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We live in an age in which high-performance computing is transforming the waywe do science. Previously intractable problems are now becoming accessible bymeans of increasingly realistic numerical simulations. One of the most enduringand most challenging of these problems is turbulence. Yet, despite theseadvances, the extreme parameter regimes encountered in space physics andastrophysics (as in atmospheric and oceanic physics) still preclude directnumerical simulation. Numerical models must take a Large Eddy Simulation (LES)approach, explicitly computing only a fraction of the active dynamical scales.The success of such an approach hinges on how well the model can represent thesubgrid-scales (SGS) that are not explicitly resolved. In addition to theparameter regime, heliophysical and astrophysical applications must also facean equally daunting challenge: magnetism. The presence of magnetic fields in aturbulent, electrically conducting fluid flow can dramatically alter thecoupling between large and small scales, with potentially profound implicationsfor LES/SGS modeling. In this review article, we summarize the state of the artin LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussingthe nature of MHD turbulence and the small-scale processes that give rise toenergy dissipation, plasma heating, and magnetic reconnection, we consider howthese processes may best be captured within an LES/SGS framework. We thenconsider several specific applications in heliophysics and astrophysics,assessing triumphs, challenges, and future directions.

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics