Riemann Solvers and Numerical Methods for Fluid Dynamics

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.
TOC: 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.