| 1 | !> @file lpm_droplet_condensation.f90 |
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| 2 | !--------------------------------------------------------------------------------! |
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| 3 | ! This file is part of PALM. |
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| 4 | ! |
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| 5 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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| 6 | ! of the GNU General Public License as published by the Free Software Foundation, |
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| 7 | ! either version 3 of the License, or (at your option) any later version. |
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| 8 | ! |
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| 9 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 10 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 11 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 12 | ! |
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| 13 | ! You should have received a copy of the GNU General Public License along with |
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| 14 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 15 | ! |
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| 16 | ! Copyright 1997-2014 Leibniz Universitaet Hannover |
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| 17 | !--------------------------------------------------------------------------------! |
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| 18 | ! |
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| 19 | ! Current revisions: |
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| 20 | ! ------------------ |
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| 21 | ! |
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| 22 | ! |
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| 23 | ! Former revisions: |
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| 24 | ! ----------------- |
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| 25 | ! $Id: lpm_droplet_condensation.f90 1683 2015-10-07 23:57:51Z knoop $ |
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| 26 | ! |
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| 27 | ! 1682 2015-10-07 23:56:08Z knoop |
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| 28 | ! Code annotations made doxygen readable |
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| 29 | ! |
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| 30 | ! 1359 2014-04-11 17:15:14Z hoffmann |
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| 31 | ! New particle structure integrated. |
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| 32 | ! Kind definition added to all floating point numbers. |
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| 33 | ! |
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| 34 | ! 1346 2014-03-27 13:18:20Z heinze |
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| 35 | ! Bugfix: REAL constants provided with KIND-attribute especially in call of |
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| 36 | ! intrinsic function like MAX, MIN, SIGN |
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| 37 | ! |
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| 38 | ! 1322 2014-03-20 16:38:49Z raasch |
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| 39 | ! REAL constants defined as wp-kind |
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| 40 | ! |
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| 41 | ! 1320 2014-03-20 08:40:49Z raasch |
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| 42 | ! ONLY-attribute added to USE-statements, |
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| 43 | ! kind-parameters added to all INTEGER and REAL declaration statements, |
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| 44 | ! kinds are defined in new module kinds, |
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| 45 | ! comment fields (!:) to be used for variable explanations added to |
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| 46 | ! all variable declaration statements |
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| 47 | ! |
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| 48 | ! 1318 2014-03-17 13:35:16Z raasch |
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| 49 | ! module interfaces removed |
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| 50 | ! |
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| 51 | ! 1092 2013-02-02 11:24:22Z raasch |
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| 52 | ! unused variables removed |
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| 53 | ! |
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| 54 | ! 1071 2012-11-29 16:54:55Z franke |
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| 55 | ! Ventilation effect for evaporation of large droplets included |
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| 56 | ! Check for unreasonable results included in calculation of Rosenbrock method |
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| 57 | ! since physically unlikely results were observed and for the same |
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| 58 | ! reason the first internal time step in Rosenbrock method should be < 1.0E02 in |
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| 59 | ! case of evaporation |
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| 60 | ! Unnecessary calculation of ql_int removed |
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| 61 | ! Unnecessary calculations in Rosenbrock method (d2rdt2, drdt_m, dt_ros_last) |
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| 62 | ! removed |
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| 63 | ! Bugfix: factor in calculation of surface tension changed from 0.00155 to |
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| 64 | ! 0.000155 |
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| 65 | ! |
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| 66 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 67 | ! code put under GPL (PALM 3.9) |
