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A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure

Abstract : Characterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average, despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone, as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement.
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Submitted on : Saturday, July 2, 2022 - 8:20:29 AM
Last modification on : Friday, August 5, 2022 - 3:37:49 PM

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M. V. Popov, R. Walder, D. Folini, T. Goffrey, I. Baraffe, et al.. A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure. Astronomy and Astrophysics - A&A, EDP Sciences, 2019, 630, ⟨10.1051/0004-6361/201834180⟩. ⟨insu-03711415⟩

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