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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1757

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1	!> @file lpm_collision_kernels.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 1997-2014 Leibniz Universitaet Hannover
17	!--------------------------------------------------------------------------------!
18	!
19	! Current revisions:
20	! -----------------
21	!
22	!
23	! Former revisions:
24	! -----------------
25	! $Id: lpm_collision_kernels.f90 1683 2015-10-07 23:57:51Z maronga $
26	!
27	! 1682 2015-10-07 23:56:08Z knoop
28	! Code annotations made doxygen readable
29	!
30	! 1519 2015-01-08 10:20:42Z hoffmann
31	! Bugfix: Using the new particle structure, particles are not sorted by size.
32	! Hence, computation of collision efficiencies must ensure that the ratio of
33	! two colliding droplets is < 1.
34	!
35	! 1359 2014-04-11 17:15:14Z hoffmann
36	! New particle structure integrated.
37	! Kind definition added to all floating point numbers.
38	!
39	! 1346 2014-03-27 13:18:20Z heinze
40	! Bugfix: REAL constants provided with KIND-attribute especially in call of
41	! intrinsic function like MAX, MIN, SIGN
42	!
43	! 1322 2014-03-20 16:38:49Z raasch
44	! REAL constants defined as wp_kind
45	!
46	! 1320 2014-03-20 08:40:49Z
47	! ONLY-attribute added to USE-statements,
48	! kind-parameters added to all INTEGER and REAL declaration statements,
49	! kinds are defined in new module kinds,
50	! revision history before 2012 removed,
51	! comment fields (!:) to be used for variable explanations added to
52	! all variable declaration statements
53	!
54	! 1092 2013-02-02 11:24:22Z raasch
55	! unused variables removed
56	!
57	! 1071 2012-11-29 16:54:55Z franke
58	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
59	!
60	! 1036 2012-10-22 13:43:42Z raasch
61	! code put under GPL (PALM 3.9)
62	!
63	! 1007 2012-09-19 14:30:36Z franke
64	! converted all units to SI units and replaced some parameters by corresponding
65	! PALM parameters
66	! Bugfix: factor in calculation of enhancement factor for collision efficencies
67	! changed from 10. to 1.0
68	!
69	! 849 2012-03-15 10:35:09Z raasch
70	! routine collision_efficiency_rogers added (moved from former advec_particles
71	! to here)
72	!
73	! 835 2012-02-22 11:21:19Z raasch $
74	! Bugfix: array diss can be used only in case of Wang kernel
75	!
76	! 828 2012-02-21 12:00:36Z raasch
77	! code has been completely reformatted, routine colker renamed
78	! recalculate_kernel,
79	! routine init_kernels added, radius is now communicated to the collision
80	! routines by array radclass
81	!
82	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
83	!
84	! 825 2012-02-19 03:03:44Z raasch
85	! routine renamed from wang_kernel to lpm_collision_kernels,
86	! turbulence_effects on collision replaced by wang_kernel
87	!
88	! 790 2011-11-29 03:11:20Z raasch
89	! initial revision
90	!
91	! Description:
92	! ------------
93	!> This module calculates collision efficiencies either due to pure gravitational
94	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
95	!> including the effects of (SGS) turbulence (Wang kernel, see Wang and
96	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
97	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
98	!> here.
99	!>
100	!> @attention Physical quantities (like g, densities, etc.) used in this module
101	!> still have to be adjusted to those values used in the main PALM code.
102	!> Also, quantities in CGS-units should be converted to SI-units eventually.
103	!------------------------------------------------------------------------------!
104	MODULE lpm_collision_kernels_mod
105
106
107	USE constants, &
108	ONLY: pi
109
110	USE kinds
111
112	USE particle_attributes, &
113	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
114
115	USE pegrid
116
117
118	IMPLICIT NONE
119
120	PRIVATE
121
122	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
123	rclass_lbound, rclass_ubound, recalculate_kernel
124
125	REAL(wp) :: epsilon !<
126	REAL(wp) :: eps2 !<
127	REAL(wp) :: rclass_lbound !<
128	REAL(wp) :: rclass_ubound !<
129	REAL(wp) :: urms !<
130	REAL(wp) :: urms2 !<
131
132	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !<
133	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !<
134	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
135
136	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
137	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
138	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
139	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
140	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
141
142	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
143
144	SAVE
145
146	!
