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A new sub-grid-scale model is developed for studying influences of the Hallterm on macroscopic aspects of magnetohydrodynamic turbulence. Although theHall term makes numerical simulations extremely expensive by excitinghigh-wave-number coefficients and makes magnetohydrodynamic equations stiff,studying macroscopic aspects of magnetohydrodynamic turbulence together withthe Hall term is meaningful since this term often influences not onlysub-ion-scales but also macroscopic scales. A new sub-ion-scale sub-grid-scalemodel for large eddy simulations of Hall magnetohydrodynamic turbulence isdeveloped in order to overcome the difficulties. Large eddy simulations by theuse of the new model successfully reproduce statistical natures such as theenergies and probability density functions of the vorticity and currentdensity, keeping some natures intrinsic to Hall magnetohydrodynamic turbulence.Our new sub-grid-scale model enables numerical simulations of homogeneous andisotropic Hall magnetohydrodynamic turbulence with a small computational cost,improving the essential resolution of an LES from that carried out with earliermodels, and retaining the ion-electron separation effects by the Hall term inthe grid scales.

Sub-grid-scale model for studying Hall effects on macroscopic aspects of magnetohydrodynamic turbulence