Three-Dimensional Lattice Boltzmann Model for High-Speed Compressible Flows

TL;DR

This paper introduces a new 3D Lattice Boltzmann model for high-speed compressible flows that improves stability and accuracy, validated through classical shock and droplet interaction benchmarks.

Contribution

The paper develops a stable, high-speed 3D LB model using the NND scheme and additional dissipation, extending previous models for better shock capturing.

Findings

Successfully simulates flows from subsonic to supersonic speeds.

Accurately captures shock wave jumps and interactions.

Matches well with exact and reported solutions.

Abstract

A highly efficient three-dimensional (3D) Lattice Boltzmann (LB) model for high speed compressible flows is proposed. This model is developed from the original one by Kataoka and Tsutahara[Phys. Rev. E 69, 056702 (2004)]. The convection term is discretized by the Non-oscillatory, containing No free parameters and Dissipative (NND) scheme, which effectively damps oscillations at discontinuities. To be more consistent with the kinetic theory of viscosity and to further improve the numerical stability, an additional dissipation term is introduced. Model parameters are chosen in such a way that the von Neumann stability criterion is satisfied. The new model is validated by well-known benchmarks, (i) Riemann problems, including the problem with Lax shock tube and a newly designed shock tube problem with high Mach number; (ii) reaction of shock wave on droplet or bubble. Good agreements are obtained between LB results and exact ones or previously reported solutions. The model is capable of simulating flows from subsonic to supersonic and capturing jumps resulted from shock waves.