A pressure compensation method for lattice Boltzmann simulation of particle-laden flows in periodic geometries

Abstract

A simple and efficient boundary treatment is proposed for periodic boundary conditions in a lattice Boltzmann method for simulating fully developed, pressure driven particle-laden flows in a complex geometry. The pressure driven effect is implemented by a simple pressure compensation method (PCM) using the pressure difference between the inlet and outlet boundaries. It eliminates the exchange of nonequilibrium distribution functions between inlet and outlet boundary nodes. It also eliminates the nonphysical oscillations of particle trajectory produced by a nonequilibrium extrapolation method when particles cross the periodic boundary. Simulation results show that the present PCM is equivalent to the body force method (BFM) for flow in a periodic straight channel with a uniform cross section. However, the BFM would significantly underestimate the fluid velocity for a flow and, hence, cannot accurately predict the particle trajectory in a periodic complex channel with a nonuniform cross section, especially at high Reynolds numbers.