A recovery-based numerical scheme for full Fokker-Planck collisions

Fokker-Planck collision model is important for accurate simulations of many problems relevant to magnetic confinement fusion, for example,

runaway electrons. However, this model is also notoriously difficult to implement self-consistently and is computationally expensive.

In this work, we build upon the successful implementation of the conservative reduced Fokker-Planck model in the Gkeyll framework, for

the continuum-kinetic Vlasov equation. The presented scheme is carefully crafted using a novel version of the discontinuous Galerkin

(DG) method based on the concepts of weak equality and recovery introduced by van Leer [van Leer et al., AIAA CFD Conference,

2007]. An integral part of this super-convergent scheme is a unique multi-dimensional recovery approach that utilizes computer algebra

tools for efficiency. The high accuracy of the scheme typically leads to decreased requirements on resolution while retaining the same

numerical uncertainty, thus, making each simulation less intense in terms of computational resources.