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

TL;DR

This paper introduces new variational multiscale turbulence models for incompressible magnetohydrodynamics, combining residual-based eddy viscosity and mixed models, which are validated through numerical experiments showing convergence to DNS solutions.

Contribution

The paper develops and tests a novel class of finite element variational multiscale turbulence models for MHD that are residual-based, dynamic, and numerically consistent.

Findings

Models accurately reproduce DNS energy evolution.

Models improve with mesh refinement.

Residual-based models are dynamically consistent.

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.