A new sub-grid-scale model is developed for studying influences of the Hall term on macroscopic aspects of magnetohydrodynamic turbulence. Although the Hall term makes numerical simulations extremely expensive by exciting high-wave-number coefficients and makes magnetohydrodynamic equations stiff, studying macroscopic aspects of magnetohydrodynamic turbulence together with the Hall term is meaningful since this term often influences not only sub-ion-scales but also macroscopic scales. Our new sub-ion-scale sub-grid-scale model for large eddy simulations of Hall magnetohydrodynamic turbulence is developed in order to overcome the difficulties. Large eddy simulations by the use of the new model successfully reproduce statistical signatures such as the energies and probability density functions of the vorticity and current density, keeping some signatures intrinsic to Hall magnetohydrodynamic turbulence. Our new sub-grid-scale model enables numerical simulations of homogeneous and isotropic Hall magnetohydrodynamic turbulence with a small computational cost, improving the effective resolution of an LES from that carried out with earlier models, and retaining the ion-electron separation effects by the Hall term in the grid scales.

开发了一种新的亚网格尺度模型，用于研究霍尔项对磁流体动力学湍流宏观方面的影响。尽管霍尔项通过激发高波数系数使数值模拟变得极其昂贵并使磁流体动力学方程变得僵硬，但与霍尔项一起研究磁流体动力学湍流的宏观方面是有意义的，因为该项通常不仅影响亚离子尺度，而且宏观尺度。为了克服这些困难，我们开发了用于霍尔磁流体动力学湍流大涡模拟的新的亚离子尺度亚网格尺度模型。使用新模型的大涡模拟成功地再现了统计特征，例如涡度和电流密度的能量和概率密度函数，保留霍尔磁流体动力学湍流固有的一些特征。我们新的亚网格尺度模型能够以较小的计算成本对均匀和各向同性霍尔磁流体动力学湍流进行数值模拟，提高 LES 的有效分辨率，并保留霍尔的离子电子分离效应网格尺度中的术语。