1 | MODULE sedmat |
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2 | !!====================================================================== |
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3 | !! *** MODULE sedmat *** |
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4 | !! Sediment : linear system of equations |
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5 | !!===================================================================== |
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6 | !! * Modules used |
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7 | !!---------------------------------------------------------------------- |
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8 | |
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9 | USE sed ! sediment global variable |
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10 | USE lib_mpp ! distribued memory computing library |
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11 | |
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12 | |
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13 | IMPLICIT NONE |
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14 | PRIVATE |
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15 | |
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16 | PUBLIC sed_mat |
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17 | |
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18 | INTERFACE sed_mat |
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19 | MODULE PROCEDURE sed_mat_dsr, sed_mat_btb |
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20 | END INTERFACE |
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21 | |
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22 | INTEGER, PARAMETER :: nmax = 30 |
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23 | |
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24 | |
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25 | !! $Id$ |
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26 | CONTAINS |
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27 | |
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28 | SUBROUTINE sed_mat_dsr( nvar, ndim, nlev, preac, psms, psol, dtsed_in ) |
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29 | !!--------------------------------------------------------------------- |
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30 | !! *** ROUTINE sed_mat_dsr *** |
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31 | !! |
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32 | !! ** Purpose : solves tridiagonal system of linear equations |
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33 | !! |
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34 | !! ** Method : |
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35 | !! 1 - computes left hand side of linear system of equations |
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36 | !! for dissolution reaction |
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37 | !! For mass balance in kbot+sediment : |
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38 | !! dz3d (:,1) = dz(1) = 0.5 cm |
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39 | !! volw3d(:,1) = dzkbot ( see sedini.F90 ) |
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40 | !! dz(2) = 0.3 cm |
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41 | !! dz3d(:,2) = 0.3 + dzdep ( see seddsr.F90 ) |
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42 | !! volw3d(:,2) and vols3d(l,2) are thickened ( see seddsr.F90 ) |
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43 | !! |
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44 | !! 2 - forward/backward substitution. |
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45 | !! |
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46 | !! History : |
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47 | !! ! 04-10 (N. Emprin, M. Gehlen ) original |
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48 | !! ! 06-04 (C. Ethe) Module Re-organization |
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49 | !!---------------------------------------------------------------------- |
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50 | !! * Arguments |
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51 | INTEGER , INTENT(in) :: nvar ! number of variable |
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52 | INTEGER , INTENT(in) :: ndim ! number of points |
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53 | INTEGER , INTENT(in) :: nlev ! number of sediment levels |
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54 | |
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55 | REAL(wp), DIMENSION(ndim,nlev), INTENT(in ) :: preac ! reaction rates |
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56 | REAL(wp), DIMENSION(ndim,nlev), INTENT(in ) :: psms ! reaction rates |
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57 | REAL(wp), DIMENSION(ndim,nlev), INTENT(inout) :: psol ! solution ( undersaturation values ) |
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58 | REAL(wp), INTENT(in) :: dtsed_in |
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59 | |
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60 | !---Local declarations |
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61 | INTEGER :: ji, jk, jn |
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62 | REAL(wp), DIMENSION(ndim,nlev) :: za, zb, zc, zr |
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63 | REAL(wp), DIMENSION(ndim) :: zbet |
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64 | REAL(wp), DIMENSION(ndim,nmax) :: zgamm |
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65 | |
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66 | REAL(wp) :: aplus,aminus |
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67 | REAL(wp) :: rplus,rminus |
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68 | REAL(wp) :: dxplus,dxminus |
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69 | |
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70 | !---------------------------------------------------------------------- |
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71 | |
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72 | IF( ln_timing ) CALL timing_start('sed_mat_dsr') |
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73 | |
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74 | ! Computation left hand side of linear system of |
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75 | ! equations for dissolution reaction |
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76 | !--------------------------------------------- |
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77 | |
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78 | |
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79 | jn = nvar |
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80 | ! first sediment level |
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81 | DO ji = 1, ndim |
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82 | aplus = ( ( volw3d(ji,1) / ( dz3d(ji,1) ) ) + & |
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83 | ( volw3d(ji,2) / ( dz3d(ji,2) ) ) ) / 2. |
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84 | dxplus = ( dz3d(ji,1) + dz3d(ji,2) ) / 2. |
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85 | rplus = ( dtsed_in / ( volw3d(ji,1) ) ) * diff(ji,1,jn) * aplus / dxplus |
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86 | |
