Almost every astrophysical fluid flow turns out to be highly turbulent. As a result, in simulating these flows one must either provide a very fine grid in order to resolve at least some of the turbulent motions or one must include a model of the turbulence. Mixing length models for turbulent convection in stellar evolution calculations are one example. My team at the University of Minnesota has been simulating astrophysical flows for many years by computing the largest turbulent motions directly on fine computational grids. Results for simulations of stellar convection will be shown and compared with mixing length models. We have also simulated the highly compressible turbulence that occurs in such flows separately, with the aim of developing models of these small-scale flows for use in numerical computations. Convergence studies for these and the convection flows show falsification of the velocity power spectrum on scales around 16 cell widths where one would otherwise expect numerical errors to be essentially negligible. We believe these errors can be corrected through use of a subgrid-scale turbulence model. From these simulations, a correlation has emerged between the topology of the local flow and the rate of energy transfer from large-scale motions to small-scale turbulence. The evidence for this correlation from very fine grid (up to 2048 cubed) simulations of Mach 1 turbulence will be shown, and the outline of a subgrid-scale model for astrophysical flows will be discussed.
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