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.
Mots clés : conservation laws, induction equation, divergence constraint, upwinded source terms
@article{M2AN_2009__43_5_825_0, author = {Fuchs, Franz G. and Karlsen, Kenneth H. and Mishra, Siddharta and Risebro, Nils H.}, title = {Stable upwind schemes for the magnetic induction equation}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {825--852}, publisher = {EDP-Sciences}, volume = {43}, number = {5}, year = {2009}, doi = {10.1051/m2an/2009006}, mrnumber = {2559735}, zbl = {1177.78057}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2009006/} }
TY - JOUR AU - Fuchs, Franz G. AU - Karlsen, Kenneth H. AU - Mishra, Siddharta AU - Risebro, Nils H. TI - Stable upwind schemes for the magnetic induction equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 825 EP - 852 VL - 43 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2009006/ DO - 10.1051/m2an/2009006 LA - en ID - M2AN_2009__43_5_825_0 ER -
%0 Journal Article %A Fuchs, Franz G. %A Karlsen, Kenneth H. %A Mishra, Siddharta %A Risebro, Nils H. %T Stable upwind schemes for the magnetic induction equation %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 825-852 %V 43 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2009006/ %R 10.1051/m2an/2009006 %G en %F M2AN_2009__43_5_825_0
Fuchs, Franz G.; Karlsen, Kenneth H.; Mishra, Siddharta; Risebro, Nils H. Stable upwind schemes for the magnetic induction equation. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 5, pp. 825-852. doi : 10.1051/m2an/2009006. http://www.numdam.org/articles/10.1051/m2an/2009006/
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