A central-moment multiple-relaxation-time collision model

TL;DR

This paper introduces a novel multiple relaxation time lattice Boltzmann model that assigns separate relaxation times to central moments, enhancing stability and accuracy in high-Reynolds number fluid simulations.

Contribution

It systematically assigns relaxation times to central moments and derives a stable, efficient LB model with correct hydrodynamics and improved numerical stability.

Findings

Accurate hydrodynamic equations via Chapman-Enskog analysis

Thermal diffusion and viscous dissipation are independent and Galilean invariant

High-Reynolds number simulations show excellent numerical stability

Abstract

We propose a multiple relaxation time Boltzmann equation collision model by systematically assigning a separate relaxation time to each of the central moments of the distribution function. The Chapman-Enskog calculation leads to correct hydrodynamic equations. The thermal diffusion and viscous dissipation are mutually independent and Galilean invariant. By transforming the central moments into the absolute reference frame and evaluating using fixed discrete velocities, an efficient lattice Boltzmann (LB) model is obtained. The LB model is found to have excellent numerical stability in high-Reynolds numbers simulations.