Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number

TL;DR

This paper introduces a novel multiple-relaxation-time lattice Boltzmann method capable of simulating high-Mach compressible flows with adjustable specific heat ratio and Prandtl number, validated through shock simulations.

Contribution

It develops a new lattice Boltzmann scheme based on a 16-velocity model that accurately recovers compressible Navier-Stokes equations with flexible thermodynamic properties.

Findings

Simulates compressible flows with Mach numbers up to 5.

Successfully models flows with strong shocks.

Recovers classical equations in the continuum limit.

Abstract

A new multiple-relaxation-time lattice Boltzmann scheme for compressible flows with arbitrary specific heat ratio and Prandtl number is presented. In the new scheme, which is based on a two-dimensional 16-discrete-velocity model, the moment space and the corresponding transformation matrix are constructed according to the seven-moment relations associated with the local equilibrium distribution function. In the continuum limit, the model recovers the compressible Navier-Stokes equations with flexible specific-heat ratio and Prandtl number. Numerical experiments show that compressible flows with strong shocks can be simulated by the present model up to Mach numbers $Ma \sim 5$.