Asymptotic Preserving scheme for strongly anisotropic parabolic equations for arbitrary anisotropy direction
For researchers simulating magnetically confined fusion plasmas, this method enables accurate and efficient simulations of anisotropic heat transport regardless of anisotropy direction, removing a key constraint of previous approaches.
This paper introduces a new Asymptotic-Preserving method for strongly anisotropic heat equations that works for arbitrary anisotropy directions, overcoming limitations of prior methods that required open field lines. The method achieves convergence independent of the anisotropy parameter on coarse Cartesian grids.
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.