A localised subgrid scale model for fluid dynamical simulations in astrophysics

Free access article

Issue		A&A Volume 450, Number 1, April IV 2006


Page(s)		265 - 281
Section		Stellar structure and evolution
DOI		http://dx.doi.org/10.1051/0004-6361:20053617

A&A 450, 265-281 (2006)
DOI: 10.1051/0004-6361:20053617

I. Theory and numerical tests

W. Schmidt^{1, 2}, J. C. Niemeyer¹ and W. Hillebrandt²

¹ Lehrstuhl für Astronomie, Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
e-mail: schmidt@astro.uni-wuerzburg.de
² Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

(Received 11 June 2005 / Accepted 19 December 2005 )

Abstract
We present a one-equation subgrid scale model that evolves the turbulence energy corresponding to unresolved velocity fluctuations in large eddy simulations. The model is derived in the context of the Germano consistent decomposition of the hydrodynamical equations. The eddy-viscosity closure for the rate of energy transfer from resolved toward subgrid scales is localised by means of a dynamical procedure for the computation of the closure parameter. Therefore, the subgrid scale model applies to arbitrary flow geometry and evolution. For the treatment of microscopic viscous dissipation a semi-statistical approach is used, and the gradient-diffusion hypothesis is adopted for turbulent transport. A priori tests of the localised eddy-viscosity closure and the gradient-diffusion closure are made by analysing data from direct numerical simulations. As an a posteriori testing case, the large eddy simulation of thermonuclear combustion in forced isotropic turbulence is discussed. We intend the formulation of the subgrid scale model in this paper as a basis for more advanced applications in numerical simulations of complex astrophysical phenomena involving turbulence.

Key words: hydrodynamics -- turbulence -- methods: numerical

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