# Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves

## TL;DR

This paper analyzes a lattice Boltzmann method for simulating linear acoustic waves, comparing different collision operators and lattice models, and demonstrating its efficiency and accuracy in heterogeneous media.

## Contribution

It introduces a detailed dispersion relation analysis for LB models and implements a grid-refinement algorithm, showing LB's competitiveness with finite-difference schemes.

## Key findings

- D2Q5 lattice is most suitable for linear acoustics
- LB scheme performance is comparable to finite-difference methods
- LB method is efficient for complex geometries and parallel computing

## Abstract

We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time (MRT) collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes. Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.