| 1 | SUBROUTINE lpm_advec |
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| 2 | |
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| 3 | !--------------------------------------------------------------------------------! |
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| 4 | ! This file is part of PALM. |
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| 5 | ! |
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| 6 | ! PALM is free software: you can redistribute it and/or modify it under the terms |
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| 7 | ! of the GNU General Public License as published by the Free Software Foundation, |
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| 8 | ! either version 3 of the License, or (at your option) any later version. |
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| 9 | ! |
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| 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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| 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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| 17 | ! Copyright 1997-2012 Leibniz University Hannover |
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| 18 | !--------------------------------------------------------------------------------! |
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| 19 | ! |
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| 20 | ! Current revisions: |
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| 21 | ! ------------------ |
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| 22 | ! |
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| 23 | ! |
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| 24 | ! Former revisions: |
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| 25 | ! ----------------- |
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| 26 | ! $Id: lpm_advec.f90 1037 2012-10-22 14:10:22Z heinze $ |
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| 27 | ! |
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| 28 | ! 1036 2012-10-22 13:43:42Z raasch |
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| 29 | ! code put under GPL (PALM 3.9) |
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| 30 | ! |
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| 31 | ! 849 2012-03-15 10:35:09Z raasch |
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| 32 | ! initial revision (former part of advec_particles) |
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| 33 | ! |
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| 34 | ! |
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| 35 | ! Description: |
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| 36 | ! ------------ |
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| 37 | ! Calculation of new particle positions due to advection using a simple Euler |
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| 38 | ! scheme. Particles may feel inertia effects. SGS transport can be included |
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| 39 | ! using the stochastic model of Weil et al. (2004, JAS, 61, 2877-2887). |
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| 40 | !------------------------------------------------------------------------------! |
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| 41 | |
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| 42 | USE arrays_3d |
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| 43 | USE control_parameters |
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| 44 | USE grid_variables |
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| 45 | USE indices |
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| 46 | USE particle_attributes |
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| 47 | USE statistics |
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| 48 | |
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| 49 | IMPLICIT NONE |
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| 50 | |
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| 51 | INTEGER :: i, j, k, n |
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| 52 | |
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| 53 | REAL :: aa, bb, cc, dd, dens_ratio, exp_arg, exp_term, gg, u_int, & |
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| 54 | u_int_l, u_int_u, v_int, v_int_l, v_int_u, w_int, w_int_l, & |
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| 55 | w_int_u, x, y |
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| 56 | |
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| 57 | |
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| 58 | INTEGER :: agp, kw, num_gp |
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| 59 | INTEGER :: gp_outside_of_building(1:8) |
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| 60 | |
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| 61 | REAL :: d_sum, de_dx_int, de_dx_int_l, de_dx_int_u, de_dy_int, & |
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| 62 | de_dy_int_l, de_dy_int_u, de_dt, de_dt_min, de_dz_int, & |
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| 63 | de_dz_int_l, de_dz_int_u, diss_int, diss_int_l, diss_int_u, & |
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| 64 | dt_gap, dt_particle, dt_particle_m, e_int, e_int_l, e_int_u, & |
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| 65 | e_mean_int, fs_int, lagr_timescale, random_gauss, vv_int |
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| 66 | |
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| 67 | REAL :: location(1:30,1:3) |
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| 68 | REAL, DIMENSION(1:30) :: de_dxi, de_dyi, de_dzi, dissi, d_gp_pl, ei |
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| 69 | |
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| 70 | |
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| 71 | DO n = 1, number_of_particles |
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| 72 | |
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| 73 | ! |
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| 74 | !-- Move particle only if the LES timestep has not (approximately) been |
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| 75 | !-- reached |
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| 76 | IF ( ( dt_3d - particles(n)%dt_sum ) < 1E-8 ) CYCLE |
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| 77 | |
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| 78 | ! |
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| 79 | !-- Interpolate u velocity-component, determine left, front, bottom |
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| 80 | !-- index of u-array |
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| 81 | i = ( particles(n)%x + 0.5 * dx ) * ddx |
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| 82 | j = particles(n)%y * ddy |
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| 83 | k = ( particles(n)%z + 0.5 * dz * atmos_ocean_sign ) / dz & |
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| 84 | + offset_ocean_nzt ! only exact if equidistant |
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| 85 | |
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| 86 | ! |
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| 87 | !-- Interpolation of the velocity components in the xy-plane |
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| 88 | x = particles(n)%x + ( 0.5 - i ) * dx |
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| 89 | y = particles(n)%y - j * dy |
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| 90 | aa = x**2 + y**2 |
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| 91 | bb = ( dx - x )**2 + y**2 |
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| 92 | cc = x**2 + ( dy - y )**2 |
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| 93 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 94 | gg = aa + bb + cc + dd |
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| 95 | |