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| 68 | ! |
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| 69 | ! 849 2012-03-15 10:35:09Z raasch |
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| 70 | ! initial revision (former part of advec_particles) |
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| 71 | ! |
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| 72 | ! |
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| 73 | ! Description: |
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| 74 | ! ------------ |
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| 75 | !> Calculates change in droplet radius by condensation/evaporation, using |
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| 76 | !> either an analytic formula or by numerically integrating the radius growth |
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| 77 | !> equation including curvature and solution effects using Rosenbrocks method |
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| 78 | !> (see Numerical recipes in FORTRAN, 2nd edition, p. 731). |
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| 79 | !> The analytical formula and growth equation follow those given in |
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| 80 | !> Rogers and Yau (A short course in cloud physics, 3rd edition, p. 102/103). |
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| 81 | !------------------------------------------------------------------------------! |
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| 82 | SUBROUTINE lpm_droplet_condensation (ip,jp,kp) |
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| 83 | |
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| 84 | |
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| 85 | USE arrays_3d, & |
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| 86 | ONLY: hyp, pt, q, ql_c, ql_v, zu |
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| 87 | |
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| 88 | USE cloud_parameters, & |
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| 89 | ONLY: bfactor, curvature_solution_effects, diff_coeff_l, & |
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| 90 | eps_ros, l_d_rv, l_v, rho_l, r_v, thermal_conductivity_l |
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| 91 | |
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| 92 | USE constants, & |
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| 93 | ONLY: pi |
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| 94 | |
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| 95 | USE control_parameters, & |
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| 96 | ONLY: atmos_ocean_sign, dt_3d, dz, message_string, & |
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| 97 | molecular_viscosity, rho_surface |
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| 98 | USE cpulog, & |
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| 99 | ONLY: cpu_log, log_point_s |
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| 100 | |
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| 101 | USE grid_variables, & |
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| 102 | ONLY: dx, ddx, dy, ddy |
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| 103 | |
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| 104 | USE lpm_collision_kernels_mod, & |
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| 105 | ONLY: rclass_lbound, rclass_ubound |
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| 106 | |
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| 107 | USE kinds |
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| 108 | |
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| 109 | USE particle_attributes, & |
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| 110 | ONLY: block_offset, grid_particles, hall_kernel, number_of_particles, & |
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| 111 | offset_ocean_nzt, offset_ocean_nzt_m1, particles, & |
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| 112 | radius_classes, use_kernel_tables, wang_kernel |
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| 113 | |
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| 114 | |
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| 115 | IMPLICIT NONE |
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| 116 | |
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| 117 | INTEGER(iwp) :: i !< |
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| 118 | INTEGER(iwp) :: ip !< |
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| 119 | INTEGER(iwp) :: internal_timestep_count !< |
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| 120 | INTEGER(iwp) :: j !< |
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| 121 | INTEGER(iwp) :: jp !< |
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| 122 | INTEGER(iwp) :: jtry !< |
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| 123 | INTEGER(iwp) :: k !< |
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| 124 | INTEGER(iwp) :: kp !< |
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| 125 | INTEGER(iwp) :: n !< |
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| 126 | INTEGER(iwp) :: nb !< |
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| 127 | INTEGER(iwp) :: ros_count !< |
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| 128 | |
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| 129 | INTEGER(iwp), PARAMETER :: maxtry = 40 !< |
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| 130 | |
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| 131 | INTEGER(iwp), DIMENSION(0:7) :: end_index !< |
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| 132 | INTEGER(iwp), DIMENSION(0:7) :: start_index !< |
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| 133 | |
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| 134 | LOGICAL :: repeat !< |
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| 135 | |
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| 136 | LOGICAL, DIMENSION(number_of_particles) :: flag_1 !< |
