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We describe an application of Berger and Colella's (1989)
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.
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