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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1996-1997 Mathematics in High Performance Computing