Increasing stability and accuracy of the lattice Boltzmann scheme: recursivity and regularization

TL;DR

This paper introduces a regularized lattice Boltzmann scheme that improves stability and accuracy for high Reynolds number flows by using a recursive regularization based on Hermite series expansion.

Contribution

The paper presents a novel regularization procedure for a single-relaxation-time lattice Boltzmann scheme, enhancing stability and accuracy over existing models.

Findings

Enhanced dispersion and dissipation relations shown by stability analysis.

Validated on 2D and 3D high Reynolds number simulations.

Outperforms MRT models in accuracy and stability.

Abstract

In the present paper a lattice Boltzmann scheme is presented which exhibits an increased stability and accuracy with respect to standard single- or multi-relaxation-time (MRT) approaches. The scheme is based on a single-relaxation-time model where a special regularization procedure is applied. This regularization is based on the fact that, for a-thermal flows, there exists a recursive way to express the velocity distribution function at any order (in the Hermite series sense) in terms of the density, velocity, and stress tensor. A linear stability analysis is conducted which shows enhanced dispersion/dissipation relations with respect to existing models. The model is then validated on two (one 2D and one 3D) moderately high Reynolds number simulations ($\mathrm{Re}\sim 1000$) at moderate Mach numbers ($\mathrm{Ma}\sim 0.5$). In both cases the results are compared with an MRT model and an enhanced accuracy and stability is shown by the present model.