Large eddy simulation models for incompressible magnetohydrodynamics derived from the variational multiscale formulation

Abstract

Novel large eddy simulation (LES) models are developed for incompressible magnetohydrodynamics (MHD). These models include the application of the variational multiscale formulation of LES to the equations of incompressible MHD. Additionally, a new residual-based eddy viscosity model is introduced for MHD. A mixed LES model that combines the strengths of both of these models is also derived. The new models result in a consistent numerical method that is relatively simple to implement. The need for a dynamic procedure in determining model coefficients is no longer required. The new LES models are tested on a decaying Taylor-Green vortex generalized to MHD and benchmarked against classical LES turbulence models. The LES simulations are run in a periodic box of size [−π, π]3 with 32 modes in each direction and are compared to a direct numerical simulation (DNS) with 512 modes in each direction. The new models are able to account for the essential MHD physics which is demonstrated via comparisons of energy spectra. We also compare the performance of our models to a DNS simulation by Pouquet et al. [“The dynamics of unforced turbulence at high Reynolds number for Taylor–Green vortices generalized to MHD,” Geophys. Astrophys. Fluid Dyn. 104, 115–134 (2010)], for which the ratio of DNS modes to LES modes is 262:144.