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© 2015

Solving Hyperbolic Equations with Finite Volume Methods

Textbook

Part of the UNITEXT book series (UNITEXT, volume 90)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT, volume 90)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Basic Concepts and Examples of Environmental and Industrial Interest

    1. Front Matter
      Pages 1-1
    2. M. Elena Vázquez-Cendón
      Pages 3-18
    3. M. Elena Vázquez-Cendón
      Pages 19-33
    4. M. Elena Vázquez-Cendón
      Pages 53-54
  3. Finite Volume Methods Applied to the Hyperbolic Conservation Laws

    1. Front Matter
      Pages 55-55
  4. MATLAB Codes for the Studied Methods

    1. Front Matter
      Pages 129-129
    2. M. Elena Vázquez-Cendón
      Pages 131-147
    3. M. Elena Vázquez-Cendón
      Pages 149-178
    4. M. Elena Vázquez-Cendón
      Pages 179-181
  5. Back Matter
    Pages 183-188

About this book

Introduction

Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).

Keywords

Finite volume method Godunov mathod Hyperbolic problems Riemann solvers Upwind schemes

Authors and affiliations

  1. 1.Department of Applied MathematicsUniversity of Santiago de CompostelaSantiago de CompostelaSpain

About the authors

Prof. M. Elena Vázquez-Cendón, Department of Applied Mathematics, University of Santiago de Compostela, Spain.

Bibliographic information

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Reviews

“The book under review provides the background necessary to understand how these numerical methods work, as well as description and analysis of finite difference, upwind, and finite volume schemes and codes for several of the classic methods in common use. ... I recommend this text to advanced undergraduates … or to graduate students looking for a companion text to go with one of the weightier books on hyperbolic conservation laws. ... I will surely recommend this edition … .” (Donna Calhoun, SIAM Review, Vol. 59 (1), March, 2017)

“This book presents an introduction to finite volume methods for hyperbolic equations. It is designed as a textbook for Master's courses in mathematical engineering or industrial mathematics. … Each part of the book closes with a short biographical summary, on Peter Lax, Sergei K. Godunov and Eleuterio F. Toro, respectively.” (Raul Borsche, Mathematical Reviews, May, 2016)