Statistics – Computation
Scientific paper
May 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992aas...180.3704c&link_type=abstract
American Astronomical Society, 180th AAS Meeting, #37.04; Bulletin of the American Astronomical Society, Vol. 24, p.787
Statistics
Computation
Scientific paper
A 2D/3D hydro code has been developed to study the dynamics of rotating stellar interiors. One of the first problems to be addressed was the modeling of the subgrid-scale (SGS) viscosity that is needed to simulate the effects of turbulence on scales smaller than the grid spacing in a computational mesh. In real stars, kinetic energy on global scales cascades down to the dissipative regime where it is transformed into thermal energy. This bottom-end scale, lambda_ {diss}, is also the size of the smallest turbulent eddies which are typically tens of centimeters in stellar interiors. Numerical simulations, however, can realistically model only scales larger than the grid separation, lambda_ {grid}, which may be 7 or 8 orders of magnitude larger than lambda_ {diss}. Therefore, an SGS viscosity is required to absorb energy that would otherwise buildup on the grid-scale and destroy the simulation. This viscosity should have the form A L rho v_t where A is a dimensionless parameter of order unity, L is a length-scale of order lambda_ {grid}, rho is the local density, and v_t is a measure of the turbulent velocity at the grid-scale. Empirically, we know that A should actually be somewhat smaller than unity in the high shear or very turbulent flows that often occur near boundaries, ``walls'', or free surfaces. In this paper, I propose a suitable algorithm (i.e., a ``law of the wall'') for determining the magnitude A of the SGS viscosity in the compressible interiors of stellar models. I also address the problem imposed by a nonuniform grid spacing and come to the conclusion that the only physically acceptable viscosity is a nonisotropic one that will guarantee at every point a rate of diffusion of momentum, energy, and mass which is independent of direction.
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