This proposal will parallelize and apply a new and innovative method that was developed for the numerical simulation of 3D hydrodynamics and gravitational clustering in cosmology. Our goal is to explain the formation of galaxies and large-scale structure in the universe by simulating the coupled effects of gravity, gas dynamics, and radiative transfer in an expanding cosmological universe. A correct solution must resolve the multi-scale, nonlinear growth of gravitational instability, which leads to anisotropic gravitational collapse, highly supersonic motions, strong shocks, radiative cooling, and many orders of magnitude of density contrast. The method is a merger of our substantially improved version of the Smoothed Particle Hydrodynamics (SPH) Method, called Adaptive SPH, or ASPH, and the well-known Particle-Particle/Particle-Mesh(P DSG1 3M) gravitational N-body method, in a cosmologically expanding, matter-dominated Friedmann universe. The ASPH method revolutionizes the standard SPH method by introducing new algorithms for time-and space-variable, anisotropic smoothing and for shock tracking to eliminate spurious heating due to artificial viscosity away from shocks. The ASPH method has significantly increased the dynamical range that can be achieved by numerical hydrodynamical simulations, and is currently the best method to achieve the resolution required to study the problems mentioned above. This project will develop and apply a new parallel computer version of our existing algorithm, that will significantly reduce the CPU time per calculation. DSG1