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87 | za(ji,1) = 0. |
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88 | zb(ji,1) = 1. + rplus |
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89 | zc(ji,1) = -rplus |
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90 | ENDDO |
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91 | |
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92 | DO jk = 2, nlev - 1 |
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93 | DO ji = 1, ndim |
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94 | aminus = ( ( volw3d(ji,jk-1) / ( dz3d(ji,jk-1) ) ) + & |
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95 | & ( volw3d(ji,jk ) / ( dz3d(ji,jk ) ) ) ) / 2. |
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96 | dxminus = ( dz3d(ji,jk-1) + dz3d(ji,jk) ) / 2. |
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97 | |
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98 | aplus = ( ( volw3d(ji,jk ) / ( dz3d(ji,jk ) ) ) + & |
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99 | & ( volw3d(ji,jk+1) / ( dz3d(ji,jk+1) ) ) ) / 2. |
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100 | dxplus = ( dz3d(ji,jk) + dz3d(ji,jk+1) ) / 2 |
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101 | ! |
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102 | rminus = ( dtsed_in / volw3d(ji,jk) ) * diff(ji,jk-1,jn) * aminus / dxminus |
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103 | rplus = ( dtsed_in / volw3d(ji,jk) ) * diff(ji,jk,jn) * aplus / dxplus |
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104 | ! |
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105 | za(ji,jk) = -rminus |
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106 | zb(ji,jk) = 1. + rminus + rplus |
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107 | zc(ji,jk) = -rplus |
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108 | END DO |
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109 | END DO |
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110 | |
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111 | DO ji = 1, ndim |
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112 | aminus = ( ( volw3d(ji,nlev-1) / dz3d(ji,nlev-1) ) + & |
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113 | & ( volw3d(ji,nlev) / dz3d(ji,nlev) ) ) / 2. |
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114 | dxminus = ( dz3d(ji,nlev-1) + dz3d(ji,nlev) ) / 2. |
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115 | rminus = ( dtsed_in / volw3d(ji,nlev) ) * diff(ji,nlev-1,jn) * aminus / dxminus |
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116 | ! |
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117 | za(ji,nlev) = -rminus |
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118 | zb(ji,nlev) = 1. + rminus |
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119 | zc(ji,nlev) = 0. |
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120 | END DO |
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121 | |
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122 | |
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123 | ! solves tridiagonal system of linear equations |
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124 | ! ----------------------------------------------- |
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125 | |
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126 | zr (:,:) = psol(:,:) + psms(:,:) |
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127 | zb (:,:) = zb(:,:) + preac(:,:) |
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128 | zbet(: ) = zb(:,1) |
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129 | psol(:,1) = zr(:,1) / zbet(:) |
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130 | |
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131 | ! |
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132 | DO jk = 2, nlev |
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133 | DO ji = 1, ndim |
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134 | zgamm(ji,jk) = zc(ji,jk-1) / zbet(ji) |
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135 | zbet(ji) = zb(ji,jk) - za(ji,jk) * zgamm(ji,jk) |
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136 | psol(ji,jk) = ( zr(ji,jk) - za(ji,jk) * psol(ji,jk-1) ) / zbet(ji) |
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137 | END DO |
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138 | ENDDO |
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139 | ! |
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140 | DO jk = nlev - 1, 1, -1 |
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141 | DO ji = 1,ndim |
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142 | psol(ji,jk) = psol(ji,jk) - zgamm(ji,jk+1) * psol(ji,jk+1) |
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143 | END DO |
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144 | ENDDO |
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145 | |
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146 | IF( ln_timing ) CALL timing_stop('sed_mat_dsr') |
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147 | |
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148 | |
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149 | END SUBROUTINE sed_mat_dsr |
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150 | |
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151 | SUBROUTINE sed_mat_btb( nvar, ndim, nlev, psol, dtsed_in ) |
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152 | !!--------------------------------------------------------------------- |
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153 | !! *** ROUTINE sed_mat_btb *** |
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154 | !! |
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155 | !! ** Purpose : solves tridiagonal system of linear equations |
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156 | !! |
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157 | !! ** Method : |
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158 | !! 1 - computes left hand side of linear system of equations |
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159 | !! for dissolution reaction |
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160 | !! |
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161 | !! 2 - forward/backward substitution. |
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162 | !! |
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163 | !! History : |
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164 | !! ! 04-10 (N. Emprin, M. Gehlen ) original |
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165 | !! ! 06-04 (C. Ethe) Module Re-organization |
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166 | !!---------------------------------------------------------------------- |
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167 | !! * Arguments |
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168 | INTEGER , INTENT(in) :: & |
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169 | nvar , & ! number of variables |
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170 | ndim , & ! number of points |
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171 | nlev ! number of sediment levels |
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172 | |
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173 | REAL(wp), DIMENSION(ndim,nlev,nvar), INTENT(inout) :: & |
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174 | psol ! solution |
