Numerical study of a nonlinear heat equation for plasma physics

TL;DR

This paper develops an efficient numerical scheme combining directional splitting and IMEX methods to accurately simulate the nonlinear heat equation governing plasma temperature in tokamak edge regions.

Contribution

The paper introduces a novel numerical approach that improves stability and efficiency for solving nonlinear plasma heat equations.

Findings

The scheme effectively captures long-term temperature evolution.

Numerical results demonstrate stability and accuracy.

The method outperforms standard approaches in plasma simulations.

Abstract

This paper is devoted to the numerical approximation of a nonlinear temperature balance equation, which describes the heat evolution of a magnetically confined plasma in the edge region of a tokamak. The nonlinearity implies some numerical difficulties, in particular long time behavior, when solved with standard methods. An efficient numerical scheme is presented in this paper, based on a combination of a directional splitting scheme and the IMEX scheme introduced in [Filbet and Jin]