An Extension of the Athena++ Framework for Fully Conservative Selfgravitating Hydrodynamics
Abstract
Numerical simulations of selfgravitating flows evolve a momentum equation and an energy equation that account for accelerations and gravitational energy releases due to a timedependent gravitational potential. In this work, we implement a fully conservative numerical algorithm for selfgravitating 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 sourcetermbased algorithm, including secondorder convergence and roundoff 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 curlfree gravity.
 Publication:

The Astrophysical Journal Supplement Series
 Pub Date:
 February 2021
 DOI:
 10.3847/15384365/abcfbd
 arXiv:
 arXiv:2012.01340
 Bibcode:
 2021ApJS..252...30M
 Keywords:

 Hydrodynamics;
 Gravitation;
 Computational methods;
 1963;
 661;
 1965;
 Astrophysics  Instrumentation and Methods for Astrophysics
 EPrint:
 34 pages, 9 figures