Approximation of the time-dependent induction equation with advection using Whitney elements: Application to dynamo action. Issue 1 (4th January 2016)

• Record Type: Journal Article
• Authors: Nore, Caroline; Zaidi, Houda; Bouillault, Frederic; Bossavit, Alain; Guermond, Jean-Luc
• Is Part Of: Compel. Volume 35:Issue 1(2016)
• Page Start: 326
• Page End: 338
• Publication Date: 2016-01-04
• Subjects: 3D FEM -- Edge element method -- Numerical simulation -- Eddy current -- Coupled phenomena -- Maxwell's equation -- Electromagnetic fields; Electrical engineering -- Data Processing -- Periodicals; Electrical engineering -- Mathematics -- Periodicals; Electrical engineering -- Periodicals; Electronics -- Data Processing -- Periodicals; Electronics -- Mathematics -- Periodicals; 621.3
• DOI: 10.1108/COMPEL-06-2015-0235
• Languages: English
• ISSNs: 0332-1649

Abstract

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.