Modern Computational Methods for Fluid and Kinetic Simulations of Plasmas 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 tutorial, I will present recently developed numerical methods to simulate plasmas at (almost) all scales. These modern methods are carefully constructed to ensure preservation of underlying physical principles (like energy and positivity) that arise from the considerations of the physics 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.

In the last such tutorial (P.J. Morrison, Phys. Plasma, 24 (5) 055502 2017) modern structure-preserving methods, that preserve geometric structure of the underlying equations were presented. Although these methods are very powerful for certain applications, equally powerful schemes can be constructed that take into account other properties of the system. For example, the proper exchange of kinetic and internal energy (critical for turbulence simulations), conservation of kinetic-energy or monotonic increase of entropy, positivity of the distribution function, monotonicity of the solution, etc. Often, structure preservation comes at the cost of these, equally important, physical properties. In the tutorial I will show how to determine the proper tradeoff between properties and choose and analyze schemes for an application at hand. I will conclude with a prospectus for the future, which will involve the discovery of more efficient and robust methods that run on modern hardware architectures.