全局吸积盘的收敛性检验
Testing Convergence for Global Accretion Disks
摘要：
全球盘模拟提供了一个强有力的工具，研究吸积和潜在的磁流体动力学湍流驱动的磁旋转不稳定性（MRI）。使用它们来准确地预测诸如应力、吸积率和表面亮度分布等量，需要理解和控制由分辨率和算法引起的纯数值效应。我们使用磁通保守雅典娜代码进行一系列的实验磁盘具有各种磁拓扑结构，以确定什么构成足够的分辨率。我们开发并应用了几个分辨率度量：Qz和Qphi，网格区域尺寸与特征MRI波长的比率，α_mag，麦克斯韦应力与磁压力的比率，以及径向与环形磁场能量的比率。对于这里考虑的初始条件，足够的分辨率的特征在于Qz > 15，Qphi > 20，alpha_mag = 0.45，以及场能量比为0.2。这些值与每个比例高度> 35个区域相关联，这与剪切盒模拟一致。数值算法也很重要。与HLLD通量求解器和三阶插值相比，使用HLLE通量求解器或二阶插值会显著降低有效分辨率。只有大量的网格区域才能达到这个标准的分辨率，网格区域的排列方式要与问题的对称性和模拟的科学目标相匹配。
英文摘要：
Global disk simulations provide a powerful tool for investigating accretion and the underlying magnetohydrodynamic turbulence driven by the magneto-rotational instability (MRI). Using them to predict accurately quantities such as stress, accretion rate, and surface brightness profile requires that purely numerical effects, arising from both resolution and algorithm, be understood and controlled. We use the flux-conservative Athena code to conduct a series of experiments on disks having a variety of magnetic topologies to determine what constitutes adequate resolution. We develop and apply several resolution metrics: Qz and Qphi, the ratio of the grid zone size to the characteristic MRI wavelength, alpha_mag, the ratio of the Maxwell stress to the magnetic pressure, and the ratio of radial to toroidal magnetic field energy. For the initial conditions considered here, adequate resolution is characterized by Qz > 15, Qphi > 20, alpha_mag = 0.45, and a field energy ratio of 0.2. These values are associated with > 35 zones per scaleheight, a result consistent with shearing box simulations. Numerical algorithm is also important. Use of the HLLE flux solver or second-order interpolation can significantly degrade the effective resolution compared to the HLLD flux solver and third-order interpolation. Resolution at this standard can be achieved only with large numbers of grid zones, arranged in a fashion that matches the symmetries of the problem and the scientific goals of the simulation.
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