Two-Dimensional Lattice Boltzmann Model For Compressible Flows With High Mach Number

TL;DR

This paper introduces an enhanced lattice Boltzmann model capable of accurately simulating high Mach number compressible flows, effectively reducing numerical oscillations and ensuring stability for shock wave analysis.

Contribution

The paper develops a novel lattice Boltzmann model combining a modified finite difference scheme and artificial viscosity for high Mach number compressible flows.

Findings

Successfully simulated Mach numbers up to 20 or higher

Reduced numerical oscillations at discontinuities

Maintained stability and accuracy in shock wave simulations

Abstract

In this paper we present an improved lattice Boltzmann model for compressible Navier-Stokes system with high Mach number. The model is composed of three components: (i) the discrete-velocity-model by Watari and Tsutahara [Phys Rev E \textbf{67},036306(2003)], (ii) a modified Lax-Wendroff finite difference scheme where reasonable dissipation and dispersion are naturally included, (iii) artificial viscosity. The improved model is convenient to compromise the high accuracy and stability. The included dispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the scheme to satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In our numerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitable for tracking shock waves with high accuracy and for investigating nonlinear nonequilibrium complex systems.