The second-order formulation of the $P_N$ equations with Marshak boundary conditions
Matthias Andres,
Florian Schneider
Abstract:We consider a reformulation of the classical P N method with Marshak boundary conditions for the approximation of the monoenergetic stationary linear transport equation as a system of second-order PDEs. Our derivation allows the automatic generation of a model hierarchy which can then be handed to standard PDE tools. This method allows for heterogeneous coefficients, irregular grids, anisotropic boundary sources and anisotropic scattering. The wide applicability is demonstrated in several numerical test cases.… Show more
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