Efficient kinetic Lattice Boltzmann simulation forthree-dimensional geospace turbulent flows

We examine the possibility of using a kinetic Lattice Boltzmann (LB) approach to perform direct numerical simulations of three-dimensional turbulentplasmas in the Hall-MHD regime. Indeed, given the small time-step required, the full dynamics at the Hall-MHD scales remains barely accessible in a parameter space close to that of plasmas in the geospace environment. The first advantage of dealing with a kinetic representation of plasma is that the spatial derivatives of the magnetic field are encompassed in the solution, allowing for an intrinsically accurate description of the small-scale current density structures. Another advantage we want to emphasize is that the novel scheme we propose is amenable to a high level of parallelism and can exploit the computational power of many-core accelerators such as GPUs, leading to unprecedented level of computational efficiency and low turnaround times. Our algorithm couples two LB schemes, for fluid dynamics, including the Lorentz force, and the magnetic induction equation with the Hall term, respectively. The LB framework we developed is tested here by means two benchmark problems routinely adopted: the three-dimensional Orszag-Tang and the Taylor-Green vortex, at high Reynolds number. Both small-scale dynamics and spectral properties of the LB runs we performed proved to be compatible with the output of analogous pseudo-spectral simulations produced with well-established pseudo-spectral codes. In the Hall regime we test the accuracy of our LB code in reproducing the small scale (fast) plasma dynamics against an exact wave solution of the Hall-MHD equations where some degree of non-linearity is kept (Mahajan, MNRAS 2005). This investigation shows how phenomenology of MHD and Hall-MHD turbulence is well captured by our LB simulations, proving its computational efficiency and a high degree of accuracy which makes it suitable to tackle problems requiring many degrees of freedom, and the comparison with the observation from the latest multi-spacecrafts magnetospheric and solar missions (MMS,SOlO,PSP).