Computational Algorithms for Shallow Water Equations / by Eleuterio F. Toro.

Format:

Book

Author/Creator:

Toro, E. F., author.

Language:

English

Subjects (All):

Numerical analysis.

Fluid mechanics.

Engineering geology.

Geotechnical engineering.

Geophysics.

Numerical Analysis.

Engineering Fluid Dynamics.

Geoengineering.

Geotechnical Engineering and Applied Earth Sciences.

Local Subjects:

Numerical Analysis.

Engineering Fluid Dynamics.

Geoengineering.

Geotechnical Engineering and Applied Earth Sciences.

Geophysics.

Physical Description:

1 online resource (413 pages)

Edition:

2nd ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

This book is a thoroughly revised and enlarged version of “Shock-capturing methods for free-surface shallow flows", first published by Wiley and Sons, 2001. The book describes mathematically free-surface flows through partial differential equations and includes modern shock-capturing methods to solve them, with strong emphasis on finite volume upwind and centred methods. Such equations and methods are fundamental in simulating shallow water flows but also atmospheric flows, dispersion of dense gases and the dynamics of mixtures of materials. The book is accompanied by numerical software in the form of sample computer programs as supplementary material. In this new edition, additional sections have been introduced to existing chapters. Also, new chapters have been included; one contains a review of the mathematics of hyperbolic partial differential equations, another introduces the numerical analysis of partial differential equations and another one deals with advanced very-high order numerical methods in the finite volume and discontinuous Galerkin frameworks. Furthermore, comprehensive modifications and corrections have been made throughout various sections of the text, and numerous figures depicting numerical results have been enhanced. This book is primarily intended for environmental scientists, applied mathematicians and engineers in academia, research laboratories, industry and consultancy organisations. Senior undergraduate and postgraduate students involved with mathematical modelling and computational methods for environmental problems will benefit from studying this book. Lecturers could use most of the material for courses on numerical methods for wave propagation problems in hydraulics, oceanography, atmospherics and other geophysical fluid dynamics contexts.

Contents:

The Shallow Water Equations

Notions on Hyperbolic Equations

Linear Shallow Water Equations

Properties of the Nonlinear Equations

Elementary Waves in Shallow Water

Exact Riemann Solver: Wet Bed

Exact Riemann Solver: Dry Bed

Tests with Exact Solution

Notions on Numerical Methods

First-Order Methods for Systems

Approximate Riemann Solvers

Second-Order Non-Linear Methods

Sources and Multidimensions

Ader High-Order Methods

Dam-Break Modelling

Mach Reflection in Tsunamis

Concluding Remarks.

Notes:

Includes bibliographical references and index.

Other Format:

Print version: Toro, Eleuterio F. Computational Algorithms for Shallow Water Equations

ISBN:

9783031613951