Multiple-relaxation-time lattice Boltzmann model for compressible fluids

TL;DR

This paper introduces an energy-conserving multiple-relaxation-time lattice Boltzmann model for simulating compressible flows with strong shocks, demonstrating improved stability and accuracy over previous models.

Contribution

A novel 16-discrete-velocity lattice Boltzmann model based on group theory for better simulation of compressible flows with shocks.

Findings

Successfully simulates strong shock compressible flows

Outperforms single-relaxation-time models in stability and accuracy

Validated with various shock and bubble interaction benchmarks

Abstract

We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. This model is based on a 16-discrete-velocity model. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The used benchmark tests include (i) shock tubes, such as the Sod, Lax, Sjogreen, Colella explosion wave and collision of two strong shocks, (ii) regular and Mach shock reflections, and (iii) shock wave reaction on cylindrical bubble problems. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version.