Efficient Turbulent Compressible Convection in the Deep Stellar Atmosphere

TL;DR

This study applies a gas-kinetic BGK scheme with SGS turbulence modeling to simulate turbulent compressible convection in deep stellar atmospheres, revealing insights into thermodynamic fluctuations and turbulence anisotropy.

Contribution

It introduces a combined gas-kinetic BGK scheme with SGS turbulence modeling for deep stellar convection simulations, analyzing parameter effects and turbulence properties.

Findings

Thermal and dynamic properties are influenced by different numerical model aspects.

Optimal parameters identified: Deardorff constant $c_=0.25$ and artificial viscosity $C_2=0$.

Preliminary study of non-local transport and turbulence anisotropy without universal constants.

Abstract

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.