Approximation of the time-dependent induction equation with advection using Whitney elements: Application to dynamo action
ISSN: 0332-1649
Article publication date: 4 January 2016
Abstract
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.
Keywords
Acknowledgements
This work has benefited from the financial support of the LabeX LaSIPS (ANR-10-LABX-0040-LaSIPS) managed by the French National Research Agency under the Investissements d’avenir program (ANR-11-IDEX-0003-02). The HPC resources for SFEMaNS were provided by GENCI-IDRIS (grant 2014-0254) in France.
Citation
Nore, C., Zaidi, H., Bouillault, F., Bossavit, A. and Guermond, J.-L. (2016), "Approximation of the time-dependent induction equation with advection using Whitney elements: Application to dynamo action", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 35 No. 1, pp. 326-338. https://doi.org/10.1108/COMPEL-06-2015-0235
Publisher
:Emerald Group Publishing Limited
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