| Preface |
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ix | |
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1 | (6) |
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7 | (6) |
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Introduction and Motivation |
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7 | (1) |
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Physics of the Mathematical Model |
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7 | (1) |
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8 | (5) |
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9 | (1) |
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9 | (1) |
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10 | (1) |
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Boundary and Initial Conditions |
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11 | (1) |
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12 | (1) |
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13 | (16) |
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13 | (1) |
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13 | (2) |
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Notations for Finite Volume Method |
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15 | (2) |
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Discretization of the Convection Equation |
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17 | (3) |
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Discretization with Higher Order |
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19 | (1) |
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Discretization of the Diffusion-Dispersion Equation |
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20 | (2) |
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Discretization of the Reaction Equation |
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22 | (2) |
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Discretization of the Convection-Reaction Equation with Embedded Analytical Solutions |
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24 | (5) |
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Operator-Splitting Methods |
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29 | (16) |
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Splitting Method of First Order |
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30 | (2) |
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Strang Splitting and Methods of Higher Order |
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32 | (1) |
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Iterative Operator-Splitting Method |
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33 | (1) |
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Application of the Splitting Methods |
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34 | (3) |
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37 | (1) |
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Nonlinear Splitting Methods |
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38 | (5) |
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The Altered Jacobian Newton Iterative Methods with Embedded Sequential Splitting Methods |
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39 | (2) |
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Iterative Operator-Splitting Method as Fixed-Point Scheme |
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41 | (1) |
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Jacobian Newton Iterative Method with Embedded Operator-Splitting Method |
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41 | (2) |
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Remarks about the Operator-Splitting Methods |
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43 | (2) |
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45 | (38) |
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Analytical Solutions for Convection-Reaction Equations with Variable Retardation Factors |
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45 | (31) |
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Application of Laplace Transformation |
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46 | (7) |
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Application of Analytical Solution for Two Components |
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53 | (1) |
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Application of Analytical Solution for Three Components |
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53 | (2) |
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Special Cases of Analytical Solutions |
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55 | (17) |
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Application of Special Analytical Solutions for Two Components |
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72 | (1) |
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Application of Special Analytical Solutions for Three Components |
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73 | (3) |
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Calculating the Analytical Solution of Mass |
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76 | (7) |
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Calculation of the Residual Mass |
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77 | (3) |
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Calculation of Total Mass |
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80 | (2) |
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Calculation of the Outflowing Mass |
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82 | (1) |
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Iterative and Multigrid Methods |
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83 | (12) |
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83 | (1) |
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83 | (2) |
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85 | (3) |
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86 | (1) |
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Gauss-Seidel Methods and SOR Methods |
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87 | (1) |
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88 | (1) |
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Introduction to Multigrid Methods |
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88 | (7) |
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89 | (1) |
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90 | (1) |
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The Hierarchy of Equation Systems |
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91 | (1) |
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91 | (4) |
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95 | (10) |
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95 | (1) |
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Rough Structuring of the Software Packages |
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95 | (1) |
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96 | (2) |
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97 | (1) |
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98 | (2) |
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99 | (1) |
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100 | (1) |
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100 | (5) |
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100 | (1) |
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100 | (1) |
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101 | (1) |
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101 | (1) |
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102 | (3) |
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105 | (36) |
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Introduction for Model Problems |
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105 | (1) |
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Error Norms and Orders of Convergence to Evaluate Numerical Results |
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106 | (1) |
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One-Dimensional Model Problems for Linear Equilibrium-Sorption |
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107 | (17) |
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Model Descriptions for Four Test Cases |
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107 | (1) |
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Model Problem with Piecewise Continuous Triangular Impulse |
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108 | (7) |
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Model Problem with Continuous Triangular Impulse |
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115 | (6) |
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Model Problem with Realistic Parameters |
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121 | (3) |
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Two-Dimensional Model Problem for Linear Equilibrium-Sorption |
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124 | (10) |
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Transformation of Two-Dimensional Model Problems into One-Dimensional Model Problems |
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124 | (5) |
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Calculation of Two-Dimensional Model Example with Rotating Pyramid |
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129 | (3) |
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Verification of Numerical Calculations for General Two-Dimensional Model Problems |
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132 | (2) |
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Realistic Model for a Potential Damage Event |
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134 | (7) |
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Motivation and Description |
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134 | (1) |
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134 | (3) |
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Three-Dimensional Modeling |
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137 | (4) |
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141 | (2) |
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141 | (2) |
| Laplace Transformation |
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143 | (4) |
| Solutions for Ordinary Differential Equations |
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147 | (2) |
| Literature |
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149 | (10) |
| Index |
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159 | |
