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Stable upwind schemes for the magnetic induction equation

Published online by Cambridge University Press:  08 April 2009

Franz G. Fuchs ,
Kenneth H. Karlsen ,
Siddharta Mishra  and
Nils H. Risebro
Franz G. Fuchs
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. franzf@math.uio.no; kennethk@math.uio.no; siddharm@cma.uio.no; nilshr@math.uio.no
Kenneth H. Karlsen
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. franzf@math.uio.no; kennethk@math.uio.no; siddharm@cma.uio.no; nilshr@math.uio.no
Siddharta Mishra
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. franzf@math.uio.no; kennethk@math.uio.no; siddharm@cma.uio.no; nilshr@math.uio.no
Nils H. Risebro
Affiliation:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway. franzf@math.uio.no; kennethk@math.uio.no; siddharm@cma.uio.no; nilshr@math.uio.no
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Abstract

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.

Keywords

Conservation lawsinduction equationdivergence constraintupwinded source terms
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 5 , September 2009 , pp. 825 - 852
Copyright
© EDP Sciences, SMAI, 2009

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