J. Ragusa, J.-L. Guermond, G. Kanschat, “A robust Sn-DG-approximation for radiation transport in optically thick and diffusive regimes”, Journal of Computational Physics, 231, 4 (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.