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