Riemann Solvers and Numerical Methods for Fluid Dynamics : A Practical Introduction - Toro, Eleuterio F.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009)
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.
Keywords: Mechanics; Mechanics, Applied; Mathematical physics; Numerical analysis; Fluids; Theoretical and Applied Mechanics; Theoretical, Mathematical and Computational Physics; Numerical Analysis; Fluid- and Aerodynamics