An Extension of the Athena++ Framework for Fully Conservative Self-Gravitating Hydrodynamics

Abstract

Numerical simulations of self-gravitating flows evolve a momentum equation and an energy equation that account for accelerations and gravitational energy releases due to a time-dependent gravitational potential. In this work, we implement a fully conservative numerical algorithm for self-gravitating flows, using source terms, in the astrophysical magnetohydrodynamics framework Athena++. We demonstrate that properly evaluated source terms are conservative when they are equivalent to the divergence of a corresponding "gravity flux" (i.e., a gravitational stress tensor or a gravitational energy flux). We provide test problems that demonstrate several advantages of the source-term-based algorithm, including second order convergence and round-off error total momentum and total energy conservation. The fully conservative scheme suppresses anomalous accelerations that arise when applying a common numerical discretization of the gravitational stress tensor that does not guarantee curl-free gravity.

arXiv comment34 pages, 9 figures

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Cited by in corpus (7)

• The Athena++ Adaptive Mesh Refinement Framework: Multigrid Solvers for Self-Gravity
• Well-balanced treatment of gravity in astrophysical fluid dynamics simulations at low Mach numbers
• Energy conserving and well-balanced discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry
• A self-gravity module for the PLUTO code
• Standing solitary waves as transitions to spiral structures in gravitationally unstable accretion disks
• Towards Higher Order Accuracy in Self-Gravitating Hydrodynamics
• GenASiS: General Astrophysical Simulation System. II. Self-gravitating Baryonic Matter