Lattice Boltzmann method for incompressible flows with large pressure gradients

Abstract

Conventional lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models can simulate incompressible flows correctly only if the Mach number $M$ and the density variation $\delta \rho$ are negligibly small. However, the equation of state $p=RT\rho$ resulting from the conventional models limits their application to incompressible flows with a rather small pressure gradient. In this paper, based on the Enskog equation, we propose a finite difference lattice BGK model for isothermal incompressible flows with the resulting equation of state and transport properties suitable for nonideal fluids. We validated this model by simulating the plane Poiseuille flow, the two dimensional Womersley flow, and the backward-facing step flow and found that the numerical results obtained by the proposed model are more accurate than those by the conventional LBGK models when the pressure gradient imposed on the flows increases.