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