Efficient turbulent compressible convection in the deep stellar atmosphere

Abstract

We report on an application of gas-kinetic BGK scheme to the computation of turbulent compressible convection in the stellar interior. After incorporating the Sub-grid Scale (SGS) turbulence model into the BGK scheme, we tested the effects of numerical parameters on the quantitative relationships among the thermodynamic variables, their fluctuations and correlations in a very deep, initially gravity-stratified stellar atmosphere. Comparison indicates that the thermal properties and dynamic properties are dominated by different aspects of numerical models separately. An adjustable Deardorff constant in the SGS model cμ.25 and an amplitude of artificial viscosity in the gas-kinetic BGK scheme C2 = 0 are appropriate for the current study. We also calculated the density-weighted auto- and cross-correlation functions in Xiong's turbulent stellar convection theory based on which the gradient type of models of the non-local transport and the anisotropy of the turbulence were preliminarily studied. No universal relations or constant parameters were found for these models.