Goal-based angular adaptivity with contributon theory for the discrete ordinates transport equation

Abstract

A goal-based angular adaptivity has been described for solving the discrete ordinates transport equation. This method uses the linear discontinuous finite element quadrature sets, allowing for local angular refinement across space-energy dimensions. Anisotropy quantified factor derived by contributon theory is introduced in this adaptivity to locate spatial regions that require more angular unknowns in every energy group for a given goal region. The goal-based error metric is considered to trigger local refinement in angle, which requires the solutions of the contributon transport equation to determine the importance to a user-defined functional. Several problems that include both one-group and multi-group transport calculations are displayed to demonstrate the effectiveness of this method. Results indicate that our goal-based adaptivity can significantly reduce computational expenses in terms of angular unknowns and computational times for a similar accuracy, as compared to uniform quadrature sets. It is expected that this adaptivity has the potential to enhance the efficiency of an even wider range of transport problems.