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| 137 | |
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| 138 | REAL(wp) :: aa !< |
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| 139 | REAL(wp) :: afactor !< |
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| 140 | REAL(wp) :: arg !< |
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| 141 | REAL(wp) :: bb !< |
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| 142 | REAL(wp) :: cc !< |
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| 143 | REAL(wp) :: dd !< |
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| 144 | REAL(wp) :: ddenom !< |
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| 145 | REAL(wp) :: delta_r !< |
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| 146 | REAL(wp) :: drdt !< |
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| 147 | REAL(wp) :: drdt_ini !< |
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| 148 | REAL(wp) :: dt_ros !< |
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| 149 | REAL(wp) :: dt_ros_next !< |
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| 150 | REAL(wp) :: dt_ros_sum !< |
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| 151 | REAL(wp) :: dt_ros_sum_ini !< |
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| 152 | REAL(wp) :: d2rdtdr !< |
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| 153 | REAL(wp) :: errmax !< |
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| 154 | REAL(wp) :: err_ros !< |
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| 155 | REAL(wp) :: g1 !< |
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| 156 | REAL(wp) :: g2 !< |
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| 157 | REAL(wp) :: g3 !< |
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| 158 | REAL(wp) :: g4 !< |
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| 159 | REAL(wp) :: gg !< |
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| 160 | REAL(wp) :: pt_int !< |
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| 161 | REAL(wp) :: pt_int_l !< |
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| 162 | REAL(wp) :: pt_int_u !< |
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| 163 | REAL(wp) :: q_int !< |
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| 164 | REAL(wp) :: q_int_l !< |
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| 165 | REAL(wp) :: q_int_u !< |
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| 166 | REAL(wp) :: r_ros !< |
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| 167 | REAL(wp) :: r_ros_ini !< |
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| 168 | REAL(wp) :: sigma !< |
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| 169 | REAL(wp) :: x !< |
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| 170 | REAL(wp) :: y !< |
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| 171 | REAL(wp) :: re_p !< |
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| 172 | |
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| 173 | !-- Parameters for Rosenbrock method |
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| 174 | REAL(wp), PARAMETER :: a21 = 2.0_wp !< |
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| 175 | REAL(wp), PARAMETER :: a31 = 48.0_wp / 25.0_wp !< |
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| 176 | REAL(wp), PARAMETER :: a32 = 6.0_wp / 25.0_wp !< |
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| 177 | REAL(wp), PARAMETER :: b1 = 19.0_wp / 9.0_wp !< |
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| 178 | REAL(wp), PARAMETER :: b2 = 0.5_wp !< |
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| 179 | REAL(wp), PARAMETER :: b3 = 25.0_wp / 108.0_wp !< |
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| 180 | REAL(wp), PARAMETER :: b4 = 125.0_wp / 108.0_wp !< |
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| 181 | REAL(wp), PARAMETER :: c21 = -8.0_wp !< |
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| 182 | REAL(wp), PARAMETER :: c31 = 372.0_wp / 25.0_wp !< |
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| 183 | REAL(wp), PARAMETER :: c32 = 12.0_wp / 5.0_wp !< |
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| 184 | REAL(wp), PARAMETER :: c41 = -112.0_wp / 125.0_wp !< |
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| 185 | REAL(wp), PARAMETER :: c42 = -54.0_wp / 125.0_wp !< |
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| 186 | REAL(wp), PARAMETER :: c43 = -2.0_wp / 5.0_wp !< |
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| 187 | REAL(wp), PARAMETER :: errcon = 0.1296_wp !< |
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| 188 | REAL(wp), PARAMETER :: e1 = 17.0_wp / 54.0_wp !< |
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| 189 | REAL(wp), PARAMETER :: e2 = 7.0_wp / 36.0_wp !< |
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| 190 | REAL(wp), PARAMETER :: e3 = 0.0_wp !< |
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| 191 | REAL(wp), PARAMETER :: e4 = 125.0_wp / 108.0_wp !< |
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| 192 | REAL(wp), PARAMETER :: gam = 0.5_wp !< |
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| 193 | REAL(wp), PARAMETER :: grow = 1.5_wp !< |
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| 194 | REAL(wp), PARAMETER :: pgrow = -0.25_wp !< |
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| 195 | REAL(wp), PARAMETER :: pshrnk = -1.0_wp /3.0_wp !< |
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| 196 | REAL(wp), PARAMETER :: shrnk = 0.5_wp !< |
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| 197 | |
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| 198 | REAL(wp), DIMENSION(number_of_particles) :: afactor_v !< |
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| 199 | REAL(wp), DIMENSION(number_of_particles) :: diff_coeff_v !< |
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| 200 | REAL(wp), DIMENSION(number_of_particles) :: e_s !< |
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| 201 | REAL(wp), DIMENSION(number_of_particles) :: e_a !< |
