Volume 49, Number 5, September-October 2015
|Page(s)||1331 - 1365|
|Published online||18 August 2015|
Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code
1 Inria Nancy grand Est, TONUS
2 Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany.
3 Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany.
Revised: 19 February 2015
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.
Mathematics Subject Classification: 65H10 / 35Q35 / 35Q60 / 76W05
Key words: MHD / instabilities / nonlinear solvers / reduction / toroidal
© EDP Sciences, SMAI 2015
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