I am doing DG calculation with deal.II for Pn equations in neutral particle transport, which is essentially a hyperbolic system. I am wondering if anyone knows a way of doing slope limiting and reconstruction for Q1 element (1, x, y, xy) with preserving the diffusion limit (or asymptotic preserving (AP) in CFD community). There are several AP schemes I know for limiting (e.g. the double minmod limiter). The difficulty is to be AP for the reconstruction. I just don't a decent scheme to be AP with the existence of xy component the Q1 element.
Someone suggests I do the limiting with AP scheme and when reconstructing, use P1 element (1, x, y), which is easy to implement. Yet it is not proved to be AP and therefore not desired.
I asked here just because the most papers on reconstruction in applied math and CFD communities are about P1 element. I just cannot find a thorough description on the algorithms.
Thanks in advance!
I do not know exactly what you mean by AP reconstruction, but some years ago in the paper
http://www.sciencedirect.com/science/article/pii/S0021999105005486
we proposed a FCT based limiting technique for DG methods that worked well for scalar transport. Maybe this could help, although I am not sure it complies with the asymptotic preserving requirements you need.
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