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| 202 | REAL(wp), DIMENSION(number_of_particles) :: new_r !< |
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| 203 | REAL(wp), DIMENSION(number_of_particles) :: p_int !< |
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| 204 | REAL(wp), DIMENSION(number_of_particles) :: thermal_conductivity_v !< |
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| 205 | REAL(wp), DIMENSION(number_of_particles) :: t_int !< |
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| 206 | REAL(wp), DIMENSION(number_of_particles) :: xv !< |
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| 207 | REAL(wp), DIMENSION(number_of_particles) :: yv !< |
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| 208 | REAL(wp), DIMENSION(number_of_particles) :: zv !< |
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| 209 | |
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| 210 | |
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| 211 | CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'start' ) |
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| 212 | |
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| 213 | start_index = grid_particles(kp,jp,ip)%start_index |
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| 214 | end_index = grid_particles(kp,jp,ip)%end_index |
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| 215 | |
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| 216 | xv = particles(1:number_of_particles)%x |
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| 217 | yv = particles(1:number_of_particles)%y |
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| 218 | zv = particles(1:number_of_particles)%z |
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| 219 | |
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| 220 | DO nb = 0,7 |
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| 221 | |
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| 222 | i = ip + block_offset(nb)%i_off |
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| 223 | j = jp + block_offset(nb)%j_off |
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| 224 | k = kp + block_offset(nb)%k_off |
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| 225 | |
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| 226 | DO n = start_index(nb), end_index(nb) |
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| 227 | ! |
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| 228 | !-- Interpolate temperature and humidity. |
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| 229 | x = xv(n) - i * dx |
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| 230 | y = yv(n) - j * dy |
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| 231 | aa = x**2 + y**2 |
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| 232 | bb = ( dx - x )**2 + y**2 |
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| 233 | cc = x**2 + ( dy - y )**2 |
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| 234 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 235 | gg = aa + bb + cc + dd |
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| 236 | |
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| 237 | pt_int_l = ( ( gg - aa ) * pt(k,j,i) + ( gg - bb ) * pt(k,j,i+1) & |
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| 238 | + ( gg - cc ) * pt(k,j+1,i) + ( gg - dd ) * pt(k,j+1,i+1) & |
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| 239 | ) / ( 3.0_wp * gg ) |
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| 240 | |
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| 241 | pt_int_u = ( ( gg-aa ) * pt(k+1,j,i) + ( gg-bb ) * pt(k+1,j,i+1) & |
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| 242 | + ( gg-cc ) * pt(k+1,j+1,i) + ( gg-dd ) * pt(k+1,j+1,i+1) & |
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| 243 | ) / ( 3.0_wp * gg ) |
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| 244 | |
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| 245 | pt_int = pt_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 246 | ( pt_int_u - pt_int_l ) |
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| 247 | |
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| 248 | q_int_l = ( ( gg - aa ) * q(k,j,i) + ( gg - bb ) * q(k,j,i+1) & |
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| 249 | + ( gg - cc ) * q(k,j+1,i) + ( gg - dd ) * q(k,j+1,i+1) & |
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| 250 | ) / ( 3.0_wp * gg ) |
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| 251 | |
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| 252 | q_int_u = ( ( gg-aa ) * q(k+1,j,i) + ( gg-bb ) * q(k+1,j,i+1) & |
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| 253 | + ( gg-cc ) * q(k+1,j+1,i) + ( gg-dd ) * q(k+1,j+1,i+1) & |
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| 254 | ) / ( 3.0_wp * gg ) |
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| 255 | |
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| 256 | q_int = q_int_l + ( zv(n) - zu(k) ) / dz * & |
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| 257 | ( q_int_u - q_int_l ) |
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| 258 | |
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| 259 | ! |
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| 260 | !-- Calculate real temperature and saturation vapor pressure |
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| 261 | p_int(n) = hyp(k) + ( particles(n)%z - zu(k) ) / dz * & |
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| 262 | ( hyp(k+1)-hyp(k) ) |
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| 263 | t_int(n) = pt_int * ( p_int(n) / 100000.0_wp )**0.286_wp |
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| 264 | |
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| 265 | e_s(n) = 611.0_wp * EXP( l_d_rv * ( 3.6609E-3_wp - 1.0_wp / & |
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| 266 | t_int(n) ) ) |
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| 267 | |
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| 268 | ! |
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| 269 | !-- Current vapor pressure |
