Stable simulation of fluid flow with high-Reynolds number using Ehrenfests' steps

TL;DR

This paper introduces a novel simulation approach for high-Reynolds number fluid flow using Ehrenfests' coarse-graining, leading to regularisers for lattice Boltzmann models that improve accuracy in standard test cases.

Contribution

It develops Ehrenfests' coarse-graining based regularisers for lattice Boltzmann models applicable to high-Reynolds flows, enhancing simulation stability and accuracy.

Findings

Effective simulation of shock tube test case.

Accurate modeling of flow past a square cylinder.

Regularisers improve high-Reynolds number flow simulations.

Abstract

The Navier--Stokes equations arise naturally as a result of Ehrenfests' coarse-graining in phase space after a period of free-flight dynamics. This point of view allows for a very flexible approach to the simulation of fluid flow for high-Reynolds number. We construct regularisers for lattice Boltzmann computational models. These regularisers are based on Ehrenfests' coarse-graining idea and could be applied to schemes with either entropic or non-entropic quasiequilibria. We give a numerical scheme which gives good results for the standard test cases of the shock tube and the flow past a square cylinder.