Discontinuous finite element method with a local numerical flux scheme for radiative transfer with strong inhomogeneity

A discontinuous finite element method (DFEM) with a local numerical flux scheme is developed for solving radiative transfer problems in participating media with strongly inhomogeneous medium properties, steep gradient source, and inhomogeneous angular radiation intensities. The discrete elements in DFEM are assumed to be discontinuous on the inner-element boundaries and the shape functions are constructed on each element. The continuity of the computation domain is maintained by modeling a numerical flux across the inner-boundaries, which makes the DFEM suitable, accurate and numerical stable for radiative transfer problems involving strong inhomogeneity. Several test cases are studied to evaluate the DFEM performance for radiative transfer equation (RTE) with strong inhomogeneity. The DFEM solutions are compared with those obtained by the meshless method and the finite element method. Our results show that the DFEM is more accurate and stable than the other two methods.