Numerical Modeling of Subgrid-Scale Flow in Turbulence, Rotation, and Convection [chapter]

Philip S. Marcus
1986 Astrophysical Radiation Hydrodynamics  
We show that it ~s impossible to simulate numerically all of the length-scales in astrophysical turbulence. We look at the effects of ignoring the unresolvable. small-scale flow. and show how numerical simulations that neglect the subgrid-scale motions produce erroneous solutions. Then we discuss the "quick fix" remedy of introducing a numerical or eddy-viscosity. We sketch how the analytic theories of turbulence attempt to model the large-scale effects of the small-scale motions. In the last
more » ... ions. In the last section of this paper we examine four anisotropic. inhomogeneous flows of astrophysical interest for which numerical and eddy-viscosities produce incorrect solutions. Improved models of the subgrid-scale flow are examined. We show how numerical simulation of large Reynolds number (but non-turbulent)· flows can guide us in modeling subgrid-scale flows in astrophysical settings. Turbulence. rotation. and convection are generally treated by astrophysicists in the same manner; they are avoided whenever possible. Jets do not become turbulent. stars do not rotate. and planetary nebulae do not convect -except when the absence of these motions contradicts common sense or when the mixing properties of these motions must be invoked to solve some astrophysical paradox. The reason we avoid calculating these flows is that the numerical computation of turbulence. in even the simplest labor~ tory settings. is usually impossible because the velocity spans a much larger range of length-scales and has many more degrees of freedom than can be accommodated in present computers. The 387 K.-H. A. Winkler and M. L. Norman (eds.), Astrophysical Radiation Hydrodynamics, 387-414.
doi:10.1007/978-94-009-4754-2_11 fatcat:wmwzlr2znja2dhcwgqomvm4pq4