适用于任意磁场的各向异性热输运方程的渐近保持半拉格朗日算法
An asymptotic-preserving semi-Lagrangian algorithm for the anisotropic heat transport equation with arbitrary magnetic fields
AI总结：
本文扩展了极强各向异性热输运方程的半拉格朗日算法，以微小修改保留解析 Green 函数等优势，使其适用于任意磁场拓扑，并通过制造解数值实验验证了准确性与通用性。
摘要：
我们将近期针对极强各向异性热输运方程提出的半拉格朗日算法〔Chacón 等人，J. Comput. Phys., 272 (2014)〕进行扩展，以处理任意磁场拓扑。原格式（展现出卓越的数值特性）仅适用于所谓的托卡马克排序区域，在该区域中，磁场强度沿磁力线不允许有大幅变化。所提出的扩展仅通过微小修改便保留了原格式的优良特性（包括对可处理性至关重要的解析 Green 函数），同时允许完全通用的磁场。通过采用解析制造解的数值实验，证明了该方法的准确性和通用性。
英文摘要：
We extend the recently proposed semi-Lagrangian algorithm for the extremely anisotropic heat transport equation [Chacón et al., J. Comput. Phys., 272 (2014)] to deal with arbitrary magnetic field topologies. The original scheme (which showed remarkable numerical properties) was valid for the so-called tokamak-ordering regime, in which the magnetic field magnitude was not allowed to vary much along field lines. The proposed extension maintains the attractive features of the original scheme (including the analytical Green's function, which is critical for tractability) with minor modifications, while allowing for completely general magnetic fields. The accuracy and generality of the approach are demonstrated by numerical experiment with an analytical manufactured solution.
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