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Approximation of mono-dimensional hyperbolic systems: A lattice Boltzmann scheme as a relaxation method

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
266
Identifiers
DOI: 10.1016/j.jcp.2014.02.017
Keywords
  • Lattice Boltzmann Scheme
  • Relaxation Method
  • Hyperbolic System

Abstract

Abstract We focus on mono-dimensional hyperbolic systems approximated by a particular lattice Boltzmann scheme. The scheme is described in the framework of the multiple relaxation times method and stability conditions are given. An analysis is done to link the scheme with an explicit finite differences approximation of the relaxation method proposed by Jin and Xin. Several numerical illustrations are given for the transport equation, Burger's equation, the p-system, and full compressible Euler's system.

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