Approximation of the time-dependent induction equation with advection using Whitney elements: Application to dynamo action

• Caroline Nore ^[2] ; Houda Zaidi ^[3] ; Frederic Bouillaul ^[3] ; Alain Bossavit ^[3] ; Jean-Luc Guermond ^[1]
  1. [1] Texas A&M University

     Texas A&M University

     Estados Unidos

     
  2. [2] Paris-Sud University
  3. [3] Gif sur Yvette

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• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 35, Nº 1, 2016, págs. 326-338
• Idioma: inglés
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• Resumen

  • Purpose – 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.

    Design/methodology/approach – Different Whitney forms are used to approximate the dependent variables. The vector potential is discretized using first-order edge elements of the first family. The velocity is approximated by using the first-order Raviart-Thomas elements. The time stepping is done by using the Crank-Nicolson scheme.

    Findings – 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. 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.

    Originality/value – The findings offer a basis to a scenario for the VKS dynamo.