Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code

TL;DR

This paper derives energy-conserving reduced MHD models for the JOREK code and introduces a non-linear solver with adaptive time stepping, improving robustness and efficiency in simulating plasma instabilities.

Contribution

It provides a rigorous derivation of energy-conserving reduced MHD models and implements a non-linear solver with adaptive time stepping in JOREK.

Findings

Energy-conserving models improve physical accuracy.

Non-linear solver enhances robustness during non-linear phases.

Larger time steps are feasible with the new approach.

Abstract

In this paper we present a rigorous derivation of the reduced MHD models with and without parallel velocity that are implemented in the non-linear MHD code JOREK. The model we obtain contains some terms that have been neglected in the implementation but might be relevant in the non-linear phase. These are necessary to guarantee exact conservation with respect to the full MHD energy. For the second part of this work, we have replaced the linearized time stepping of JOREK by a non-linear solver based on the Inexact Newton method including adaptive time stepping. We demonstrate that this approach is more robust especially with respect to numerical errors in the saturation phase of an instability and allows to use larger time steps in the non-linear phase.