Gravitational Collapse and Fragmentation in Molecular Clouds with   Adaptive Mesh Refinement
  We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method 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 for the solution of problems in a manner that is both more efficient and more versatile than other fixed and variable resolution methods. The application of AMR to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation, is discussed. Such simulations involve many orders of magnitude of variation in length scale as fragments form. In this paper we briefly describe the methodology and present an illustrative application for nonisothermal cloud collapse. We describe the numerical Jeans condition, a criterion for stability of self-gravitational hydrodynamics problems. We show the first well-resolved nonisothermal evolutionary sequence beginning with a perturbed dense molecular cloud core 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. 
Richard I. Klein, Robert T. Fisher, Christopher F. McKee, J. Kelly   Truelove