1 | MODULE advect_mod |
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2 | USE icosa |
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3 | IMPLICIT NONE |
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4 | |
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5 | PRIVATE |
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6 | |
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7 | PUBLIC :: init_advect, compute_backward_traj, compute_gradq3d, compute_advect_horiz |
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8 | |
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9 | CONTAINS |
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10 | |
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11 | !========================================================================== |
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12 | |
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13 | SUBROUTINE init_advect(normal,tangent) |
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14 | IMPLICIT NONE |
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15 | REAL(rstd),INTENT(OUT) :: normal(3*iim*jjm,3) |
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16 | REAL(rstd),INTENT(OUT) :: tangent(3*iim*jjm,3) |
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17 | |
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18 | INTEGER :: i,j,n |
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19 | |
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20 | DO j=jj_begin-1,jj_end+1 |
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21 | DO i=ii_begin-1,ii_end+1 |
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22 | n=(j-1)*iim+i |
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23 | |
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24 | CALL cross_product2(xyz_v(n+z_rdown,:),xyz_v(n+z_rup,:),normal(n+u_right,:)) |
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25 | normal(n+u_right,:)=normal(n+u_right,:)/sqrt(sum(normal(n+u_right,:)**2)+1e-50)*ne(n,right) |
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26 | |
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27 | CALL cross_product2(xyz_v(n+z_up,:),xyz_v(n+z_lup,:),normal(n+u_lup,:)) |
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28 | normal(n+u_lup,:)=normal(n+u_lup,:)/sqrt(sum(normal(n+u_lup,:)**2)+1e-50)*ne(n,lup) |
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29 | |
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30 | CALL cross_product2(xyz_v(n+z_ldown,:),xyz_v(n+z_down,:),normal(n+u_ldown,:)) |
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31 | normal(n+u_ldown,:)=normal(n+u_ldown,:)/sqrt(sum(normal(n+u_ldown,:)**2)+1e-50)*ne(n,ldown) |
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32 | |
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33 | tangent(n+u_right,:)=xyz_v(n+z_rup,:)-xyz_v(n+z_rdown,:) |
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34 | tangent(n+u_right,:)=tangent(n+u_right,:)/sqrt(sum(tangent(n+u_right,:)**2)+1e-50) |
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35 | |
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36 | tangent(n+u_lup,:)=xyz_v(n+z_lup,:)-xyz_v(n+z_up,:) |
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37 | tangent(n+u_lup,:)=tangent(n+u_lup,:)/sqrt(sum(tangent(n+u_lup,:)**2)+1e-50) |
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38 | |
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39 | tangent(n+u_ldown,:)=xyz_v(n+z_down,:)-xyz_v(n+z_ldown,:) |
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40 | tangent(n+u_ldown,:)=tangent(n+u_ldown,:)/sqrt(sum(tangent(n+u_ldown,:)**2)+1e-50) |
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41 | END DO |
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42 | ENDDO |
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43 | |
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44 | END SUBROUTINE init_advect |
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45 | |
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46 | !======================================================================================= |
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47 | |
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48 | SUBROUTINE compute_gradq3d(qi,gradq3d) |
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49 | IMPLICIT NONE |
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50 | REAL(rstd),INTENT(IN) :: qi(iim*jjm,llm) |
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51 | REAL(rstd),INTENT(OUT) :: gradq3d(iim*jjm,llm,3) |
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52 | REAL(rstd) :: maxq,minq,minq_c,maxq_c |
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53 | REAL(rstd) :: alphamx,alphami,alpha ,maggrd,leng |
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54 | REAL(rstd) :: leng1,leng2 |
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55 | REAL(rstd) :: arr(2*iim*jjm) |
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56 | REAL(rstd) :: gradtri(2*iim*jjm,llm,3) |
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57 | REAL(rstd) :: ar |
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58 | INTEGER :: i,j,n,k,ind,l |
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59 | |
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60 | ! TODO : precompute ar, drop arr as output argument of gradq ? |
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61 | |
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62 | !========================================================================================== GRADIENT |
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63 | ! Compute gradient at triangles solving a linear system |
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64 | ! arr = area of triangle joining centroids of hexagons |
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65 | Do l = 1,llm |
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66 | DO j=jj_begin-1,jj_end+1 |
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67 | DO i=ii_begin-1,ii_end+1 |
