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Shock-Capturing Methods for Free-Surface Shallow Flows

Eleuterio Francisco Toro

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Abstract

Preface. Introduction. The Shallow Water Equations. Properties of the Equations. Linearised Shallow Water. Exact Riemann Solver: Wet Bed. Exact Riemann Solver: Dry Bed. Tests with Exact Solution. Basics on Numerical Methods. First-Order Methods. Approximate Riemann Solvers. TVD Methods. Sources and Multi-Dimensions. Dam-Break Modelling. Mach Reflection of Bores. Concluding Remarks. References. Index.

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What this paper is about

Preface. Introduction. The Shallow Water Equations. Properties of the Equations. Linearised Shallow Water. Exact Riemann Solver: Wet Bed. Exact Riemann Solver: Dry Bed. Tests with Exact Solution. Basics on Numerical Methods. First-Order Methods. Approximate Riemann Solvers. TVD Methods. Sources and Multi-Dimensions. Dam-Break Modelling. Mach Reflection of Bores. Concluding Remarks. References. Index.

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Available abstract

Preface. Introduction. The Shallow Water Equations. Properties of the Equations. Linearised Shallow Water. Exact Riemann Solver: Wet Bed. Exact Riemann Solver: Dry Bed. Tests with Exact Solution. Basics on Numerical Methods. First-Order Methods. Approximate Riemann Solvers. TVD Methods. Sources and Multi-Dimensions. Dam-Break Modelling. Mach Reflection of Bores. Concluding Remarks. References. Index.

Key concepts: Riemann solver, Riemann problem, Shallow water equations, Solver, Riemann hypothesis, Mach reflection, Waves and shallow water, Roe solver

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