Radiative Transfer in Turbulent Flow using Spacetime Discontinuous Galerkin Finite Element Method

The radiative transfer equation for a problem that involves scattering, absorption and radiation is solved using spacetime discontinuous Galerkin (SDG) method. The strength of finite element method to handle scattering problems in heterogeneous media with complex geometries is well known. Adaptive operations in spacetime facilitates very accurate and efficient solution algorithm. We investigated the accuracy of the SDG method by using the method of manufactured solutions. For the case of harmonic phase functions we illustrate how the L2 norm error decreases with the choice of high order polynomial and more refined element size. Key merits of the use of SDG for our problem enamates from its linear solution cost, and the ability to obtain the solution for a wide frequency spectrum in one time domain simulation.