Entropy and weak solutions in the LBGK model

TL;DR

This paper develops entropy functions for the Lattice Boltzmann method to better recover Euler-like equations, supported by numerical examples demonstrating the theoretical findings.

Contribution

It introduces new entropy functions tailored for the LBGK model to improve the derivation of Euler-like equations.

Findings

Entropy functions compatible with LBGK model derived

Numerical examples confirm theoretical predictions

Enhanced understanding of entropy in Lattice Boltzmann methods

Abstract

In this paper, we derive entropy functions whose local equilibria are suitable to recover the Euler-like equations in the framework of the Lattice Boltzmann method. Numerical examples are also given, which are consistent with the above theoretical arguments.