Nonequilibrium entropy limiters in lattice Boltzmann methods

R.A. Brownlee, A.N. Gorban and J. Levesley

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 2, 385-406

Abstract: We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity — nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy “trimming”) and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimation of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100×100 grid. All limiter constructions are applicable both for entropic and for non-entropic equilibria.

Keywords: Lattice Boltzmann method; Numerical regularisation; Entropy (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:2:p:385-406

DOI: 10.1016/j.physa.2007.09.031

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