Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak

TL;DR

This paper develops an asymptotic-preserving numerical method for a 2D nonlinear model of electrical potential in tokamak edge plasma, effectively handling the stiff problem caused by low parallel resistivity.

Contribution

It introduces a micro-macro decomposition-based method that remains well-posed as parallel resistivity approaches zero, supported by numerical validation.

Findings

Bounded condition number in numerical tests

Method remains stable for low resistivity

Theoretical analysis confirms numerical results

Abstract

A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a micro-macro decomposition is studied in order to have a well-posed problem, even when the parallel resistivity goes to $0$. Numerical tests with a finite difference scheme show a bounded condition number for the linearised discrete problem solved at each time step, which confirms the theoretical analysis on the continuous problem.