An asymptotic preserving method for strongly anisotropic diffusion equations based on field line integration

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Tang, Min¹ 

[1] Shanghai Jiao Tong Univ, Inst Nat Sci, Shanghai 200240, Peoples R China

关键词: Anisotropic diffusion;    Asymptotic preserving;    Uniform convergence;    Field line integration;   

DOI  :  10.1016/j.jcp.2016.10.062

来源: Elsevier

【 摘 要 】

In magnetized plasma, the magnetic field confines the particles around the field lines. The anisotropy intensity in the viscosity and heat conduction may reach the order of 10(12). When the boundary conditions are periodic or Neumann, the strong diffusion leads to an ill-posed limiting problem. To remove the ill-conditionedness in the highly anisotropic diffusion equations, we introduce a simple but very efficient asymptotic preserving reformulation in this paper.The key idea is that, instead of discretizing the Neumann boundary conditions locally, we replace one of the Neumann boundary condition by the integration of the original problem along the field line, the singular 1/epsilon terms can be replaced by O(1) terms after the integration, which yields a well-posed problem. Small modifications to the original code are required and no change of coordinates nor mesh adaptation are needed. Uniform convergence with respect to the anisotropy strength 1/epsilon can be observed numerically and the condition number does not scale with the anisotropy. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free