Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Extension of the Athena++ 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.

12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org