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| 96 | u_int_l = ( ( gg - aa ) * u(k,j,i) + ( gg - bb ) * u(k,j,i+1) & |
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| 97 | + ( gg - cc ) * u(k,j+1,i) + ( gg - dd ) * u(k,j+1,i+1) & |
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| 98 | ) / ( 3.0 * gg ) - u_gtrans |
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| 99 | IF ( k+1 == nzt+1 ) THEN |
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| 100 | u_int = u_int_l |
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| 101 | ELSE |
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| 102 | u_int_u = ( ( gg-aa ) * u(k+1,j,i) + ( gg-bb ) * u(k+1,j,i+1) & |
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| 103 | + ( gg-cc ) * u(k+1,j+1,i) + ( gg-dd ) * u(k+1,j+1,i+1) & |
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| 104 | ) / ( 3.0 * gg ) - u_gtrans |
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| 105 | u_int = u_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 106 | ( u_int_u - u_int_l ) |
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| 107 | ENDIF |
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| 108 | |
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| 109 | ! |
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| 110 | !-- Same procedure for interpolation of the v velocity-component (adopt |
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| 111 | !-- index k from u velocity-component) |
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| 112 | i = particles(n)%x * ddx |
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| 113 | j = ( particles(n)%y + 0.5 * dy ) * ddy |
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| 114 | |
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| 115 | x = particles(n)%x - i * dx |
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| 116 | y = particles(n)%y + ( 0.5 - j ) * dy |
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| 117 | aa = x**2 + y**2 |
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| 118 | bb = ( dx - x )**2 + y**2 |
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| 119 | cc = x**2 + ( dy - y )**2 |
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| 120 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 121 | gg = aa + bb + cc + dd |
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| 122 | |
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| 123 | v_int_l = ( ( gg - aa ) * v(k,j,i) + ( gg - bb ) * v(k,j,i+1) & |
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| 124 | + ( gg - cc ) * v(k,j+1,i) + ( gg - dd ) * v(k,j+1,i+1) & |
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| 125 | ) / ( 3.0 * gg ) - v_gtrans |
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| 126 | IF ( k+1 == nzt+1 ) THEN |
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| 127 | v_int = v_int_l |
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| 128 | ELSE |
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| 129 | v_int_u = ( ( gg-aa ) * v(k+1,j,i) + ( gg-bb ) * v(k+1,j,i+1) & |
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| 130 | + ( gg-cc ) * v(k+1,j+1,i) + ( gg-dd ) * v(k+1,j+1,i+1) & |
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| 131 | ) / ( 3.0 * gg ) - v_gtrans |
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| 132 | v_int = v_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 133 | ( v_int_u - v_int_l ) |
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| 134 | ENDIF |
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| 135 | |
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| 136 | ! |
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| 137 | !-- Same procedure for interpolation of the w velocity-component (adopt |
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| 138 | !-- index i from v velocity-component) |
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| 139 | IF ( vertical_particle_advection(particles(n)%group) ) THEN |
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| 140 | j = particles(n)%y * ddy |
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| 141 | k = particles(n)%z / dz + offset_ocean_nzt_m1 |
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| 142 | |
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| 143 | x = particles(n)%x - i * dx |
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| 144 | y = particles(n)%y - j * dy |
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| 145 | aa = x**2 + y**2 |
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| 146 | bb = ( dx - x )**2 + y**2 |
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| 147 | cc = x**2 + ( dy - y )**2 |
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| 148 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 149 | gg = aa + bb + cc + dd |
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| 150 | |
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| 151 | w_int_l = ( ( gg - aa ) * w(k,j,i) + ( gg - bb ) * w(k,j,i+1) & |
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| 152 | + ( gg - cc ) * w(k,j+1,i) + ( gg - dd ) * w(k,j+1,i+1) & |
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| 153 | ) / ( 3.0 * gg ) |
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| 154 | IF ( k+1 == nzt+1 ) THEN |
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| 155 | w_int = w_int_l |
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| 156 | ELSE |
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| 157 | w_int_u = ( ( gg-aa ) * w(k+1,j,i) + & |
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| 158 | ( gg-bb ) * w(k+1,j,i+1) + & |
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| 159 | ( gg-cc ) * w(k+1,j+1,i) + & |
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| 160 | ( gg-dd ) * w(k+1,j+1,i+1) & |
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| 161 | ) / ( 3.0 * gg ) |
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| 162 | w_int = w_int_l + ( particles(n)%z - zw(k) ) / dz * & |
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| 163 | ( w_int_u - w_int_l ) |
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| 164 | ENDIF |
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| 165 | ELSE |
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| 166 | w_int = 0.0 |
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| 167 | ENDIF |
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| 168 | |
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| 169 | ! |
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| 170 | !-- Interpolate and calculate quantities needed for calculating the SGS |
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| 171 | !-- velocities |
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| 172 | IF ( use_sgs_for_particles ) THEN |
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| 173 | ! |
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| 174 | !-- Interpolate TKE |
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| 175 | i = particles(n)%x * ddx |
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| 176 | j = particles(n)%y * ddy |
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| 177 | k = ( particles(n)%z + 0.5 * dz * atmos_ocean_sign ) / dz & |
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| 178 | + offset_ocean_nzt ! only exact if eq.dist |
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| 179 | |
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| 180 | IF ( topography == 'flat' ) THEN |
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| 181 | |
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| 182 | x = particles(n)%x - i * dx |
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| 183 | y = particles(n)%y - j * dy |
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| 184 | aa = x**2 + y**2 |
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| 185 | bb = ( dx - x )**2 + y**2 |
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| 186 | cc = x**2 + ( dy - y )**2 |
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| 187 | dd = ( dx - x )**2 + ( dy - y )**2 |