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| 270 | e_a(n) = q_int * p_int(n) / ( 0.378_wp * q_int + 0.622_wp ) |
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| 271 | |
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| 272 | ENDDO |
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| 273 | ENDDO |
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| 274 | |
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| 275 | new_r = 0.0_wp |
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| 276 | flag_1 = .false. |
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| 277 | |
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| 278 | DO n = 1, number_of_particles |
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| 279 | ! |
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| 280 | !-- Change in radius by condensation/evaporation |
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| 281 | IF ( particles(n)%radius >= 4.0E-5_wp .AND. & |
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| 282 | e_a(n)/e_s(n) < 1.0_wp ) THEN |
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| 283 | ! |
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| 284 | !-- Approximation for large radii, where curvature and solution effects |
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| 285 | !-- can be neglected but ventilation effect has to be included in case of |
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| 286 | !-- evaporation. |
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| 287 | !-- First calculate the droplet's Reynolds number |
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| 288 | re_p = 2.0_wp * particles(n)%radius * ABS( particles(n)%speed_z ) / & |
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| 289 | molecular_viscosity |
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| 290 | ! |
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| 291 | !-- Ventilation coefficient (Rogers and Yau, 1989): |
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| 292 | IF ( re_p > 2.5_wp ) THEN |
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| 293 | afactor_v(n) = 0.78_wp + 0.28_wp * SQRT( re_p ) |
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| 294 | ELSE |
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| 295 | afactor_v(n) = 1.0_wp + 0.09_wp * re_p |
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| 296 | ENDIF |
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| 297 | flag_1(n) = .TRUE. |
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| 298 | ELSEIF ( particles(n)%radius >= 1.0E-6_wp .OR. & |
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| 299 | .NOT. curvature_solution_effects ) THEN |
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| 300 | ! |
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| 301 | !-- Approximation for larger radii in case that curvature and solution |
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| 302 | !-- effects are neglected and ventilation effects does not play a role |
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| 303 | afactor_v(n) = 1.0_wp |
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| 304 | flag_1(n) = .TRUE. |
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| 305 | ENDIF |
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| 306 | ENDDO |
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| 307 | |
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| 308 | DO n = 1, number_of_particles |
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| 309 | ! |
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| 310 | !-- Thermal conductivity for water (from Rogers and Yau, Table 7.1), |
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| 311 | !-- diffusivity for water vapor (after Hall und Pruppacher, 1976) |
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| 312 | thermal_conductivity_v(n) = 7.94048E-05_wp * t_int(n) + 0.00227011_wp |
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| 313 | diff_coeff_v(n) = 0.211E-4_wp * & |
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| 314 | ( t_int(n) / 273.15_wp )**1.94_wp * ( 101325.0_wp / p_int(n)) |
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| 315 | |
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| 316 | IF(flag_1(n)) then |
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| 317 | arg = particles(n)%radius**2 + 2.0_wp * dt_3d * afactor_v(n) * & |
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| 318 | ( e_a(n) / e_s(n) - 1.0_wp ) / & |
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| 319 | ( ( l_d_rv / t_int(n) - 1.0_wp ) * l_v * rho_l / t_int(n) / & |
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| 320 | thermal_conductivity_v(n) + & |
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| 321 | rho_l * r_v * t_int(n) / diff_coeff_v(n) / e_s(n) ) |
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| 322 | |
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| 323 | arg = MAX( arg, 1.0E-16_wp ) |
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| 324 | new_r(n) = SQRT( arg ) |
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| 325 | ENDIF |
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| 326 | ENDDO |
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| 327 | |
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| 328 | DO n = 1, number_of_particles |
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| 329 | IF ( curvature_solution_effects .AND. & |
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| 330 | ( ( particles(n)%radius < 1.0E-6_wp ) .OR. & |
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| 331 | ( new_r(n) < 1.0E-6_wp ) ) ) THEN |
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| 332 | ! |
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| 333 | !-- Curvature and solutions effects are included in growth equation. |
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| 334 | !-- Change in Radius is calculated with 4th-order Rosenbrock method |
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| 335 | !-- for stiff o.d.e's with monitoring local truncation error to adjust |
