Computational Plasma Physics at (Almost) all Scales

Computational plasma physics is a uniquely challenging field due to the extreme scales and disparate physical phenomena involved in the plasma universe. From electron cyclotron motion to resistive time-scales, from the plasma environment around black-holes to fusion machines, plasmas are ubiquitous in the visible universe. In this talk I will summarize the recent sophisticated numerical methods developed to simulate plasmas at (almost) all scales. These modern methods are carefully constructed to ensure preservation of underlying physical principles (like energy and positivity) and often arise from the considerations of the underlying Hamiltonian and Lagrangian structure of the equations. Based on higher-order finite-element or finite-volume schemes, these methods allow simulating a wide variety of problems, from laboratory to space plasmas. I will focus on modern discontinuous Galerkin (DG) schemes for kinetic equations, in which the 6D phase-space is directly discretized, in contrast to the standard particle-in-cell methods. I will show a variety of applications, from simulating planetary magnetospheres to turbulence in fusion machines. I will conclude with a prospectus for the future, which will likely involve the discovery of more efficient and robust methods that run on modern hardware architectures.