147	!-- Public interfaces
148	INTERFACE collision_efficiency_rogers
149	MODULE PROCEDURE collision_efficiency_rogers
150	END INTERFACE collision_efficiency_rogers
151
152	INTERFACE init_kernels
153	MODULE PROCEDURE init_kernels
154	END INTERFACE init_kernels
155
156	INTERFACE recalculate_kernel
157	MODULE PROCEDURE recalculate_kernel
158	END INTERFACE recalculate_kernel
159
160
161	CONTAINS
162
163
164	!------------------------------------------------------------------------------!
165	! Description:
166	! ------------
167	!> Initialization of the collision efficiency matrix with fixed radius and
168	!> dissipation classes, calculated at simulation start only.
169	!------------------------------------------------------------------------------!
170
171	SUBROUTINE init_kernels
172
173	IMPLICIT NONE
174
175	INTEGER(iwp) :: i !<
176	INTEGER(iwp) :: j !<
177	INTEGER(iwp) :: k !<
178
179
180	!
181	!-- Calculate collision efficiencies for fixed radius- and dissipation
182	!-- classes
183	IF ( collision_kernel(6:9) == 'fast' ) THEN
184
185	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
186	0:dissipation_classes), epsclass(1:dissipation_classes), &
187	radclass(1:radius_classes) )
188
189	!
190	!-- Calculate the radius class bounds with logarithmic distances
191	!-- in the interval [1.0E-6, 2.0E-4] m
192	rclass_lbound = LOG( 1.0E-6_wp )
193	rclass_ubound = LOG( 2.0E-4_wp )
194	radclass(1) = 1.0E-6_wp
195	DO i = 2, radius_classes
196	radclass(i) = EXP( rclass_lbound + &
197	( rclass_ubound - rclass_lbound ) * &
198	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
199	ENDDO
200
201	!
202	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
203	DO i = 1, dissipation_classes
204	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
205	ENDDO
206	!
207	!-- Calculate collision efficiencies of the Wang/ayala kernel
208	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
209	ecf(1:radius_classes,1:radius_classes), &
210	gck(1:radius_classes,1:radius_classes), &
211	winf(1:radius_classes) )
212
213	DO k = 1, dissipation_classes
214
215	epsilon = epsclass(k)
216	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
217
218	CALL turbsd
219	CALL turb_enhance_eff
220	CALL effic
221
222	DO j = 1, radius_classes
223	DO i = 1, radius_classes
224	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
225	ENDDO
226	ENDDO
227
228	ENDDO
229
230	!
231	!-- Calculate collision efficiencies of the Hall kernel
232	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
233	hwratio(1:radius_classes,1:radius_classes) )
234
235	CALL fallg
236	CALL effic
237
238	DO j = 1, radius_classes
239	DO i = 1, radius_classes
240	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
241	* ec(i,j) * ABS( winf(j) - winf(i) )
242	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
243	ENDDO
244	ENDDO
245
246	!
247	!-- Test output of efficiencies
248	IF ( j == -1 ) THEN
249
250	PRINT, '** Hall kernel'
251	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
252	i = 1,radius_classes )
253	DO j = 1, radius_classes
254	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
255	( hkernel(i,j), i = 1,radius_classes )
256	ENDDO
257
258	DO k = 1, dissipation_classes
259	DO i = 1, radius_classes
260	DO j = 1, radius_classes
261	IF ( hkernel(i,j) == 0.0_wp ) THEN
262	hwratio(i,j) = 9999999.9_wp
263	ELSE
264	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
265	ENDIF
266	ENDDO
267	ENDDO
268
269	PRINT, '** epsilon = ', epsclass(k)
270	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
271	i = 1,radius_classes )
272	DO j = 1, radius_classes
273	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
274	( hwratio(i,j), i = 1,radius_classes )
275	ENDDO
276	ENDDO
277
278	ENDIF
279
280	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
281
282	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
283	THEN
284	!
285	!-- Initial settings for Hall- and Wang-Kernel
286	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
287	ENDIF
288
289	END SUBROUTINE init_kernels
290
291
292	!------------------------------------------------------------------------------!
293	! Description:
294	! ------------
295	!> Calculation of collision kernels during each timestep and for each grid box
296	!------------------------------------------------------------------------------!
