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

Abstract. 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.