source: palm/trunk/SOURCE/lpm_droplet_collision.f90 @ 2281

!> @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 <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2017 Leibniz Universitaet Hannover
!------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
! 
! 
! Former revisions:
! -----------------
! $Id: lpm_droplet_collision.f90 2274 2017-06-09 13:27:48Z suehring $
! Changed error messages
!
! 2123 2017-01-18 12:34:59Z hoffmann
!
! 2122 2017-01-18 12:22:54Z hoffmann
! Some reformatting of the code.
!
! 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 factor'
                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 factor'
                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