http://arxiv.org/abs/1904.04099
The use of Large Eddy Simulations in compressible, turbulent MHD is often limited to the implementation of purely dissipative sub-grid scale models. While such models work well in the hydrodynamic case due to the universality of the spectrum, they do not fully describe the complex dynamics of MHD, where the transfer of energy between internal, kinetic and magnetic energies at small scales are less trivial. For this reason, a sub-grid scale model based on the gradients of the fields entering in each non-linear term of the equations has already been proposed and studied in the literature, for the momentum and induction equations. Here, we consider the full set of compressible, ideal MHD equations, with an ideal gas equation of state, and we proposed a generalization of the gradient model, including the energy equation. We focus on the residuals coming from the whole set of equations, by filtering accurate high-resolution simulations of the turbulent Newtonian Kelvin-Helmholtz instability in a periodic box. We employ the same high-resolution shock capturing methods typically used in relativistic MHD, applicable in particular to neutron star mergers. The a-priori test, i.e. the fit between the sub-filter residuals and the model, allows us to confirm that the gradient model outperforms any other, in terms of accuracy of the fit and small deviations of the best-fit pre-coefficient from the expected value. Such results are validated for 2D and 3D, for a range of different problems, and are shown, for the first time, to hold also for the energy evolution equation. This paper is the first step, based on a solid theoretical and numerical basis, towards the near-future extension of the sub-grid scale gradient model to the relativistic MHD, and a future implementation in a full General Relativity LES.
D. Viganò and C. Palenzuela
Tue, 9 Apr 19
77/105
Comments: 22 pages, 17 figures, 2 tables. Submitted