A Novel Velocity Discretization for Lattice Boltzmann Method: Application to Compressible Flow

TL;DR

This paper introduces a new velocity discretization technique for the Lattice Boltzmann Method that improves its application to compressible flows by accurately capturing the necessary moments of the Maxwell-Boltzmann distribution.

Contribution

The paper presents a novel velocity discretization approach using a bump function, enabling LBM to better simulate compressible fluid dynamics.

Findings

Successfully recovers macroscopic equations for compressible fluids

Validates the method with benchmark simulations

Enhances LBM applicability to high-speed flows

Abstract

The Lattice Boltzmann Method (LBM) has emerged as a powerful tool in computational fluid dynamics and material science. However, standard LBM formulation imposes some limitations on the applications of the method, particularly compressible fluids. In this paper, we introduce a new velocity discretization method to overcome some of these challenges. In this new formulation, the particle populations are discretized using a bump function that has a mean and a variance. This introduces enough independent degrees of freedom to set the equilibrium moments to the moments of Maxwell-Boltzmann distribution up to and including the third moments. Consequently, the correct macroscopic fluid dynamics equations for compressible fluids are recovered. We validate our method using several benchmark simulations.