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.
Highlights
In a wide range of astrophysical objects, the balance between gravitation and gas pressure is a key element, on top of which additional physics may take place
We adopt the scheme of KM16, the key aspects of which we summarize here
We examine two 2D setups analogous to H84 and show that we obtain similar results, notably similar convection patterns and energy fluxes
Summary
In a wide range of astrophysical objects, the balance between gravitation and gas pressure is a key element, on top of which additional physics may take place. Energy transport via convection is often essential in maintaining a globally quasi-static state This is notably the case for the outer parts of low mass stars and the inner regions of high mass stars, where energy transport via radiation is not efficient enough. Multidimensional simulations of such transport processes contribute to the 321D link for stellar modeling (e.g., Arnett et al 2015), that is, the effort to improve one-dimensional stellar evolution models via simulating short episodes in 2D and 3D. We mention the vertical structure of accretion disks and supernova explosions, notably the moment just before the onset of the collapse and again when the prompt shock stalls (Couch & Ott 2013; Müller et al 2016, 2017)
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