Implicit filtered P_N method in cylindrical coordinates for thermal radiation transport

In this paper, we present an implicit time-integration method for solving the time-dependent thermal radiation transport equations in cylindrical coordinates. We use a so-called filtered spherical harmonics (FP_N) expansion. The filtering approach - introduced by McClarren and Flauck in [1] - enables to efficiently attenuate the oscillations and negativity in the solution by smoothing out the steep variations thereof in angle. Implicit time-integration allows to simulate particles travelling at the speed of light with high CFL number but requires to inverse a large linear system at every time step. Previous work by the authors has shown that the filter not only gives better solutions - compared to reference solutions such as Implicit Monte Carlo (IMC) - but also helps the solver to converge faster. The purpose of the present work is to extend this method to cylindrical problems by first deriving the streaming operator expression [2]. After implementing the method, we compare the results with IMC calculations on a standard problem, known as the Crooked Pipe test problem. We find that our method indeed gives much more satisfying results than unfiltered calculations. Even better results can be obtained by allowing the filtering to be space-dependent.