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68 | n=(j-1)*iim+i |
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69 | CALL gradq(n,n+t_rup,n+t_lup,n+z_up,qi(:,l),gradtri(n+z_up,l,:),arr(n+z_up)) |
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70 | CALL gradq(n,n+t_ldown,n+t_rdown,n+z_down,qi(:,l),gradtri(n+z_down,l,:),arr(n+z_down)) |
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71 | END DO |
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72 | END DO |
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73 | END DO |
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74 | |
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75 | ! Do l =1,llm |
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76 | DO j=jj_begin,jj_end |
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77 | DO i=ii_begin,ii_end |
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78 | n=(j-1)*iim+i |
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79 | gradq3d(n,:,:) = gradtri(n+z_up,:,:) + gradtri(n+z_down,:,:) + & |
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80 | gradtri(n+z_rup,:,:) + gradtri(n+z_ldown,:,:) + & |
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81 | gradtri(n+z_lup,:,:)+ gradtri(n+z_rdown,:,:) |
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82 | ar = arr(n+z_up)+arr(n+z_lup)+arr(n+z_ldown)+arr(n+z_down)+arr(n+z_rdown)+arr(n+z_rup) |
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83 | gradq3d(n,:,:) = gradq3d(n,:,:)/(ar+1.e-50) |
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84 | END DO |
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85 | END DO |
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86 | ! END DO |
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87 | |
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88 | !============================================================================================= LIMITING |
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89 | ! GO TO 120 |
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90 | DO l =1,llm |
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91 | DO j=jj_begin,jj_end |
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92 | DO i=ii_begin,ii_end |
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93 | n=(j-1)*iim+i |
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94 | maggrd = dot_product(gradq3d(n,l,:),gradq3d(n,l,:)) |
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95 | maggrd = sqrt(maggrd) |
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96 | leng = max(sum((xyz_v(n+z_up,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_down,:) - xyz_i(n,:))**2), & |
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97 | sum((xyz_v(n+z_rup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_rdown,:) - xyz_i(n,:))**2), & |
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98 | sum((xyz_v(n+z_lup,:) - xyz_i(n,:))**2),sum((xyz_v(n+z_ldown,:) - xyz_i(n,:))**2)) |
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99 | maxq_c = qi(n,l) + maggrd*sqrt(leng) |
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100 | minq_c = qi(n,l) - maggrd*sqrt(leng) |
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101 | maxq = max(qi(n,l),qi(n+t_right,l),qi(n+t_lup,l),qi(n+t_rup,l),qi(n+t_left,l), & |
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102 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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103 | minq = min(qi(n,l),qi(n+t_right,l),qi(n+t_lup,l),qi(n+t_rup,l),qi(n+t_left,l), & |
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104 | qi(n+t_rdown,l),qi(n+t_ldown,l)) |
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105 | alphamx = (maxq - qi(n,l)) ; alphamx = alphamx/(maxq_c - qi(n,l) ) |
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106 | alphamx = max(alphamx,0.0) |
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107 | alphami = (minq - qi(n,l)); alphami = alphami/(minq_c - qi(n,l)) |
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108 | alphami = max(alphami,0.0) |
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109 | alpha = min(alphamx,alphami,1.0) |
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110 | gradq3d(n,l,:) = alpha*gradq3d(n,l,:) |
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111 | END DO |
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112 | END DO |
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113 | END DO |
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114 | END SUBROUTINE compute_gradq3d |
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115 | |
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116 | ! Backward trajectories, for use with Miura approach |
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117 | SUBROUTINE compute_backward_traj(normal,tangent,ue,tau, cc) |
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118 | IMPLICIT NONE |
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119 | REAL(rstd),INTENT(IN) :: normal(3*iim*jjm,3) |
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120 | REAL(rstd),INTENT(IN) :: tangent(3*iim*jjm,3) |
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121 | REAL(rstd),INTENT(IN) :: ue(iim*3*jjm,llm) |
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122 | REAL(rstd),INTENT(OUT) :: cc(3*iim*jjm,llm,3) ! start of backward trajectory |
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123 | REAL(rstd),INTENT(IN) :: tau |
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124 | |
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125 | REAL(rstd) :: v_e(3), up_e, qe, ed(3) |
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126 | INTEGER :: i,j,n,l |
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127 | |
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128 | ! TODO : compute normal displacement ue*tau as hfluxt / mass(upwind) then reconstruct tangential displacement |
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129 | |
