Luc Mieussens

AP space discretizations of kinetic equations

We discuss the problem of space discretizations of kinetic equations
for small mean free path regimes. The model problem we consider is the
stationary linear transport equation used in neutron transport or
radiative transfer problems. We present the standard asymptotic
analysis that shows the existence of boundary layers in case of non
equilibrium boundary values. We show why standard upwind finite
difference methods fail to capture the solution when the boundary
layer is not resolved, and we explain the surprising result of Larsen
and Morel who were first to show that the linear discontinuous
Galerkin method works much better. We also discuss the recent work of
Guermond and Kanschat who have revisited the previous result in a
modern finite element framework. Finally, we give some examples in
other fields (like rarefied gas dynamics) where this work might be
very useful.