Abstract
The development of a new method, called Adaptive Smoothed Particle Hydrodynamics (ASPH), generalized for cosmology and coupled to the Particle Mesh (PM) method for solving the Poisson Equation, for the simulation of galaxy and large-scale structure formation, will be described. The accurate numerical simulation of the highly nonlinear phenomena of shocks and caustics which occur generically in the process of structure formation requires enormous dynamic range and resolution. Existing numerical methods cannot achieve the required resolution with current computer technology. Progress toward the solution of this problem will be presented.
