Asymptotic Preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction
arXiv:1303.5219 · doi:10.1016/j.cpc.2014.08.018
Abstract
This paper deals with the numerical study of a strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. Furthermore, the recently proposed Asymptotic-Preserving method [arXiv:1203.6739] allows to perform simulations regardless of the anisotropy strength but its application is limited to the case, where the anisotropy direction is given by a field with all field lines open. In this paper we introduce a new Asymptotic-Preserving method, which overcomes those limitations without any loss of precision or increase in the computational costs. The convergence of the method is shown to be independent of the anisotropy parameter $0 < \eps <1$, and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.
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Cited by in corpus (6)
- Asymptotic-Preserving methods and multiscale models for plasma physics
- The effect of magnetic islands on ITG turbulence driven transport
- An Asymptotic Preserving method for strongly anisotropic diffusion equations based on field line integration
- Preserving the accuracy of numerical methods discretizing anisotropic elliptic problems
- Numerical analysis of an asymptotic-preserving scheme for anisotropic elliptic equations
- Uniform convergent scheme for strongly anisotropic diffusion equations with closed field lines