Louis H. Howell

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

We describe a new code for numerical solution of three-dimensional self-gravitational hydrodynamics problems. This code utilizes the technique of local adaptive mesh refinement (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 fixed 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 refinement 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 finer 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 finite pressured cloud. 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. Our results provide numerical confirmation of recent work by Inutsuka & Miyama on this scenario of isothermal filament formation.

An Adaptive Mesh Projection Method for Viscous Incompressible Flow

Many fluid flow problems of practical interest---particularly at high Reynolds number---are characterized by small regions of complex and rapidly varying fluid motion surrounded by larger regions of relatively smooth flow. Efficient solution of such problems requires an adaptive mesh refinement capability to concentrate computational effort where it is most needed. We present in this paper a fractional step version of Chorins projection method for incompressible flow, with adaptive mesh refinement, which is second-order accurate in both space and time. Convection terms are handled by a high-resolution upwind method which provides excellent resolution of small-scale features of the flow, while a multilevel iterative scheme efficiently solves the parabolic and elliptic equations associated with viscosity and the projection. Numerical examples demonstrate the performance of the method on two-dimensional problems involving vortex spindown with viscosity and inviscid vortex merger.