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.

针对辐射传递方程（RTE），提出了一种新的多重弛豫时间（MRT）晶格玻尔兹曼模型。在本文中，讨论和实现仅限于灰色（与频率无关）的辐射传递方程。我们通过将RTE视为没有扩散项的特定对流扩散方程来建立该模型。构造了RTE的平衡分布函数，并通过弥散标度下的Maxwell迭代从晶格Boltzmann方程中严格导出RTE。进行了几种数值情况，包括一维，二维和三维瞬态和稳态情况。结果表明，该MRT格子Boltzmann模型对于解决参与介质中的瞬态和稳态辐射传递问题是准确而稳定的。此外，该模型还具有二阶精度和收敛速度。该模型可以进一步扩展到参与媒体中的各种辐射传输问题。