Abstract : FreeFem++ is a software for the numerical solution of partial differential equations. It is based on finite element method. The FreeFem++ platform aims at facilitating teaching and basic research through prototyping. For the moment this platform is restricted to the numerical simulations of problems which admit a variational formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic equations arising in Fusion Plasma in the context of the ITER project. First we consider the Grad-Shafranov equation, which is derived from the static ideal MHD equations assuming axisymetry. Some of the properties of the equation and its analytical solutions are discussed. Second we discretize a reduced resistive MHD model which admits solutions of the Grad-Shafranov equation as stationary solutions. Then the physical stability of these stationary solutions is investigated through numerical experiments and the numerical stability of the algorithm is discussed.
https://hal-univ-tln.archives-ouvertes.fr/hal-00976962
Contributeur : Gloria Faccanoni
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Soumis le : mercredi 16 avril 2014 - 09:57:01
Dernière modification le : jeudi 7 février 2019 - 16:07:18
Document(s) archivé(s) le : lundi 10 avril 2017 - 11:49:45
Erwan Deriaz, Bruno Després, Gloria Faccanoni, Kirill Gostaf, Lise-Marie Imbert-Gérard, et al.. Magnetic Equations with FreeFem++: the Grad-Shafranov Equation & the Current Hole. ESAIM: Proceedings, EDP Sciences, 2011, 32, pp.76-94. 〈10.1051/proc/2011013〉. 〈hal-00976962〉
