Discontinuous spectral element approach for solving transient radiative transfer equations

A discontinuous spectral element method is presented to solve transient radiative heat transfer in multidimensional semitransparent media. The transient term is discretized by the Crank-Nicolson scheme, and the spatial discretization is conducted using the discontinuous spectral element approach. The salient features of the discontinuous spectral element method are that it possesses high-order accuracy, has properties such as local conservation, and its solutions are allowed to be discontinuous across interelement boundaries. The inherent discontinuity acceptable property of the discontinuous spectral element method allows efficient and accurate capturing of the sharp wave front of the transient radiative transfer process. A special treatment for the problem with diffuse irradiation at the boundary Is presented to mitigate the ray effect encountered In solving the transient radiative transfer equation. The performance of the discontinuous spectral element method is verified by three test cases. The predicted results by the discontinuous spectral element method agree well with reported benchmark solutions in the references.