!> @file lpm_droplet_collision.f90
!------------------------------------------------------------------------------!
! This file is part of PALM.
!
! PALM is free software: you can redistribute it and/or modify it under the
! terms of the GNU General Public License as published by the Free Software
! Foundation, either version 3 of the License, or (at your option) any later
! version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see .
!
! Copyright 1997-2017 Leibniz Universitaet Hannover
!------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
!
!
! Former revisions:
! -----------------
! $Id: lpm_droplet_collision.f90 2101 2017-01-05 16:42:31Z suehring $
!
! 2000 2016-08-20 18:09:15Z knoop
! Forced header and separation lines into 80 columns
!
! 1884 2016-04-21 11:11:40Z hoffmann
! Conservation of mass should only be checked if collisions took place.
!
! 1860 2016-04-13 13:21:28Z hoffmann
! Interpolation of dissipation rate adjusted to more reasonable values.
!
! 1822 2016-04-07 07:49:42Z hoffmann
! Integration of a new collision algortithm based on Shima et al. (2009) and
! Soelch and Kaercher (2010) called all_or_nothing. The previous implemented
! collision algorithm is called average_impact. Moreover, both algorithms are
! now positive definit due to their construction, i.e., no negative weighting
! factors should occur.
!
! 1682 2015-10-07 23:56:08Z knoop
! Code annotations made doxygen readable
!
! 1359 2014-04-11 17:15:14Z hoffmann
! New particle structure integrated.
! Kind definition added to all floating point numbers.
!
! 1322 2014-03-20 16:38:49Z raasch
! REAL constants defined as wp_kind
!
! 1320 2014-03-20 08:40:49Z raasch
! ONLY-attribute added to USE-statements,
! kind-parameters added to all INTEGER and REAL declaration statements,
! kinds are defined in new module kinds,
! revision history before 2012 removed,
! comment fields (!:) to be used for variable explanations added to
! all variable declaration statements
!
! 1092 2013-02-02 11:24:22Z raasch
! unused variables removed
!
! 1071 2012-11-29 16:54:55Z franke
! Calculation of Hall and Wang kernel now uses collision-coalescence formulation
! proposed by Wang instead of the continuous collection equation (for more
! information about new method see PALM documentation)
! Bugfix: message identifiers added
!
! 1036 2012-10-22 13:43:42Z raasch
! code put under GPL (PALM 3.9)
!
! 849 2012-03-15 10:35:09Z raasch
! initial revision (former part of advec_particles)
!
!
! Description:
! ------------
!> Calculates change in droplet radius by collision. Droplet collision is
!> calculated for each grid box seperately. Collision is parameterized by
!> using collision kernels. Two different kernels are available:
!> Hall kernel: Kernel from Hall (1980, J. Atmos. Sci., 2486-2507), which
!> considers collision due to pure gravitational effects.
!> Wang kernel: Beside gravitational effects (treated with the Hall-kernel) also
!> the effects of turbulence on the collision are considered using
!> parameterizations of Ayala et al. (2008, New J. Phys., 10,
!> 075015) and Wang and Grabowski (2009, Atmos. Sci. Lett., 10,
!> 1-8). This kernel includes three possible effects of turbulence:
!> the modification of the relative velocity between the droplets,
!> the effect of preferential concentration, and the enhancement of
!> collision efficiencies.
!------------------------------------------------------------------------------!
SUBROUTINE lpm_droplet_collision (i,j,k)
USE arrays_3d, &
ONLY: diss, ql_v, ql_vp
USE cloud_parameters, &
ONLY: rho_l
USE constants, &
ONLY: pi
USE control_parameters, &
ONLY: dt_3d, message_string, dz
USE cpulog, &
ONLY: cpu_log, log_point_s
USE grid_variables, &
ONLY: dx, dy
USE kinds
USE lpm_collision_kernels_mod, &
ONLY: ckernel, recalculate_kernel
USE particle_attributes, &
ONLY: all_or_nothing, average_impact, dissipation_classes, &
hall_kernel, iran_part, number_of_particles, particles, &
particle_type, prt_count, use_kernel_tables, wang_kernel
USE random_function_mod, &
ONLY: random_function
USE pegrid
IMPLICIT NONE
INTEGER(iwp) :: eclass !<
INTEGER(iwp) :: i !<
INTEGER(iwp) :: j !<
INTEGER(iwp) :: k !<
INTEGER(iwp) :: n !<
INTEGER(iwp) :: m !<
INTEGER(iwp) :: rclass_l !<
INTEGER(iwp) :: rclass_s !<
REAL(wp) :: collection_probability !< probability for collection
REAL(wp) :: ddV !< inverse grid box volume
REAL(wp) :: epsilon !< dissipation rate
REAL(wp) :: factor_volume_to_mass !< 4.0 / 3.0 * pi * rho_l
REAL(wp) :: xm !< mean mass of droplet m
REAL(wp) :: xn !< mean mass of droplet n
REAL(wp), DIMENSION(:), ALLOCATABLE :: weight !< weighting factor
REAL(wp), DIMENSION(:), ALLOCATABLE :: mass !< total mass of super droplet
CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'start' )
number_of_particles = prt_count(k,j,i)
factor_volume_to_mass = 4.0_wp / 3.0_wp * pi * rho_l
ddV = 1 / ( dx * dy * dz )
!
