Adaptive time-stepping in fusion plasma simulations with MFEM

The simulation of magnetized plasma transport using the fluid approximation is ubiquitous in the study of fusion devices. However, the extreme anisotropy of the diffusion coefficients and their non-linear dependence on state variables make time-step selection both very important and non-trivial. The nature of the diffusion equation suggests that small time-steps are needed whenever small scale structure must be captured by the simulation and much larger time-steps can be appropriate as the solution approaches a steady state. Unfortunately, the non-linear character of the diffusion coefficients make these general rules-of-thumb difficult to use in practice. We investigate time-step selection based on a proportional-integral-derivative controller (PID controller) which is a type of feedback control system. The controller makes use of an estimate of the solution error and attempts to choose the largest time-step which restricts this error below some target. Here we present progress on using this technique coupled with a high-order finite element simulation of a non-linear advection-diffusion transport equation.