Lattice Boltzmann methods with anisotropic equilibrium distributions.

Authors

Benjamin Kellers, Julius Weinmiller, Arnulf Latz, Timo Danner

Published in

Physical review. E. Volume 114. Issue 3-2. Pages 035307.

Abstract

Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a full derivation of the resulting lattice Boltzmann method. We ensure that our method correctly reproduces macroscopic behavior via Chapman-Enskog analysis for a single-relaxation time collision operator. As a result, we are able to show that a properly discretized anisotropic Maxwell-Boltzmann equilibrium does macroscopically in fact lead to an anisotropic variation of the Navier-Stokes equations. All desired properties of lattice Boltzmann methods, such as locality of the collision operator, isotropic discrete position and velocity space, or mass and momentum conservation are retained. While it is explicitly shown in the context of fluid flow, the presented scheme is straightforward to adopt to advection-diffusion problems.

PMID:
42888822
Bibliographic data and abstract were imported from PubMed on 17 Oct 2026.

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