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175 | |
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176 | REAL(wp), INTENT(in) :: dtsed_in |
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177 | |
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178 | !---Local declarations |
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179 | INTEGER :: & |
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180 | ji, jk, jn |
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181 | |
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182 | REAL(wp) :: & |
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183 | aplus,aminus , & |
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184 | rplus,rminus , & |
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185 | dxplus,dxminus |
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186 | |
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187 | REAL(wp), DIMENSION(nlev) :: za, zb, zc |
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188 | REAL(wp), DIMENSION(ndim,nlev) :: zr |
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189 | REAL(wp), DIMENSION(nmax) :: zgamm |
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190 | REAL(wp) :: zbet |
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191 | |
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192 | |
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193 | !---------------------------------------------------------------------- |
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194 | |
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195 | ! Computation left hand side of linear system of |
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196 | ! equations for dissolution reaction |
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197 | !--------------------------------------------- |
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198 | |
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199 | |
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200 | IF( ln_timing ) CALL timing_start('sed_mat_btb') |
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201 | |
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202 | ! first sediment level |
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203 | DO ji = 1, ndim |
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204 | aplus = ( ( vols(2) / dz(2) ) + ( vols(3) / dz(3) ) ) / 2. |
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205 | dxplus = ( dz(2) + dz(3) ) / 2. |
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206 | rplus = ( dtsed_in / vols(2) ) * db(ji,2) * aplus / dxplus |
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207 | |
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208 | za(1) = 0. |
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209 | zb(1) = 1. + rplus |
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210 | zc(1) = -rplus |
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211 | |
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212 | |
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213 | DO jk = 2, nlev - 1 |
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214 | aminus = ( ( vols(jk) / dz(jk) ) + ( vols(jk+1) / dz(jk+1) ) ) / 2. |
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215 | dxminus = ( dz(jk) + dz(jk+1) ) / 2. |
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216 | rminus = ( dtsed_in / vols(jk+1) ) * db(ji,jk) * aminus / dxminus |
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217 | ! |
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218 | aplus = ( ( vols(jk+1) / dz(jk+1 ) ) + ( vols(jk+2) / dz(jk+2) ) ) / 2. |
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219 | dxplus = ( dz(jk+1) + dz(jk+2) ) / 2. |
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220 | rplus = ( dtsed_in / vols(jk+1) ) * db(ji,jk+1) * aplus / dxplus |
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221 | ! |
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222 | za(jk) = -rminus |
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223 | zb(jk) = 1. + rminus + rplus |
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224 | zc(jk) = -rplus |
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225 | ENDDO |
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226 | |
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227 | aminus = ( ( vols(nlev) / dz(nlev) ) + ( vols(nlev+1) / dz(nlev+1) ) ) / 2. |
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228 | dxminus = ( dz(nlev) + dz(nlev+1) ) / 2. |
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229 | rminus = ( dtsed_in / vols(nlev+1) ) * db(ji,nlev) * aminus / dxminus |
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230 | ! |
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231 | za(nlev) = -rminus |
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232 | zb(nlev) = 1. + rminus |
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233 | zc(nlev) = 0. |
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234 | |
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235 | |
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236 | ! solves tridiagonal system of linear equations |
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237 | ! ----------------------------------------------- |
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238 | DO jn = 1, nvar |
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239 | |
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240 | DO jk = 1, nlev |
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241 | zr (ji,jk) = psol(ji,jk,jn) |
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242 | END DO |
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243 | zbet = zb(1) |
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244 | psol(ji,1,jn) = zr(ji,1) / zbet |
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245 | ! |
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246 | DO jk = 2, nlev |
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247 | zgamm(jk) = zc(jk-1) / zbet |
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248 | zbet = zb(jk) - za(jk) * zgamm(jk) |
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249 | psol(ji,jk,jn) = ( zr(ji,jk) - za(jk) * psol(ji,jk-1,jn) ) / zbet |
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250 | ENDDO |
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251 | ! |
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252 | DO jk = nlev - 1, 1, -1 |
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253 | psol(ji,jk,jn) = psol(ji,jk,jn) - zgamm(jk+1) * psol(ji,jk+1,jn) |
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254 | ENDDO |
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255 | |
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256 | ENDDO |
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257 | |
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258 | END DO |
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259 | ! |
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260 | IF( ln_timing ) CALL timing_stop('sed_mat_btb') |
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261 | |
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262 | |
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263 | END SUBROUTINE sed_mat_btb |
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264 | |
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265 | END MODULE sedmat |
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