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| 188 | gg = aa + bb + cc + dd |
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| 189 | |
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| 190 | e_int_l = ( ( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) & |
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| 191 | + ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1) & |
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| 192 | ) / ( 3.0 * gg ) |
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| 193 | |
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| 194 | IF ( k+1 == nzt+1 ) THEN |
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| 195 | e_int = e_int_l |
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| 196 | ELSE |
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| 197 | e_int_u = ( ( gg - aa ) * e(k+1,j,i) + & |
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| 198 | ( gg - bb ) * e(k+1,j,i+1) + & |
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| 199 | ( gg - cc ) * e(k+1,j+1,i) + & |
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| 200 | ( gg - dd ) * e(k+1,j+1,i+1) & |
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| 201 | ) / ( 3.0 * gg ) |
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| 202 | e_int = e_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 203 | ( e_int_u - e_int_l ) |
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| 204 | ENDIF |
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| 205 | |
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| 206 | ! |
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| 207 | !-- Interpolate the TKE gradient along x (adopt incides i,j,k and |
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| 208 | !-- all position variables from above (TKE)) |
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| 209 | de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + & |
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| 210 | ( gg - bb ) * de_dx(k,j,i+1) + & |
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| 211 | ( gg - cc ) * de_dx(k,j+1,i) + & |
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| 212 | ( gg - dd ) * de_dx(k,j+1,i+1) & |
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| 213 | ) / ( 3.0 * gg ) |
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| 214 | |
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| 215 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
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| 216 | de_dx_int = de_dx_int_l |
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| 217 | ELSE |
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| 218 | de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + & |
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| 219 | ( gg - bb ) * de_dx(k+1,j,i+1) + & |
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| 220 | ( gg - cc ) * de_dx(k+1,j+1,i) + & |
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| 221 | ( gg - dd ) * de_dx(k+1,j+1,i+1) & |
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| 222 | ) / ( 3.0 * gg ) |
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| 223 | de_dx_int = de_dx_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 224 | ( de_dx_int_u - de_dx_int_l ) |
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| 225 | ENDIF |
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| 226 | |
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| 227 | ! |
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| 228 | !-- Interpolate the TKE gradient along y |
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| 229 | de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + & |
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| 230 | ( gg - bb ) * de_dy(k,j,i+1) + & |
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| 231 | ( gg - cc ) * de_dy(k,j+1,i) + & |
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| 232 | ( gg - dd ) * de_dy(k,j+1,i+1) & |
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| 233 | ) / ( 3.0 * gg ) |
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| 234 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
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| 235 | de_dy_int = de_dy_int_l |
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| 236 | ELSE |
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| 237 | de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + & |
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| 238 | ( gg - bb ) * de_dy(k+1,j,i+1) + & |
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| 239 | ( gg - cc ) * de_dy(k+1,j+1,i) + & |
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| 240 | ( gg - dd ) * de_dy(k+1,j+1,i+1) & |
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| 241 | ) / ( 3.0 * gg ) |
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| 242 | de_dy_int = de_dy_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 243 | ( de_dy_int_u - de_dy_int_l ) |
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| 244 | ENDIF |
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| 245 | |
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| 246 | ! |
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| 247 | !-- Interpolate the TKE gradient along z |
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| 248 | IF ( particles(n)%z < 0.5 * dz ) THEN |
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| 249 | de_dz_int = 0.0 |
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| 250 | ELSE |
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| 251 | de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + & |
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| 252 | ( gg - bb ) * de_dz(k,j,i+1) + & |
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| 253 | ( gg - cc ) * de_dz(k,j+1,i) + & |
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| 254 | ( gg - dd ) * de_dz(k,j+1,i+1) & |
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| 255 | ) / ( 3.0 * gg ) |
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| 256 | |
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| 257 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
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| 258 | de_dz_int = de_dz_int_l |
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| 259 | ELSE |
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| 260 | de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + & |
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| 261 | ( gg - bb ) * de_dz(k+1,j,i+1) + & |
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| 262 | ( gg - cc ) * de_dz(k+1,j+1,i) + & |
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| 263 | ( gg - dd ) * de_dz(k+1,j+1,i+1) & |
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| 264 | ) / ( 3.0 * gg ) |
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| 265 | de_dz_int = de_dz_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 266 | ( de_dz_int_u - de_dz_int_l ) |
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| 267 | ENDIF |
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| 268 | ENDIF |
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| 269 | |
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| 270 | ! |
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| 271 | !-- Interpolate the dissipation of TKE |
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| 272 | diss_int_l = ( ( gg - aa ) * diss(k,j,i) + & |
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| 273 | ( gg - bb ) * diss(k,j,i+1) + & |
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| 274 | ( gg - cc ) * diss(k,j+1,i) + & |
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| 275 | ( gg - dd ) * diss(k,j+1,i+1) & |
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| 276 | ) / ( 3.0 * gg ) |
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| 277 | |
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| 278 | IF ( k+1 == nzt+1 ) THEN |
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| 279 | diss_int = diss_int_l |
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| 280 | ELSE |
