Preface |
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vii | |
Introduction |
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ix | |
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1 Equations of Hydrodynamics |
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1 | (22) |
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1.1 Features of the Problems in the Formulation of Mathematical Physics |
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1 | (2) |
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1.2 Classification of Linear Differential Equations with Partial Derivatives of the Second Order |
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3 | (2) |
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1.3 Nonlinear Equations of Fluid Dynamics |
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5 | (4) |
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1.4 Methods for Solving Nonlinear Equations |
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9 | (2) |
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1.5 The Basic Laws of Hydrodynamics of an Ideal Fluid |
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11 | (5) |
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1.6 Linear Equations of Hydrodynamic Waves |
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16 | (7) |
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20 | (3) |
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2 Modeling of Wave Phenomena on the Shallow Water Surface |
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23 | (42) |
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2.1 Waves on the Sea Surface |
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23 | (3) |
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2.2 Review of Research on Surface Gravity Waves |
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26 | (13) |
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2.3 Investigation of Surface Gravity Waves |
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39 | (11) |
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2.4 Spatial modeling of Wave Phenomena on Shallow Water Surface |
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50 | (7) |
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2.5 Actual Observations of Wave Phenomena on the Surface of Shallow Water |
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57 | (1) |
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2.6 Ship Waves. "Reactive" Ducks of the Alexander Garden |
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58 | (7) |
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64 | (1) |
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3 Modeling of Nonlinear Surface Gravity Waves in Shallow Water |
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65 | (54) |
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3.1 Overview of Studies on Nonlinear Surface Gravity Waves in Shallow Water |
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65 | (9) |
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3.2 Nonlinear Models of Surface Gravity Waves in Shallow Water |
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74 | (7) |
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3.3 Solution of the Nonlinear Shallow Water Equation by the Method of Successive Approximations |
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81 | (5) |
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3.4 Modeling the Propagation of Nonlinear Surface Gravity Waves in Shallow Water |
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86 | (13) |
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3.5 Modeling the Refraction of Nonlinear Surface Gravity Waves |
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99 | (10) |
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3.6 Modeling of Propagation and Refraction of Nonlinear Surface Gravity Waves Under Shallow Water Conditions with Account of Dispersion |
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109 | (10) |
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117 | (2) |
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4 Numerical Simulation of Nonlinear Surface Gravity Waves in Shallow Water |
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119 | (36) |
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4.1 Review of Studies on Computational Modeling of Surface Waves |
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119 | (13) |
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4.2 Statement of the Problem |
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132 | (6) |
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4.3 The Research of a Discrete Model |
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138 | (1) |
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4.4 Results of Numerical Modeling based on Shallow Water Equations |
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139 | (9) |
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4.5 Discussion and Comparison of Results |
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148 | (7) |
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152 | (3) |
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5 Two-Dimensional Numerical Simulation of the Run-Up of Nonlinear Surface Gravity Waves |
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155 | (36) |
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5.1 Statement of the Problem |
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155 | (5) |
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5.2 Construction of a Discrete Finite-Volume Model |
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160 | (9) |
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5.3 Discrete Model Research |
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169 | (2) |
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5.4 Results of Two-Dimensional Numerical Modeling and Their Analysis |
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171 | (14) |
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5.5 Discussion and Comparison of Results |
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185 | (6) |
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188 | (3) |
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6 Three-Dimensional Numerical Modeling of the Runup of Nonlinear Surface Gravity Waves |
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191 | (54) |
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6.1 Statement of the Problem. Boundary and Initial Conditions |
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191 | (4) |
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6.2 Construction of a Discrete Model |
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195 | (11) |
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6.3 The Construction of a Discrete Finite-Volume Model |
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206 | (23) |
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6.4 Discrete Model Research |
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229 | (1) |
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6.5 Results of Three-Dimensional Numerical Modeling and Their Analysis |
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230 | (11) |
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6.6 Discussion and Comparison of Results |
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241 | (4) |
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242 | (3) |
Conclusion |
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245 | (2) |
References |
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247 | (14) |
Index |
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261 | |