论文标题
估计磁性prandtl数量和应用于太阳表面小规模发电机模拟的方法
Methodology for estimating the magnetic Prandtl number and application to solar surface small-scale dynamo simulations
论文作者
论文摘要
语境。太阳大气中的小规模发电机的数值研究的关键步骤包括精确测定磁性prandtl数量，PRM，由辐射磁磁氢动力学（MHD）模拟引起。目标。其目的是提供一种可靠的方法来估算有效的雷诺和磁性雷诺数，re和rem及其比率prm = rem/re（磁性prandlt数字），以表征MHD模拟，并根据这些无尺寸无尺寸的无尺寸无尺度仿真对这些小尺度发电机进行分类。方法。用于计算RE和REM提出的方法基于对适当元素的投影方法，它依赖于使用较高阶准精确数值运算符进行的后处理步骤，而不是模拟代码中的操作员。使用CO5bold代码进行了许多具有不同有效粘度和等离子体电阻率的辐射MHD模拟，并以RE和REM的形式表征了磁能和饱和磁场强度的生长速率。结果。总体而言，提出的方法提供了影响MHD模拟代码动量和诱导方程的耗散系数的稳定估计，因此对表征数值结果的磁性prandtl数量进行了可靠的评估。此外，发现小规模的发电机是活跃的，并且可以将小的种子磁场放大至CO5BOLD模拟中的显着值，而网格间距小于H = 12 km，即使在PRM = 0.65处也是如此。但是，很明显，很难单独将发电机仿真分类，因为估计耗散系数的幅度不仅重要，而且在哪些尺度上发生了能量耗散的幅度。
Context. A crucial step in the numerical investigation of small-scale dynamos in the solar atmosphere consists of an accurate determination of the magnetic Prandtl number, Prm, stemming from radiative magneto-hydrodynamic (MHD) simulations. Aims. The aims are to provide a reliable methodology for estimating the effective Reynolds and magnetic Reynolds numbers, Re and Rem, and their ratio Prm=Rem/Re (the magnetic Prandlt number), that characterise MHD simulations and to categorise small-scale dynamo simulations in terms of these dimensionless parameters. Methods. The methodology proposed for computing Re and Rem is based on the method of projection on proper elements and it relies on a post-processing step carried out using higher order accurate numerical operators than the ones in the simulation code. A number of radiative MHD simulations with different effective viscosities and plasma resistivities were carried out with the CO5BOLD code, and the resulting growth rate of the magnetic energy and saturated magnetic field strengths were characterised in terms of Re and Rem. Results. Overall, the proposed methodology provides a solid estimate of the dissipation coefficients affecting the momentum and induction equations of MHD simulation codes, and consequently also a reliable evaluation of the magnetic Prandtl number characterising the numerical results. Additionally, it is found that small-scale dynamos are active and can amplify a small seed magnetic field up to significant values in CO5BOLD simulations with a grid spacing smaller than h=12 km, even at Prm=0.65. However, it is also evident that it is difficult to categorise dynamo simulations in terms of Prm alone, because it is not only important to estimate the amplitude of the dissipation coefficients, but also at which scales energy dissipation takes place.
