Moment Closures in Radiation Transport and How to Efficiently Solve Them
Radiation transport computations require the numerical approximation
of integro-differential equations in a high-dimensional phase space.
We start off by contrasting different moment methods aimed at
minimizing spurious Gibbs phenomenon oscillations. We then discuss
high-order methods to solve the resulting moment systems, with a
particular focus on asymptotic preserving properties, meaning that the
diffusive nature of radiation transport in the optically dense regime
is reproduced automatically by the numerical scheme, even when
under-resolved. A particularly simple approach, based on staggered
grids and exponential integrators, implemented in the free and
open-source software StaRMAP, is shown in a radiation dose simulation
as it arises in cancer therapy.