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Generalized Riemann Problems in Computational Fluid Dynamics

Part of Cambridge Monographs on Applied and Computational Mathematics

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


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About the Authors
  • Numerical simulation of compressible, inviscid time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate representation of the time evolution of complex flow patterns, involving interactions of shocks, interfaces, and rarefaction waves. The Generalized Riemann Problem (GRP) algorithm, developed by the authors for this purpose, provides a unifying 'shell' which comprises some of the most commonly used numerical schemes of this process. This monograph gives a systematic presentation of the GRP methodology, starting from the underlying mathematical principles, through basic scheme analysis and scheme extensions (such as reacting flow or two-dimensional flows involving moving or stationary boundaries). An array of instructive examples illustrates the range of applications, extending from (simple) scalar equations to computational fluid dynamics. Background material from mathematical analysis and fluid dynamics is provided, making the book accessible to both 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

    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

  • Authors

    Matania Ben-Artzi, Hebrew University of Jerusalem

    Joseph Falcovitz, Hebrew University of Jerusalem

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