Unstructured lattice Boltzmann model for radiative transfer in homogeneous media

In the past decades, the lattice Boltzmann method (LBM) has been a great success in convection and heat conduction. Recently, based on its advanced numerical properties, LBM has some progress in radiative transfer. Some lattice Boltzmann (LB) models for radiative transfer have been established successively. However, all these LB models for radiative transfer are standard LB models which are limited to uniform Cartesian grids. The unstructured LB model for radiative transfer is still lacking. The unstructured model is important for radiative transfer problems in complex geometric enclosures. Developing an unstructured LB model for radiative transfer is of great significance. This paper proposes an unstructured LB model for radiative transfer in homogeneous media. We establish this model by using the Chapman-Enskog (CE) analysis and the finite volume discretization. In this model, the equilibrium distribution function is reconstructed on interfaces of unstructured grids. Through the CE analysis, we rigorously derive the radiative transfer equation (RTE) from the proposed unstructured LB model. Several numerical cases are conducted to test the performance of the unstructured LB model. Numerical results show that the present unstructured LB model is stable and accurate for solving steady and transient radiative transfer in homogeneous media with complex geometries. Besides, the proposed unstructured LB model can greatly reduce the computational time compared to the standard LB model due to eliminating the streaming process on the uniform lattice.