Highly anisotropic temperature balance equation and its\n asymptotic-preserving resolution

2012/03/30 by Alexei Lozinski, Jacek Narski, Lozinski, Alexei +3 · 1 citation
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Magnetic confinement fusion research #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1203.6739

openalex publication_date 2012/03/30 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

This paper deals with the numerical study of a nonlinear, strongly\nanisotropic heat equation. The use of standard schemes in this situation leads\nto poor results, due to the high anisotropy. An Asymptotic-Preserving method is\nintroduced in this paper, which is second-order accurate in both, temporal and\nspacial variables. The discretization in time is done using an L-stable\nRunge-Kutta scheme. The convergence of the method is shown to be independent of\nthe anisotropy parameter 0 < eps <1, and this for fixed coarse Cartesian\ngrids and for variable anisotropy directions. The context of this work are\nmagnetically confined fusion plasmas.\n

Citations

• The basis of anisotropic water diffusion in the nervous system – a technical review

Cited by

• Uniform convergent scheme for strongly anisotropic diffusion equations with closed field lines

Related

• An accurate SUPG-stabilized continuous Galerkin discretization for anisotropic heat flux in magnetic confinement fusion
• Numerical study of a nonlinear heat equation for plasma physics
• A fast algebraic multigrid solver and accurate discretization for highly anisotropic heat flux I: open field lines
• An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields
• A robust fourth-order finite-difference discretization for the strongly anisotropic transport equation in magnetized plasmas