297	SUBROUTINE recalculate_kernel( i1, j1, k1 )
298
299	USE arrays_3d, &
300	ONLY: diss
301
302	USE particle_attributes, &
303	ONLY: prt_count, radius_classes, wang_kernel
304
305	IMPLICIT NONE
306
307	INTEGER(iwp) :: i !<
308	INTEGER(iwp) :: i1 !<
309	INTEGER(iwp) :: j !<
310	INTEGER(iwp) :: j1 !<
311	INTEGER(iwp) :: k1 !<
312	INTEGER(iwp) :: pend !<
313	INTEGER(iwp) :: pstart !<
314
315
316	pstart = 1
317	pend = prt_count(k1,j1,i1)
318	radius_classes = prt_count(k1,j1,i1)
319
320	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
321	radclass(1:radius_classes), winf(1:radius_classes) )
322
323	!
324	!-- Store particle radii on the radclass array
325	radclass(1:radius_classes) = particles(pstart:pend)%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:radius_classes,1:radius_classes), &
338	ecf(1:radius_classes,1:radius_classes) )
339
340	CALL turbsd
341	CALL turb_enhance_eff
342	CALL effic
343
344	DO j = 1, radius_classes
345	DO i = 1, radius_classes
346	ckernel(pstart+i-1,pstart+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, radius_classes
359	DO i = 1, radius_classes
360	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
361	( radclass(j) + radclass(i) )**2 &
362	* ec(i,j) * ABS( winf(j) - winf(i) )
363	ENDDO
364	ENDDO
365
366	ENDIF
367
368	DEALLOCATE( ec, radclass, winf )
369
370	END SUBROUTINE recalculate_kernel
371
372
373	!------------------------------------------------------------------------------!
374	! Description:
375	! ------------
376	!> Calculation of gck
377	!> This is from Aayala 2008b, page 37ff.
378	!> Necessary input parameters: water density, radii of droplets, air density,
379	!> air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
380	!> gravitational acceleration --> to be replaced by PALM parameters
381	!------------------------------------------------------------------------------!
382	SUBROUTINE turbsd
383
384	USE control_parameters, &
385	ONLY: g, molecular_viscosity
386
387	USE particle_attributes, &
388	ONLY: radius_classes
389
390	IMPLICIT NONE
391
392	LOGICAL, SAVE :: first = .TRUE. !<
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 !<
442	REAL(wp), DIMENSION(1:radius_classes) :: tau !<
443
444	!
445	!-- Initial assignment of constants
446	IF ( first ) THEN
447
448	first = .FALSE.
449
450	ENDIF
451
452	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
453	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
454	tl = urms**2 / epsilon ! in s
455	lf = 0.5_wp * urms**3 / epsilon ! in m
456	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
457	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
458	vk = eta / tauk
459
460	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
461	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
462
463	CALL fallg ! gives winf in m/s
464
465	DO i = 1, radius_classes
466	tau(i) = winf(i) / g ! in s
467	st(i) = tau(i) / tauk
468	ENDDO
469
470	!
471	!-- Calculate wr (from Aayala 2008b, page 38f)
472	z = tt / tl
473	be = SQRT( 2.0_wp ) * lambda / lf
474	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
475	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
476	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
477	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
478	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
479	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
480	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
481	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
482	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
483	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
484
485	DO i = 1, radius_classes
486
487	v1 = winf(i) ! in m/s
488	t1 = tau(i) ! in s
489
490	DO j = 1, i
491	rrp = radclass(i) + radclass(j)
492	v2 = winf(j) ! in m/s
493	t2 = tau(j) ! in s
494
495	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
496	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
497	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
498	vrms1xy = SQRT( v1xysq ) ! in m/s
499
500	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
501	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
502	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
503	vrms2xy = SQRT( v2xysq ) ! in m/s
504
505	IF ( winf(i) >= winf(j) ) THEN
506	v1 = winf(i)
507	t1 = tau(i)
508	v2 = winf(j)
509	t2 = tau(j)
510	ELSE
511	v1 = winf(j)
512	t1 = tau(j)
513	v2 = winf(i)
514	t2 = tau(i)
515	ENDIF
516
517	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
518	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
519	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
520	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
521	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
522	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
523	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
524	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
525	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
526	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
527
528	!
529	!-- Calculate gr
530	IF ( st(j) > st(i) ) THEN
531	sst = st(j)
532	ELSE
533	sst = st(i)
534	ENDIF
535
536	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
537	sst*2 + 5.3406_wp sst
538	IF ( xx < 0.0_wp ) xx = 0.0_wp
539	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
540
541	c1_gr = xx / ( g / vk * tauk )**yy
542
543	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
544	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
545	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
546
547	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
548	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
549
550	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
551	gck(j,i) = gck(i,j)
552
553	ENDDO
554	ENDDO
555
556	END SUBROUTINE turbsd
557
558
559	!------------------------------------------------------------------------------!
