Geodesic
Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1701-1724

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

DOI : 10.1051/m2an/2014016
Classification : 65N30, 65Z05, 35K20
Keywords: anisotropic parabolic equation, ill-conditioned problem, singular perturbation model, limit model, asymptotic preserving scheme 
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     title = {Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1701--1724},
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Lozinski, Alexei; Narski, Jacek; Negulescu, Claudia. Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1701-1724. doi: 10.1051/m2an/2014016

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