Lattice Boltzmann Approach to High-Speed Compressible Flows

TL;DR

This paper introduces an enhanced lattice Boltzmann model capable of simulating high-speed compressible flows up to Mach 30, demonstrating stability and accuracy in benchmark tests and shock reflection simulations.

Contribution

It develops a flexible, stable lattice Boltzmann scheme for high-speed flows by incorporating a dissipation term and finite-difference scheme, extending applicability to supersonic regimes.

Findings

Works for Mach numbers up to 30

Accurately simulates Riemann problems with high pressure/density ratios

Successfully reproduces shock reflections

Abstract

We present an improved lattice Boltzmann model for high-speed compressible flows. The model is composed of a discrete-velocity model by Kataoka and Tsutahara [Phys. Rev. E \textbf{69}, 056702 (2004)] and an appropriate finite-difference scheme combined with an additional dissipation term. With the dissipation term parameters in the model can be flexibly chosen so that the von Neumann stability condition is satisfied. The influence of the various model parameters on the numerical stability is analyzed and some reference values of parameter are suggested. The new scheme works for both subsonic and supersonic flows with a Mach number up to 30 (or higher), which is validated by well-known benchmark tests. Simulations on Riemann problems with very high ratios ($1000:1$) of pressure and density also show good accuracy and stability. Successful recovering of regular and double Mach shock reflections shows the potential application of the lattice Boltzmann model to fluid systems where non-equilibrium processes are intrinsic. The new scheme for stability can be easily extended to other lattice Boltzmann models.