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130 | ! reconstruct tangential wind then 3D wind at edge then cc = edge midpoint - u*tau |
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131 | DO l = 1,llm |
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132 | DO j=jj_begin-1,jj_end+1 |
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133 | DO i=ii_begin-1,ii_end+1 |
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134 | n=(j-1)*iim+i |
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135 | |
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136 | up_e =1/de(n+u_right)*( & |
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137 | wee(n+u_right,1,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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138 | wee(n+u_right,2,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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139 | wee(n+u_right,3,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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140 | wee(n+u_right,4,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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141 | wee(n+u_right,5,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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142 | wee(n+u_right,1,2)*le(n+t_right+u_ldown)*ue(n+t_right+u_ldown,l)+ & |
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143 | wee(n+u_right,2,2)*le(n+t_right+u_rdown)*ue(n+t_right+u_rdown,l)+ & |
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144 | wee(n+u_right,3,2)*le(n+t_right+u_right)*ue(n+t_right+u_right,l)+ & |
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145 | wee(n+u_right,4,2)*le(n+t_right+u_rup)*ue(n+t_right+u_rup,l)+ & |
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146 | wee(n+u_right,5,2)*le(n+t_right+u_lup)*ue(n+t_right+u_lup,l) & |
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147 | ) |
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148 | v_e = ue(n+u_right,l)*normal(n+u_right,:) + up_e*tangent(n+u_right,:) |
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149 | cc(n+u_right,l,:) = xyz_e(n+u_right,:) - v_e*tau |
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150 | |
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151 | up_e=1/de(n+u_lup)*( & |
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152 | wee(n+u_lup,1,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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153 | wee(n+u_lup,2,1)*le(n+u_ldown)*ue(n+u_ldown,l)+ & |
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154 | wee(n+u_lup,3,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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155 | wee(n+u_lup,4,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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156 | wee(n+u_lup,5,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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157 | wee(n+u_lup,1,2)*le(n+t_lup+u_right)*ue(n+t_lup+u_right,l)+ & |
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158 | wee(n+u_lup,2,2)*le(n+t_lup+u_rup)*ue(n+t_lup+u_rup,l)+ & |
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159 | wee(n+u_lup,3,2)*le(n+t_lup+u_lup)*ue(n+t_lup+u_lup,l)+ & |
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160 | wee(n+u_lup,4,2)*le(n+t_lup+u_left)*ue(n+t_lup+u_left,l)+ & |
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161 | wee(n+u_lup,5,2)*le(n+t_lup+u_ldown)*ue(n+t_lup+u_ldown,l) & |
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162 | ) |
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163 | v_e = ue(n+u_lup,l)*normal(n+u_lup,:) + up_e*tangent(n+u_lup,:) |
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164 | cc(n+u_lup,l,:) = xyz_e(n+u_lup,:) - v_e*tau |
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165 | |
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166 | up_e=1/de(n+u_ldown)*( & |
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167 | wee(n+u_ldown,1,1)*le(n+u_rdown)*ue(n+u_rdown,l)+ & |
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168 | wee(n+u_ldown,2,1)*le(n+u_right)*ue(n+u_right,l)+ & |
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169 | wee(n+u_ldown,3,1)*le(n+u_rup)*ue(n+u_rup,l)+ & |
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170 | wee(n+u_ldown,4,1)*le(n+u_lup)*ue(n+u_lup,l)+ & |
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171 | wee(n+u_ldown,5,1)*le(n+u_left)*ue(n+u_left,l)+ & |
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172 | wee(n+u_ldown,1,2)*le(n+t_ldown+u_lup)*ue(n+t_ldown+u_lup,l)+ & |
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173 | wee(n+u_ldown,2,2)*le(n+t_ldown+u_left)*ue(n+t_ldown+u_left,l)+ & |
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174 | wee(n+u_ldown,3,2)*le(n+t_ldown+u_ldown)*ue(n+t_ldown+u_ldown,l)+ & |
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175 | wee(n+u_ldown,4,2)*le(n+t_ldown+u_rdown)*ue(n+t_ldown+u_rdown,l)+ & |
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176 | wee(n+u_ldown,5,2)*le(n+t_ldown+u_right)*ue(n+t_ldown+u_right,l) & |
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177 | ) |
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178 | v_e = ue(n+u_ldown,l)*normal(n+u_ldown,:) + up_e*tangent(n+u_ldown,:) |
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179 | cc(n+u_ldown,l,:) = xyz_e(n+u_ldown,:) - v_e*tau |
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180 | ENDDO |
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181 | ENDDO |
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182 | END DO |
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183 | END SUBROUTINE compute_backward_traj |
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184 | |
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185 | ! Horizontal transport (S. Dubey, T. Dubos) |
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186 | ! Slope-limited van Leer approach with hexagons |
