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Book Description:

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Synopsis:

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

Table of Contents:

Preface to the First Edition
1: The Equations of Fluid Dynamics
2: Notions on Hyperbolic Partial Differential Equations
3: Some Properties of the Euler Equations
4: The Riemann Problem for the Euler Equations
5: Notions on Numerical Methods
6: The Method of Godunov for Non-linear Systems7: Random Choice and Related Methods
8: Flux Vector Splitting Methods
9: Approximate-State Riemann Solvers
10: The HLL and HLLC Riemann Solvers
11: The Riemann Solver of Roe
12: The Riemann Solver of Osher
13: High-Order and TVD Methods for Scalar Equations
14: High-Order and TVD Schemes for Non-Linear Systems
15: Splitting Schemes for PDEs with Source Terms
16: Methods for Multi-Dimensional PDEs
17: Multidimensional Test Problems
18: Concluding Remarks
References
Index