Recovering the full Navier Stokes equations with lattice Boltzmann schemes

TL;DR

This paper demonstrates how to recover the full thermal Navier-Stokes equations using lattice Boltzmann schemes with two particle distributions, focusing on stability and nonlinear wave simulations.

Contribution

It introduces a coupling method for dissipation coefficients in multi relaxation time lattice Boltzmann schemes to accurately model thermal fluid dynamics.

Findings

Successful simulation of nonlinear acoustic waves with shocks

Linear stability analysis guides dissipation coefficient coupling

Numerical results validate the scheme's effectiveness

Abstract

We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentum and dissipation of volumic entropy.Linear stability is taken into consideration to determine a coupling between two coefficients of dissipation.We present interesting numerical results for one-dimensional strong nonlinear acoustic waves with shocks.