A Collision-Based Hybrid Method for Multiscale, Linear Transport

We present a hybrid method for simulating kinetic equations with multi-scale phenomena in the context of linear transport. The method consists of (i) partitioning the kinetic equation into collisional and non-collisional components; (ii) applying a different numerical method to each compo-nent; and (iii) re-partitioning the kinetic distribution after each time step in the algorithm. Preliminary results show that for a wide range of test problems, the combination of a low-order method for the collisional compo-nent and a high-order method for the non-collisional component provides a level of accuracy that is comparable to a uniform, high-order treatment of the entire system. Background Problem Setup. We consider a single-group, linear transport equation of the for