Skip to Main content Skip to Navigation
Journal articles

Stabilized finite element formulation applied to the kinematic Ponomarenko dynamo problem

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

https://hal-insu.archives-ouvertes.fr/insu-00499298
Contributor : Pascale Talour <>
Submitted on : Friday, July 9, 2010 - 10:55:39 AM
Last modification on : Friday, September 25, 2020 - 3:13:44 AM

Links full text

Identifiers

Collections

Citation

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

Share

Metrics

Record views

185