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| 281 | diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + & |
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| 282 | ( gg - bb ) * diss(k+1,j,i+1) + & |
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| 283 | ( gg - cc ) * diss(k+1,j+1,i) + & |
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| 284 | ( gg - dd ) * diss(k+1,j+1,i+1) & |
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| 285 | ) / ( 3.0 * gg ) |
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| 286 | diss_int = diss_int_l + ( particles(n)%z - zu(k) ) / dz * & |
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| 287 | ( diss_int_u - diss_int_l ) |
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| 288 | ENDIF |
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| 289 | |
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| 290 | ELSE |
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| 291 | |
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| 292 | ! |
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| 293 | !-- In case that there are buildings it has to be determined |
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| 294 | !-- how many of the gridpoints defining the particle box are |
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| 295 | !-- situated within a building |
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| 296 | !-- gp_outside_of_building(1): i,j,k |
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| 297 | !-- gp_outside_of_building(2): i,j+1,k |
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| 298 | !-- gp_outside_of_building(3): i,j,k+1 |
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| 299 | !-- gp_outside_of_building(4): i,j+1,k+1 |
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| 300 | !-- gp_outside_of_building(5): i+1,j,k |
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| 301 | !-- gp_outside_of_building(6): i+1,j+1,k |
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| 302 | !-- gp_outside_of_building(7): i+1,j,k+1 |
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| 303 | !-- gp_outside_of_building(8): i+1,j+1,k+1 |
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| 304 | |
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| 305 | gp_outside_of_building = 0 |
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| 306 | location = 0.0 |
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| 307 | num_gp = 0 |
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| 308 | |
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| 309 | IF ( k > nzb_s_inner(j,i) .OR. nzb_s_inner(j,i) == 0 ) THEN |
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| 310 | num_gp = num_gp + 1 |
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| 311 | gp_outside_of_building(1) = 1 |
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| 312 | location(num_gp,1) = i * dx |
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| 313 | location(num_gp,2) = j * dy |
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| 314 | location(num_gp,3) = k * dz - 0.5 * dz |
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| 315 | ei(num_gp) = e(k,j,i) |
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| 316 | dissi(num_gp) = diss(k,j,i) |
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| 317 | de_dxi(num_gp) = de_dx(k,j,i) |
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| 318 | de_dyi(num_gp) = de_dy(k,j,i) |
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| 319 | de_dzi(num_gp) = de_dz(k,j,i) |
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| 320 | ENDIF |
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| 321 | |
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| 322 | IF ( k > nzb_s_inner(j+1,i) .OR. nzb_s_inner(j+1,i) == 0 ) & |
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| 323 | THEN |
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| 324 | num_gp = num_gp + 1 |
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| 325 | gp_outside_of_building(2) = 1 |
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| 326 | location(num_gp,1) = i * dx |
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| 327 | location(num_gp,2) = (j+1) * dy |
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| 328 | location(num_gp,3) = k * dz - 0.5 * dz |
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| 329 | ei(num_gp) = e(k,j+1,i) |
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| 330 | dissi(num_gp) = diss(k,j+1,i) |
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| 331 | de_dxi(num_gp) = de_dx(k,j+1,i) |
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| 332 | de_dyi(num_gp) = de_dy(k,j+1,i) |
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| 333 | de_dzi(num_gp) = de_dz(k,j+1,i) |
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| 334 | ENDIF |
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| 335 | |
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| 336 | IF ( k+1 > nzb_s_inner(j,i) .OR. nzb_s_inner(j,i) == 0 ) THEN |
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| 337 | num_gp = num_gp + 1 |
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| 338 | gp_outside_of_building(3) = 1 |
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| 339 | location(num_gp,1) = i * dx |
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| 340 | location(num_gp,2) = j * dy |
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| 341 | location(num_gp,3) = (k+1) * dz - 0.5 * dz |
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| 342 | ei(num_gp) = e(k+1,j,i) |
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| 343 | dissi(num_gp) = diss(k+1,j,i) |
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| 344 | de_dxi(num_gp) = de_dx(k+1,j,i) |
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| 345 | de_dyi(num_gp) = de_dy(k+1,j,i) |
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| 346 | de_dzi(num_gp) = de_dz(k+1,j,i) |
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| 347 | ENDIF |
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| 348 | |
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| 349 | IF ( k+1 > nzb_s_inner(j+1,i) .OR. nzb_s_inner(j+1,i) == 0 ) & |
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| 350 | THEN |
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| 351 | num_gp = num_gp + 1 |
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| 352 | gp_outside_of_building(4) = 1 |
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| 353 | location(num_gp,1) = i * dx |
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| 354 | location(num_gp,2) = (j+1) * dy |
|---|
| 355 | location(num_gp,3) = (k+1) * dz - 0.5 * dz |
|---|
| 356 | ei(num_gp) = e(k+1,j+1,i) |
|---|
| 357 | dissi(num_gp) = diss(k+1,j+1,i) |
|---|
| 358 | de_dxi(num_gp) = de_dx(k+1,j+1,i) |
|---|
| 359 | de_dyi(num_gp) = de_dy(k+1,j+1,i) |
|---|
| 360 | de_dzi(num_gp) = de_dz(k+1,j+1,i) |
|---|
| 361 | ENDIF |
|---|
| 362 | |
|---|
| 363 | IF ( k > nzb_s_inner(j,i+1) .OR. nzb_s_inner(j,i+1) == 0 ) & |
|---|
| 364 | THEN |
|---|
| 365 | num_gp = num_gp + 1 |
|---|
| 366 | gp_outside_of_building(5) = 1 |
|---|
| 367 | location(num_gp,1) = (i+1) * dx |
|---|
| 368 | location(num_gp,2) = j * dy |
|---|
| 369 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 370 | ei(num_gp) = e(k,j,i+1) |
|---|
| 371 | dissi(num_gp) = diss(k,j,i+1) |
|---|
| 372 | de_dxi(num_gp) = de_dx(k,j,i+1) |
|---|
| 373 | de_dyi(num_gp) = de_dy(k,j,i+1) |
|---|
| 374 | de_dzi(num_gp) = de_dz(k,j,i+1) |
|---|
| 375 | ENDIF |
|---|
| 376 | |
|---|
| 377 | IF ( k > nzb_s_inner(j+1,i+1) .OR. nzb_s_inner(j+1,i+1) == 0 ) & |
|---|
| 378 | THEN |
|---|
| 379 | num_gp = num_gp + 1 |
|---|
| 380 | gp_outside_of_building(6) = 1 |
|---|
| 381 | location(num_gp,1) = (i+1) * dx |
|---|
| 382 | location(num_gp,2) = (j+1) * dy |
|---|
| 383 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 384 | ei(num_gp) = e(k,j+1,i+1) |
|---|
| 385 | dissi(num_gp) = diss(k,j+1,i+1) |
|---|
| 386 | de_dxi(num_gp) = de_dx(k,j+1,i+1) |
|---|
| 387 | de_dyi(num_gp) = de_dy(k,j+1,i+1) |
