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Highly anisotropic nonlinear temperature balance equation andits numerical solution using asymptotic-preserving schemes of second order in time

Published online by Cambridge University Press:  26 September 2014

Alexei Lozinski
Affiliation:
Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France.. jacek.narski@math.univ-toulouse.fr; claudia.negulescu@math.univ-toulouse.fr Laboratoire de Mathematiques CNRS UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon cedex, France.; alexei.lozinski@univ-fcomte.fr
Jacek Narski
Affiliation:
Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France.. jacek.narski@math.univ-toulouse.fr; claudia.negulescu@math.univ-toulouse.fr
Claudia Negulescu
Affiliation:
Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, 118 route de Narbonne, 31062 Toulouse, France.. jacek.narski@math.univ-toulouse.fr; claudia.negulescu@math.univ-toulouse.fr
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Abstract

This paper deals with the numerical study of a nonlinear, strongly anisotropic heatequation. The use of standard schemes in this situation leads to poor results, due to thehigh anisotropy. An Asymptotic-Preserving method is introduced in this paper, which issecond-order accurate in both, temporal and spacial variables. The discretization in timeis done using an L-stable Runge−Kutta scheme. The convergence of the method is shown to beindependent of the anisotropy parameter , andthis for fixed coarse Cartesian grids and for variable anisotropy directions. The contextof this work are magnetically confined fusion plasmas.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2014

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