A multiple-relaxation-time lattice Boltzmann model for radiative transfer equation

A novel multiple-relaxation-time (MRT) lattice Boltzmann model is proposed for the radiative transfer equation (RTE). In this paper, the discussion and implementation are restricted to the grey (frequency-independent) radiative transfer equation. We establish this model by regarding the RTE as a particular convection–diffusion equation without the diffusion term. The equilibrium distribution function for the RTE is constructed, and the RTE is rigorously derived from the lattice Boltzmann equation via the Maxwell iteration under the diffusive scaling. Several numerical cases are conducted, including one-dimensional, two-dimensional and three-dimensional transient and steady cases. Results demonstrate that this MRT lattice Boltzmann model is accurate and stable for solving transient and steady radiative transfer problems in participating media. Besides, the second-order accuracy and convergence rate are observed for this model. This model may be further extended to various radiative transfer problems in participating media.