High Order Numerical Schemes for Lattice Boltzmann Models: Applications to Flow With Variable Knudsen Number

摘要

Lattice Boltzmann (LB) models are effective for problems where both mesoscopic dynamics and microscopic statistics become important, as in the case of microchannel flows. In this report, we investigate the applications of the two-dimensional (2D) thermal finite difference Lattice Boltzmann (FDLB) model appropriate boundary conditions. Two separate cases were considered: the pressure-driven case and the external force-driven case. A characteristics of the Lattice Boltzmann model is the recovery of the density, temperature, velocity and pressure fields from the local values of the discretized set of distribution functions, whose evolution is governed by the Boltzmann equation, which is easier to manage than the Navier-Stokes or Burnett equations. Entrance and exit effects are present in the pressure-driven case and are clearly seen especially in the longitudinal temperature and velocity profiles when the fluid flows in a short channel. In long channels, the non-linear pressure profile along the center line, the rarefaction effects, as well as the existence of the so-called Knudsen minimum in the plot of mass flow rate vs. Knudsen number were found to be in good agreement with literature results.