Discrete Rotational Symmetry, Moment Isotropy, and High Order Lattice Boltzmann Models

TL;DR

This paper explores the relationship between discrete rotational symmetry and moment isotropy in lattice Boltzmann models, providing a systematic way to develop higher order models for more accurate physical simulations.

Contribution

It introduces a geometric framework linking rotational symmetry to moment isotropy and offers a systematic method to construct higher order lattice Boltzmann models.

Findings

Moment isotropy is related to the rotational symmetry of vector sets.

The paper provides a systematic procedure for constructing higher order models.

Popular models are explained through geometric understanding.

Abstract

Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this paper, we present some basic results on moment isotropy and its relationship to the rotational symmetry of a generating discrete vector set. The anslysis provides a geometric understanding for popular lattice Boltzmann models, while offering a systematic procedure to construct higher order models.