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187 | SUBROUTINE compute_advect_horiz(update_mass,hfluxt,cc,gradq3d, mass,qi) |
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188 | IMPLICIT NONE |
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189 | LOGICAL, INTENT(IN) :: update_mass |
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190 | REAL(rstd), INTENT(IN) :: gradq3d(iim*jjm,llm,3) |
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191 | REAL(rstd), INTENT(IN) :: hfluxt(3*iim*jjm,llm) ! mass flux |
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192 | REAL(rstd), INTENT(IN) :: cc(3*iim*jjm,llm,3) ! barycenter of quadrilateral, where q is evaluated (1-point quadrature) |
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193 | REAL(rstd), INTENT(INOUT) :: mass(iim*jjm,llm) |
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194 | REAL(rstd), INTENT(INOUT) :: qi(iim*jjm,llm) |
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195 | |
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196 | REAL(rstd) :: dq,dmass,qe,ed(3), newmass |
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197 | REAL(rstd) :: qflux(3*iim*jjm,llm) |
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198 | INTEGER :: i,j,n,k,l |
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199 | |
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200 | ! evaluate tracer field at point cc using piecewise linear reconstruction |
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201 | ! q(cc)= q0 + gradq.(cc-xyz_i) with xi centroid of hexagon |
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202 | ! ne*hfluxt>0 iff outgoing |
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203 | DO l = 1,llm |
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204 | DO j=jj_begin-1,jj_end+1 |
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205 | DO i=ii_begin-1,ii_end+1 |
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206 | n=(j-1)*iim+i |
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207 | if (ne(n,right)*hfluxt(n+u_right,l)>0) then |
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208 | ed = cc(n+u_right,l,:) - xyz_i(n,:) |
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209 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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210 | else |
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211 | ed = cc(n+u_right,l,:) - xyz_i(n+t_right,:) |
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212 | qe = qi(n+t_right,l)+sum2(gradq3d(n+t_right,l,:),ed) |
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213 | endif |
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214 | qflux(n+u_right,l) = hfluxt(n+u_right,l)*qe |
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215 | |
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216 | if (ne(n,lup)*hfluxt(n+u_lup,l)>0) then |
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217 | ed = cc(n+u_lup,l,:) - xyz_i(n,:) |
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218 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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219 | else |
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220 | ed = cc(n+u_lup,l,:) - xyz_i(n+t_lup,:) |
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221 | qe = qi(n+t_lup,l)+sum2(gradq3d(n+t_lup,l,:),ed) |
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222 | endif |
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223 | qflux(n+u_lup,l) = hfluxt(n+u_lup,l)*qe |
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224 | |
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225 | if (ne(n,ldown)*hfluxt(n+u_ldown,l)>0) then |
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226 | ed = cc(n+u_ldown,l,:) - xyz_i(n,:) |
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227 | qe = qi(n,l)+sum2(gradq3d(n,l,:),ed) |
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228 | else |
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229 | ed = cc(n+u_ldown,l,:) - xyz_i(n+t_ldown,:) |
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230 | qe = qi(n+t_ldown,l)+sum2(gradq3d(n+t_ldown,l,:),ed) |
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231 | endif |
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232 | qflux(n+u_ldown,l) = hfluxt(n+u_ldown,l)*qe |
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233 | end do |
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234 | end do |
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235 | END DO |
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236 | |
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237 | ! update q and, if update_mass, update mass |
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238 | DO l = 1,llm |
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239 | DO j=jj_begin,jj_end |
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240 | DO i=ii_begin,ii_end |
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241 | n=(j-1)*iim+i |
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242 | ! sign convention as Ringler et al. (2010) eq. 21 |
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243 | dmass = hfluxt(n+u_right,l)*ne(n,right) & |
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244 | + hfluxt(n+u_lup,l) *ne(n,lup) & |
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245 | + hfluxt(n+u_ldown,l)*ne(n,ldown) & |
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246 | + hfluxt(n+u_rup,l) *ne(n,rup) & |
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247 | + hfluxt(n+u_left,l) *ne(n,left) & |
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248 | + hfluxt(n+u_rdown,l)*ne(n,rdown) |
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249 | |
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250 | dq = qflux(n+u_right,l) *ne(n,right) & |
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251 | + qflux(n+u_lup,l) *ne(n,lup) & |
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252 | + qflux(n+u_ldown,l) *ne(n,ldown) & |
