New formulations of grid-based Vlasov solvers: relativity, flexible coordinates, and more.

Grid-based solvers for the Vlasov equation have grown in popularity in recent years as an alternative to the classical particle-in-cell algorithm, especially for problems which require delicate, detailed resolution of phase space and the elimination of particle noise in the subsequent analysis. However, the extension of these methods to more general kinetic systems remains challenging, such as extreme astrophysical environments which require relativity, radiation, photon dynamics, and QED effects such as pair production.

In this presentation, I will demonstrate an extension to the Vlasov solver in the Gkeyll simulation framework using a Hamiltonian formulation that makes the inclusion of relativity straightforward, and even allows for a clean interface for photon dynamics. I will show how this same formulation has been extended to more flexible momentum-space meshes to handle the significant dynamic range in energies needed to model compact objects. I will conclude with simulations utilizing this new formulation which allow for new insights into kinetic instabilities likely present around pulsars.