Derivation and Analysis of Lattice Boltzmann Schemes for the Linearized Euler Equations

TL;DR

This paper derives second-order Lattice Boltzmann schemes for the Linearized Euler Equations in multiple dimensions, analyzes their stability, and validates their effectiveness through numerical experiments, aiming for future coupling with Navier-Stokes and finite volume methods.

Contribution

The paper introduces a novel derivation of second-order Lattice Boltzmann schemes for linearized Euler equations using an analytical Maxwellian, including stability analysis and numerical validation.

Findings

Schemes are second-order accurate in multiple dimensions

L2-stability of the schemes is established

Numerical results confirm the validity of the approach

Abstract

We derive Lattice Boltzmann (LBM) schemes to solve the Linearized Euler Equations in 1D, 2D, and 3D with the future goal of coupling them to an LBM scheme for Navier Stokes Equations and an Finite Volume scheme for Linearized Euler Equations. The derivation uses the analytical Maxwellian in a BGK model. In this way, we are able to obtain second-order schemes. In addition, we perform an $L^2$-stability analysis. Numerical results validate the approach.