Improved angular discretization and error analysis of the lattice Boltzmann method for solving radiative heat transfer in a participating medium

Abstract

Purpose

The purpose of this paper is to present and validate some improvements to the lattice Boltzmann method (LBM) for solving radiative heat transfer in a participating medium. Validation of the model is performed by investigating the effects of spatial and angular discretizations and extinction coefficient on the solution. The error analysis and the order of convergence of the scheme are also reported.

Design/methodology/approach

LB scheme is derived from the radiative transfer equation, where isotropic scattering and radiative equilibrium condition are assumed. Azimuthal angle is discretized according to the lattice velocities on the computational plane, while, concerning the polar angle, an additional component of the discrete velocity normal to the plane is introduced. Radiative LB scheme is used to solve a 2‐D square enclosure benchmark problem. In order to validate the model, results of LB scheme are compared with a reference solution obtained through a Richardson extrapolation of the results of a standard finite volume method.

Findings

The proposed improvements drastically increase the accuracy of the previous method. Radiative LB scheme is found to be (at most) first order accurate. Numerical results show that solution gets more accurate when spatial and azimuthal angle discretizations are improved, but a saturation threshold exists. With regard to polar angle, minimum error occurs when a particular subdivision is considered.

Originality/value

The paper provides simple but effective improvements to the recently proposed lattice Boltzmann method for solving radiative heat transfer in a participating medium.

Citation

Fabio Di Rienzo, A., Asinari, P., Borchiellini, R. and Mishra, S.C. (2011), "Improved angular discretization and error analysis of the lattice Boltzmann method for solving radiative heat transfer in a participating medium", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 5, pp. 640-662. https://doi.org/10.1108/09615531111135873