Improved angular discretization and error analysis of the lattice Boltzmann method for solving radiative heat transfer in a participating medium Antonio Fabio Di Rienzo, Pietro Asinari and Romano Borchiellini Politecnico di Torino, Torino, Italy, and Sunhash C. Mishra Indian Institute of Technology Guwahati, Guwahati, India 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. Keywords Radiation, Heat transfer, Modelling, Error analysis Paper type Research paper Nomenclature c ¼ speed of light c v ¼ specific heat at constant volume ~ e ¼ velocity on the lattice ~ E ¼ total velocity Err ¼ global error G ¼ incident radiation The current issue and full text archive of this journal is available at www.emeraldinsight.com/0961-5539.htm Sunhash C. Mishra gratefully acknowledges the support of the Politecnico di Torino under the Visiting Professor Program, which contributed to this work during his stay in Politecnico di Torino. HFF 21,5 640 Received 30 December 2009 Revised 24 April 2010 Accepted 28 October 2010 International Journal of Numerical Methods for Heat & Fluid Flow Vol. 21 No. 5, 2011 pp. 640-662 q Emerald Group Publishing Limited 0961-5539 DOI 10.1108/09615531111135873