Discontinuous Finite Element Approach for Transient Radiative Transfer Equation

摘要

A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.