Local spherical collapsing box in ATHENA++: Numerical implementation and benchmark tests

¹ Univ Lyon, Univ Lyon 1, ENS de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574, 69230 Saint-Genis-Laval, France
e-mail: elliot.lynch@ens-lyon.fr
² Center for Star and Planet Formation, GLOBE Institute, University of Copenhagen, Øster Voldgade 5–7, 1350 Copenhagen, Denmark
e-mail: ziyan.xu@sund.ku.dk

Received: 20 March 2024
Accepted: 23 June 2024

Abstract

We implement a local model for a spherical collapsing or expanding gas cloud in the ATHENA++ magnetohydrodynamic code. This local model consists of a Cartesian periodic box with time-dependent geometry. We present a series of benchmark test problems, including nonlinear solutions and linear perturbations of the local model, confirming the code’s desired performance. During a spherical collapse, a horizontal shear flow is amplified, corresponding to angular momentum conservation of zonal flows in the global problem; wave speed and the amplitude of sound waves increase in the local frame, due to the reduction in the characteristic length scale of the box, which can lead to an anisotropic effective sound speed in the local box. Our code conserves both mass and momentum-to-machine precision. This numerical implementation of the local model has potential applications to the study of local physics and hydrodynamic instabilities during protostellar collapse, providing a powerful framework for better understanding the earliest stages of star and planet formation.