An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields

TL;DR

This paper introduces an extended semi-Lagrangian algorithm for anisotropic heat transport equations that works with arbitrary magnetic fields, maintaining high accuracy and numerical stability in complex magnetic topologies.

Contribution

The authors extend a previous semi-Lagrangian scheme to handle arbitrary magnetic field configurations, broadening its applicability beyond tokamak-like regimes.

Findings

The extended algorithm accurately solves heat transport with complex magnetic fields.

Numerical experiments confirm the scheme's stability and precision.

The method preserves the analytical Green's function for tractability.

Abstract

We extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chac\'on et al., J. Comput. Phys., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.