Self‐gravitational Hydrodynamics with Three‐dimensional Adaptive Mesh Refinement: Methodology and Applications to Molecular Cloud Collapse and Fragmentation

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Abstract

We describe a new code for numerical solution of three-dimensional self-gravitational hydrodynamics problems. This code utilizes the technique of local adaptive mesh renement (AMR), employing multiple grids at multiple levels of resolution and automatically and dynamically adding and removing these grids as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with a code using xed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. In particular, we apply this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation. The simulation involves many orders of magnitude of variation in length scale as fragments form at positions that are not a priori discernible from general initial conditions. In this paper, we describe the methodology behind this new code and present several illustrative applications. The criterion that guides the degree of adaptive mesh renement is critical to the success of the scheme, and, for the isothermal problems considered here, we employ the Jeans condition for this purpose. By maintaining resolution ner than the local Jeans length, we set new benchmarks of accuracy by which to measure other codes on each problem we consider, including the uniform collapse of a nite pressured cloud. We nd that the uniformly rotating, spherical clouds treated here rst collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form lamentary singularities that do not fragment while isothermal. Our results provide numerical conrmation of recent work by Inutsuka & Miyama on this scenario of isothermal lament formation.

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