高斯矩松弛闭合用于等离子体快速磁重联可验证数值模拟
Gaussian-Moment Relaxation Closures for Verifiable Numerical Simulation of Fast Magnetic Reconnection in Plasma
AI总结：
本文研究了等离子体流体模型中最小要求以实现与动能模拟一致的收敛模拟，提出高斯矩两流体MHD模型并引入压力张量各向同性以解决奇异问题，提出10时刻旋向热通量闭合以提高模拟稳定性。
摘要：
本论文的动机是确定流体模型中等离子体的最小要求，以允许收敛模拟与收敛动能模拟一致。我们证明截断闭合偏差压力或热通量会导致奇点。由于压力各向异性强烈，我们研究了高斯矩两流体MHD模型，压力张量各向同性。对于GEM磁重联挑战问题，我们的偏差压力张量在重联峰值时与已发表的动能模拟一致，但此后数值解变得不可预测并发展出近奇点，除非应用正性限制器。为解释这些困难，我们表明稳态重联需要热通量。具体而言，对于二维问题在X点处180度旋转对称，X点附近熵生产是重联必需的，并导致保守模型缺乏热通量时解变得奇异。这促使需要10时刻旋向热通量闭合。使用Chapman-Enskog展开和Gaussian-BGK碰撞算子得到磁化10时刻带电气体的热通量闭合，推广了McDonald和Groth的闭合。
英文摘要：
The motivating question for this dissertation was to identify the minimal requirements for fluid models of plasma to allow converged simulations that agree well with converged kinetic simulations of fast magnetic reconnection. We show that truncation closure for the deviatoric pressure or for the heat flux results in singularities. Due to the strong pressure anisotropies that arise, we study magnetic reconnection with a Gaussian-moment two-fluid MHD with isotropization of the pressure tensor. For the GEM magnetic reconnection challenge problem, our deviatoric pressure tensor agrees well with published kinetic simulations at the time of peak reconnection, but sometime thereafter the numerical solution becomes unpredictable and develops near-singularities that crash the simulation unless positivity limiters are applied. To explain these difficulties, we show that steady reconnection requires heat flux. Specifically, for two-dimensional problems invariant under 180-degree rotation about the X-point, entropy production in the vicinity of the X-point is necessary for reconnection and causes solutions to become singular for conservative models that lack heat flux. This prompts the need for a 10-moment gyrotropic heat flux closure. Using a Chapman-Enskog expansion with a Gaussian-BGK collision operator yields a heat flux closure for a magnetized 10-moment charged gas which generalizes the closure of McDonald and Groth.
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