科研之友
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摘要
In magnetized plasma, the magnetic field confines particles around field lines. The ratio between the intensity of the parallel and perpendicular viscosities or heat conductions may reach the order of 10(12). Due to the closed field lines, the coefficient matrices of numerical discretizations using field aligned coordinates are badly conditioned in the strongly anisotropic limit, while the convergence orders of most known schemes with nonaligned grids depend on the anisotropy strength. This paper introduces a simple but very efficient asymptotic preserving reformulation for the magnetic field that has closed field lines. The new reformulated system removes the ill-posedness in the strongly anisotropic limit. Numerical discretiztions for the reformulated system based on nonaligned Cartesian grids are presented. On the one hand, the scheme exhibits uniform second convergence with respect to the anisotropy strength, while on the other hand, the condition numbers do not scale with the the anisotropy strength. Moreover, since the reformulation is different from the original system at only one single point on each closed field line, merely slight modifications to standard discretizations are needed.
- 出版日期2018
- 单位上海交通大学
