7 research outputs found
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
Pictoris.Comment: 10 pages, 6 figures (color postscript). To appear in the proceedings
of Numerical Astrophysics 1998, Tokyo, March 10-13, 199
A rarefaction-tracking method for hyperbolic conservation laws
We present a numerical method for scalar conservation laws in one space
dimension. The solution is approximated by local similarity solutions. While
many commonly used approaches are based on shocks, the presented method uses
rarefaction and compression waves. The solution is represented by particles
that carry function values and move according to the method of characteristics.
Between two neighboring particles, an interpolation is defined by an analytical
similarity solution of the conservation law. An interaction of particles
represents a collision of characteristics. The resulting shock is resolved by
merging particles so that the total area under the function is conserved. The
method is variation diminishing, nevertheless, it has no numerical dissipation
away from shocks. Although shocks are not explicitly tracked, they can be
located accurately. We present numerical examples, and outline specific
applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding