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

Alexei Lozinski; Jacek Narski; Claudia Negulescu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 6, page 1701-1724
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Lozinski, Alexei, Narski, Jacek, and 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 - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1701-1724. <http://eudml.org/doc/273107>.

@article{Lozinski2014,
abstract = {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.},
author = {Lozinski, Alexei, Narski, Jacek, Negulescu, Claudia},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {anisotropic parabolic equation; ill-conditioned problem; singular perturbation model; limit model; asymptotic preserving scheme; stability; nonlinear heat equation; Runge-Kutta scheme},
language = {eng},
number = {6},
pages = {1701-1724},
publisher = {EDP-Sciences},
title = {Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time},
url = {http://eudml.org/doc/273107},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Lozinski, Alexei
AU - Narski, Jacek
AU - Negulescu, Claudia
TI - Highly anisotropic nonlinear temperature balance equation and its numerical solution using asymptotic-preserving schemes of second order in time
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 6
SP - 1701
EP - 1724
AB - 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.
LA - eng
KW - anisotropic parabolic equation; ill-conditioned problem; singular perturbation model; limit model; asymptotic preserving scheme; stability; nonlinear heat equation; Runge-Kutta scheme
UR - http://eudml.org/doc/273107
ER -

References

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