Stabilized finite element formulation applied to the kinematic Ponomarenko dynamo problem

Ridha Touihri (1) , Azzedine Soulaimani (2) , Franck Plunian (3)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
2 ETS - Ecole de Technologie Supérieure [Montréal]
3 LGIT - Laboratoire de Géophysique Interne et Tectonophysique

A stabilized finite element (B, q) formulation is developed to solve the kinematic dynamo problem. As a test case, we solve the induction equation for a given solid body helical flow, embedded in a cylindrical conducting shell. This problem corresponds to the well-known Ponomarenko dynamo. It has the interesting property to have an exact dispersion relation giving the magnetic growth rate as a function of the flow properties. Therefore, it is a good benchmark to test our kinematic dynamo code. We calculated the dynamo threshold and plotted the geometry of the generated magnetic field. We also evaluated the residual error due to our stabilized formulation.

Mots clés: Magnetohydrodynamics; Finite element; Stabilized formulation; Kinematic dynamo

Ridha Touihri, Azzedine Soulaimani, Franck Plunian. Stabilized finite element formulation applied to the kinematic Ponomarenko dynamo problem. Theoretical and Computational Fluid Dynamics, 2009, 23 (6), pp.431-437. ⟨10.1007/s00162-009-0143-4⟩. ⟨insu-00499298⟩