Dominique d'Humières, Irina Ginzburg, Manfred Krafczyk, Pierre Lallemand and Li-Shi Luo

Multiple-Relaxation-Time Lattice Boltzmann Models in Three Dimensions, Phil. Trans. R. Soc. A, 360, 437-451

This article features an overview of the probably most commonly used Multiple-Relaxation-Time (MRT) model. In this model, the relaxation times of the ghost modes are given by ad-hoc numerical values. These values are derived from a linear stability analysis, and are mentioned explicitly in the article. The presented models are extensions of the “incompressible lattice Boltzmann” scheme. In stationary flows, they exhibit therefore a smaller compressibility error than fully compressible schemes (such as BGK). On the other hand, they have lost the ability of the BGK and related models to simulate weakly compressible flows. The article is implementation-oriented and delivers all required information to write a MRT code.

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