560	! Description:
561	! ------------
562	!> phi_w as a function
563	!------------------------------------------------------------------------------!
564	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
565
566	IMPLICIT NONE
567
568	REAL(wp) :: a !<
569	REAL(wp) :: aa1 !<
570	REAL(wp) :: b !<
571	REAL(wp) :: tau0 !<
572	REAL(wp) :: vsett !<
573
574	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
575	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
576
577	END FUNCTION phi_w
578
579
580	!------------------------------------------------------------------------------!
581	! Description:
582	! ------------
583	!> zhi as a function
584	!------------------------------------------------------------------------------!
585	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
586
587	IMPLICIT NONE
588
589	REAL(wp) :: a !<
590	REAL(wp) :: aa1 !<
591	REAL(wp) :: aa2 !<
592	REAL(wp) :: aa3 !<
593	REAL(wp) :: aa4 !<
594	REAL(wp) :: aa5 !<
595	REAL(wp) :: aa6 !<
596	REAL(wp) :: b !<
597	REAL(wp) :: tau1 !<
598	REAL(wp) :: tau2 !<
599	REAL(wp) :: vsett1 !<
600	REAL(wp) :: vsett2 !<
601
602	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
603	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
604	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
605	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
606	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
607	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
608	vsett1 / vsett2
609	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
610	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
611	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
612	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
613
614	END FUNCTION zhi
615
616
617	!------------------------------------------------------------------------------!
618	! Description:
619	! ------------
620	!> Calculation of terminal velocity winf following Equations 10-138 to 10-145
621	!> from (Pruppacher and Klett, 1997)
622	!------------------------------------------------------------------------------!
623	SUBROUTINE fallg
624
625	USE cloud_parameters, &
626	ONLY: rho_l
627
628	USE control_parameters, &
629	ONLY: g
630
631	USE particle_attributes, &
632	ONLY: radius_classes
633
634
635	IMPLICIT NONE
636
637	INTEGER(iwp) :: i !<
638	INTEGER(iwp) :: j !<
639
640	LOGICAL, SAVE :: first = .TRUE. !<
641
642	REAL(wp), SAVE :: cunh !<
643	REAL(wp), SAVE :: eta !<
644	REAL(wp), SAVE :: phy !<
645	REAL(wp), SAVE :: py !<
646	REAL(wp), SAVE :: rho_a !<
647	REAL(wp), SAVE :: sigma !<
648	REAL(wp), SAVE :: stb !<
649	REAL(wp), SAVE :: stok !<
650	REAL(wp), SAVE :: xlamb !<
651
652	REAL(wp) :: bond !<
653	REAL(wp) :: x !<
654	REAL(wp) :: xrey !<
655	REAL(wp) :: y !<
656
657	REAL(wp), DIMENSION(1:7), SAVE :: b !<
658	REAL(wp), DIMENSION(1:6), SAVE :: c !<
659
660	!
661	!-- Initial assignment of constants
662	IF ( first ) THEN
663
664	first = .FALSE.
665	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
666	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
667	-0.327815E-5_wp /)
668	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
669	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
670
671	!
672	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
673	eta = 1.818E-5_wp ! in kg/(m s)
674	xlamb = 6.6E-8_wp ! in m
675	rho_a = 1.204_wp ! in kg/m**3
676	cunh = 1.26_wp * xlamb ! in m
677	sigma = 0.07363_wp ! in kg/s**2
678	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
679	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
680	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
681	py = phy**( 1.0_wp / 6.0_wp )
682
683	ENDIF
684
685	DO j = 1, radius_classes
686
687	IF ( radclass(j) <= 1.0E-5_wp ) THEN
688
689	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
690
691	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
692
693	x = LOG( stb * radclass(j)**3 )
694	y = 0.0_wp
695
696	DO i = 1, 7
697	y = y + b(i) * x**(i-1)
698	ENDDO
699	!
