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Riemann Solvers and Numerical Methods for Fluid Dynamics

A Practical Introduction

  • Book
  • © 1999

Overview

Authors:
  1. Eleuterio F. Toro

    1. Department of Computing and Mathematics, Manchester Metropolitan University, Manchester, UK

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  • Comprehensive treatment of subject, practical approach given in details
  • Useful in practice
  • Self-contained presentation of methods

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XIX
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  2. The Equations of Fluid Dynamics

    • Eleuterio F. Toro
    Pages 1-40

  3. Notions on Hyperbolic Partial Differential Equations

    • Eleuterio F. Toro
    Pages 41-85

  4. Some Properties of the Euler Equations

    • Eleuterio F. Toro
    Pages 87-113

  5. The Riemann Problem for the Euler Equations

    • Eleuterio F. Toro
    Pages 115-162

  6. Notions on Numerical Methods

    • Eleuterio F. Toro
    Pages 163-212

  7. The Method of Godunov for Non-linear Systems

    • Eleuterio F. Toro
    Pages 213-235

  8. Random Choice and Related Methods

    • Eleuterio F. Toro
    Pages 237-264

  9. Flux Vector Splitting Methods

    • Eleuterio F. Toro
    Pages 265-291

  10. Approximate-State Riemann Solvers

    • Eleuterio F. Toro
    Pages 293-313

  11. The HLL and HLLC Riemann Solvers

    • Eleuterio F. Toro
    Pages 315-339

  12. The Riemann Solver of Roe

    • Eleuterio F. Toro
    Pages 341-372

  13. The Riemann Solver of Osher

    • Eleuterio F. Toro
    Pages 373-407

  14. High-Order and TVD Methods for Scalar Equations

    • Eleuterio F. Toro
    Pages 409-488

  15. High-Order and TVD Schemes for Non-Linear Systems

    • Eleuterio F. Toro
    Pages 489-525

  16. Splitting Schemes for PDEs with Source Terms

    • Eleuterio F. Toro
    Pages 527-538

  17. Methods for Multi-Dimensional PDEs

    • Eleuterio F. Toro
    Pages 539-579

  18. Multidimensional Test Problems

    • Eleuterio F. Toro
    Pages 581-592

  19. Concluding Remarks

    • Eleuterio F. Toro
    Pages 593-598

  20. Back Matter

    Pages 599-624
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Keywords

About this book

High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.

Authors and Affiliations

  • Department of Computing and Mathematics, Manchester Metropolitan University, Manchester, UK

    Eleuterio F. Toro

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