  This paper reports 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 $c_\mu=0.25$ and an amplitude of artificial viscosity
in the gas-kinetic BGK scheme $C_2=0$ are appropriate for current study. We
also calculated the density-weighted auto- and cross-correlation functions in
Xiong's (\cite{xiong77}) turbulent stellar convection theories based on which
the gradient type of models of the non-local transport and the anisotropy of
the turbulence are preliminarily studied. No universal relations or constant
parameters were found for these models.
