	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
713	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
714	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
715	0.90_wp, 0.95_wp, 1.00_wp /)
716
717	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
718	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
719	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
720	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
721	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
722	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
723	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
724	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
725	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
726	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
727	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
728	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
729	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
730	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
731	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
732	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
733	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
734	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
735	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
736	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
737	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
738	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
739	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
740	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
741	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
742	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
743	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
744	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
745	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
746	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
747	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
748	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
749	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
750	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
751	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
752	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
753	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
754	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
755	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
756	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
757	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
758	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
759	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
760	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
761	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
762	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
763	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
764	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
765	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
766	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
767	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
768	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
769	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
770	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
771	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
772	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
773	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
774	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
775	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
776	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
777	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
778	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
779	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
780	ENDIF
781
782	!
783	!-- Calculate the radius class index of particles with respect to array r
784	!-- Radius has to be in microns
785	ALLOCATE( ira(1:radius_classes) )
786	DO j = 1, radius_classes
787	particle_radius = radclass(j) * 1.0E6_wp
788	DO k = 1, 15
789	IF ( particle_radius < r0(k) ) THEN
790	ira(j) = k
791	EXIT
792	ENDIF
793	ENDDO
794	IF ( particle_radius >= r0(15) ) ira(j) = 16
795	ENDDO
796
797	!
798	!-- Two-dimensional linear interpolation of the collision efficiency.
799	!-- Radius has to be in microns
800	DO j = 1, radius_classes
801	DO i = 1, j
802
803	ir = MAX( ira(i), ira(j) )
804	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
805	iq = INT( rq * 20 ) + 1
806	iq = MAX( iq , 2)
807
808	IF ( ir < 16 ) THEN
809	IF ( ir >= 2 ) THEN
810	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
811	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
812	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
813	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
814	* ecoll(ir-1,iq-1) &
815	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
816	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
817	+ pp * qq * ecoll(ir,iq)
818	ELSE
819	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
820	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
821	ENDIF
822	ELSE
823	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
824	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
825	ec(j,i) = MIN( ek, 1.0_wp )
826	ENDIF
827
828	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
829
830	ec(i,j) = ec(j,i)
831
832	ENDDO
833	ENDDO
834
835	DEALLOCATE( ira )
836
837	END SUBROUTINE effic
838
839
840	!------------------------------------------------------------------------------!
841	! Description:
842	! ------------
843	!> Interpolation of turbulent enhancement factor for collision efficencies
844	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
845	!------------------------------------------------------------------------------!
846	SUBROUTINE turb_enhance_eff
847
848	USE particle_attributes, &
849	ONLY: radius_classes
850
851	IMPLICIT NONE
852
853	INTEGER(iwp) :: i !<
854	INTEGER(iwp) :: iq !<
855	INTEGER(iwp) :: ir !<
856	INTEGER(iwp) :: j !<
857	INTEGER(iwp) :: k !<
858	INTEGER(iwp) :: kk !<
859
860	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
861
862	LOGICAL, SAVE :: first = .TRUE. !<
863
864	REAL(wp) :: particle_radius !<
865	REAL(wp) :: pp !<
866	REAL(wp) :: qq !<
867	REAL(wp) :: rq !<
868	REAL(wp) :: y1 !<
869	REAL(wp) :: y2 !<
870	REAL(wp) :: y3 !<
871
872	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
873	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
874
875	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
876	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
877
878	!
879	!-- Initial assignment of constants
880	IF ( first ) THEN
881
882	first = .FALSE.
883
884	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
885	100.0_wp /)
886
887	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
888	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
889	!
890	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
891	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
892	1.207_wp, 1.207_wp, 1.0_wp /)
893	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
894	1.069_wp, 1.069_wp, 1.0_wp /)
895	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
896	1.000_wp, 1.000_wp, 1.0_wp /)
897	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
898	1.025_wp, 1.025_wp, 1.0_wp /)
899	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
900	1.056_wp, 1.056_wp, 1.0_wp /)
901	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
902	1.028_wp, 1.028_wp, 1.0_wp /)
903	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
904	1.046_wp, 1.046_wp, 1.0_wp /)
905	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
906	1.029_wp, 1.029_wp, 1.0_wp /)
907	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
908	1.021_wp, 1.021_wp, 1.0_wp /)
909	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
910	1.088_wp, 1.088_wp, 1.0_wp /)
911	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
912	2.60_wp, 2.60_wp, 1.0_wp /)
913	!
914	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
915	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
916	1.445_wp, 1.445_wp, 1.0_wp /)
917	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
918	1.201_wp, 1.201_wp, 1.0_wp /)
919	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
920	1.150_wp, 1.150_wp, 1.0_wp /)
921	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
922	1.126_wp, 1.126_wp, 1.0_wp /)
923	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
924	1.092_wp, 1.092_wp, 1.0_wp /)
925	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
926	1.051_wp, 1.051_wp, 1.0_wp /)
927	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
928	1.086_wp, 1.086_wp, 1.0_wp /)
929	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
930	1.063_wp, 1.063_wp, 1.0_wp /)
931	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
932	1.100_wp, 1.100_wp, 1.0_wp /)
933	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
934	1.120_wp, 1.120_wp, 1.0_wp /)
935	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
936	26.0_wp, 26.0_wp, 1.0_wp /)
937
938	ENDIF
939
940	!
941	!-- Calculate the radius class index of particles with respect to array r0
942	!-- The droplet radius has to be given in microns.
943	ALLOCATE( ira(1:radius_classes) )
944
945	DO j = 1, radius_classes
946	particle_radius = radclass(j) * 1.0E6_wp
947	DO k = 1, 7
948	IF ( particle_radius < r0(k) ) THEN
949	ira(j) = k
950	EXIT
951	ENDIF
952	ENDDO
953	IF ( particle_radius >= r0(7) ) ira(j) = 8
954	ENDDO
955
956	!
957	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
958	!-- The droplet radius has to be given in microns.
959	DO j = 1, radius_classes
960	DO i = 1, j
961
962	ir = MAX( ira(i), ira(j) )
963	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
964
965	DO kk = 2, 11
966	IF ( rq <= rat(kk) ) THEN
967	iq = kk
968	EXIT
969	ENDIF
970	ENDDO
971
972	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
973
974	IF ( ir < 8 ) THEN
975	IF ( ir >= 2 ) THEN
976	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
977	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
978	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
979	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
980	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
981	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
982	pp * qq * ecoll_100(ir,iq)
983	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
984	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
985	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
986	pp * qq * ecoll_400(ir,iq)
987	ELSE
988	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
989	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
990	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
991	ENDIF
992	ELSE
993	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
994	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
995	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
996	ENDIF
997	!
998	!-- Linear interpolation of turbulent enhancement factor
999	IF ( epsilon <= 0.01_wp ) THEN
1000	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
1001	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
1002	ELSEIF ( epsilon <= 0.06_wp ) THEN
1003	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1004	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1005	ELSE
1006	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1007	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1008	ENDIF
1009
1010	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
1011
1012	ecf(i,j) = ecf(j,i)
1013
1014	ENDDO
1015	ENDDO
1016
1017	END SUBROUTINE turb_enhance_eff
1018
1019	END MODULE lpm_collision_kernels_mod

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