On the equivalence of discontinuous finite element methods and discrete ordinates methods for the angular discretization of the linearized Boltzmann equation in slab geometry

Abstract~We describe the equivalence of discontinuous finite element methods and discrete ordinates methods for the angular discretization of the Boltzmann equation in slab geometry. We use the spectral Greenʹs function (SGF) numerical method to solve the discrete ordinates equations on a digital computer. The SGF method is completely free from spatial truncation errors; therefore, we use the ʹexactʹ solution generated by the SGF method to reconstruct the flux profile inside each node of the spatial grid. This scheme is referred to as the domain decomposition reconstruction scheme. Numerical results to three typical problems are presented.