!-- Collision requires at least one super droplet inside the box
IF ( number_of_particles > 0 ) THEN
!
!-- Now apply the different kernels
IF ( use_kernel_tables ) THEN
!
!-- Fast method with pre-calculated collection kernels for
!-- discrete radius- and dissipation-classes.
!--
!-- Determine dissipation class index of this gridbox
IF ( wang_kernel ) THEN
eclass = INT( diss(k,j,i) * 1.0E4_wp / 600.0_wp * &
dissipation_classes ) + 1
epsilon = diss(k,j,i)
ELSE
epsilon = 0.0_wp
ENDIF
IF ( hall_kernel .OR. epsilon * 1.0E4_wp < 0.001_wp ) THEN
eclass = 0 ! Hall kernel is used
ELSE
eclass = MIN( dissipation_classes, eclass )
ENDIF
!
!-- Droplet collision are calculated using collision-coalescence
!-- formulation proposed by Wang (see PALM documentation)
!-- Temporary fields for total mass of super-droplet and weighting factors
!-- are allocated.
ALLOCATE(mass(1:number_of_particles), weight(1:number_of_particles))
mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
particles(1:number_of_particles)%radius**3 * &
factor_volume_to_mass
weight(1:number_of_particles) = particles(1:number_of_particles)%weight_factor
IF ( average_impact ) THEN ! select collision algorithm
DO n = 1, number_of_particles
rclass_l = particles(n)%class
xn = mass(n) / weight(n)
DO m = n, number_of_particles
rclass_s = particles(m)%class
xm = mass(m) / weight(m)
IF ( xm .LT. xn ) THEN
!
!-- Particle n collects smaller particle m
collection_probability = ckernel(rclass_l,rclass_s,eclass) * &
weight(n) * ddV * dt_3d
mass(n) = mass(n) + mass(m) * collection_probability
weight(m) = weight(m) - weight(m) * collection_probability
mass(m) = mass(m) - mass(m) * collection_probability
ELSEIF ( xm .GT. xn ) THEN
!
!-- Particle m collects smaller particle n
collection_probability = ckernel(rclass_l,rclass_s,eclass) * &
weight(m) * ddV * dt_3d
mass(m) = mass(m) + mass(n) * collection_probability
weight(n) = weight(n) - weight(n) * collection_probability
mass(n) = mass(n) - mass(n) * collection_probability
ELSE
!
!-- Same-size collections. If n = m, weight is reduced by the
!-- number of possible same-size collections; the total mass
!-- is not changed during same-size collection.
!-- Same-size collections of different
!-- particles ( n /= m ) are treated as same-size collections
!-- of ONE partilce with weight = weight(n) + weight(m) and
!-- mass = mass(n) + mass(m).
!-- Accordingly, each particle loses the same number of
!-- droplets to the other particle, but this has no effect on
!-- total mass mass, since the exchanged droplets have the
!-- same radius.
!-- Note: For m = n this equation is an approximation only
!-- valid for weight >> 1 (which is usually the case). The
!-- approximation is weight(n)-1 = weight(n).
weight(n) = weight(n) - 0.5_wp * weight(n) * &
ckernel(rclass_l,rclass_s,eclass) * &
weight(m) * ddV * dt_3d
IF ( n .NE. m ) THEN
weight(m) = weight(m) - 0.5_wp * weight(m) * &
ckernel(rclass_l,rclass_s,eclass) * &
weight(n) * ddV * dt_3d
ENDIF
ENDIF
ENDDO
ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
ENDDO
ELSEIF ( all_or_nothing ) THEN ! select collision algorithm
DO n = 1, number_of_particles
rclass_l = particles(n)%class
xn = mass(n) / weight(n) ! mean mass of droplet n
DO m = n, number_of_particles
rclass_s = particles(m)%class
xm = mass(m) / weight(m) ! mean mass of droplet m
IF ( weight(n) .LT. weight(m) ) THEN
!