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| 336 | !-- stepsize (see Numerical recipes in FORTRAN, 2nd edition, p. 731). |
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| 337 | !-- For larger radii the simple analytic method (see ELSE) gives |
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| 338 | !-- almost the same results. |
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| 339 | |
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| 340 | ros_count = 0 |
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| 341 | repeat = .TRUE. |
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| 342 | ! |
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| 343 | !-- Carry out the Rosenbrock algorithm. In case of unreasonable results |
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| 344 | !-- the switch "repeat" will be set true and the algorithm will be carried |
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| 345 | !-- out again with the internal time step set to its initial (small) value. |
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| 346 | !-- Unreasonable results may occur if the external conditions, especially |
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| 347 | !-- the supersaturation, has significantly changed compared to the last |
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| 348 | !-- PALM timestep. |
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| 349 | DO WHILE ( repeat ) |
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| 350 | |
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| 351 | repeat = .FALSE. |
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| 352 | ! |
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| 353 | !-- Surface tension (Straka, 2009): |
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| 354 | sigma = 0.0761_wp - 0.000155_wp * ( t_int(n) - 273.15_wp ) |
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| 355 | |
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| 356 | r_ros = particles(n)%radius |
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| 357 | dt_ros_sum = 0.0_wp ! internal integrated time (s) |
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| 358 | internal_timestep_count = 0 |
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| 359 | |
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| 360 | ddenom = 1.0_wp / ( rho_l * r_v * t_int(n) / ( e_s(n) * & |
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| 361 | diff_coeff_v(n) ) + ( l_v / & |
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| 362 | ( r_v * t_int(n) ) - 1.0_wp ) * & |
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| 363 | rho_l * l_v / ( thermal_conductivity_v(n) * & |
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| 364 | t_int(n) ) & |
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| 365 | ) |
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| 366 | |
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| 367 | afactor = 2.0_wp * sigma / ( rho_l * r_v * t_int(n) ) |
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| 368 | |
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| 369 | ! |
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| 370 | !-- Take internal time step values from the end of last PALM time step |
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| 371 | dt_ros_next = particles(n)%rvar1 |
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| 372 | |
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| 373 | ! |
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| 374 | !-- Internal time step should not be > 1.0E-2 in case of evaporation |
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| 375 | !-- because larger values may lead to secondary solutions which are |
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| 376 | !-- physically unlikely |
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| 377 | IF ( dt_ros_next > 1.0E-2_wp .AND. e_a(n)/e_s(n) < 1.0_wp ) THEN |
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| 378 | dt_ros_next = 1.0E-3_wp |
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| 379 | ENDIF |
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| 380 | ! |
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| 381 | !-- If calculation of Rosenbrock method is repeated due to unreasonalble |
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| 382 | !-- results during previous try the initial internal time step has to be |
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| 383 | !-- reduced |
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| 384 | IF ( ros_count > 1 ) THEN |
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| 385 | dt_ros_next = dt_ros_next - ( 0.2_wp * dt_ros_next ) |
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| 386 | ELSEIF ( ros_count > 5 ) THEN |
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| 387 | ! |
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| 388 | !-- Prevent creation of infinite loop |
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| 389 | message_string = 'ros_count > 5 in Rosenbrock method' |
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| 390 | CALL message( 'lpm_droplet_condensation', 'PA0018', 2, 2, & |
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| 391 | 0, 6, 0 ) |
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| 392 | ENDIF |
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| 393 | |
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| 394 | ! |
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| 395 | !-- Internal time step must not be larger than PALM time step |
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| 396 | dt_ros = MIN( dt_ros_next, dt_3d ) |
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| 397 | ! |
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| 398 | !-- Integrate growth equation in time unless PALM time step is reached |
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| 399 | DO WHILE ( dt_ros_sum < dt_3d ) |
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| 400 | |