|---|
| 388 | de_dzi(num_gp) = de_dz(k,j+1,i+1) |
|---|
| 389 | ENDIF |
|---|
| 390 | |
|---|
| 391 | IF ( k+1 > nzb_s_inner(j,i+1) .OR. nzb_s_inner(j,i+1) == 0 ) & |
|---|
| 392 | THEN |
|---|
| 393 | num_gp = num_gp + 1 |
|---|
| 394 | gp_outside_of_building(7) = 1 |
|---|
| 395 | location(num_gp,1) = (i+1) * dx |
|---|
| 396 | location(num_gp,2) = j * dy |
|---|
| 397 | location(num_gp,3) = (k+1) * dz - 0.5 * dz |
|---|
| 398 | ei(num_gp) = e(k+1,j,i+1) |
|---|
| 399 | dissi(num_gp) = diss(k+1,j,i+1) |
|---|
| 400 | de_dxi(num_gp) = de_dx(k+1,j,i+1) |
|---|
| 401 | de_dyi(num_gp) = de_dy(k+1,j,i+1) |
|---|
| 402 | de_dzi(num_gp) = de_dz(k+1,j,i+1) |
|---|
| 403 | ENDIF |
|---|
| 404 | |
|---|
| 405 | IF ( k+1 > nzb_s_inner(j+1,i+1) .OR. nzb_s_inner(j+1,i+1) == 0)& |
|---|
| 406 | THEN |
|---|
| 407 | num_gp = num_gp + 1 |
|---|
| 408 | gp_outside_of_building(8) = 1 |
|---|
| 409 | location(num_gp,1) = (i+1) * dx |
|---|
| 410 | location(num_gp,2) = (j+1) * dy |
|---|
| 411 | location(num_gp,3) = (k+1) * dz - 0.5 * dz |
|---|
| 412 | ei(num_gp) = e(k+1,j+1,i+1) |
|---|
| 413 | dissi(num_gp) = diss(k+1,j+1,i+1) |
|---|
| 414 | de_dxi(num_gp) = de_dx(k+1,j+1,i+1) |
|---|
| 415 | de_dyi(num_gp) = de_dy(k+1,j+1,i+1) |
|---|
| 416 | de_dzi(num_gp) = de_dz(k+1,j+1,i+1) |
|---|
| 417 | ENDIF |
|---|
| 418 | |
|---|
| 419 | ! |
|---|
| 420 | !-- If all gridpoints are situated outside of a building, then the |
|---|
| 421 | !-- ordinary interpolation scheme can be used. |
|---|
| 422 | IF ( num_gp == 8 ) THEN |
|---|
| 423 | |
|---|
| 424 | x = particles(n)%x - i * dx |
|---|
| 425 | y = particles(n)%y - j * dy |
|---|
| 426 | aa = x**2 + y**2 |
|---|
| 427 | bb = ( dx - x )**2 + y**2 |
|---|
| 428 | cc = x**2 + ( dy - y )**2 |
|---|
| 429 | dd = ( dx - x )**2 + ( dy - y )**2 |
|---|
| 430 | gg = aa + bb + cc + dd |
|---|
| 431 | |
|---|
| 432 | e_int_l = (( gg-aa ) * e(k,j,i) + ( gg-bb ) * e(k,j,i+1) & |
|---|
| 433 | + ( gg-cc ) * e(k,j+1,i) + ( gg-dd ) * e(k,j+1,i+1)& |
|---|
| 434 | ) / ( 3.0 * gg ) |
|---|
| 435 | |
|---|
| 436 | IF ( k+1 == nzt+1 ) THEN |
|---|
| 437 | e_int = e_int_l |
|---|
| 438 | ELSE |
|---|
| 439 | e_int_u = ( ( gg - aa ) * e(k+1,j,i) + & |
|---|
| 440 | ( gg - bb ) * e(k+1,j,i+1) + & |
|---|
| 441 | ( gg - cc ) * e(k+1,j+1,i) + & |
|---|
| 442 | ( gg - dd ) * e(k+1,j+1,i+1) & |
|---|
| 443 | ) / ( 3.0 * gg ) |
|---|
| 444 | e_int = e_int_l + ( particles(n)%z - zu(k) ) / dz * & |
|---|
| 445 | ( e_int_u - e_int_l ) |
|---|
| 446 | ENDIF |
|---|
| 447 | |
|---|
| 448 | ! |
|---|
| 449 | !-- Interpolate the TKE gradient along x (adopt incides i,j,k |
|---|
| 450 | !-- and all position variables from above (TKE)) |
|---|
| 451 | de_dx_int_l = ( ( gg - aa ) * de_dx(k,j,i) + & |
|---|
| 452 | ( gg - bb ) * de_dx(k,j,i+1) + & |
|---|
| 453 | ( gg - cc ) * de_dx(k,j+1,i) + & |
|---|
| 454 | ( gg - dd ) * de_dx(k,j+1,i+1) & |
|---|
| 455 | ) / ( 3.0 * gg ) |
|---|
| 456 | |
|---|
| 457 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
|---|
| 458 | de_dx_int = de_dx_int_l |
|---|
| 459 | ELSE |
|---|
| 460 | de_dx_int_u = ( ( gg - aa ) * de_dx(k+1,j,i) + & |
|---|
| 461 | ( gg - bb ) * de_dx(k+1,j,i+1) + & |
|---|
| 462 | ( gg - cc ) * de_dx(k+1,j+1,i) + & |
|---|
| 463 | ( gg - dd ) * de_dx(k+1,j+1,i+1) & |
|---|
| 464 | ) / ( 3.0 * gg ) |
|---|
| 465 | de_dx_int = de_dx_int_l + ( particles(n)%z - zu(k) ) / & |
|---|
| 466 | dz * ( de_dx_int_u - de_dx_int_l ) |
|---|
| 467 | ENDIF |
|---|
| 468 | |
|---|
| 469 | ! |
|---|
| 470 | !-- Interpolate the TKE gradient along y |
|---|
| 471 | de_dy_int_l = ( ( gg - aa ) * de_dy(k,j,i) + & |
|---|
| 472 | ( gg - bb ) * de_dy(k,j,i+1) + & |
|---|
| 473 | ( gg - cc ) * de_dy(k,j+1,i) + & |
|---|
| 474 | ( gg - dd ) * de_dy(k,j+1,i+1) & |
|---|
| 475 | ) / ( 3.0 * gg ) |
|---|
| 476 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
|---|
| 477 | de_dy_int = de_dy_int_l |
|---|
| 478 | ELSE |
|---|
| 479 | de_dy_int_u = ( ( gg - aa ) * de_dy(k+1,j,i) + & |
|---|
| 480 | ( gg - bb ) * de_dy(k+1,j,i+1) + & |
|---|
| 481 | ( gg - cc ) * de_dy(k+1,j+1,i) + & |
|---|
| 482 | ( gg - dd ) * de_dy(k+1,j+1,i+1) & |
|---|
| 483 | ) / ( 3.0 * gg ) |
|---|
| 484 | de_dy_int = de_dy_int_l + ( particles(n)%z - zu(k) ) / & |
|---|
| 485 | dz * ( de_dy_int_u - de_dy_int_l ) |
|---|
| 486 | ENDIF |
|---|
| 487 | |
|---|
| 488 | ! |
|---|
| 489 | !-- Interpolate the TKE gradient along z |
|---|
| 490 | IF ( particles(n)%z < 0.5 * dz ) THEN |
|---|
| 491 | de_dz_int = 0.0 |
|---|
| 492 | ELSE |
|---|
| 493 | de_dz_int_l = ( ( gg - aa ) * de_dz(k,j,i) + & |
|---|
| 494 | ( gg - bb ) * de_dz(k,j,i+1) + & |
|---|
| 495 | ( gg - cc ) * de_dz(k,j+1,i) + & |
|---|
| 496 | ( gg - dd ) * de_dz(k,j+1,i+1) & |
|---|
| 497 | ) / ( 3.0 * gg ) |
|---|
| 498 | |
|---|
| 499 | IF ( ( k+1 == nzt+1 ) .OR. ( k == nzb ) ) THEN |
|---|
| 500 | de_dz_int = de_dz_int_l |
|---|
| 501 | ELSE |
|---|
| 502 | de_dz_int_u = ( ( gg - aa ) * de_dz(k+1,j,i) + & |
|---|
| 503 | ( gg - bb ) * de_dz(k+1,j,i+1) + & |
|---|
| 504 | ( gg - cc ) * de_dz(k+1,j+1,i) + & |
|---|
| 505 | ( gg - dd ) * de_dz(k+1,j+1,i+1) & |
|---|
| 506 | ) / ( 3.0 * gg ) |
|---|
| 507 | de_dz_int = de_dz_int_l + ( particles(n)%z - zu(k) ) /& |
|---|
| 508 | dz * ( de_dz_int_u - de_dz_int_l ) |
|---|
| 509 | ENDIF |
|---|
| 510 | ENDIF |
|---|
| 511 | |
|---|
| 512 | ! |
|---|
| 513 | !-- Interpolate the dissipation of TKE |
|---|
| 514 | diss_int_l = ( ( gg - aa ) * diss(k,j,i) + & |
|---|
| 515 | ( gg - bb ) * diss(k,j,i+1) + & |
|---|
| 516 | ( gg - cc ) * diss(k,j+1,i) + & |
|---|
| 517 | ( gg - dd ) * diss(k,j+1,i+1) & |
|---|
| 518 | ) / ( 3.0 * gg ) |
|---|
| 519 | |
|---|
| 520 | IF ( k+1 == nzt+1 ) THEN |
|---|
| 521 | diss_int = diss_int_l |
|---|
| 522 | ELSE |
|---|
| 523 | diss_int_u = ( ( gg - aa ) * diss(k+1,j,i) + & |
|---|
| 524 | ( gg - bb ) * diss(k+1,j,i+1) + & |
|---|
| 525 | ( gg - cc ) * diss(k+1,j+1,i) + & |
|---|
| 526 | ( gg - dd ) * diss(k+1,j+1,i+1) & |
|---|
| 527 | ) / ( 3.0 * gg ) |
|---|
| 528 | diss_int = diss_int_l + ( particles(n)%z - zu(k) ) / dz *& |
|---|
| 529 | ( diss_int_u - diss_int_l ) |
|---|
| 530 | ENDIF |
|---|
| 531 | |
|---|
| 532 | ELSE |
|---|
| 533 | |
|---|
| 534 | ! |
|---|
| 535 | !-- If wall between gridpoint 1 and gridpoint 5, then |
|---|
| 536 | !-- Neumann boundary condition has to be applied |
|---|
| 537 | IF ( gp_outside_of_building(1) == 1 .AND. & |
|---|
| 538 | gp_outside_of_building(5) == 0 ) THEN |
|---|
| 539 | num_gp = num_gp + 1 |
|---|
| 540 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 541 | location(num_gp,2) = j * dy |
|---|
| 542 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 543 | ei(num_gp) = e(k,j,i) |
|---|
| 544 | dissi(num_gp) = diss(k,j,i) |
|---|
| 545 | de_dxi(num_gp) = 0.0 |
|---|
| 546 | de_dyi(num_gp) = de_dy(k,j,i) |
|---|
| 547 | de_dzi(num_gp) = de_dz(k,j,i) |
|---|
| 548 | ENDIF |
|---|
| 549 | |
|---|
| 550 | IF ( gp_outside_of_building(5) == 1 .AND. & |
|---|
| 551 | gp_outside_of_building(1) == 0 ) THEN |
|---|
| 552 | num_gp = num_gp + 1 |
|---|
| 553 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 554 | location(num_gp,2) = j * dy |
|---|
| 555 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 556 | ei(num_gp) = e(k,j,i+1) |
|---|
| 557 | dissi(num_gp) = diss(k,j,i+1) |
|---|
| 558 | de_dxi(num_gp) = 0.0 |
|---|
| 559 | de_dyi(num_gp) = de_dy(k,j,i+1) |
|---|
| 560 | de_dzi(num_gp) = de_dz(k,j,i+1) |
|---|
| 561 | ENDIF |
|---|
| 562 | |
|---|
| 563 | ! |
|---|
| 564 | !-- If wall between gridpoint 5 and gridpoint 6, then |
|---|
| 565 | !-- then Neumann boundary condition has to be applied |
|---|
| 566 | IF ( gp_outside_of_building(5) == 1 .AND. & |
|---|
| 567 | gp_outside_of_building(6) == 0 ) THEN |
|---|
| 568 | num_gp = num_gp + 1 |
|---|
| 569 | location(num_gp,1) = (i+1) * dx |
|---|
| 570 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 571 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 572 | ei(num_gp) = e(k,j,i+1) |
|---|
| 573 | dissi(num_gp) = diss(k,j,i+1) |
|---|
| 574 | de_dxi(num_gp) = de_dx(k,j,i+1) |
|---|
| 575 | de_dyi(num_gp) = 0.0 |
|---|
| 576 | de_dzi(num_gp) = de_dz(k,j,i+1) |
|---|
