Fully implicit solution methods for fluid plasma equations with physics-based pre-conditioning

Many problems of interest in plasma modelling are subject to the ‘tyranny of scales’, specifically, problems that encompass physical processes that operate on timescales that are separated by many orders of magnitude. Investigating such problems therefore requires the use of implicit time-integration schemes, which advance problem solutions on the timescale of interest, while incorporating the physics of the fast-timescales. One promising route to develop these implicit solvers is the combination of Jacobian-Free Newton-Krylov methods, combined with physics-based pre-conditioners based on Schur complement analysis of the physical system.