Discontinuous Galerkin Studies of Collisional Dynamics in Continuum-Kinetic Plasma

Numerical investigations of collisional physics have historically been impeded by the issue of computational expense. While the continuum-kinetic Vlasov-Maxwell-Fokker-Planck system is well-established in theory and has been used as the basis for many approximate fluid equations, simulations utilizing the distribution function are relatively uncommon, due primarily to the high dimensionality of the problem. However, advances in numerical methods are steadily making these models more accessible. In this work, we utilize the Gkeyll framework, which applies a novel, highly efficient discontinuous Galerkin (DG) finite element method to the Vlasov-Maxwell-Fokker-Planck system.

We first investigate the Rayleigh-Taylor (RT) instability in a neutral gas in regimes of finite collisionality which are inaccessible to the fluid codes that are traditionally applied to this instability. Utilizing a spatially constant, finite collision frequency, we demonstrate the ability of the Vlasov-Boltzmann model to approach the fluid result at high collision frequency while also accessing a regime of intermediate collisionality in which the RT instability deviates greatly from classic fluid behavior. We then extend upon this finding by choosing a collision frequency that varies spatially, resulting in new dynamics with asymmetric diffusion affecting the development of the RT instability.

Having demonstrated the utility of collisional kinetic modeling even in the simple case of a neutral gas with a basic collision operator, we transition to development and implementation of a fully-conservative, recovery-based DG algorithm for the full nonlinear Rosenbluth/Fokker-Planck collision operator (FPO). Details of the novel recovery scheme for the cross-derivatives and conservation enforcement are presented, and we show that the scheme converges and exhibits stability criteria as expected. Finally, the FPO is applied to test cases that demonstrate the importance of accurate handling of the velocity-dependent collision frequency as compared to an approximate model.