Negative Flux Fixups in Finite Element Radiation Transport

Steven Hamilton, Emory University

In solving the radiation transport equation, all higher-order-accurate linear discretizations can potentially produce non-physical negative solutions. These negative solutions are highly undesirable, as they can introduce instabilities into coupled multiphysics solvers or acceleration strategies. We propose a new fixup strategy which guarantees non-negativity of the solution while preserving a basic conservation condition. Numerical experiments on several 2-D test problems indicate that the new discretization is quite successful at eliminating non-physical behavior and actually increases the overall accuracy of the underlying method. Because the resulting function to be solved is nonlinear, standard linear solution strategies cannot be applied in a straightforward manner. Thus, we introduce a new hybrid Richardson/Krylov solver to more effectively solve the system. Numerical tests on this algorithm suggest that it is quite robust and can significantly reduce the computational work required to converge to the solution.

Abstract Author(s): Steven Hamilton, Jim Warsa, Michele Benzi