Abstract
In these notes we present an introduction to the theory of kinetic schemes for gas dynamics. Several ideas developed in recent years on stability and entropy analysis are reviewed. This compendium is intended to be self-contained and self-consistent even though some results are not entirely proved and a preliminary knowledge of elementary hyperbolic theory is supposed (cf Serre [28], Smoller [29], Lax [15]).
Several subjects are not treated: the modifications proposed by Prendergast & Xu [22], [31] and Deshpande [7] for improving accuracy, the early works by Brenier [1] and Giga & Miyakawa [9] on scalar equations, those of Kaniel [12] on gas dynamics with entropy conservation, discrete velocity schemes and the related subject of relaxation schemes.
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Perthame, B. (1999). An Introduction to Kinetic Schemes for Gas Dynamics. In: Kröner, D., Ohlberger, M., Rohde, C. (eds) An Introduction to Recent Developments in Theory and Numerics for Conservation Laws. Lecture Notes in Computational Science and Engineering, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58535-7_1
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