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| 401 | internal_timestep_count = internal_timestep_count + 1 |
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| 402 | |
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| 403 | ! |
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| 404 | !-- Derivative at starting value |
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| 405 | drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - afactor / & |
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| 406 | r_ros + bfactor / r_ros**3 ) |
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| 407 | drdt_ini = drdt |
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| 408 | dt_ros_sum_ini = dt_ros_sum |
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| 409 | r_ros_ini = r_ros |
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| 410 | |
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| 411 | ! |
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| 412 | !-- Calculate radial derivative of dr/dt |
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| 413 | d2rdtdr = ddenom * ( ( 1.0_wp - e_a(n)/e_s(n) ) / r_ros**2 + & |
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| 414 | 2.0_wp * afactor / r_ros**3 - & |
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| 415 | 4.0_wp * bfactor / r_ros**5 ) |
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| 416 | ! |
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| 417 | !-- Adjust stepsize unless required accuracy is reached |
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| 418 | DO jtry = 1, maxtry+1 |
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| 419 | |
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| 420 | IF ( jtry == maxtry+1 ) THEN |
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| 421 | message_string = 'maxtry > 40 in Rosenbrock method' |
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| 422 | CALL message( 'lpm_droplet_condensation', 'PA0347', 2, & |
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| 423 | 2, 0, 6, 0 ) |
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| 424 | ENDIF |
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| 425 | |
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| 426 | aa = 1.0_wp / ( gam * dt_ros ) - d2rdtdr |
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| 427 | g1 = drdt_ini / aa |
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| 428 | r_ros = r_ros_ini + a21 * g1 |
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| 429 | drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - & |
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| 430 | afactor / r_ros + & |
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| 431 | bfactor / r_ros**3 ) |
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| 432 | |
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| 433 | g2 = ( drdt + c21 * g1 / dt_ros )& |
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| 434 | / aa |
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| 435 | r_ros = r_ros_ini + a31 * g1 + a32 * g2 |
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| 436 | drdt = ddenom / r_ros * ( e_a(n) / e_s(n) - 1.0_wp - & |
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| 437 | afactor / r_ros + & |
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| 438 | bfactor / r_ros**3 ) |
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| 439 | |
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| 440 | g3 = ( drdt + & |
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| 441 | ( c31 * g1 + c32 * g2 ) / dt_ros ) / aa |
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| 442 | g4 = ( drdt + & |
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| 443 | ( c41 * g1 + c42 * g2 + c43 * g3 ) / dt_ros ) / aa |
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| 444 | r_ros = r_ros_ini + b1 * g1 + b2 * g2 + b3 * g3 + b4 * g4 |
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| 445 | |
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| 446 | dt_ros_sum = dt_ros_sum_ini + dt_ros |
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| 447 | |
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| 448 | IF ( dt_ros_sum == dt_ros_sum_ini ) THEN |
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| 449 | message_string = 'zero stepsize in Rosenbrock method' |
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| 450 | CALL message( 'lpm_droplet_condensation', 'PA0348', 2, & |
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| 451 | 2, 0, 6, 0 ) |
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| 452 | ENDIF |
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| 453 | ! |
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| 454 | !-- Calculate error |
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| 455 | err_ros = e1 * g1 + e2 * g2 + e3 * g3 + e4 * g4 |
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| 456 | errmax = 0.0_wp |
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| 457 | errmax = MAX( errmax, ABS( err_ros / r_ros_ini ) ) / eps_ros |
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| 458 | ! |
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| 459 | !-- Leave loop if accuracy is sufficient, otherwise try again |
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| 460 | !-- with a reduced stepsize |
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| 461 | IF ( errmax <= 1.0_wp ) THEN |
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| 462 | EXIT |
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| 463 | ELSE |
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| 464 | dt_ros = SIGN( MAX( ABS( 0.9_wp * dt_ros * & |
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| 465 | errmax**pshrnk ), & |
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| 466 | shrnk * ABS( dt_ros ) ), dt_ros ) |
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| 467 | ENDIF |
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| 468 | |
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| 469 | ENDDO ! loop for stepsize adjustment |
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| 470 | |