!-- Particle n collects weight(n) droplets of particle m
collection_probability = ckernel(rclass_l,rclass_s,eclass) * &
weight(m) * ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(n) = mass(n) + weight(n) * xm
weight(m) = weight(m) - weight(n)
mass(m) = mass(m) - weight(n) * xm
ENDIF
ELSEIF ( weight(m) .LT. weight(n) ) THEN
!
!-- Particle m collects weight(m) droplets of particle n
collection_probability = ckernel(rclass_l,rclass_s,eclass) * &
weight(n) * ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(m) = mass(m) + weight(m) * xn
weight(n) = weight(n) - weight(m)
mass(n) = mass(n) - weight(m) * xn
ENDIF
ELSE
!
!-- Collisions of particles of the same weighting factor.
!-- Particle n collects 1/2 weight(n) droplets of particle m,
!-- particle m collects 1/2 weight(m) droplets of particle n.
!-- The total mass mass changes accordingly.
!-- If n = m, the first half of the droplets coalesces with the
!-- second half of the droplets; mass is unchanged because
!-- xm = xn for n = m.
!-- Note: For m = n this equation is an approximation only
!-- valid for weight >> 1 (which is usually the case). The
!-- approximation is weight(n)-1 = weight(n).
collection_probability = ckernel(rclass_l,rclass_s,eclass) * &
weight(n) * ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(n) = mass(n) + 0.5_wp * weight(n) * ( xm - xn )
mass(m) = mass(m) + 0.5_wp * weight(m) * ( xn - xm )
weight(n) = weight(n) - 0.5_wp * weight(m)
weight(m) = weight(n)
ENDIF
ENDIF
ENDDO
ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
ENDDO
ENDIF
IF ( ANY(weight < 0.0_wp) ) THEN
WRITE( message_string, * ) 'negative weighting'
CALL message( 'lpm_droplet_collision', 'PA0028', &
2, 2, -1, 6, 1 )
ENDIF
particles(1:number_of_particles)%radius = ( mass(1:number_of_particles) / &
( weight(1:number_of_particles) &
* factor_volume_to_mass &
) &
)**0.33333333333333_wp
particles(1:number_of_particles)%weight_factor = weight(1:number_of_particles)
DEALLOCATE(weight, mass)
ELSEIF ( .NOT. use_kernel_tables ) THEN
!
!-- Collection kernels are calculated for every new
!-- grid box. First, allocate memory for kernel table.
!-- Third dimension is 1, because table is re-calculated for
!-- every new dissipation value.
ALLOCATE( ckernel(1:number_of_particles,1:number_of_particles,1:1) )
!
!-- Now calculate collection kernel for this box. Note that
!-- the kernel is based on the previous time step
CALL recalculate_kernel( i, j, k )
!
!-- Droplet collision are calculated using collision-coalescence
!-- formulation proposed by Wang (see PALM documentation)
!-- Temporary fields for total mass of super-droplet and weighting factors
!-- are allocated.
ALLOCATE(mass(1:number_of_particles), weight(1:number_of_particles))
mass(1:number_of_particles) = particles(1:number_of_particles)%weight_factor * &
particles(1:number_of_particles)%radius**3 * &
factor_volume_to_mass
weight(1:number_of_particles) = particles(1:number_of_particles)%weight_factor
IF ( average_impact ) THEN ! select collision algorithm
DO n = 1, number_of_particles
xn = mass(n) / weight(n) ! mean mass of droplet n
DO m = n, number_of_particles
xm = mass(m) / weight(m) !mean mass of droplet m
IF ( xm .LT. xn ) THEN
!
!-- Particle n collects smaller particle m
collection_probability = ckernel(n,m,1) * weight(n) * &
ddV * dt_3d
mass(n) = mass(n) + mass(m) * collection_probability
weight(m) = weight(m) - weight(m) * collection_probability
mass(m) = mass(m) - mass(m) * collection_probability
ELSEIF ( xm .GT. xn ) THEN
!
!-- Particle m collects smaller particle n
collection_probability = ckernel(n,m,1) * weight(m) * &
ddV * dt_3d
mass(m) = mass(m) + mass(n) * collection_probability
weight(n) = weight(n) - weight(n) * collection_probability
mass(n) = mass(n) - mass(n) * collection_probability
ELSE
!
!-- Same-size collections. If n = m, weight is reduced by the
!-- number of possible same-size collections; the total mass
!-- mass is not changed during same-size collection.