700	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
701	!-- for correct version see (Beard, 1976)
702	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
703
704	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
705
706	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
707
708	IF ( radclass(j) > 0.0035_wp ) THEN
709	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
710	ELSE
711	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
712	ENDIF
713
714	x = LOG( 16.0_wp * bond * py / 3.0_wp )
715	y = 0.0_wp
716
717	DO i = 1, 6
718	y = y + c(i) * x**(i-1)
719	ENDDO
720
721	xrey = py * EXP( y )
722
723	IF ( radclass(j) > 0.0035_wp ) THEN
724	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
725	ELSE
726	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
727	ENDIF
728
729	ENDIF
730
731	ENDDO
732
733	END SUBROUTINE fallg
734
735
736	!------------------------------------------------------------------------------!
737	! Description:
738	! ------------
739	!> Calculation of collision efficiencies for the Hall kernel
740	!------------------------------------------------------------------------------!
741	SUBROUTINE effic
742
743	USE particle_attributes, &
744	ONLY: radius_classes
745
746	IMPLICIT NONE
747
748	INTEGER(iwp) :: i !<
749	INTEGER(iwp) :: iq !<
750	INTEGER(iwp) :: ir !<
751	INTEGER(iwp) :: j !<
752	INTEGER(iwp) :: k !<
753
754	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
755
756	LOGICAL, SAVE :: first = .TRUE. !<
757
758	REAL(wp) :: ek !<
759	REAL(wp) :: particle_radius !<
760	REAL(wp) :: pp !<
761	REAL(wp) :: qq !<
762	REAL(wp) :: rq !<
763
764	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
765
766	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
767
768	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
769
770	!
771	!-- Initial assignment of constants
772	IF ( first ) THEN
773
774	first = .FALSE.
775	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
776	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
777	150.0_wp, 200.0_wp, 300.0_wp /)
778
779	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
780	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
781	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
782	0.90_wp, 0.95_wp, 1.00_wp /)
783
784	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
785	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
786	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
787	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
788	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
789	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
790	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
791	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
792	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
793	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
794	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
795	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
796	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
797	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
798	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
799	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
800	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
801	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
802	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
803	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
804	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
805	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
806	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
807	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
808	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
809	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
810	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
811	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
812	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
813	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
814	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
815	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
816	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
817	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
818	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
819	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
820	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
821	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
822	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
823	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
824	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
825	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
826	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
827	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
828	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
829	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
830	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
831	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
832	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
833	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
834	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
835	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
836	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
837	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
838	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
839	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
840	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
841	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
842	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
843	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
844	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
845	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
846	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
847	ENDIF
848
849	!
850	!-- Calculate the radius class index of particles with respect to array r
851	!-- Radius has to be in Âµm
852	ALLOCATE( ira(1:radius_classes) )
853	DO j = 1, radius_classes
854	particle_radius = radclass(j) * 1.0E6_wp
855	DO k = 1, 15
856	IF ( particle_radius < r0(k) ) THEN
857	ira(j) = k
858	EXIT
859	ENDIF
860	ENDDO
861	IF ( particle_radius >= r0(15) ) ira(j) = 16
862	ENDDO
863
864	!
865	!-- Two-dimensional linear interpolation of the collision efficiency.
866	!-- Radius has to be in Âµm
867	DO j = 1, radius_classes
868	DO i = 1, j
869
870	ir = ira(j)
871	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
872	iq = INT( rq * 20 ) + 1
873	iq = MAX( iq , 2)
874
875	IF ( ir < 16 ) THEN
876	IF ( ir >= 2 ) THEN
877	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
878	( r0(ir) - r0(ir-1) )
879	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
880	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
881	* ecoll(ir-1,iq-1) &
882	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
883	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
884	+ pp * qq * ecoll(ir,iq)
885	ELSE
886	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
887	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
888	ENDIF
889	ELSE
890	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
891	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
892	ec(j,i) = MIN( ek, 1.0_wp )
893	ENDIF
894
895	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
896
897	ec(i,j) = ec(j,i)
898
899	ENDDO
900	ENDDO
901
902	DEALLOCATE( ira )
903
904	END SUBROUTINE effic
905
906
907	!------------------------------------------------------------------------------!
908	! Description:
909	! ------------
910	!> Calculation of enhancement factor for collision efficencies due to turbulence
911	!------------------------------------------------------------------------------!
