Lattice Boltzmann model on unstructured grids for radiative transfer in graded-index media

Abstract

The lattice Boltzmann method (LBM) has already been extended to radiative transfer. Radiative transfer in graded-index media is of great interest in many practical processes and is particularly challenging to solve. Currently, some lattice Boltzmann (LB) models have been developed for radiative transfer in graded-index media. These LB models are limited to uniform Cartesian grids and only applicable to simple geometries, thus limiting its application to practical processes. Here we develop a LB model on unstructured grids for radiative transfer in graded-index media. We adopt the relationship between the equilibrium distribution function and the radiative intensity in the standard LB model to establish this LB model on unstructured grids. In this unstructured LB model, the key is that the equilibrium distribution function is reconstructed on the interface of the unstructured grids. This unstructured LB model can solve the radiative transfer equation of graded-index media directly without using the streaming process on each lattice, thus significantly shortening the computational time compared to the standard LB model. This unstructured LB model allows for a simple and efficient geometrical implementation of complex boundaries for radiative transfer in graded-index media. Numerical results show that this unstructured LB model is well suited for radiative transfer in graded-index media with complex geometries and has good accuracy and stability.