9410800 Liu This research seeks to develop new methods to solve the Navier-Stokes equations using advanced two-equation turbulence models. These new methods will permit the prediction of unsteady aerodynamic loads and hence will have applications in the design of turbines and compressors. Current knowledge in these areas is based on steady flow models whereas the actual flows are highly unsteady. The proposed work has both analytical and numerical components including: development of a flux-limited pressure split dissipation model and k-w turbulence model, algorithms for massively parallel computers and new techniques for solving both the Navier Stokes equations and the turbulence equations. ***