Force-free plasmas are a good approximation where the plasma pressure is tiny compared with the magnetic pressure, which is the case during the cold vertical displacement event (VDE) of a major disruption in a tokamak. On time scales long compared with the transit time of Alfven waves, the evolution of a force-free plasma is most efficiently described by the quasi-static magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we consider a regularized quasi-static MHD model for force-free plasmas in tokamak disruptions and propose a mimetic finite difference (MFD) algorithm. The full geometry of an ITER-like tokamak reactor is treated, with a blanket module region, a vacuum vessel region, and the plasma region. Specifically, we develop a parallel, fully implicit, and scalable MFD solver based on PETSc and its DMStag data structure for the discretization of the five-field quasi-static perpendicular plasma dynamics model on a 3D structured mesh. The MFD spatial discretization is coupled with a fully implicit DIRK scheme. The algorithm exactly preserves the divergence-free condition of the magnetic field under the resistive Ohm's law. The preconditioner employed is a four-level fieldsplit preconditioner, which is created by combining separate preconditioners for individual fields, that calls multigrid or direct solvers for sub-blocks or exact factorization on the separate fields. The numerical results confirm the divergence-free constraint is strongly satisfied and demonstrate the performance of the fieldsplit preconditioner and overall algorithm. The simulation of ITER VDE cases over the actual plasma current diffusion time is also presented.

翻译：无力等离子体是等离子体压强远小于磁压强的良好近似，这对应于托卡马克大破裂期间冷垂直位移事件（VDE）的状态。在远长于阿尔芬波渡越时间的时间尺度上，无力等离子体的演化最有效的描述方式是忽略等离子体惯性的准静态磁流体力学（MHD）模型。本文针对托卡马克破裂中的无力等离子体，考虑正则化准静态MHD模型，提出一种拟有限差分（MFD）算法。我们处理了类ITER托卡马克反应堆的全几何结构，包括包层模块区域、真空室区域和等离子体区域。具体而言，基于PETSc及其DMStag数据结构，针对三维结构化网格上五场准静态垂直等离子体动力学模型的离散化，开发了并行、全隐式、可扩展的MFD求解器。MFD空间离散化与全隐式DIRK格式耦合。该算法在电阻性欧姆定律下精确保持磁场无散条件。所采用的预处理器为四级场分裂预处理器，通过组合各场的独立预处理器构建，对子块调用多重网格或直接求解器，或对各场进行精确分解。数值结果验证了无散约束被严格满足，并展示了场分裂预处理器及整体算法的性能。同时给出了基于实际等离子体电流扩散时间的ITER VDE算例模拟结果。