Riemann Solvers and Numerical Methods for Fluid Dynamics : A Practical Introduction

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#x2014;linear Systems.- Random Choice and Related Methods.- Flux Vector Splitting Methods.- Approximate#x2014;State Riemann Solvers.- The HLL and HLLC Riemann Solvers.- The Riemann Solver of Roe.- The Riemann Solver of Osher.- High#x2013;Order and TVD Methods for Scalar Equations.- High#x2013;Order and TVD Schemes for Non#x2013;Linear Systems.- Splitting Schemes for PDEs with Source Terms.- Methods for Multi#x2013;Dimensional PDEs.- Multidimensional Test Problems.- FORCE Fluxes in Multiple Space Dimensions.- The Generalized Riemann Problem.- The ADER Approach.- Concluding Remarks.