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253 | + qflux(n+u_rup,l) *ne(n,rup) & |
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254 | + qflux(n+u_left,l) *ne(n,left) & |
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255 | + qflux(n+u_rdown,l) *ne(n,rdown) |
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256 | |
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257 | newmass = mass(n,l) - dmass/Ai(n) |
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258 | qi(n,l) = (qi(n,l)*mass(n,l) - dq/Ai(n) ) / newmass |
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259 | IF(update_mass) mass(n,l) = newmass |
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260 | END DO |
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261 | END DO |
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262 | END DO |
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263 | |
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264 | CONTAINS |
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265 | |
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266 | !==================================================================================== |
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267 | PURE REAL(rstd) FUNCTION sum2(a1,a2) |
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268 | IMPLICIT NONE |
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269 | REAL(rstd),INTENT(IN):: a1(3), a2(3) |
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270 | sum2 = a1(1)*a2(1)+a1(2)*a2(2)+a1(3)*a2(3) |
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271 | ! sum2 = 0. ! Godunov scheme |
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272 | END FUNCTION sum2 |
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273 | |
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274 | END SUBROUTINE compute_advect_horiz |
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275 | |
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276 | !========================================================================== |
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277 | PURE SUBROUTINE gradq(n0,n1,n2,n3,q,dq,det) |
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278 | IMPLICIT NONE |
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279 | INTEGER, INTENT(IN) :: n0,n1,n2,n3 |
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280 | REAL(rstd), INTENT(IN) :: q(iim*jjm) |
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281 | REAL(rstd), INTENT(OUT) :: dq(3), det |
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282 | |
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283 | REAL(rstd) ::detx,dety,detz |
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284 | INTEGER :: info |
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285 | INTEGER :: IPIV(3) |
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286 | |
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287 | REAL(rstd) :: A(3,3) |
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288 | REAL(rstd) :: B(3) |
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289 | |
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290 | ! TODO : replace A by A1,A2,A3 |
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291 | A(1,1)=xyz_i(n1,1)-xyz_i(n0,1); A(1,2)=xyz_i(n1,2)-xyz_i(n0,2); A(1,3)=xyz_i(n1,3)-xyz_i(n0,3) |
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292 | A(2,1)=xyz_i(n2,1)-xyz_i(n0,1); A(2,2)=xyz_i(n2,2)-xyz_i(n0,2); A(2,3)=xyz_i(n2,3)-xyz_i(n0,3) |
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293 | A(3,1)=xyz_v(n3,1); A(3,2)= xyz_v(n3,2); A(3,3)=xyz_v(n3,3) |
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294 | |
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295 | dq(1) = q(n1)-q(n0) |
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296 | dq(2) = q(n2)-q(n0) |
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297 | dq(3) = 0.0 |
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298 | ! CALL DGESV(3,1,A,3,IPIV,dq(:),3,info) |
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299 | CALL determinant(A(:,1),A(:,2),A(:,3),det) |
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300 | CALL determinant(dq,A(:,2),A(:,3),detx) |
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301 | CALL determinant(A(:,1),dq,A(:,3),dety) |
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302 | CALL determinant(A(:,1),A(:,2),dq,detz) |
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303 | dq(1) = detx |
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304 | dq(2) = dety |
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305 | dq(3) = detz |
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306 | END SUBROUTINE gradq |
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307 | |
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308 | !========================================================================== |
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309 | PURE SUBROUTINE determinant(a1,a2,a3,det) |
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310 | IMPLICIT NONE |
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311 | REAL(rstd), DIMENSION(3), INTENT(IN) :: a1,a2,a3 |
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312 | REAL(rstd), INTENT(OUT) :: det |
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313 | REAL(rstd) :: x1,x2,x3 |
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314 | x1 = a1(1) * (a2(2) * a3(3) - a2(3) * a3(2)) |
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315 | x2 = a1(2) * (a2(1) * a3(3) - a2(3) * a3(1)) |
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316 | x3 = a1(3) * (a2(1) * a3(2) - a2(2) * a3(1)) |
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317 | det = x1 - x2 + x3 |
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318 | END SUBROUTINE determinant |
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319 | |
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320 | END MODULE advect_mod |
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