!-- Same-size collections of different
!-- particles ( n /= m ) are treated as same-size collections
!-- of ONE partilce with weight = weight(n) + weight(m) and
!-- mass = mass(n) + mass(m).
!-- Accordingly, each particle loses the same number of
!-- droplets to the other particle, but this has no effect on
!-- total mass mass, since the exchanged droplets have the
!-- same radius.
!--
!-- Note: For m = n this equation is an approximation only
!-- valid for weight >> 1 (which is usually the case). The
!-- approximation is weight(n)-1 = weight(n).
weight(n) = weight(n) - 0.5_wp * weight(n) * &
ckernel(n,m,1) * weight(m) * &
ddV * dt_3d
IF ( n .NE. m ) THEN
weight(m) = weight(m) - 0.5_wp * weight(m) * &
ckernel(n,m,1) * weight(n) * &
ddV * dt_3d
ENDIF
ENDIF
ENDDO
ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
ENDDO
ELSEIF ( all_or_nothing ) THEN ! select collision algorithm
DO n = 1, number_of_particles
xn = mass(n) / weight(n) ! mean mass of droplet n
DO m = n, number_of_particles
xm = mass(m) / weight(m) !mean mass of droplet m
IF ( weight(n) .LT. weight(m) ) THEN
!
!-- Particle n collects smaller particle m
collection_probability = ckernel(n,m,1) * weight(m) * &
ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(n) = mass(n) + weight(n) * xm
weight(m) = weight(m) - weight(n)
mass(m) = mass(m) - weight(n) * xm
ENDIF
ELSEIF ( weight(m) .LT. weight(n) ) THEN
!
!-- Particle m collects smaller particle n
collection_probability = ckernel(n,m,1) * weight(n) * &
ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(m) = mass(m) + weight(m) * xn
weight(n) = weight(n) - weight(m)
mass(n) = mass(n) - weight(m) * xn
ENDIF
ELSE
!
!-- Collisions of particles of the same weighting factor.
!-- Particle n collects 1/2 weight(n) droplets of particle m,
!-- particle m collects 1/2 weight(m) droplets of particle n.
!-- The total mass mass changes accordingly.
!-- If n = m, the first half of the droplets coalesces with the
!-- second half of the droplets; mass is unchanged because
!-- xm = xn for n = m.
!--
!-- Note: For m = n this equation is an approximation only
!-- valid for weight >> 1 (which is usually the case). The
!-- approximation is weight(n)-1 = weight(n).
collection_probability = ckernel(n,m,1) * weight(n) * &
ddV * dt_3d
IF ( collection_probability .GT. random_function( iran_part ) ) THEN
mass(n) = mass(n) + 0.5_wp * weight(n) * ( xm - xn )
mass(m) = mass(m) + 0.5_wp * weight(m) * ( xn - xm )
weight(n) = weight(n) - 0.5_wp * weight(m)
weight(m) = weight(n)
ENDIF
ENDIF
ENDDO
ql_vp(k,j,i) = ql_vp(k,j,i) + mass(n) / factor_volume_to_mass
ENDDO
ENDIF
IF ( ANY(weight < 0.0_wp) ) THEN
WRITE( message_string, * ) 'negative weighting'
CALL message( 'lpm_droplet_collision', 'PA0028', &
2, 2, -1, 6, 1 )
ENDIF
particles(1:number_of_particles)%radius = ( mass(1:number_of_particles) / &
( weight(1:number_of_particles) &
* factor_volume_to_mass &
) &
)**0.33333333333333_wp
particles(1:number_of_particles)%weight_factor = weight(1:number_of_particles)
DEALLOCATE( weight, mass, ckernel )
ENDIF
!
!-- Check if LWC is conserved during collision process
IF ( ql_v(k,j,i) /= 0.0_wp ) THEN
IF ( ql_vp(k,j,i) / ql_v(k,j,i) >= 1.0001_wp .OR. &
ql_vp(k,j,i) / ql_v(k,j,i) <= 0.9999_wp ) THEN
WRITE( message_string, * ) ' LWC is not conserved during', &
' collision! ', &
' LWC after condensation: ', ql_v(k,j,i), &
' LWC after collision: ', ql_vp(k,j,i)
CALL message( 'lpm_droplet_collision', 'PA0040', 2, 2, -1, 6, 1 )
ENDIF
ENDIF
ENDIF
CALL cpu_log( log_point_s(43), 'lpm_droplet_coll', 'stop' )
END SUBROUTINE lpm_droplet_collision