Local Dynamic Subgrid Closure for Compressible MHD Turbulence Simulation

A Local Dynamic Kinetic Energy Model (LDKM) for large-eddy simulation (LES) of magnetohydrodynamicis (MHD) turbulence is proposed. The proposed MHD turbulence model evaluates all model coefficients locally and dynamically without any ad hoc aver-aging. This model does not assume low magnetic Reynolds numbers. The turbulent residual-helicity effect (α-effect) appearing in the magnetic induction equation is success-fully modeled and consistently remains a pseudo-scalar. This paper uses the MHD-LDKM LES model to compute high-Re decaying isotropic turbulence in a magnetic field. A decay model is used for validation. It is observed that the energy spectrum follows a k−5/3 law in DNS and LDKM results. For further validation, the long time behavior of ideal invariants: energy (E), cross helicity (Hc), and magnetic helicity (Hm) are examined. The expected selective decay is observed when Hc is finite. This MHD LDKM model is applicable to wide variety of high/low magnetic Reynolds number applications. Nomenclature (∗)sgs subgrid scale value α-effect force to generate a poloidal electric current from the poloidal magnetic field Ω̄k resolved vorticity āij resolved part of MHD shear stress B̄i resolved magnetic field M̄ij resolved rate of magnetic strain β turbulent closure coefficient b magnetic dissipation term v kinetic dissipation term ijk alternating tensor f ̂ test filtered k sgs,b subgrid magnetic energy k sgs subgrid kinetic enregy κ thermal conductivity λ magnetic diffusivity µb permeability ν viscosity νat magnetic diffusivity related to τ sgs,v,a ij νvt turbulent viscosity νe effective viscosity ∆ local grid width ρ density σ electric conductivit