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Generalized Riemann Problems in Computational Fluid Dynamics

$43.99 (C)

Part of Cambridge Monographs on Applied and Computational Mathematics

  • Date Published: July 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521173278

$ 43.99 (C)
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About the Authors
  • The primary goal of numerical simulation of compressible, inviscid time-dependent flow is to represent the time evolution of complex flow patterns. Developed by Matania Ben-Artzi and Joseph Falcovitz, the Generalized Riemann Problem (GRP) algorithm comprises some of the most commonly used numerical schemes of this process. This monograph presents the GRP methodology ranging from underlying mathematical principles through basic scheme analysis and scheme extensions. The book is intended for researchers and graduate students of applied mathematics, science and engineering.

    • Presents the relevant mathematical background along with systematic analysis of the GRP methods
    • Introduces basic mathematical concepts first in simpler scalar conservation laws, repeats the process for more general settings
    • Includes detailed 'construction' tables, allowing for the actual writing of suitable computer codes
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    Reviews & endorsements

    Review of the hardback: '… a welcome addition to the literature.' Journal of Fluid Mechanics

    Review of the hardback: '… book is well written, exhibits a nice balance between mathematics and fluid dynamics, and can serve as a reference work for GRP-based methods.' Zentralblatt fur Mathematik

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    Product details

    • Date Published: July 2011
    • format: Paperback
    • isbn: 9780521173278
    • length: 366 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.54kg
    • availability: Available
  • Table of Contents

    Preface
    List of figures
    1. Introduction
    Part I. Basic Theory:
    2. Scalar conservation laws
    Appendix A: entropy conditions for scalar conservation laws
    3. The GRP method for scalar conservation laws
    Appendix B: convergence of the Godunov scheme
    4. Systems of conservation laws
    Appendix C: Riemann solver for a y-law gas
    5. The generalized Riemann problem (GRP) for compressible fluid dynamics
    Appendix D: the MUSCL scheme
    6. Analytical and numerical treatment of fluid dynamical problems
    Part II. Numerical Implementation:
    7. From the GRP algorithm to scientific computing
    8. Geometric extensions
    9. A physical extension: reacting flow
    10. Wave interaction in a duct - a comparative study
    Bibliography
    Glossary
    Index.

  • Authors

    Matania Ben-Artzi, Hebrew University of Jerusalem

    Joseph Falcovitz, Hebrew University of Jerusalem

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