GTP Large-Eddy Simulations of MHD Turbulence


Large Eddy Simulations (LES) provide a means to model turbulent flows in extreme parameter regimes that are inaccessible to Direct Numerical Simulation (DNS). However, LES require some strategy to deal with the sub-grid scale (SGS) motions that cannot be explicitly resolved. Devising reliable SGS models is particularly challenging in electrically conducting fluids where magnetohydrodynamic (MHD) interactions link large and small scales, promoting self-organization processes and small-scale anisotropy that have no counterpart in neutral fluids in the absence of external agents such as rotation and stratification.

- Participation in this workshop is by invitation only.

In this workshop we will explore LES/SGS modeling strategies for turbulent MHD flows in geophysical, heliophysical, and astrophysical applications. Sessions on specific focus topics to be addressed include:

  1. SGS Modeling vs filtering vs AMR
    Leaders: M. Miesch (NCAR, USA): miesch@ and P. Sagaut (UPMC, France): pierre.sagaut@

    Is it necessary to model explicitly the spectral transfer for SGS motions or is it sufficient to minimize large-scale dissipation through filtering or grid-based diffusion schemes? Can Adaptive Mesh Refinement (AMR) be used to capture the dynamics of small scales in lieu of LES, at a reasonable computational expense? Might novel physical, mathematical or algorithmic approaches improve the reliability and computational efficiency of SGS models?

  2. Anisotropy and Kinetic Effects
    Leaders: C. Cambon (Lyon, France): claude.cambon@ and F. Jenko (IPP-MPG, Germany): fsj@

    Dynamical interactions between flows and magnetic fields make all scales inherently anisotropic in MHD turbulence. What is the nature of this anisotropy and can it be reliably captured within an LES/SGS modeling framework? Should it and at what cost?

  3. Magnetic Reconnection
    Leaders: D. Uzdensky (Univ. of Colorado): uzdensky@ and M. Velli (JPL/Cal Tech, USA): mvelli@

    Energy dissipation and global magnetic topology in MHD are intimately linked to magnetic reconnection. Can the subtleties of small-scale reconnection in MHD turbulence be reliably captured by SGS modeling or filtering, the simplest example being turbulent diffusion? Can such modeling substitute for plasma kinetic effects reasonably well? What about eddy noise?

  4. Helicity
    Leaders: A. Brandenburg (Nordita, Sweden): brandenb@ and W. Matthaeus (Univ Delaware, USA): whm@

    How do magnetic, kinetic, and cross helicity regulate spectral transfer among scales and how might LES/SGS models best take these invariants into account?

  5. Geometry and Boundary Conditions
    Leaders: E. King (UC, Berkeley, USA): eric.king@ and S. Tobias (Univ. Leeds, UK): smt@

    Can SGS models in MHD be devised that are universal or are small-scale dynamics inextricably linked to the large-scale geometry (at least in practical applications)? What role do boundaries play in global dynamics and dynamo processes?

  6. Applications and the MHD-LES Challenge
    Leaders:  J. Stone (Princeton Univ., USA): jstone@ and J. Toomre (Univ. Colorado/JILA, USA): jtoomre@

    Are there untapped opportunities in geophysics, heliophysics, astrophysics, and industry where LES of MHD phenomena might foster substantial progress if it is more fully exploited? What particular challenges do each of these applications pose with regard to large-scale instabilities, kinetic, compressibility, or other effects? Can and should we define benchmark problems that can be used to assess the viability of different modeling strategies?

As part of Session 6, workshop participants will work together to define and embark upon an LES-MHD Challenge to be carried out within one year of the workshop. The challenge will consist of a few care-fully selected benchmark problems sampling different physical conditions with regard to geometry, helicity, shear, rotation, and stratification. Issues of variable magnetic Prantdl number will also be explored. An example of a benchmark problem is the Orszag-Tang vortex and its extension to 3D. For each benchmark, different research teams will contribute an entry into the Challenge consisting of one reference DNS plus one or more exploratory LES models designed to anticipate the behavior of the system at much higher Reynolds and magnetic Reynolds numbers. The fidelity of the exploratory LES models will be assessed with higher-resolution DNS. Although this is not a new strategy, we believe that it is an increasingly important one as continuing advances in high-performance computing technology enable intermediate-resolution LES models with wide enough dynamical range to capture large-scale anisotropy and transport together with the smaller-scale self-similarity that many SGS models rely on.

Scientific Organizing Committee

N. Featherstone (HAO/NCAR and University of Colorado)
M. Miesch (NCAR)
P. Mininni (University of Buenos Aires/NCAR)
A. Petrosyan (Space Res. Inst., Russian Acad. Sci.)
A. Pouquet (NCAR)
J. Toomre (JILA/University of Colorado)