A recovery-based discontinous Galerkin scheme for the Fokker-Planck collision operator.

Continuum-kinetic simulations offer the ability to capture kinetic-scale physics without tracking individual particles, producing noise-free solutions. The motivation for this work is to study kinetic plasma dynamics for a range of applications from high-energy-density plasma instabilities to plasma-material interactions including collisionless, intermediate, and high collisionality regimes. In collisional systems, the choice of collision operator naturally affects the dynamics of the system. Simulations performed with reduced collision operators like the Lenard-Bernstein operator work well for a number of problems but are not accurate when tail population collisions need to be accounted for. The full Fokker-Planck collision operator is necessary to accurately capture kinetic phenomena but is computationally expensive and difficult to implement. Specifically, it is non-trivial to derive a discontinuous Galerkin scheme that accurately captures cross-derivatives to high order of accuracy. In this work, a conservative, recovery-based discontinuous Galerkin scheme for the Fokker-Planck operator is implemented in the plasma simulation framework Gkeyll. The details of the scheme will be presented along with initial results.