| 577 | ENDIF |
|---|
| 578 | |
|---|
| 579 | IF ( gp_outside_of_building(6) == 1 .AND. & |
|---|
| 580 | gp_outside_of_building(5) == 0 ) THEN |
|---|
| 581 | num_gp = num_gp + 1 |
|---|
| 582 | location(num_gp,1) = (i+1) * dx |
|---|
| 583 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 584 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 585 | ei(num_gp) = e(k,j+1,i+1) |
|---|
| 586 | dissi(num_gp) = diss(k,j+1,i+1) |
|---|
| 587 | de_dxi(num_gp) = de_dx(k,j+1,i+1) |
|---|
| 588 | de_dyi(num_gp) = 0.0 |
|---|
| 589 | de_dzi(num_gp) = de_dz(k,j+1,i+1) |
|---|
| 590 | ENDIF |
|---|
| 591 | |
|---|
| 592 | ! |
|---|
| 593 | !-- If wall between gridpoint 2 and gridpoint 6, then |
|---|
| 594 | !-- Neumann boundary condition has to be applied |
|---|
| 595 | IF ( gp_outside_of_building(2) == 1 .AND. & |
|---|
| 596 | gp_outside_of_building(6) == 0 ) THEN |
|---|
| 597 | num_gp = num_gp + 1 |
|---|
| 598 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 599 | location(num_gp,2) = (j+1) * dy |
|---|
| 600 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 601 | ei(num_gp) = e(k,j+1,i) |
|---|
| 602 | dissi(num_gp) = diss(k,j+1,i) |
|---|
| 603 | de_dxi(num_gp) = 0.0 |
|---|
| 604 | de_dyi(num_gp) = de_dy(k,j+1,i) |
|---|
| 605 | de_dzi(num_gp) = de_dz(k,j+1,i) |
|---|
| 606 | ENDIF |
|---|
| 607 | |
|---|
| 608 | IF ( gp_outside_of_building(6) == 1 .AND. & |
|---|
| 609 | gp_outside_of_building(2) == 0 ) THEN |
|---|
| 610 | num_gp = num_gp + 1 |
|---|
| 611 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 612 | location(num_gp,2) = (j+1) * dy |
|---|
| 613 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 614 | ei(num_gp) = e(k,j+1,i+1) |
|---|
| 615 | dissi(num_gp) = diss(k,j+1,i+1) |
|---|
| 616 | de_dxi(num_gp) = 0.0 |
|---|
| 617 | de_dyi(num_gp) = de_dy(k,j+1,i+1) |
|---|
| 618 | de_dzi(num_gp) = de_dz(k,j+1,i+1) |
|---|
| 619 | ENDIF |
|---|
| 620 | |
|---|
| 621 | ! |
|---|
| 622 | !-- If wall between gridpoint 1 and gridpoint 2, then |
|---|
| 623 | !-- Neumann boundary condition has to be applied |
|---|
| 624 | IF ( gp_outside_of_building(1) == 1 .AND. & |
|---|
| 625 | gp_outside_of_building(2) == 0 ) THEN |
|---|
| 626 | num_gp = num_gp + 1 |
|---|
| 627 | location(num_gp,1) = i * dx |
|---|
| 628 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 629 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 630 | ei(num_gp) = e(k,j,i) |
|---|
| 631 | dissi(num_gp) = diss(k,j,i) |
|---|
| 632 | de_dxi(num_gp) = de_dx(k,j,i) |
|---|
| 633 | de_dyi(num_gp) = 0.0 |
|---|
| 634 | de_dzi(num_gp) = de_dz(k,j,i) |
|---|
| 635 | ENDIF |
|---|
| 636 | |
|---|
| 637 | IF ( gp_outside_of_building(2) == 1 .AND. & |
|---|
| 638 | gp_outside_of_building(1) == 0 ) THEN |
|---|
| 639 | num_gp = num_gp + 1 |
|---|
| 640 | location(num_gp,1) = i * dx |
|---|
| 641 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 642 | location(num_gp,3) = k * dz - 0.5 * dz |
|---|
| 643 | ei(num_gp) = e(k,j+1,i) |
|---|
| 644 | dissi(num_gp) = diss(k,j+1,i) |
|---|
| 645 | de_dxi(num_gp) = de_dx(k,j+1,i) |
|---|
| 646 | de_dyi(num_gp) = 0.0 |
|---|
| 647 | de_dzi(num_gp) = de_dz(k,j+1,i) |
|---|
| 648 | ENDIF |
|---|
| 649 | |
|---|
| 650 | ! |
|---|
| 651 | !-- If wall between gridpoint 3 and gridpoint 7, then |
|---|
| 652 | !-- Neumann boundary condition has to be applied |
|---|
| 653 | IF ( gp_outside_of_building(3) == 1 .AND. & |
|---|
| 654 | gp_outside_of_building(7) == 0 ) THEN |
|---|
| 655 | num_gp = num_gp + 1 |
|---|
| 656 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 657 | location(num_gp,2) = j * dy |
|---|
| 658 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 659 | ei(num_gp) = e(k+1,j,i) |
|---|
| 660 | dissi(num_gp) = diss(k+1,j,i) |
|---|
| 661 | de_dxi(num_gp) = 0.0 |
|---|
| 662 | de_dyi(num_gp) = de_dy(k+1,j,i) |
|---|
| 663 | de_dzi(num_gp) = de_dz(k+1,j,i) |
|---|
| 664 | ENDIF |
|---|
| 665 | |
|---|
| 666 | IF ( gp_outside_of_building(7) == 1 .AND. & |
|---|
| 667 | gp_outside_of_building(3) == 0 ) THEN |
|---|
| 668 | num_gp = num_gp + 1 |
|---|
| 669 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 670 | location(num_gp,2) = j * dy |
|---|
| 671 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 672 | ei(num_gp) = e(k+1,j,i+1) |
|---|
| 673 | dissi(num_gp) = diss(k+1,j,i+1) |
|---|
| 674 | de_dxi(num_gp) = 0.0 |
|---|
| 675 | de_dyi(num_gp) = de_dy(k+1,j,i+1) |
|---|
| 676 | de_dzi(num_gp) = de_dz(k+1,j,i+1) |
|---|
| 677 | ENDIF |
|---|
| 678 | |
|---|
| 679 | ! |
|---|
| 680 | !-- If wall between gridpoint 7 and gridpoint 8, then |
|---|
| 681 | !-- Neumann boundary condition has to be applied |
|---|
| 682 | IF ( gp_outside_of_building(7) == 1 .AND. & |
|---|
| 683 | gp_outside_of_building(8) == 0 ) THEN |
|---|
| 684 | num_gp = num_gp + 1 |
|---|
| 685 | location(num_gp,1) = (i+1) * dx |
|---|
| 686 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 687 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 688 | ei(num_gp) = e(k+1,j,i+1) |
|---|
| 689 | dissi(num_gp) = diss(k+1,j,i+1) |
|---|
| 690 | de_dxi(num_gp) = de_dx(k+1,j,i+1) |
|---|
| 691 | de_dyi(num_gp) = 0.0 |
|---|
| 692 | de_dzi(num_gp) = de_dz(k+1,j,i+1) |
|---|
| 693 | ENDIF |
|---|
| 694 | |
|---|
| 695 | IF ( gp_outside_of_building(8) == 1 .AND. & |
|---|
| 696 | gp_outside_of_building(7) == 0 ) THEN |
|---|
| 697 | num_gp = num_gp + 1 |
|---|
| 698 | location(num_gp,1) = (i+1) * dx |
|---|
| 699 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 700 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 701 | ei(num_gp) = e(k+1,j+1,i+1) |
|---|
| 702 | dissi(num_gp) = diss(k+1,j+1,i+1) |
|---|
| 703 | de_dxi(num_gp) = de_dx(k+1,j+1,i+1) |
|---|
| 704 | de_dyi(num_gp) = 0.0 |
|---|
| 705 | de_dzi(num_gp) = de_dz(k+1,j+1,i+1) |
|---|
| 706 | ENDIF |
|---|
| 707 | |
|---|
| 708 | ! |
|---|
| 709 | !-- If wall between gridpoint 4 and gridpoint 8, then |
|---|
| 710 | !-- Neumann boundary condition has to be applied |
|---|
| 711 | IF ( gp_outside_of_building(4) == 1 .AND. & |
|---|
| 712 | gp_outside_of_building(8) == 0 ) THEN |
|---|
| 713 | num_gp = num_gp + 1 |
|---|
| 714 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 715 | location(num_gp,2) = (j+1) * dy |
|---|
| 716 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 717 | ei(num_gp) = e(k+1,j+1,i) |
|---|
| 718 | dissi(num_gp) = diss(k+1,j+1,i) |
|---|
| 719 | de_dxi(num_gp) = 0.0 |
|---|
| 720 | de_dyi(num_gp) = de_dy(k+1,j+1,i) |
|---|
| 721 | de_dzi(num_gp) = de_dz(k+1,j+1,i) |
|---|
| 722 | ENDIF |
|---|
| 723 | |
|---|
| 724 | IF ( gp_outside_of_building(8) == 1 .AND. & |
|---|
| 725 | gp_outside_of_building(4) == 0 ) THEN |
|---|
| 726 | num_gp = num_gp + 1 |
|---|
| 727 | location(num_gp,1) = i * dx + 0.5 * dx |
|---|
| 728 | location(num_gp,2) = (j+1) * dy |
|---|
| 729 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 730 | ei(num_gp) = e(k+1,j+1,i+1) |
|---|
| 731 | dissi(num_gp) = diss(k+1,j+1,i+1) |
|---|
| 732 | de_dxi(num_gp) = 0.0 |
|---|
| 733 | de_dyi(num_gp) = de_dy(k+1,j+1,i+1) |
|---|
| 734 | de_dzi(num_gp) = de_dz(k+1,j+1,i+1) |
|---|
| 735 | ENDIF |
|---|
| 736 | |
|---|
| 737 | ! |
|---|
| 738 | !-- If wall between gridpoint 3 and gridpoint 4, then |
|---|
| 739 | !-- Neumann boundary condition has to be applied |
|---|
| 740 | IF ( gp_outside_of_building(3) == 1 .AND. & |
|---|
| 741 | gp_outside_of_building(4) == 0 ) THEN |
|---|
| 742 | num_gp = num_gp + 1 |
|---|
| 743 | location(num_gp,1) = i * dx |
|---|
| 744 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 745 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 746 | ei(num_gp) = e(k+1,j,i) |
|---|
| 747 | dissi(num_gp) = diss(k+1,j,i) |
|---|
| 748 | de_dxi(num_gp) = de_dx(k+1,j,i) |
|---|
| 749 | de_dyi(num_gp) = 0.0 |
|---|
| 750 | de_dzi(num_gp) = de_dz(k+1,j,i) |
|---|
| 751 | ENDIF |
|---|
| 752 | |
|---|
| 753 | IF ( gp_outside_of_building(4) == 1 .AND. & |
|---|
| 754 | gp_outside_of_building(3) == 0 ) THEN |
|---|
| 755 | num_gp = num_gp + 1 |
|---|
| 756 | location(num_gp,1) = i * dx |
|---|
| 757 | location(num_gp,2) = j * dy + 0.5 * dy |
|---|
| 758 | location(num_gp,3) = k * dz + 0.5 * dz |
|---|
| 759 | ei(num_gp) = e(k+1,j+1,i) |
|---|
