The second-order formulation of the $P_N$ equations with Marshak boundary conditions
Numerical Analysis
2019-11-04 v1 Numerical Analysis
Abstract
We consider a reformulation of the classical 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. We make our implementation available online, which allows for fast prototyping.
Keywords
Cite
@article{arxiv.1911.00468,
title = {The second-order formulation of the $P_N$ equations with Marshak boundary conditions},
author = {Matthias Andres and Florian Schneider},
journal= {arXiv preprint arXiv:1911.00468},
year = {2019}
}