A Simple Method to Construct Local Equilibrium Function for One Dimensional Lattice Boltzmann Method

TL;DR

This paper introduces a straightforward approach to construct local equilibrium functions for one-dimensional lattice Boltzmann methods, enabling accurate simulation of compressible flows with variable specific heat ratios.

Contribution

The paper presents a novel, simple method for constructing local equilibrium functions in 1D LBM that accommodates compressible flows with flexible specific heat ratios.

Findings

Favorable results in Sod and Lax flow tests.

Method successfully models compressible flows with variable specific heat.

Potential for broader application in 1D LBM simulations.

Abstract

We have developed a simple method to construct local equilibrium function for one dimensional lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one dimensional Sod flow and one dimensional Lax flow are presented. Favorable results are obtained using proposed new method, indicating that the proposed method is potentially capable of constructing of the local equilibrium function for one dimensional LBM.