Temporal Regularization of the $P_N$ Equations
Abstract: The $P_N$ equations are a linear hyperbolic system of PDE that are used to describe the transport of dilute particles through a material medium. Like the kinetic transport equation from which they are derived, the $P_N$ equations possess a diffusive limit in collision-dominated regimes. The development of efficient algorithms which accurately capture this limit is the subject of on-going research. In this talk, I will introduce a regularization of the $P_N$ equations based on a temporal splitting of fast and slow dynamics. The regularization captures the proper diffusion limit in collision-dominated regimes and allows for relatively large times steps when the original $P_N$ system is stiff. In particular, in simulations for which the computational mesh does not resolve the particle mean-free-path, the regularization admits a simple scheme that is free of any stability-induced restrictions on the time step.