  We describe an application of Berger and Colella's structured adaptive mesh
refinement algorithm to the field of cosmological astrophysics. Simulations in
this area must include not just a gaseous component which follows the
hyperbolic equations of compressible gas dynamics, but also a collisionless
component (such as dark matter or stars) described by the Newtonian dynamical
equations. The two fluids interact via gravity which requires an elliptic
solver. The challenge for AMR is twofold. First, the collisionless material is
most easily modeled by following trajectories of individual objects, a method
often referred to as an N-body scheme. The introduction of particles poses a
number of difficulties, both physical (how do they interact accurately with the
fluid in the mesh) and algorithmic (how to efficiently add a new data
structure). The second challenge is to incorporate the gravitational
interaction between the two components. We discuss our solutions to both of
these issues and briefly present very encouraging results.
