2020/12/02 by P. D. Mullen, Tomoyuki Hanawa, C. F. Gammie · 16 citations
Physics and Astronomy · #Convergence (economics) #Cosmology and Gravitation Theories #Discretization #Divergence (linguistics) #Energy–momentum relation #Gamma-ray bursts and supernovae #Gravitation #Gravitational energy #Gravitational field #Momentum (technical analysis) #Pulsars and Gravitational Waves Research #Tensor (intrinsic definition) #astro-ph.IM
paper · pdf · doi:10.3847/1538-4365/abcfbd
published in The Astrophysical Journal Supplement Series 252(2), 30 (Institute of Physics) · 34 pages, 9 figures
arxiv created 2020/12/02 · openalex created_date 2020/12/07 · openalex publication_date 2021/02/01 · arxiv updated 2021/02/17 · openalex updated_date 2026/08/06
Abstract 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.