Lattice Boltzmann method for radiative transfer in curvilinear coordinate systems.

Abstract

Radiative transfer in curvilinear geometries has wide applications across engineering and scientific fields. However, solving the radiative transfer equation (RTE) in curvilinear coordinate systems remains challenging due to its complexity. A universal and simple numerical method is still lacking. This paper presents a lattice Boltzmann method (LBM) for radiative transfer in curvilinear coordinates. Through Chapman-Enskog analysis, the LB model is rigorously derived from the curvilinear RTE. By incorporating the metric tensor and a curvilinear radiative transfer operator, the method maintains simplicity while being applicable to curvilinear systems. Numerical tests confirm its accuracy and stability, and asymptotic analysis proves second-order convergence. As an application, we study thermal radiative transfer in fiber lasers, providing insights for optimized fiber design. The proposed LBM offers an efficient tool for curvilinear radiative transfer problems.