Application of the Lattice-Boltzmann Method to Sub-Continuum Heat Conduction

Abstract

The Lattice Boltzmann Method (LBM) is introduced in this paper as a method to simulate heat conduction across broad length scales in which continuum and sub-continuum effects exist. The paper describes the implementation of the method in both one and two dimensions. Results are presented for cases involving problems with existing solutions and show close agreement with both continuum and subcontinuum solutions of one-dimensional heat transfer through thin films. Results for a two-dimensional continuum problem agree with a known solution to within one percent. These results, combined with relative small computational effort, indicate that the LBM is a useful analysis tool for simulation of multiscale heat conduction.