Accelerated Solution of Discrete Ordinates Approximation to the Boltzmann Transport Equation for a Gray Absorbing–Emitting Medium Via Model Reduction

Abstract

This work applies a projection-based model-reduction approach to make high-order quadrature (HOQ) computationally feasible for the discrete ordinates approximation of the radiative transfer equation (RTE) for purely absorbing applications. In contrast to traditional discrete ordinates variants, the proposed method provides easily evaluated error estimates associated with the angular discretization as well as an efficient approach for reducing this error to an arbitrary level. In particular, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model (ROM) constructed from this reduced basis. This strategy results in a much more accurate solution than might have been achieved using only the ordinate directions used to construct the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.