# Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

Erwan Deriaz; Bruno Despres; Gloria Faccanoni; Kirill Pichon Gostaf; Lise-Marie Imbert-Gérard; Georges Sadaka; Remy Sart

ESAIM: Proceedings (2011)

- Volume: 32, page 76-94
- ISSN: 1270-900X

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topDeriaz, Erwan, et al. Cancès, E., et al, eds. "Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole." ESAIM: Proceedings 32 (2011): 76-94. <http://eudml.org/doc/251193>.

@article{Deriaz2011,

abstract = {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.},

author = {Deriaz, Erwan, Despres, Bruno, Faccanoni, Gloria, Pichon Gostaf, Kirill, Imbert-Gérard, Lise-Marie, Sadaka, Georges, Sart, Remy},

editor = {Cancès, E., Crouseilles, N., Guillard, H., Nkonga, B., Sonnendrücker, E.},

journal = {ESAIM: Proceedings},

language = {eng},

month = {11},

pages = {76-94},

publisher = {EDP Sciences},

title = {Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole},

url = {http://eudml.org/doc/251193},

volume = {32},

year = {2011},

}

TY - JOUR

AU - Deriaz, Erwan

AU - Despres, Bruno

AU - Faccanoni, Gloria

AU - Pichon Gostaf, Kirill

AU - Imbert-Gérard, Lise-Marie

AU - Sadaka, Georges

AU - Sart, Remy

AU - Cancès, E.

AU - Crouseilles, N.

AU - Guillard, H.

AU - Nkonga, B.

AU - Sonnendrücker, E.

TI - Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

JO - ESAIM: Proceedings

DA - 2011/11//

PB - EDP Sciences

VL - 32

SP - 76

EP - 94

AB - 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.

LA - eng

UR - http://eudml.org/doc/251193

ER -

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