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

TL;DR

This paper extends the A-MaZe simulation toolkit to accurately model stratified stellar convection by implementing a well-balanced scheme that preserves energy and momentum, enabling more reliable 2D and 3D stellar simulations.

Contribution

The authors developed a well-balanced, energy-preserving extension of the A-MaZe hydrodynamics solver for stellar convection simulations, demonstrating improved accuracy and stability.

Findings

The scheme maintains static balance between gravity and pressure to machine precision.

It preserves gas energy on average despite local convective motions.

Qualitative agreement with implicit codes confirms its reliability.

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.