An axisymmetric poloidal flow damping calculation is performed to benchmark the implementation. It is first shown that the kinetic aspects of the implementation give results for the steady-state poloidal flow that agree both with other codes, analytics, and a fixed-background (i.e. $f_0$ a stationary Maxwellian) $\delta f$ implementation in NIMROD. It is then shown that the flow dynamics in the full CEL approach agree well both with analytics, and with results from the fixed-background $\delta f$ implementation.
A von Neumann linear stability analysis of the full fluid-kinetic system is also performed to help elucidate methods to make the time advance of the full system numerically stable. It is shown that numerical stability is impossible to achieve without explicitly enforcing key tenets of the CEL closure approach, in particular, that the $n$, $\mathbf{u}$, and $T$ moments of the kinetic distortion remain small in time. In addition, it is shown that centering the heat flux at the beginning of the time step and the ion temperature at the end of the time step in the kinetic equation allows for a numerically-stable time advance of the coupled fluid-kinetic system. Furthermore, these linear stability results are seen to remain applicable when running NIMROD fully nonlinearly.
The methodology of applying the CEL approach to non-axisymmetric problems is also discussed. Future work will include applying this closure approach to the problem of forced magnetic reconnection in toroidal geometry, as well as to accurate simulation of neoclassical tearing modes (NTMs) in tokamaks.