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Numerical Approximation of Hyperbolic Systems of Conservation Laws

  • Book
  • © 2021

Overview

Authors:
  1. Edwige Godlewski

    1. Laboratoire Jacques-Louis Lions, Sorbonne University, Paris, France

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    You can also search for this author in PubMed   Google Scholar

  2. Pierre-Arnaud Raviart

    1. Laboratoire Jacques-Louis Lions, Sorbonne University, Paris, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Revised version which completes the first 1996 publication
  • Presents the state of the art concerning finite volume methods
  • More examples and details added
  • An expanding field
  • Excellent up-to-date review of the current research trends in this area
  • Rigorous theoretical framework for the numerical approximation of nonlinear hyperbolic systems of conservation laws by finite volume methods with emphasis on fluid models in the context of compressible flows

Part of the book series: Applied Mathematical Sciences (AMS, volume 118)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 1-53

  3. Nonlinear Hyperbolic Systems in One Space Dimension

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 55-139

  4. Gas Dynamics and Reacting Flows

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 141-213

  5. Finite Volume Schemes for One-Dimensional Systems

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 215-423

  6. The Case of Multidimensional Systems

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 425-579

  7. An Introduction to Boundary Conditions

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 581-625

  8. Source Terms

    • Edwige Godlewski, Pierre-Arnaud Raviart
    Pages 627-747

  9. Back Matter

    Pages 749-840
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Keywords

About this book

This monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors. Since the earlier work concentrated on the mathematical theory of multidimensional scalar conservation laws, this book will focus on systems and the theoretical aspects which are needed in the applications, such as the solution of the Riemann problem and further insights into more sophisticated problems, with special attention to the system of gas dynamics. This new edition includes more examples such as MHD and shallow water, with an insight on multiphase flows. Additionally, the text includes source terms and well-balanced/asymptotic preserving schemes, introducing relaxation schemes and addressing problems related to resonance and discontinuous fluxes while adding details on the low Mach number situation.

Authors and Affiliations

  • Laboratoire Jacques-Louis Lions, Sorbonne University, Paris, France

    Edwige Godlewski, Pierre-Arnaud Raviart

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