Riemann Solvers and Numerical Methods for Fluid Dynamics
Subtitle: A Practical Introduction
By: by Eleuterio F. Toro
Edition: 2nd Edition.
Publisher: Springer Berlin Heidelberg
Published: 1999
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 624
ISBN-13: 9783662039175; 9783662039151
Subjects: Mathematics; Engineering; Computer science; Hydraulic engineering
Description: This textbook gives a comprehensive and practical treatment of all existing Riemann solvers for compressible fluid dynamics and their use in the upwind method of Godunov and its high-order extensions. Related upwind methods of the Flux Vector Splitting type are also included, as are modern centred TVD methods. Methodologies for solving realistic problems in one, two and three space dimensions for both Cartesian and non-Cartesian geometries are presented in detail. Additional information is provided on further developments of the techniques and possible applications to practical problems in a variety of disciplines. A list of over 400 relevant references is given. The book is most useful for post-graduate students in Applied Mathematics, Engineering, Physics, Computing and other scientific disciplines such as Meteorology, Oceanography, Hydraulics and Chemistry, for example. It can be used as a means for self-study by academics and computational practioners in indusstry and research laboratories or as a teaching aid for postgraduate and final-year undergraduate courses on numerical methods etc.
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Table of contents: title: The Equations of Fluid Dynamics; title: Notions on Hyperbolic Partial Differential Equations; title: Some Properties of the Euler Equations; title: The Riemann Problem for the Euler Equations; title: Notions on Numerical Methods; title: The Method of Godunov for Non-linear Systems; title: Random Choice and Related Methods; title: Flux Vector Splitting Methods; title: Approximate-State Riemann Solvers; title: The HLL and HLLC Riemann Solvers; title: The Riemann Solver of Roe; title: The Riemann Solver of Osher; title: High-Order and TVD Methods for Scalar Equations; title: High-Order and TVD Schemes for Non-linear Systems; title: Splitting Schemes for PDEs with Source Terms; title: Methods for Multi-Dimensional PDEs; title: Multidimensional Test Problems; title: Concluding Remarks.