J.M. Zhao, L.H. Liu. Spectral Element Method with Adaptive Artificial Diffusion for Solving Radiative Transfer Equation. Numerical Heat Transfer Part B, 2008, 53(6): 536-554. download

Abstract: An adaptive isotropically artificial diffusion (AISO) scheme is developed for the spectral element method to mitigate the ray effects encountered in the solution of radiative transfer problems. By considering the coupled manner of ray effects and false scattering, the artificial diffusion coefficient is determined heuristically from both local angular discretization scale and local spatial discretization scale. The scheme is easily and efficiently implemented under the spectral or finite-element method framework. The performance of various artificial diffusion schemes is studied and compared. The streamwise artificial diffusion schemes are only responsible for stabilization of strong convection-induced instability, while the isotropically artificial diffusion scheme shows very good performance in mitigating the ‘‘wiggles’’ in both low- and high-order spatial approximation. Numerical experiments show that the spectral element method with the AISO scheme is stable, high-order-accurate, and effective for solving radiative transfer in simple and complex geometries, and also robust for mitigating ray effects of various origins.