912	SUBROUTINE turb_enhance_eff
913
914	USE particle_attributes, &
915	ONLY: radius_classes
916
917	IMPLICIT NONE
918
919	INTEGER(iwp) :: i !<
920	INTEGER(iwp) :: iq !<
921	INTEGER(iwp) :: ir !<
922	INTEGER(iwp) :: j !<
923	INTEGER(iwp) :: k !<
924	INTEGER(iwp) :: kk !<
925
926	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
927
928	LOGICAL, SAVE :: first = .TRUE. !<
929
930	REAL(wp) :: particle_radius !<
931	REAL(wp) :: pp !<
932	REAL(wp) :: qq !<
933	REAL(wp) :: rq !<
934	REAL(wp) :: y1 !<
935	REAL(wp) :: y2 !<
936	REAL(wp) :: y3 !<
937
938	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
939
940	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
941
942	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
943	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
944
945	!
946	!-- Initial assignment of constants
947	IF ( first ) THEN
948
949	first = .FALSE.
950
951	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
952	100.0_wp /)
953
954	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
955	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
956	!
957	!-- for 100 cm2/s3
958	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
959	1.207_wp, 1.207_wp, 1.0_wp /)
960	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
961	1.069_wp, 1.069_wp, 1.0_wp /)
962	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
963	1.000_wp, 1.000_wp, 1.0_wp /)
964	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
965	1.025_wp, 1.025_wp, 1.0_wp /)
966	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
967	1.056_wp, 1.056_wp, 1.0_wp /)
968	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
969	1.028_wp, 1.028_wp, 1.0_wp /)
970	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
971	1.046_wp, 1.046_wp, 1.0_wp /)
972	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
973	1.029_wp, 1.029_wp, 1.0_wp /)
974	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
975	1.021_wp, 1.021_wp, 1.0_wp /)
976	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
977	1.088_wp, 1.088_wp, 1.0_wp /)
978	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
979	2.60_wp, 2.60_wp, 1.0_wp /)
980	!
981	!-- for 400 cm2/s3
982	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
983	1.445_wp, 1.445_wp, 1.0_wp /)
984	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
985	1.201_wp, 1.201_wp, 1.0_wp /)
986	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
987	1.150_wp, 1.150_wp, 1.0_wp /)
988	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
989	1.126_wp, 1.126_wp, 1.0_wp /)
990	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
991	1.092_wp, 1.092_wp, 1.0_wp /)
992	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
993	1.051_wp, 1.051_wp, 1.0_wp /)
994	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
995	1.086_wp, 1.086_wp, 1.0_wp /)
996	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
997	1.063_wp, 1.063_wp, 1.0_wp /)
998	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
999	1.100_wp, 1.100_wp, 1.0_wp /)
1000	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
1001	1.120_wp, 1.120_wp, 1.0_wp /)
1002	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
1003	26.0_wp, 26.0_wp, 1.0_wp /)
1004
1005	ENDIF
1006
1007	!
1008	!-- Calculate the radius class index of particles with respect to array r0
1009	!-- Radius has to be in Âµm
1010	ALLOCATE( ira(1:radius_classes) )
1011
1012	DO j = 1, radius_classes
1013	particle_radius = radclass(j) * 1.0E6_wp
1014	DO k = 1, 7
1015	IF ( particle_radius < r0(k) ) THEN
1016	ira(j) = k
1017	EXIT
1018	ENDIF
1019	ENDDO
1020	IF ( particle_radius >= r0(7) ) ira(j) = 8
1021	ENDDO
1022
1023	!
1024	!-- Two-dimensional linear interpolation of the collision efficiencies
1025	!-- Radius has to be in Âµm
1026	DO j = 1, radius_classes
1027	DO i = 1, j
1028
1029	ir = ira(j)
1030	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
1031
1032	DO kk = 2, 11
1033	IF ( rq <= rat(kk) ) THEN
1034	iq = kk
1035	EXIT
1036	ENDIF
1037	ENDDO
1038
1039	y1 = 0.0001_wp ! for 0 m2/s3
1040
1041	IF ( ir < 8 ) THEN
1042	IF ( ir >= 2 ) THEN
1043	pp = ( radclass(j)*1.0E6_wp - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
1044	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1045	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
1046	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
1047	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
1048	pp * qq * ecoll_100(ir,iq)
1049	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
1050	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
1051	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
1052	pp * qq * ecoll_400(ir,iq)
1053	ELSE
1054	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1055	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
1056	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
1057	ENDIF
1058	ELSE
1059	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1060	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
1061	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
1062	ENDIF
1063	!
