Godunov-type Schemes book cover

Godunov-type Schemes

An Introduction for Engineers

Godunov-type schemes appear as good candidates for the next generation of commercial modelling software packages, the capability of which to handle discontinuous solution will be a basic requirement. It is in the interest of practising engineers and developers to be familiar with the specific features of discontinuous wave propagation problems and to be aware of the possibilities offered by Godunov-type schemes for their solution.

This book aims to present the principles of such schemes in a way that is easily understandable to practising engineers.The features of hyperbolic conservation laws and their solutions are presented in the first two chapters. The principles of Godunov-type schemes are outlined in a third chapter. Chapters 4 and 5 cover the application of the original Godunov scheme to scalar laws and to hyperbolic systems of conservation laws respectively. Chapter 6 is devoted to higher-order schemes in one dimension of space. The design of such a scheme is described for the general case and applied to some well-known schemes such as the MUSCL and PPM schemes. Chapter 7 focuses on multidimensional problems. The classical alternate directions and finite volume approaches are presented together with the wave splitting technique that is described in depth with an application to two-dimensional systems. Chapter 8 deals with large-time step algorithms. These include front tracking-based methods, explicit-implicit techniques and the time-line interpolation technique. Three appendices provide notions on accuracy and stability issues, Riemann solvers and the user instructions for the computational codes provided in the enclosed CD-ROM.

Hardbound, 508 pages

Published: January 2003

Imprint: Elsevier

ISBN: 978-0-444-51155-3

Reviews

  • ...This is, quite simply, a remarkable book. It has admirably achieved its objective as articulated by the author at the opening to the concluding chapter: "The purpose of the present book was to introduce the basics of Godunov-type schemes to the engineering public". The unassuming succinctness, brevity, and clarity of this statement are characteristic of the entire work. ...Once the author has had a chance to catch his breath after the considerable effort devoted to this book, one hopes that he will consider authoring a second edition that could include chapters devoted to practical issues such as incorporation of hydraulic works in channels, and mobile-bed hydraulics, in the context of Godunov-type schemes.
    F.M. Holly Jr., Journal of Hydraulic Research

Contents

  • Preface. Acknowledgements. Notation. 1. Scalar conservation laws. 2. Hyperbolic systems of conservation laws. 3. An outline of Godunov-type schemes. 4. The Godunov method for scalar laws in one dimension. 5. The Godunov method for systems of conservation laws. 6. Higher-order schemes. 7. Multidimensional schemes. 8. Large-time-step algorithms. 9. Concluding remarks. Appendix A. Notions in mathematics. Appendix B. Riemann solvers. Appendix C. Sample codes. References. Index.

Advertisement

advert image