An extension of the athena++ framework for fully conservative self-gravitating hydrodynamics

P. D. Mullen, Tomoyuki Hanawa, C. F. Gammie

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article numberabcfbd
JournalAstrophysical Journal, Supplement Series
Issue number2
StatePublished - Feb 2021

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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