SELF-GRAVITATIONAL HYDRODYNAMICS WITH 3-DIMENSIONAL ADAPTIVE MESH REFINEMENT - METHODOLOGY AND APPLICATIONS TO MOLECULAR CLOUD COLLAPSE ANDFRAGMENTATION

We describe a new code for numerical solution of three-dimensional sel f-gravitational hydrodynamics problems. This code utilizes the techniq ue of local adaptive mesh refinement (AMR), employing multiple grids a t multiple levels of resolution and automatically and dynamically addi ng and removing these grids as necessary to maintain adequate resoluti on. This technology allows solution of problems that would be prohibit ively expensive with a code using fixed resolution, and it is more ver satile and efficient than competing methods of achieving variable reso lution. In particular, we apply this technique to simulate the collaps e and fragmentation of a molecular cloud, a key step in star formation . The simulation involves many orders of magnitude of variation in len gth scale as fragments form at positions that are not a priori discern ible from general initial conditions. In this paper, we describe the m ethodology behind this new code and present several illustrative appli cations. The criterion that guides the degree of adaptive mesh refinem ent is critical to the success of the scheme, and, for the isothermal problems considered here, we employ the Jeans condition for this purpo se. By maintaining resolution finer than the local Jeans length, we se t new benchmarks of accuracy by which to measure other codes on each p roblem we consider, including the uniform collapse of a finite pressur ed cloud. We find that the uniformly rotating, spherical clouds treate d here first collapse to disks in the equatorial plane and then, in th e presence of applied perturbations, form filamentary singularities th at do not fragment while isothermal. Our results provide numerical con firmation of recent work by Inutsuka & Miyama on this scenario of isot hermal filament formation.