Discrete ellipsoidal statistical BGK model and Burnett equations

TL;DR

This paper introduces a discrete ES-BGK model for simulating non-equilibrium flows, capable of capturing Burnett level effects with flexible Prandtl number and a novel distribution recovery scheme.

Contribution

The paper develops a discrete ES-BGK model at Burnett level with two velocity models and a new distribution recovery method applicable to hydrodynamic equations.

Findings

Model verified through four benchmark tests.

Flexible Prandtl number implementation.

Effective distribution function recovery scheme.

Abstract

To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in Burnett level, two kinds of discrete velocity model are introduced; the relations between non-equilibrium quantities and the viscous stress and heat flux in Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, based on the Navier-Stokes, the Burnett equations, etc.