1Laboratoire de Mécanique, Modélisation et Procédés Propres, 38 rue Frédéric Joliot-Curie 13451 Marseille, France 2Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris, France 3Institut de mathématiques de Toulon et du Var, Université du Sud Toulon-Var, 83957 La Garde, France 4Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, 33 rue Saint-Leu, 80039 Amiens, France 5École Supérieure d’Ingénieurs Léonard de Vinci, 92916 Paris, France
ESAIM. Proceedings, Tome 32 (2011), pp. 76-94
Cet article a éte moissonné depuis la source EDP Sciences
FreeFem++ [11] 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.
1
Laboratoire de Mécanique, Modélisation et Procédés Propres, 38 rue Frédéric Joliot-Curie 13451 Marseille, France
2
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 75252 Paris, France
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
@article{EP_2011_32_a6,
author = {Erwan Deriaz and Bruno Despres and Gloria Faccanoni and Kirill Pichon Gostaf and Lise-Marie Imbert-G\'erard and Georges Sadaka and Remy Sart},
title = {Magnetic equations with {FreeFem++:} {The} {Grad-Shafranov} equation & the current hole},
journal = {ESAIM. Proceedings},
pages = {76--94},
year = {2011},
volume = {32},
doi = {10.1051/proc/2011013},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2011013/}
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TY - JOUR
AU - Erwan Deriaz
AU - Bruno Despres
AU - Gloria Faccanoni
AU - Kirill Pichon Gostaf
AU - Lise-Marie Imbert-Gérard
AU - Georges Sadaka
AU - Remy Sart
TI - Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole
JO - ESAIM. Proceedings
PY - 2011
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EP - 94
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DO - 10.1051/proc/2011013
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%0 Journal Article
%A Erwan Deriaz
%A Bruno Despres
%A Gloria Faccanoni
%A Kirill Pichon Gostaf
%A Lise-Marie Imbert-Gérard
%A Georges Sadaka
%A Remy Sart
%T Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole
%J ESAIM. Proceedings
%D 2011
%P 76-94
%V 32
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/2011013/
%R 10.1051/proc/2011013
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%F EP_2011_32_a6
Erwan Deriaz; Bruno Despres; Gloria Faccanoni; Kirill Pichon Gostaf; Lise-Marie Imbert-Gérard; Georges Sadaka; Remy Sart. Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole. ESAIM. Proceedings, Tome 32 (2011), pp. 76-94. doi: 10.1051/proc/2011013
