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Other titles in the Cambridge Monographs on Applied and Computational Mathematics series:
Generalized Riemann Problems in Computatby Matania Ben-artzi
Synopses & Reviews
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.
The Generalized Riemann Problem (GRP) algorithm comprises common schemes of numerical simulation of compressible, inviscid time-dependent flow. This monograph, including examples illustrating the algorithm's applications, presents the GRP methodology beginning with its underlying mathematical principles. The book is accessible to researchers and graduate students of applied mathematics, science and engineering.
This monograph presents the GRP algorithm and is accessible to researchers and graduate students alike.
Includes bibliographical references (p. 337-343) and index.
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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