| 760 | dissi(num_gp) = diss(k+1,j+1,i) |
|---|
| 761 | de_dxi(num_gp) = de_dx(k+1,j+1,i) |
|---|
| 762 | de_dyi(num_gp) = 0.0 |
|---|
| 763 | de_dzi(num_gp) = de_dz(k+1,j+1,i) |
|---|
| 764 | ENDIF |
|---|
| 765 | |
|---|
| 766 | ! |
|---|
| 767 | !-- If wall between gridpoint 1 and gridpoint 3, then |
|---|
| 768 | !-- Neumann boundary condition has to be applied |
|---|
| 769 | !-- (only one case as only building beneath is possible) |
|---|
| 770 | IF ( gp_outside_of_building(1) == 0 .AND. & |
|---|
| 771 | gp_outside_of_building(3) == 1 ) THEN |
|---|
| 772 | num_gp = num_gp + 1 |
|---|
| 773 | location(num_gp,1) = i * dx |
|---|
| 774 | location(num_gp,2) = j * dy |
|---|
| 775 | location(num_gp,3) = k * dz |
|---|
| 776 | ei(num_gp) = e(k+1,j,i) |
|---|
| 777 | dissi(num_gp) = diss(k+1,j,i) |
|---|
| 778 | de_dxi(num_gp) = de_dx(k+1,j,i) |
|---|
| 779 | de_dyi(num_gp) = de_dy(k+1,j,i) |
|---|
| 780 | de_dzi(num_gp) = 0.0 |
|---|
| 781 | ENDIF |
|---|
| 782 | |
|---|
| 783 | ! |
|---|
| 784 | !-- If wall between gridpoint 5 and gridpoint 7, then |
|---|
| 785 | !-- Neumann boundary condition has to be applied |
|---|
| 786 | !-- (only one case as only building beneath is possible) |
|---|
| 787 | IF ( gp_outside_of_building(5) == 0 .AND. & |
|---|
| 788 | gp_outside_of_building(7) == 1 ) THEN |
|---|
| 789 | num_gp = num_gp + 1 |
|---|
| 790 | location(num_gp,1) = (i+1) * dx |
|---|
| 791 | location(num_gp,2) = j * dy |
|---|
| 792 | location(num_gp,3) = k * dz |
|---|
| 793 | ei(num_gp) = e(k+1,j,i+1) |
|---|
| 794 | dissi(num_gp) = diss(k+1,j,i+1) |
|---|
| 795 | de_dxi(num_gp) = de_dx(k+1,j,i+1) |
|---|
| 796 | de_dyi(num_gp) = de_dy(k+1,j,i+1) |
|---|
| 797 | de_dzi(num_gp) = 0.0 |
|---|
| 798 | ENDIF |
|---|
| 799 | |
|---|
| 800 | ! |
|---|
| 801 | !-- If wall between gridpoint 2 and gridpoint 4, then |
|---|
| 802 | !-- Neumann boundary condition has to be applied |
|---|
| 803 | !-- (only one case as only building beneath is possible) |
|---|
| 804 | IF ( gp_outside_of_building(2) == 0 .AND. & |
|---|
| 805 | gp_outside_of_building(4) == 1 ) THEN |
|---|
| 806 | num_gp = num_gp + 1 |
|---|
| 807 | location(num_gp,1) = i * dx |
|---|
| 808 | location(num_gp,2) = (j+1) * dy |
|---|
| 809 | location(num_gp,3) = k * dz |
|---|
| 810 | ei(num_gp) = e(k+1,j+1,i) |
|---|
| 811 | dissi(num_gp) = diss(k+1,j+1,i) |
|---|
| 812 | de_dxi(num_gp) = de_dx(k+1,j+1,i) |
|---|
| 813 | de_dyi(num_gp) = de_dy(k+1,j+1,i) |
|---|
| 814 | de_dzi(num_gp) = 0.0 |
|---|
| 815 | ENDIF |
|---|
| 816 | |
|---|
| 817 | ! |
|---|
| 818 | !-- If wall between gridpoint 6 and gridpoint 8, then |
|---|
| 819 | !-- Neumann boundary condition has to be applied |
|---|
| 820 | !-- (only one case as only building beneath is possible) |
|---|
| 821 | IF ( gp_outside_of_building(6) == 0 .AND. & |
|---|
| 822 | gp_outside_of_building(8) == 1 ) THEN |
|---|
| 823 | num_gp = num_gp + 1 |
|---|
| 824 | location(num_gp,1) = (i+1) * dx |
|---|
| 825 | location(num_gp,2) = (j+1) * dy |
|---|
| 826 | location(num_gp,3) = k * dz |
|---|
| 827 | ei(num_gp) = e(k+1,j+1,i+1) |
|---|
| 828 | dissi(num_gp) = diss(k+1,j+1,i+1) |
|---|
| 829 | de_dxi(num_gp) = de_dx(k+1,j+1,i+1) |
|---|
| 830 | de_dyi(num_gp) = de_dy(k+1,j+1,i+1) |
|---|
| 831 | de_dzi(num_gp) = 0.0 |
|---|
| 832 | ENDIF |
|---|
| 833 | |
|---|
| 834 | ! |
|---|
| 835 | !-- Carry out the interpolation |
|---|
| 836 | IF ( num_gp == 1 ) THEN |
|---|
| 837 | ! |
|---|
| 838 | !-- If only one of the gridpoints is situated outside of the |
|---|
| 839 | !-- building, it follows that the values at the particle |
|---|
| 840 | !-- location are the same as the gridpoint values |
|---|
| 841 | e_int = ei(num_gp) |
|---|
| 842 | diss_int = dissi(num_gp) |
|---|
| 843 | de_dx_int = de_dxi(num_gp) |
|---|
| 844 | de_dy_int = de_dyi(num_gp) |
|---|
| 845 | de_dz_int = de_dzi(num_gp) |
|---|
| 846 | ELSE IF ( num_gp > 1 ) THEN |
|---|
| 847 | |
|---|
| 848 | d_sum = 0.0 |
|---|
| 849 | ! |
|---|
| 850 | !-- Evaluation of the distances between the gridpoints |
|---|
| 851 | !-- contributing to the interpolated values, and the particle |
|---|
| 852 | !-- location |
|---|
| 853 | DO agp = 1, num_gp |
|---|
| 854 | d_gp_pl(agp) = ( particles(n)%x-location(agp,1) )**2 & |
|---|
| 855 | + ( particles(n)%y-location(agp,2) )**2 & |
|---|
| 856 | + ( particles(n)%z-location(agp,3) )**2 |
|---|
| 857 | d_sum = d_sum + d_gp_pl(agp) |
|---|
| 858 | ENDDO |
|---|
| 859 | |
|---|
| 860 | ! |
|---|
| 861 | !-- Finally the interpolation can be carried out |
|---|
| 862 | e_int = 0.0 |
|---|
| 863 | diss_int = 0.0 |
|---|
| 864 | de_dx_int = 0.0 |
|---|
| 865 | de_dy_int = 0.0 |
|---|
| 866 | de_dz_int = 0.0 |
|---|
| 867 | DO agp = 1, num_gp |
|---|
| 868 | e_int = e_int + ( d_sum - d_gp_pl(agp) ) * & |
|---|
| 869 | ei(agp) / ( (num_gp-1) * d_sum ) |
|---|
| 870 | diss_int = diss_int + ( d_sum - d_gp_pl(agp) ) * & |
|---|
| 871 | dissi(agp) / ( (num_gp-1) * d_sum ) |
|---|
| 872 | de_dx_int = de_dx_int + ( d_sum - d_gp_pl(agp) ) * & |
|---|
| 873 | de_dxi(agp) / ( (num_gp-1) * d_sum ) |
|---|
| 874 | de_dy_int = de_dy_int + ( d_sum - d_gp_pl(agp) ) * & |
|---|
| 875 | de_dyi(agp) / ( (num_gp-1) * d_sum ) |
|---|
| 876 | de_dz_int = de_dz_int + ( d_sum - d_gp_pl(agp) ) * & |
|---|
| 877 | de_dzi(agp) / ( (num_gp-1) * d_sum ) |
|---|
| 878 | ENDDO |
|---|
| 879 | |
|---|
| 880 | ENDIF |
|---|
| 881 | |
|---|
| 882 | ENDIF |
|---|
| 883 | |
|---|
| 884 | ENDIF |
|---|
| 885 | |
|---|
| 886 | ! |
|---|
| 887 | !-- Vertically interpolate the horizontally averaged SGS TKE and |
|---|
| 888 | !-- resolved-scale velocity variances and use the interpolated values |
|---|
| 889 | !-- to calculate the coefficient fs, which is a measure of the ratio |
|---|
| 890 | !-- of the subgrid-scale turbulent kinetic energy to the total amount |
|---|
| 891 | !-- of turbulent kinetic energy. |
|---|
| 892 | IF ( k == 0 ) THEN |
|---|
| 893 | e_mean_int = hom(0,1,8,0) |
|---|
| 894 | ELSE |
|---|
| 895 | e_mean_int = hom(k,1,8,0) + & |
|---|
| 896 | ( hom(k+1,1,8,0) - hom(k,1,8,0) ) / & |
|---|
| 897 | ( zu(k+1) - zu(k) ) * & |
|---|
| 898 | ( particles(n)%z - zu(k) ) |
|---|
| 899 | ENDIF |
|---|
| 900 | |
|---|
| 901 | kw = particles(n)%z / dz |
|---|
| 902 | |
|---|
| 903 | IF ( k == 0 ) THEN |
|---|
| 904 | aa = hom(k+1,1,30,0) * ( particles(n)%z / & |
|---|
| 905 | ( 0.5 * ( zu(k+1) - zu(k) ) ) ) |
|---|
| 906 | bb = hom(k+1,1,31,0) * ( particles(n)%z / & |
|---|
| 907 | ( 0.5 * ( zu(k+1) - zu(k) ) ) ) |
|---|
| 908 | cc = hom(kw+1,1,32,0) * ( particles(n)%z / & |
|---|
| 909 | ( 1.0 * ( zw(kw+1) - zw(kw) ) ) ) |
|---|
| 910 | ELSE |
|---|
| 911 | aa = hom(k,1,30,0) + ( hom(k+1,1,30,0) - hom(k,1,30,0) ) * & |
|---|
| 912 | ( ( particles(n)%z - zu(k) ) / ( zu(k+1) - zu(k) ) ) |
|---|
| 913 | bb = hom(k,1,31,0) + ( hom(k+1,1,31,0) - hom(k,1,31,0) ) * & |
|---|
| 914 | ( ( particles(n)%z - zu(k) ) / ( zu(k+1) - zu(k) ) ) |
|---|
| 915 | cc = hom(kw,1,32,0) + ( hom(kw+1,1,32,0)-hom(kw,1,32,0) ) *& |
|---|
| 916 | ( ( particles(n)%z - zw(kw) ) / ( zw(kw+1)-zw(kw) ) ) |
|---|
| 917 | ENDIF |
|---|
| 918 | |
|---|
| 919 | vv_int = ( 1.0 / 3.0 ) * ( aa + bb + cc ) |
|---|
| 920 | |
|---|
| 921 | fs_int = ( 2.0 / 3.0 ) * e_mean_int / & |
|---|
| 922 | ( vv_int + ( 2.0 / 3.0 ) * e_mean_int ) |
|---|
| 923 | |
|---|
| 924 | ! |
|---|
| 925 | !-- Calculate the Lagrangian timescale according to Weil et al. (2004). |
|---|
| 926 | lagr_timescale = ( 4.0 * e_int ) / & |
|---|
| 927 | ( 3.0 * fs_int * c_0 * diss_int ) |
|---|
| 928 | |
|---|
| 929 | ! |
|---|
| 930 | !-- Calculate the next particle timestep. dt_gap is the time needed to |
|---|
| 931 | !-- complete the current LES timestep. |
|---|
| 932 | dt_gap = dt_3d - particles(n)%dt_sum |
|---|
| 933 | dt_particle = MIN( dt_3d, 0.025 * lagr_timescale, dt_gap ) |
|---|
| 934 | |
|---|
| 935 | ! |
|---|
| 936 | !-- The particle timestep should not be too small in order to prevent |
|---|
| 937 | !-- the number of particle timesteps of getting too large |
|---|
| 938 | IF ( dt_particle < dt_min_part .AND. dt_min_part < dt_gap ) & |
|---|
| 939 | THEN |
|---|
| 940 | dt_particle = dt_min_part |
|---|
| 941 | ENDIF |
