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

Abstract

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 highReynolds 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.

Stabilization of the Lattice Boltzmann Method Using Information Theory

“…The EF-LBM collision rule equips the LBM with an entropy limiter which monitors the simulation for lattice points at which some type of local entropic criteria is violated [42]. This approach has been shown to be successful in reducing instabilities in 1-D shock tube [39,40,42,45,60,61] and 2D lid driven cavity flow [45] simulations.…”

“…It should be noted that this form of the discretized entropy is the frequently used form of the discretized entropy used in some LBM simulations ( [28,39,40,45,61,66,67] for example).…”