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| 471 | ! |
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| 472 | !-- Calculate next internal time step |
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| 473 | IF ( errmax > errcon ) THEN |
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| 474 | dt_ros_next = 0.9_wp * dt_ros * errmax**pgrow |
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| 475 | ELSE |
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| 476 | dt_ros_next = grow * dt_ros |
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| 477 | ENDIF |
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| 478 | |
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| 479 | ! |
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| 480 | !-- Estimated time step is reduced if the PALM time step is exceeded |
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| 481 | IF ( ( dt_ros_next + dt_ros_sum ) >= dt_3d ) THEN |
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| 482 | dt_ros = dt_3d - dt_ros_sum |
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| 483 | ELSE |
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| 484 | dt_ros = dt_ros_next |
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| 485 | ENDIF |
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| 486 | |
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| 487 | ENDDO |
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| 488 | ! |
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| 489 | !-- Store internal time step value for next PALM step |
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| 490 | particles(n)%rvar1 = dt_ros_next |
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| 491 | |
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| 492 | new_r(n) = r_ros |
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| 493 | ! |
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| 494 | !-- Radius should not fall below 1E-8 because Rosenbrock method may |
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| 495 | !-- lead to errors otherwise |
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| 496 | new_r(n) = MAX( new_r(n), 1.0E-8_wp ) |
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| 497 | ! |
|---|
| 498 | !-- Check if calculated droplet radius change is reasonable since in |
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| 499 | !-- case of droplet evaporation the Rosenbrock method may lead to |
|---|
| 500 | !-- secondary solutions which are physically unlikely. |
|---|
| 501 | !-- Due to the solution effect the droplets may grow for relative |
|---|
| 502 | !-- humidities below 100%, but change of radius should not be too |
|---|
| 503 | !-- large. In case of unreasonable droplet growth the Rosenbrock |
|---|
| 504 | !-- method is recalculated using a smaller initial time step. |
|---|
| 505 | !-- Limiting values are tested for droplets down to 1.0E-7 |
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| 506 | IF ( new_r(n) - particles(n)%radius >= 3.0E-7_wp .AND. & |
|---|
| 507 | e_a(n)/e_s(n) < 0.97_wp ) THEN |
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| 508 | ros_count = ros_count + 1 |
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| 509 | repeat = .TRUE. |
|---|
| 510 | ENDIF |
|---|
| 511 | |
|---|
| 512 | ENDDO ! Rosenbrock method |
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| 513 | |
|---|
| 514 | ENDIF |
|---|
| 515 | |
|---|
| 516 | delta_r = new_r(n) - particles(n)%radius |
|---|
| 517 | |
|---|
| 518 | ! |
|---|
| 519 | !-- Sum up the change in volume of liquid water for the respective grid |
|---|
| 520 | !-- volume (this is needed later in lpm_calc_liquid_water_content for |
|---|
| 521 | !-- calculating the release of latent heat) |
|---|
| 522 | i = ip |
|---|
| 523 | j = jp |
|---|
| 524 | k = kp |
|---|
| 525 | ! only exact if equidistant |
|---|
| 526 | |
|---|
| 527 | ql_c(k,j,i) = ql_c(k,j,i) + particles(n)%weight_factor * & |
|---|
| 528 | rho_l * 1.33333333_wp * pi * & |
|---|
| 529 | ( new_r(n)**3 - particles(n)%radius**3 ) / & |
|---|
| 530 | ( rho_surface * dx * dy * dz ) |
|---|
| 531 | IF ( ql_c(k,j,i) > 100.0_wp ) THEN |
|---|
| 532 | WRITE( message_string, * ) 'k=',k,' j=',j,' i=',i, & |
|---|
| 533 | ' ql_c=',ql_c(k,j,i), ' &part(',n,')%wf=', & |
|---|
| 534 | particles(n)%weight_factor,' delta_r=',delta_r |
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| 535 | CALL message( 'lpm_droplet_condensation', 'PA0143', 2, 2, -1, 6, 1 ) |
|---|
| 536 | ENDIF |
|---|
| 537 | |
|---|
| 538 | ! |
|---|
| 539 | !-- Change the droplet radius |
|---|
| 540 | IF ( ( new_r(n) - particles(n)%radius ) < 0.0_wp .AND. & |
|---|
| 541 | new_r(n) < 0.0_wp ) THEN |
|---|
| 542 | WRITE( message_string, * ) '#1 k=',k,' j=',j,' i=',i, & |
|---|
| 543 | ' e_s=',e_s(n), ' e_a=',e_a(n),' t_int=',t_int(n), & |
|---|
| 544 | ' &delta_r=',delta_r, & |
|---|
| 545 | ' particle_radius=',particles(n)%radius |
|---|
| 546 | CALL message( 'lpm_droplet_condensation', 'PA0144', 2, 2, -1, 6, 1 ) |
|---|
| 547 | ENDIF |
|---|
| 548 | |
|---|
| 549 | ! |
|---|
| 550 | !-- Sum up the total volume of liquid water (needed below for |
|---|
| 551 | !-- re-calculating the weighting factors) |
|---|
| 552 | ql_v(k,j,i) = ql_v(k,j,i) + particles(n)%weight_factor * new_r(n)**3 |
|---|
| 553 | |
|---|
| 554 | particles(n)%radius = new_r(n) |
|---|
| 555 | |
|---|
| 556 | ! |
|---|
| 557 | !-- Determine radius class of the particle needed for collision |
|---|
| 558 | IF ( ( hall_kernel .OR. wang_kernel ) .AND. use_kernel_tables ) & |
|---|
| 559 | THEN |
|---|
| 560 | particles(n)%class = ( LOG( new_r(n) ) - rclass_lbound ) / & |
|---|
| 561 | ( rclass_ubound - rclass_lbound ) * & |
|---|
| 562 | radius_classes |
|---|
| 563 | particles(n)%class = MIN( particles(n)%class, radius_classes ) |
|---|
| 564 | particles(n)%class = MAX( particles(n)%class, 1 ) |
|---|
| 565 | ENDIF |
|---|
| 566 | |
|---|
| 567 | ENDDO |
|---|
| 568 | |
|---|
| 569 | CALL cpu_log( log_point_s(42), 'lpm_droplet_condens', 'stop' ) |
|---|
| 570 | |
|---|
| 571 | |
|---|
| 572 | END SUBROUTINE lpm_droplet_condensation |
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