A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows

Abstract

A lattice Boltzmann model for simulating isothermal micro flows has been proposed by us recently [Niu XD, Chew YT, Shu C. A lattice Boltzmann BGK model for simulation of micro flows. Europhys Lett 2004;67(4):600]. In this paper, we extend the model to simulate the micro thermal flows. In particular, the thermal lattice Boltzmann equation (TLBE) [He X, Chen S, Doolen GD. A novel thermal model for the lattice Boltzmann method in incompressible limit. J Comput Phys 1998;146:282] is used with modification of the relaxation times linking to the Knudsen number. The diffuse scattering boundary condition (DSBC) derived in our early model is extended to consider temperature jump at wall boundaries. Simple theoretical analyses of the DSBC are presented and the results are found to be consistent with the conventional velocity slip and temperature jump boundary conditions. Numerical validations are carried out by simulating two-dimensional thermal Couette flows and developing thermal flows in a microchannel, and the obtained results are found to be in good agreement with those given from the direct simulation Monte Carlo (DSMC), the molecular dynamics (MD) approaches and the Maxwell theoretical prediction. © 2006 Elsevier Ltd. All rights reserved.