Stabilization of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea

The lattice Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modeling complex fluid flow. However, it is acknowledged that the method can demonstrate numerical instabilities, e.g., in the vicinity of shocks. W...

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Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 74; no. 3 Pt 2; p. 037703
Main Authors Brownlee, R A, Gorban, A N, Levesley, J
Format Journal Article
LanguageEnglish
Published United States 01.09.2006
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Summary:The lattice Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modeling complex fluid flow. However, it is acknowledged that the method can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We propose a simple technique to stabilize the LBM by monitoring the difference between microscopic and macroscopic entropy. Populations are returned to their equilibrium states if a threshold value is exceeded. We coin the name Ehrenfests' steps for this procedure in homage to the vehicle that we use to introduce the procedure, namely, the Ehrenfests' coarse-graining idea.
ISSN:1539-3755
DOI:10.1103/PhysRevE.74.037703