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

Deriaz, 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 -