We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with unprecendented resolution. This code utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution. These grids are automatically and dynamically added and removed as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with methods using fixed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. The application of this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation is discussed. The simulation involves many orders of magnitude of variation in length scale as fragments form. In this paper we describe the methodology and present illustrative applications for both isothermal and nonisothermal cloud collapse. We describe the numerical Jeans condition, a new criterion for stability of self-gravitational gas dynamic problems. We find that the uniformly rotating, spherical clouds treated here first collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form filamentary singularities that do not fragment while isothermal. As the collapse enters the non-isothermal phase, we show the evolutionary sequence that leads to the formation of a binary system consisting of protostellar cores surrounded by distinct protostellar disks. The scale of the disks, of order 100 AU, is consistent with observations of gaseous disks surrounding single T-Tauri stars and debris disks surrounding systems such as Beta Pictoris. © 1999 Elsevier Science B.V.
Klein, R. I. (1999). Star formation with 3-D adaptive mesh refinement: The collapse and fragmentation of molecular clouds. Journal of Computational and Applied Mathematics, 109(1–2), 123–152. https://doi.org/10.1016/S0377-0427(99)00156-9