J. Ragusa, J.-L. Guermond, and G. Kanschat,
"A robust Sn-DG-approximation for radiation transport in optically thick and diffusive regimes,"
Journal of Computational Physics
231(4), 1947-1962 (2012).
We introduce a new discontinuous Galerkin (DG) method with
reduced upwind stabilization for the linear Boltzmann equation
applied to particle transport. The asymptotic analysis demonstrates
that the new formulation does not suffer from the limitations of
standard upwind methods in the thick diffusive regime; in
particular, the new method yields the correct diffusion limit for
any approximation order, including piecewise constant discontinuous
finite elements. Numerical tests on well-established benchmark
problems demonstrate the superiority of the new method. The
improvement is particularly significant when employing piecewise
constant DG approximation for which standard upwinding is known to
perform poorly in the thick diffusion limit.
Associated Project(s):SHIELD (Smuggled HEU Interdiction through Enhanced anaLysis and Detection): A Framework for Developing Novel Detection Systems Focused on Interdicting Shielded HEU