Volume 630, October 2019
|Number of page(s)||12|
|Section||Numerical methods and codes|
|Published online||04 October 2019|
A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure
Centre de Recherche Astrophysique de Lyon UMR5574, Univ. Lyon, Ens de Lyon, Univ. Lyon1, CNRS, 69364 Lyon Cedex 07, France
2 College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
3 Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303, USA
4 Seminar of Applied Mathematics, ETH-Zürich, Switzerland
Accepted: 30 August 2019
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.
Key words: methods: numerical / stars: interiors / hydrodynamics / convection
© M. V. Popov et al. 2019
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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