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

TL;DR

This paper introduces a fully conservative numerical algorithm for simulating self-gravitating flows within the Athena++ framework, ensuring accurate conservation of momentum and energy, and demonstrating improved stability and convergence.

Contribution

The authors develop and implement a source-term-based conservative scheme for self-gravitating hydrodynamics in Athena++, addressing issues with non-conservative discretizations.

Findings

Second order convergence demonstrated in tests

Total momentum and energy are conserved to round-off error

Suppression of anomalous accelerations in simulations

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.