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Approximation of the time-dependent induction equation with advection using Whitney elements

Abstract : The purpose of this paper is to present a new formulation for taking into account the convective term due to an imposed velocity field in the induction equation in a code based on Whitney elements called DOLMEN. Different Whitney forms are used to approximate the dependent variables. The authors study the kinematic dynamo action in a von Kármán configuration and obtain results in good agreement with those provided by another well validated code called SFEMaNS. DOLMEN is developed to investigate the dynamo action in non-axisymmetric domains like the impeller driven flow of the von Kármán Sodium (VKS) experiment. The authors show that a 3D magnetic field dominated by an axisymmetric vertical dipole can grow in a kinematic dynamo configuration using an analytical velocity field.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-01264162
Contributor : Frederic Bouillault <>
Submitted on : Thursday, January 28, 2016 - 6:11:16 PM
Last modification on : Wednesday, September 16, 2020 - 5:48:56 PM

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Caroline Nore, Houda Zaidi, Frédéric Bouillault, Alain Bossavit, Jean-Luc Guermond. Approximation of the time-dependent induction equation with advection using Whitney elements. COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald, 2016, 35 (1), pp.326-338. ⟨10.1108/COMPEL-06-2015-0235⟩. ⟨hal-01264162⟩

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