An Extension of the Athena++ Framework for Fully Conservative Self-Gravitating Hydrodynamics. (arXiv:2012.01340v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Mullen_P/0/1/0/all/0/1">P. D. Mullen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hanawa_T/0/1/0/all/0/1">Tomoyuki Hanawa</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gammie_C/0/1/0/all/0/1">C. F. Gammie</a>
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.
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.
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