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Full Description
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.
Contents
The Equations of Fluid Dynamics.- Notions on Hyperbolic Partial Differential Equations.- Some Properties of the Euler Equations.- The Riemann Problem for the Euler Equations.- Notions on Numerical Methods.- The Method of Godunov for Non-linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate-State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High-Order and TVD Methods for Scalar Equations.- High-Order and TVD Schemes for Non-linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi-Dimensional PDEs.- Multidimensional Test Problems.- Concluding Remarks.