|---|
| 942 | |
|---|
| 943 | ! |
|---|
| 944 | !-- Calculate the SGS velocity components |
|---|
| 945 | IF ( particles(n)%age == 0.0 ) THEN |
|---|
| 946 | ! |
|---|
| 947 | !-- For new particles the SGS components are derived from the SGS |
|---|
| 948 | !-- TKE. Limit the Gaussian random number to the interval |
|---|
| 949 | !-- [-5.0*sigma, 5.0*sigma] in order to prevent the SGS velocities |
|---|
| 950 | !-- from becoming unrealistically large. |
|---|
| 951 | particles(n)%rvar1 = SQRT( 2.0 * sgs_wfu_part * e_int ) * & |
|---|
| 952 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) |
|---|
| 953 | particles(n)%rvar2 = SQRT( 2.0 * sgs_wfv_part * e_int ) * & |
|---|
| 954 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) |
|---|
| 955 | particles(n)%rvar3 = SQRT( 2.0 * sgs_wfw_part * e_int ) * & |
|---|
| 956 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) |
|---|
| 957 | |
|---|
| 958 | ELSE |
|---|
| 959 | |
|---|
| 960 | ! |
|---|
| 961 | !-- Restriction of the size of the new timestep: compared to the |
|---|
| 962 | !-- previous timestep the increase must not exceed 200% |
|---|
| 963 | |
|---|
| 964 | dt_particle_m = particles(n)%age - particles(n)%age_m |
|---|
| 965 | IF ( dt_particle > 2.0 * dt_particle_m ) THEN |
|---|
| 966 | dt_particle = 2.0 * dt_particle_m |
|---|
| 967 | ENDIF |
|---|
| 968 | |
|---|
| 969 | ! |
|---|
| 970 | !-- For old particles the SGS components are correlated with the |
|---|
| 971 | !-- values from the previous timestep. Random numbers have also to |
|---|
| 972 | !-- be limited (see above). |
|---|
| 973 | !-- As negative values for the subgrid TKE are not allowed, the |
|---|
| 974 | !-- change of the subgrid TKE with time cannot be smaller than |
|---|
| 975 | !-- -e_int/dt_particle. This value is used as a lower boundary |
|---|
| 976 | !-- value for the change of TKE |
|---|
| 977 | |
|---|
| 978 | de_dt_min = - e_int / dt_particle |
|---|
| 979 | |
|---|
| 980 | de_dt = ( e_int - particles(n)%e_m ) / dt_particle_m |
|---|
| 981 | |
|---|
| 982 | IF ( de_dt < de_dt_min ) THEN |
|---|
| 983 | de_dt = de_dt_min |
|---|
| 984 | ENDIF |
|---|
| 985 | |
|---|
| 986 | particles(n)%rvar1 = particles(n)%rvar1 - fs_int * c_0 * & |
|---|
| 987 | diss_int * particles(n)%rvar1 * dt_particle /& |
|---|
| 988 | ( 4.0 * sgs_wfu_part * e_int ) + & |
|---|
| 989 | ( 2.0 * sgs_wfu_part * de_dt * & |
|---|
| 990 | particles(n)%rvar1 / & |
|---|
| 991 | ( 2.0 * sgs_wfu_part * e_int ) + de_dx_int & |
|---|
| 992 | ) * dt_particle / 2.0 + & |
|---|
| 993 | SQRT( fs_int * c_0 * diss_int ) * & |
|---|
| 994 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) * & |
|---|
| 995 | SQRT( dt_particle ) |
|---|
| 996 | |
|---|
| 997 | particles(n)%rvar2 = particles(n)%rvar2 - fs_int * c_0 * & |
|---|
| 998 | diss_int * particles(n)%rvar2 * dt_particle /& |
|---|
| 999 | ( 4.0 * sgs_wfv_part * e_int ) + & |
|---|
| 1000 | ( 2.0 * sgs_wfv_part * de_dt * & |
|---|
| 1001 | particles(n)%rvar2 / & |
|---|
| 1002 | ( 2.0 * sgs_wfv_part * e_int ) + de_dy_int & |
|---|
| 1003 | ) * dt_particle / 2.0 + & |
|---|
| 1004 | SQRT( fs_int * c_0 * diss_int ) * & |
|---|
| 1005 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) * & |
|---|
| 1006 | SQRT( dt_particle ) |
|---|
| 1007 | |
|---|
| 1008 | particles(n)%rvar3 = particles(n)%rvar3 - fs_int * c_0 * & |
|---|
| 1009 | diss_int * particles(n)%rvar3 * dt_particle /& |
|---|
| 1010 | ( 4.0 * sgs_wfw_part * e_int ) + & |
|---|
| 1011 | ( 2.0 * sgs_wfw_part * de_dt * & |
|---|
| 1012 | particles(n)%rvar3 / & |
|---|
| 1013 | ( 2.0 * sgs_wfw_part * e_int ) + de_dz_int & |
|---|
| 1014 | ) * dt_particle / 2.0 + & |
|---|
| 1015 | SQRT( fs_int * c_0 * diss_int ) * & |
|---|
| 1016 | ( random_gauss( iran_part, 5.0 ) - 1.0 ) * & |
|---|
| 1017 | SQRT( dt_particle ) |
|---|
| 1018 | |
|---|
| 1019 | ENDIF |
|---|
| 1020 | |
|---|
| 1021 | u_int = u_int + particles(n)%rvar1 |
|---|
| 1022 | v_int = v_int + particles(n)%rvar2 |
|---|
| 1023 | w_int = w_int + particles(n)%rvar3 |
|---|
| 1024 | |
|---|
| 1025 | ! |
|---|
| 1026 | !-- Store the SGS TKE of the current timelevel which is needed for |
|---|
| 1027 | !-- for calculating the SGS particle velocities at the next timestep |
|---|
| 1028 | particles(n)%e_m = e_int |
|---|
| 1029 | |
|---|
| 1030 | ELSE |
|---|
| 1031 | ! |
|---|
| 1032 | !-- If no SGS velocities are used, only the particle timestep has to |
|---|
| 1033 | !-- be set |
|---|
| 1034 | dt_particle = dt_3d |
|---|
| 1035 | |
|---|
| 1036 | ENDIF |
|---|
| 1037 | |
|---|
| 1038 | ! |
|---|
| 1039 | !-- Store the old age of the particle ( needed to prevent that a |
|---|
| 1040 | !-- particle crosses several PEs during one timestep, and for the |
|---|
| 1041 | !-- evaluation of the subgrid particle velocity fluctuations ) |
|---|
| 1042 | particles(n)%age_m = particles(n)%age |
|---|
| 1043 | |
|---|
| 1044 | |
|---|
| 1045 | ! |
|---|
| 1046 | !-- Particle advection |
|---|
| 1047 | IF ( particle_groups(particles(n)%group)%density_ratio == 0.0 ) THEN |
|---|
| 1048 | ! |
|---|
| 1049 | !-- Pure passive transport (without particle inertia) |
|---|
| 1050 | particles(n)%x = particles(n)%x + u_int * dt_particle |
|---|
| 1051 | particles(n)%y = particles(n)%y + v_int * dt_particle |
|---|
| 1052 | particles(n)%z = particles(n)%z + w_int * dt_particle |
|---|
| 1053 | |
|---|
| 1054 | particles(n)%speed_x = u_int |
|---|
| 1055 | particles(n)%speed_y = v_int |
|---|
| 1056 | particles(n)%speed_z = w_int |
|---|
| 1057 | |
|---|
| 1058 | ELSE |
|---|
| 1059 | ! |
|---|
| 1060 | !-- Transport of particles with inertia |
|---|
| 1061 | particles(n)%x = particles(n)%x + particles(n)%speed_x * & |
|---|
| 1062 | dt_particle |
|---|
| 1063 | particles(n)%y = particles(n)%y + particles(n)%speed_y * & |
|---|
| 1064 | dt_particle |
|---|
| 1065 | particles(n)%z = particles(n)%z + particles(n)%speed_z * & |
|---|
| 1066 | dt_particle |
|---|
| 1067 | |
|---|
| 1068 | ! |
|---|
| 1069 | !-- Update of the particle velocity |
|---|
| 1070 | dens_ratio = particle_groups(particles(n)%group)%density_ratio |
|---|
| 1071 | IF ( cloud_droplets ) THEN |
|---|
| 1072 | exp_arg = 4.5 * dens_ratio * molecular_viscosity / & |
|---|
| 1073 | ( particles(n)%radius )**2 * & |
|---|
| 1074 | ( 1.0 + 0.15 * ( 2.0 * particles(n)%radius * & |
|---|
| 1075 | SQRT( ( u_int - particles(n)%speed_x )**2 + & |
|---|
| 1076 | ( v_int - particles(n)%speed_y )**2 + & |
|---|
| 1077 | ( w_int - particles(n)%speed_z )**2 ) / & |
|---|
| 1078 | molecular_viscosity )**0.687 & |
|---|
| 1079 | ) |
|---|
| 1080 | exp_term = EXP( -exp_arg * dt_particle ) |
|---|
| 1081 | ELSEIF ( use_sgs_for_particles ) THEN |
|---|
| 1082 | exp_arg = particle_groups(particles(n)%group)%exp_arg |
|---|
| 1083 | exp_term = EXP( -exp_arg * dt_particle ) |
|---|
| 1084 | ELSE |
|---|
| 1085 | exp_arg = particle_groups(particles(n)%group)%exp_arg |
|---|
| 1086 | exp_term = particle_groups(particles(n)%group)%exp_term |
|---|
| 1087 | ENDIF |
|---|
| 1088 | particles(n)%speed_x = particles(n)%speed_x * exp_term + & |
|---|
| 1089 | u_int * ( 1.0 - exp_term ) |
|---|
| 1090 | particles(n)%speed_y = particles(n)%speed_y * exp_term + & |
|---|
| 1091 | v_int * ( 1.0 - exp_term ) |
|---|
| 1092 | particles(n)%speed_z = particles(n)%speed_z * exp_term + & |
|---|
| 1093 | ( w_int - ( 1.0 - dens_ratio ) * g / exp_arg )& |
|---|
| 1094 | * ( 1.0 - exp_term ) |
|---|
| 1095 | ENDIF |
|---|
| 1096 | |
|---|
| 1097 | ! |
|---|
| 1098 | !-- Increment the particle age and the total time that the particle |
|---|
| 1099 | !-- has advanced within the particle timestep procedure |
|---|
| 1100 | particles(n)%age = particles(n)%age + dt_particle |
|---|
| 1101 | particles(n)%dt_sum = particles(n)%dt_sum + dt_particle |
|---|
| 1102 | |
|---|
| 1103 | ! |
|---|
| 1104 | !-- Check whether there is still a particle that has not yet completed |
|---|
| 1105 | !-- the total LES timestep |
|---|
| 1106 | IF ( ( dt_3d - particles(n)%dt_sum ) > 1E-8 ) THEN |
|---|
| 1107 | dt_3d_reached_l = .FALSE. |
|---|
| 1108 | ENDIF |
|---|
| 1109 | |
|---|
| 1110 | ENDDO |
|---|
| 1111 | |
|---|
| 1112 | |
|---|
| 1113 | END SUBROUTINE lpm_advec |
|---|
