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.
DOI : 10.1051/m2an/2015014
Mots clés : MHD, instabilities, nonlinear solvers, reduction, toroidal
@article{M2AN_2015__49_5_1331_0, author = {Franck, Emmanuel and H\"olzl, Matthias and Lessig, Alexander and Sonnendr\"ucker, Eric}, title = {Energy conservation and numerical stability for the reduced {MHD} models of the non-linear {JOREK} code}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1331--1365}, publisher = {EDP-Sciences}, volume = {49}, number = {5}, year = {2015}, doi = {10.1051/m2an/2015014}, zbl = {1329.76382}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015014/} }
TY - JOUR AU - Franck, Emmanuel AU - Hölzl, Matthias AU - Lessig, Alexander AU - Sonnendrücker, Eric TI - Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1331 EP - 1365 VL - 49 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015014/ DO - 10.1051/m2an/2015014 LA - en ID - M2AN_2015__49_5_1331_0 ER -
%0 Journal Article %A Franck, Emmanuel %A Hölzl, Matthias %A Lessig, Alexander %A Sonnendrücker, Eric %T Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1331-1365 %V 49 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015014/ %R 10.1051/m2an/2015014 %G en %F M2AN_2015__49_5_1331_0
Franck, Emmanuel; Hölzl, Matthias; Lessig, Alexander; Sonnendrücker, Eric. Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1331-1365. doi : 10.1051/m2an/2015014. http://www.numdam.org/articles/10.1051/m2an/2015014/
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