Discrete-Ordinate Discontinuous Galerkin Methods for Solving the Radiative Transfer Equation

The radiative transfer equation (RTE) occurs in a wide variety of applications. In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE. The numerical methods are formed in two steps. In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semi-discrete hyperbolic system. In the second step, the spatial discontinuous Galerkin method is applied to discretize the semi-discrete system. A stability and error analysis is performed on the numerical methods. Some numerical examples are included to demonstrate the convergence behavior of the methods. Key words. radiative transfer equation, discrete-ordinate discontinuous Galerkin method, stability, convergence, error estimation AMS subject classifications. 65N30, 65R20

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Weimin Han, Jianguo Huang, Joseph A. Eichholz
• Keywords: Discontinuous Galerkin Method, Discrete-ordinate Discontinuous Galerkin, Radiative Transfer Equation, SIAMSC 2010