Dr. Benz will investigate two main themes in computational astrophysics: the modeling of stellar collisions and the simulation of hydrodynamical behavior in supernova explosions. He will use a 3-D Smooth Particle Hydrodynamics (SPH) computer code to extend previous work on stellar collisions and disruptions to include encounters involving main sequence stars of unequal mass and compact objects. The long range goal is to obtain cross- sections for merging, mass-loss and binary formation for all possible stellar encounters. Knowledge of these cross-sections is an essential ingredient for models of the evolution of globular cluster cores and active galactic nuclei. The need for a better understanding of hydrodynamical instabilities occurring in supernova explosions has been demonstrated by the unexpected early detection of x-rays from SN1987A. Dr. Benz will also study the subsonic flame propagation and off-center ignition in type Ia supernova. Because SPH is a relatively new method to solve the hydrodynamical equations, emphasis in this study is given to comparisons between results from SPH and state-of-the-art finite difference methods. The various tests envisioned go far beyond the usual simple shock tube problem and will deal with complicated multidimensional flows. This should provide a better understanding of the capabilities of SPH at a time when this method is becoming increasingly popular.