Skip to Main content Skip to Navigation
Journal articles

Magnetic Equations with FreeFem++: the Grad-Shafranov Equation & the Current Hole

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.
Complete list of metadata

Cited literature [1 references]  Display  Hide  Download
Contributor : Gloria Faccanoni Connect in order to contact the contributor
Submitted on : Wednesday, April 16, 2014 - 9:57:01 AM
Last modification on : Friday, August 5, 2022 - 11:23:11 AM
Long-term archiving on: : Monday, April 10, 2017 - 11:49:45 AM


Publisher files allowed on an open archive



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⟩



Record views


Files downloads