An Extension of the Athena plus plus Framework for Fully Conservative Self-gravitating Hydrodynamics

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.

Automated summary

In this study, a fully conservative numerical algorithm for self-gravitating flows was implemented using source terms, demonstrating advantages such as second-order convergence and conservation of total momentum and total energy. The scheme suppresses anomalous accelerations arising from the common numerical discretization of the gravitational stress tensor that does not guarantee curl-free gravity.