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This paper reports an application of gas-kinetic BGK scheme to thecomputation of turbulent compressible convection in the stellar interior. Afterincorporating the Sub-grid Scale (SGS) turbulence model into the BGK scheme, wetested the effects of numerical parameters on the quantitative relationshipsamong the thermodynamic variables, their fluctuations and correlations in avery deep, initially gravity-stratified stellar atmosphere. Comparisonindicates that the thermal properties and dynamic properties are dominated bydifferent aspects of numerical models separately. An adjustable Deardorffconstant in the SGS model $c_\mu=0.25$ and an amplitude of artificial viscosityin the gas-kinetic BGK scheme $C_2=0$ are appropriate for current study. Wealso calculated the density-weighted auto- and cross-correlation functions inXiong's (\cite{xiong77}) turbulent stellar convection theories based on whichthe gradient type of models of the non-local transport and the anisotropy ofthe turbulence are preliminarily studied. No universal relations or constantparameters were found for these models.

Efficient Turbulent Compressible Convection in the Deep Stellar Atmosphere