Stable upwind schemes for the magnetic induction equation
Centre of Mathematics for Applications (CMA),
University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. email@example.com; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Revised: 26 October 2008
We consider the magnetic induction equation for the evolution of a magnetic field in a plasma where the velocity is given. The aim is to design a numerical scheme which also handles the divergence constraint in a suitable manner. We design and analyze an upwind scheme based on the symmetrized version of the equations in the non-conservative form. The scheme is shown to converge to a weak solution of the equations. Furthermore, the discrete divergence produced by the scheme is shown to be bounded. We report several numerical experiments that show that the stable upwind scheme of this paper is robust.
Mathematics Subject Classification: 65M12 / 35L65
Key words: Conservation laws / induction equation / divergence constraint / upwinded source terms
© EDP Sciences, SMAI, 2009