Numerical convergence of 2D solar convection in implicit large-eddy simulations

Abstract

Large-eddy simulations (LES) and implicit LES (ILES) are wise and affordable alternatives to the unfeasible direct numerical simulations (DNS) of turbulent flows at high Reynolds numbers (Re). However, for systems with few observational constraints, it is a formidable challenge to determine if these strategies adequately capture the physics of the system. Here we address this problem by analyzing numerical convergence of ILES of turbulent convection in 2D, with resolutions between $64^2$ and $2048^2$ grid points, along with the estimation of their effective viscosities, resulting in effective Reynolds numbers between $1$ and $\sim 10^4$. The thermodynamic structure of our model resembles the solar interior, including a fraction of the radiative zone and the convection zone. In the convective layer, the ILES solutions converge for the simulations with $\ge 512^2$ grid points, as evidenced by the integral properties of the flow and its power spectra. Most importantly, we found that even a resolution of $128^2$ grid points, Re$\sim 10$, is sufficient to capture the dynamics of the large scales accurately. This is a consequence of the ILES method allowing that the energy contained in these scales is the same in simulations with low and high resolution. Special attention is needed in regions with a small density scale height driving the formation of fine structures unresolved by the numerical grid. In the stable layer we found the excitation of internal gravity waves, yet high resolution is needed to capture their development and interaction.

arXiv comment15 pages, 9 figures, accepted for publication in The Astrophysical Journal

References in corpus (14)

• Turbulent thermal superstructures in Rayleigh-Bénard convection
• Seismic Sounding of Convection in the Sun
• High-resolution calculation of the solar global convection with the reduced speed of sound technique: II. Near surface shear layer with the rotation
• On the role of tachoclines in solar and stellar dynamos
• The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime
• Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer
• Numerical Calculation of Convection with Reduced Speed of Sound Technique
• On the sensitivity of magnetic cycles in global simulations of solar-like stars
• Supergranulation as the largest buoyantly driven convective scale of the Sun
• Understanding solar torsional oscillations from global dynamo models
• Modelling turbulent stellar convection zones: sub-grid scales effects
• Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations
• Effect of the radiative background flux in convection
• Dynamics of Turbulent Convection and Convective Overshoot in a Moderate Mass Star

Cited by in corpus (1)

• Implicit large eddy simulations of global solar convection: effects of numerical resolution in non-rotating and rotating cases