Highly anisotropic temperature balance equation and its asymptotic-preserving resolution
For researchers in plasma physics and numerical methods, this work provides a robust solver for anisotropic heat transport, though it is an incremental improvement over existing asymptotic-preserving techniques.
The paper introduces an asymptotic-preserving method for solving a strongly anisotropic heat equation, achieving second-order accuracy in time and space with convergence independent of the anisotropy parameter. The method is validated for magnetically confined fusion plasmas.
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 $0 < \eps <1$, and this for fixed coarse Cartesian grids and for variable anisotropy directions. The context of this work are magnetically confined fusion plasmas.