AI 中文总结
针对真实托卡马克几何下电阻磁流体力学的刚性磁波耦合问题，提出基于IMIM时间分裂、旋度协调有限元的高效求解器，在三维托卡马克测试中验证了其效率、准确性与稳定性。
AI 中文摘要
我们针对真实托卡马克几何下电阻磁流体力学（MHD）中产生的刚性磁波耦合问题，提出了一种高效的求解器框架。该方法基于隐式-隐式（IMIM）时间分裂技术，将快速磁波和各向异性热输运与较慢的声学动力学分离，同时保留完全耦合性（Krzysik等人，2026年）。在该公式中，磁式子系统呈现为各向异性的旋度-旋度算子，可使用可扩展的辅助空间麦克斯韦（AMS）多重网格求解器。为在离散层面利用该结构，我们对磁场采用旋度协调有限元空间，并设计速度空间以保留洛伦兹力耦合诱导的旋度-旋度结构。所得的相容离散化方法在保持离散磁散度约束的同时，生成可直接适配高效AMS求解器的线性系统。我们在完全非线性的三维托卡马克测试案例上，验证了该求解器的效率以及所得保结构离散化方法的准确性和稳定性。
英文摘要
We present an efficient solver framework for the stiff magnetic wave coupling arising in resistive magnetohydrodynamics (MHD) on realistic tokamak geometries. The approach builds on an implicit-implicit (IMIM) time-splitting that separates fast magnetic waves and anisotropic heat transport from slower acoustic dynamics while retaining full coupling (Krzysik et al. 2026). Within this formulation, the magnetic wave subsystem appears as an anisotropic curl-curl operator, enabling the use of scalable auxiliary-space Maxwell (AMS) multigrid solvers. To exploit this structure at the discrete level, we employ curl-conforming finite element spaces for the magnetic field and design the velocity space to preserve the curl-curl structure induced by the Lorentz-force coupling. The resulting compatible discretization preserves the discrete magnetic divergence constraint while producing linear systems directly amenable to efficient AMS-based solvers. We demonstrate solver efficiency as well as the accuracy and stability of the resulting structure-preserving discretization on fully nonlinear three-dimensional tokamak test cases.
Comments29 pages, 6 figures
