A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics

Abstract

New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulations are introduced. The new models include the variational multiscale formulation, a residual-based eddy viscosity model, and a mixed model that combines both of these component models. Each model contains terms that are proportional to the residual of the incompressible MHD equations and is therefore numerically consistent. Moreover, each model is also dynamic, in that its effect vanishes when this residual is small. The new models are tested on the decaying MHD Taylor Green vortex at low and high Reynolds numbers. The evaluation of the models is based on comparisons with available data from direct numerical simulations (DNS) of the time evolution of energies as well as energy spectra at various discrete times. A numerical study, on a sequence of meshes, is presented that demonstrates that the large eddy simulation approaches the DNS solution for these quantities with spatial mesh refinement.

30 pages, 14 figures, submitted to the Journal of Computational Physics

References in corpus (11)

• Spectrum of magnetohydrodynamic turbulence
• The Spectral Slope and Kolmogorov Constant of MHD turbulence
• Scale-Locality of Magnetohydrodynamic Turbulence
• On the lack of universality in decaying magnetohydrodynamic turbulence
• Simulation of induction at low magnetic Prandtl number
• Hydrodynamic and hydromagnetic energy spectra from large eddy simulations
• Spectral Modeling of Magnetohydrodynamic Turbulent Flows
• The dynamics of unforced turbulence at high Reynolds number for Taylor-Green vortices generalized to MHD
• A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• The origins of $k^{-2}$ spectrum in the decaying Taylor-Green magnetohydrodynamic turbulent flows

Cited by in corpus (1)

• Extension of the sub-grid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities