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Approximation of mono-dimensional hyperbolic systems: a lattice Boltzmann scheme as a relaxation method. (English) Zbl 1310.76145
Summary: 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 S. Jin and Z. Xin [Commun. Pure Appl. Math. 48, No. 3, 235–276 (1995; Zbl 0826.65078)]. Several numerical illustrations are given for the transport equation, Burger’s equation, the p-system, and full compressible Euler’s system.

MSC:
76M28 Particle methods and lattice-gas methods
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