1064	!-- Linear interpolation of dissipation rate in m2/s3
1065	IF ( epsilon <= 0.01_wp ) THEN
1066	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
1067	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
1068	ELSEIF ( epsilon <= 0.06_wp ) THEN
1069	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1070	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1071	ELSE
1072	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1073	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1074	ENDIF
1075
1076	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
1077
1078	ecf(i,j) = ecf(j,i)
1079
1080	ENDDO
1081	ENDDO
1082
1083	END SUBROUTINE turb_enhance_eff
1084
1085
1086
1087	!------------------------------------------------------------------------------!
1088	! Description:
1089	! ------------
1090	!> Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
1091	!> Values are calculated from table by bilinear interpolation.
1092	!------------------------------------------------------------------------------!
1093
1094	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
1095
1096	IMPLICIT NONE
1097
1098	INTEGER(iwp) :: i !<
1099	INTEGER(iwp) :: j !<
1100	INTEGER(iwp) :: k !<
1101
1102	LOGICAL, SAVE :: first = .TRUE. !<
1103
1104	REAL(wp) :: aa !<
1105	REAL(wp) :: bb !<
1106	REAL(wp) :: cc !<
1107	REAL(wp) :: dd !<
1108	REAL(wp) :: dx !<
1109	REAL(wp) :: dy !<
1110	REAL(wp) :: e !<
1111	REAL(wp) :: gg !<
1112	REAL(wp) :: mean_r !<
1113	REAL(wp) :: mean_rm !<
1114	REAL(wp) :: r !<
1115	REAL(wp) :: rm !<
1116	REAL(wp) :: x !<
1117	REAL(wp) :: y !<
1118
1119	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !<
1120
1121	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !<
1122
1123	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !<
1124
1125	mean_rm = mean_r * 1.0E06_wp
1126	rm = r * 1.0E06_wp
1127
1128	IF ( first ) THEN
1129
1130	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
1131	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
1132	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
1133	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
1134	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
1135	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
1136
1137	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
1138	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
1139	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
1140	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
1141	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
1142	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
1143	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
1144	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
1145	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
1146	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
1147	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
1148	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
1149	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
1150	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
1151	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
1152	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
1153	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
1154	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
1155	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
1156	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
1157	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
1158	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1159	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
1160	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1161	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
1162	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1163	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
1164	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1165	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
1166	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1167	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
1168	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
1169	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
1170	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
1171	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
1172	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
1173	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
1174	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
1175
1176	ENDIF
1177
1178	DO k = 1, 8
1179	IF ( collected_r(k) <= mean_rm ) i = k
1180	ENDDO
1181
1182	DO k = 1, 18
1183	IF ( collector_r(k) <= rm ) j = k
1184	ENDDO
1185
1186	IF ( rm < 10.0_wp ) THEN
1187	e = 0.0_wp
1188	ELSEIF ( mean_rm < 2.0_wp ) THEN
1189	e = 0.001_wp
1190	ELSEIF ( mean_rm >= 25.0_wp ) THEN
1191	IF( j <= 2 ) e = 0.0_wp
1192	IF( j == 3 ) e = 0.47_wp
1193	IF( j == 4 ) e = 0.8_wp
1194	IF( j == 5 ) e = 0.9_wp
1195	IF( j >=6 ) e = 1.0_wp
1196	ELSEIF ( rm >= 3000.0_wp ) THEN
1197	IF( i == 1 ) e = 0.02_wp
1198	IF( i == 2 ) e = 0.16_wp
1199	IF( i == 3 ) e = 0.33_wp
1200	IF( i == 4 ) e = 0.55_wp
1201	IF( i == 5 ) e = 0.71_wp
1202	IF( i == 6 ) e = 0.81_wp
1203	IF( i == 7 ) e = 0.90_wp
1204	IF( i >= 8 ) e = 0.94_wp
1205	ELSE
1206	x = mean_rm - collected_r(i)
1207	y = rm - collector_r(j)
1208	dx = collected_r(i+1) - collected_r(i)
1209	dy = collector_r(j+1) - collector_r(j)
1210	aa = x2 + y2
1211	bb = ( dx - x )2 + y2
1212	cc = x2 + ( dy - y )2
1213	dd = ( dx - x )2 + ( dy - y )2
1214	gg = aa + bb + cc + dd
1215
1216	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
1217	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
1218	ENDIF
1219
1220	END SUBROUTINE collision_efficiency_rogers
1221
1222	END MODULE lpm_collision_kernels_mod

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