Analysis of Transient Conduction and Radiation Problems Using the Lattice Boltzmann and Discrete Ordinates Methods

Abstract

In this paper, the lattice Boltzmann method (LBM) and the discrete ordinates method (DOM) are coupled to solve transient conduction and radiation heat transfer problems. These are used to solve the energy equation and obtain the radiative heat source, respectively. To avoid additional interpolations between these two solvers when adding the radiative heat source to the energy equation, we propose using the same grid systems for both LBM and DOM. This is achieved by adopting a halfway bounce-back boundary scheme for LBM. This scheme is shown to be invalid in regard to solving 1D conduction problems with the D1Q2 lattice structure, while D1Q3 is shown to be correct and is adopted in this work. Good agreement with the available literature is obtained for both 1D and 2D conditions. The effects of conduction–radiation parameter and scattering albedo on the transient temperature distribution are presented and discussed. The method proposed in this study can readily solve combined conduction and radiation problems.