Modelling turbulent stellar convection zones: sub-grid scales effects

TL;DR

This study compares two global models of turbulent stellar convection to evaluate how different treatments of sub-grid scales affect large-scale flow simulations, aiming to improve robustness in stellar interior modeling.

Contribution

It provides a detailed comparison of sub-grid scale effects between the ASH and EULAG codes using energy budgets and derived diffusivities, advancing understanding of numerical robustness.

Findings

Good agreement in large-scale flows between models in hydrodynamic regime

Derived eddy-diffusion coefficients effectively characterize sub-grid effects

Encourages further MHD regime investigations for dynamo solutions

Abstract

The impressive development of global numerical simulations of turbulent stellar interiors unveiled a variety of possible differential rotation (solar or anti-solar), meridional circulation (single or multi-cellular), and dynamo states (stable large scale toroidal field or periodically reversing magnetic fields). Various numerical schemes, based on the so-called anelastic set of equations, were used to obtain these results. It appears today mandatory to assess their robustness with respect to the details of the numerics, and in particular to the treatment of turbulent sub-grid scales. We report on an ongoing comparison between two global models, the ASH and EULAG codes. In EULAG the sub-grid scales are treated implicitly by the numerical scheme, while in ASH their effect is generally modelled by using enhanced dissipation coefficients. We characterize the sub-grid scales effect in a turbulent convection simulation with EULAG. We assess their effect at each resolved scale with a detailed energy budget. We derive equivalent eddy-diffusion coefficients and use the derived diffusivities in twin ASH numerical simulations. We find a good agreement between the large-scale flows developing in the two codes in the hydrodynamic regime, which encourages further investigation in the magnetohydrodynamic regime for various dynamo solutions.