An implicit, adaptive solver for a relativistic drift-kinetic Fokker-Planck-Boltzmann model

We develop a scalable, fully implicit, adaptive solver for a relativistic drift-kinetic model that describes runaway electrons in the tokamak disruption. This runaway electron solver can dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the adaptive mesh refinement (AMR) algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies. We further present a series of numerical benchmark and physics studies using the new solver. The numerical benchmark study focuses on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations. The physics study focuses on understanding the impact of different low-energy boundary conditions and the impact of large-angle collision operators with different fidelity.