Numerical Method of Weakly Compressible Poiseuille Flow Using Lattice Boltzmann Method

Abstract

The present work focuses on the numerical simulation of isothermal and weakly compressible Poiseuille flow in a planar channel using the Lattice Boltzmann method with multiple times of relaxation (MRT-LBE) coupled to the Finite Difference method (FDM). The active fluid considered is the air under low Mach number assumption. The flow is two-dimensional, laminar and all the physical properties are constants except the density which varies in the sense of the Boussinesq approximation. The effects of the compressibility, the inclination angle and the Reynolds number on the dynamical and thermal fields are studied numerically. The results are presented in terms of streamlines, isotherms and transverse velocity.