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Generalized Riemann Problems in Computational Fluid Dynamics

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Generalized Riemann Problems in Computational Fluid Dynamics

Generalized Riemann Problems in Computational Fluid Dynamics

Matania Ben-Artzi, Hebrew University of Jerusalem
Joseph Falcovitz, Hebrew University of Jerusalem
July 2011
Paperback
9780521173278
    Description

    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

    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

    See more reviews

    Product details

    July 2011
    Paperback
    9780521173278
    366 pages
    229 × 152 × 21 mm
    0.54kg
    Available

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    Contents

    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.
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