A large-eddy simulation methodology (LES) has been developed for predicting the turbulent physics of an incompressible flow in simple and complex geometries. The Cartesian form of the governing equations was first verified, and then later used to investigate a three-dimensional shear-driven cavity flow. The investigation involved Reynolds numbers of 2000, 3200, 5000 and 10000 and focused on the unsteadiness and turbulent characteristics of the flow. At the low Reynolds numbers (Re ~ 5000) where the cavity flow is fully laminar, direct numerical simulations (DNS) were conducted whereas the LES methodology was adopted to predict the cavity flow at the higher Reynolds number (Re = 10000). Determining the parameters in the damped subgrid scale (SGS) turbulence model for this complex flow was guided by the DNS results at Re = 5000. The SGS model was also verified against DNS results at Re = 7500 where the cavity flow was known through laboratory experimentation to be locally transitional. The LES results using the damped SGS model verified the published experimental evidence as well as uncovered new flow features within the cavity. LES computations were also carried-out of the three-dimensional shear driven cavity flow at a high Reynolds number where the SGS turbulent field was represented by a dynamic model. Lilly's least-squares expression was tested for determining Smagorinsky's coefficient in the model without ad hoc measures such as ensemble-averaging or filtering. However, zero cutoff of negative total viscosity (kinematic plus turbulent eddy viscosity) was necessary to maintain stable solutions. A discretized filter function was derived for the test filter. Both qualitative and quantitative comparisons to experimental data show that the dynamic model performed quite well. The dynamic model gave better comparisons to the experimental evidence than the damped model did. Vortex formation in the wake of a circular cylinder and their subsequent downstream transport was also numerically investigated by LES. Here however, the curvilinear form of the governing equations was necessary to perform the computations. A new generalized dynamic model was derived to represent the SGS stress field in the curvilinear space. This new model introduced the contravariant velocity components as part of the field variables. New downstream boundary conditions were also formulated to permit the shed vortices to exit with minimum disturbance. The focus of the investigation was at Re = 5600 with some verification of the computations at Re = 200 and Re = 3000. At all of these Reynolds numbers. the upstream boundary layer was laminar but the wake was fully turbulent at Re = 3000 and Re = 5600. The LES results of the many interesting characteristics of the wake showed good comparisons to the experimental data. / Ph. D.