Many plasma systems, from here on Earth in fusion reactors and lab plasma experiments to far away compact objects and galaxy clusters, are magnetized. The underlying dynamic magnetic field imposes some structure to the plasma’s evolution, affecting the transport of momentum and energy parallel vs. perpendicular to the magnetic field. A variety of asymptotic models have been derived utilizing the importance of the plasma’s magnetic field for its dynamics. Many of these models are highly non-trivial and their robust, accurate numerical discretization an even grander challenge.

I will present an overview of the Gkeyll simulation framework, which has implemented a number of models for modeling magnetized plasmas for diverse applications, from fusion to astrophysical applications. I will discuss subtleties and developments to create energy-conserving schemes using the discontinuous Galerkin finite element method. I will focus in particular on a novel parallel-kinetic-perpendicular-moment model, which performs a spectral expansion of only the perpendicular degrees of freedom, analogous to spectral methods which have grown in popularity in recent years for gyrokinetics, while retaining the complete dynamics parallel to the magnetic field. Finally, I will demonstrate the utility of Gkeyll’s implementation of these models on a variety of benchmarks and production problems.