Godunov-type Schemes
：An Introduction for Engineers
Publication subTitle ：An Introduction for Engineers
Publisher： Elsevier Science
Publication year： 2003
E-ISBN: 9780080532585
P-ISBN(Paperback): 9780444511553
P-ISBN(Hardback): 9780444511553
Subject： O241 数值分析;O35 hydrodynamics
Language： ENG
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Description
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 tech
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