Volume 32, October 2011CEMRACS'10 research achievements: Numerical modeling of fusion
|Page(s)||76 - 94|
|Published online||03 November 2011|
Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole
Laboratoire de Mécanique, Modélisation et Procédés
Propres, 38 rue Frédéric
2 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris, France
e-mail: firstname.lastname@example.org & email@example.com & firstname.lastname@example.org
3 Institut de mathématiques de Toulon et du Var, Université du Sud Toulon-Var, 83957 La Garde, France
4 Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France
5 École Supérieure d’Ingénieurs Léonard de Vinci, 92916 Paris, France
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.
© EDP Sciences, SAIM 2011
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