Linear Analysis on Multiple-relaxation-time Lattice Boltzmann Method

TL;DR

This paper provides a linear analysis of the MRT Lattice Boltzmann method, deriving physically consistent schemes through eigenvalue decomposition and validating them via Navier-Stokes equivalence and simulations.

Contribution

It introduces a method to derive physically consistent MRT-LBM schemes using eigenvalue decomposition, improving the theoretical foundation and applicability.

Findings

Derived physically consistent MRT-LBM schemes

Validated schemes through Navier-Stokes equivalence

Confirmed effectiveness via numerical simulations

Abstract

The development of multiple-relaxation-time (MRT) Lattice Boltzmann method (LBM) is a significant contribution in improving the numerical behavior, revealing the math and physics mechanism and extending the application of LBM. However, some of the MRT schemes proposed previously are not physically-consistent. In this work, we take D2Q9 as a example to show how to derive physically-consistent MRT-LBM schemes by eigenvalue decomposition of the collision operator. In addition, the scheme is validated by the equivalence to Navier-Stokes equations and numerical simulations.