计算广义相对论无力电动力学：II。数值扩散率的表征
Computational General Relativistic Force-Free Electrodynamics: II. Characterization of Numerical Diffusivity
摘要：
科学代码是理论和实验之间不可或缺的纽带;在（天文）等离子体物理中，这样的数值工具是了解宇宙最极端能量流动的一个窗口。麦克斯韦方程组的离散化-需要使高度磁化（天文）物理等离子体服从其数值模拟-引入数值扩散。它作为耗散源独立于系统的物理成分。了解科学代码的数值扩散是对其可靠性进行分类的关键。它给出了具体的限制，其中数值实验的结果是物理的。我们的目标是量化和表征的数值扩散特性，我们最近开发的数值工具的模拟广义相对论性无力电动力学，通过校准和比较它与文献中发现的其他策略。我们的代码正确地模拟了高磁化等离子体的平滑波。我们评估的范围内的电流片和撕裂模不稳定性的广义相对论无力电动力学。我们确定，电流平行于磁场（$\mathbf{j}_\parallel$），结合广义相对论无力电动力学的故障在电流片，损害电阻不稳定性的物理建模。我们发现，每个感兴趣的特征尺寸（例如，在等离子体波的波长或电流片的横向宽度）至少需要八个数值单元，以找到数值和物理起源的电阻率之间的一致性。高阶离散化的无力电流使我们能够提供几乎理想的订单收敛（光滑）等离子体波动力学。电阻层的物理建模需要合适的电流处方或子网格建模以用于$\mathbf{j}_\parallel$的演变。
英文摘要：
Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe's most extreme flows of energy. The discretization of Maxwell's equations - needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling - introduces numerical diffusion. It acts as a source of dissipation independent of the system's physical constituents. Understanding the numerical diffusion of scientific codes is the key to classify their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics, by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field ($\mathbf{j}_\parallel$), in combination with the break-down of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g. the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of $\mathbf{j}_\parallel$.
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