A New Stabilized Finite Element Formulation for Solving Radiative Transfer Equation

Abstract

A new stabilized finite element formulation for solving radiative transfer equation is presented. It owns the salient feature of least-squares finite element method (LSFEM), i.e., free of the tuning parameter that appears in the streamline upwind/Petrov–Galerkin (SUPG) finite element method. The new finite element formulation is based on a second-order form of the radiative transfer equation. The second-order term will provide essential diffusion as the artificial diffusion introduced in traditional stabilized schemes to ensure stability. The performance of the new method was evaluated using challenging test cases featuring strong medium inhomogeneity and large gradient of radiative intensity field. It is demonstrated to be computationally efficient and capable of solving radiative heat transfer in strongly inhomogeneous media with even better accuracy than the LSFEM, and hence a promising alternative finite element formulation for solving complex radiative transfer problems.