Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes

¹ Heidelberger Institut für Theoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
e-mail: robert.andrassy@h-its.org
² LCSE and Department of Astronomy, University of Minnesota, Minneapolis, MN, 55455, USA
³ Astrophysics Group, Keele University, Keele, Staffordshire, ST5 5BG, UK
⁴ Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK
⁵ Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ, 85721, USA
⁶ École Normale Supérieure, Lyon, CRAL (UMR CNRS 5574), Université de Lyon, France
⁷ School of Physics and Astronomy, Monash University, Victoria, 3800, Australia
⁸ ARC Centre of Excellence for All Sky Astrophysics in Three Dimensions (ASTRO-3D), Australia
⁹ X Computational Physics (XCP) Division and Center for Theoretical Astrophysics (CTA), Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
¹⁰ Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
¹¹ Department of Physics and Astronomy, University of Victoria, Victoria, BC, V8W 2Y2, Canada
¹² Joint Institute for Nuclear Astrophysics, Center for the Evolution of the Elements, Michigan State University, 640 South Shaw Lane, East Lansing, MI, 48824, USA
¹³ Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
¹⁴ Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut, Mönchhofstr. 12-14, 69120 Heidelberg, Germany
¹⁵ Pasadena Consulting Group, 1075 N Mar Vista Ave, Pasadena, CA, 91104, USA
¹⁶ Department of Physics and Astronomy, Georgia State University, Atlanta, GA, 30303, USA
¹⁷ Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany

Received: 31 October 2021
Accepted: 29 December 2021

Abstract

Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH, MUSIC, PPMSTAR, PROMPI, and SLH, which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within ≲3σ of the mean of all simulations on a given grid (128³ and 256³ grid cells), where σ describes the statistical variation due to the flow’s time dependence. They also agree well with a 512³ reference run. The 128³ and 256³ simulations agree within 9% and 4%, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.