It has been well known for some time that discretizations with good spatial conservation properties in terms of mass, momentum, and kinetic energy produce superior results when applied to the direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flow. The importance of temporal conservation has received much less attention. In this thesis, a second-order accurate finite difference discretization of the incompressible Navier-Stokes equations has been developed for structured Cartesian grids that discretely conserves mass, momentum, and kinetic energy (in the invisdd limit) in both space and time. The discrete conservation properties are retained for both uniform and non-uniform grid spacing. A second discretization has also been considered and shown through numerical experiments to have similar properties. This second discretization has the desirable property of linearity in each time step while still m aintaining second-order accuracy, although an energy conservation principle could not be rigorously derived.

For the case of either discretization, a novel multiple semicoarsened grid (MSG) multigrid method has been developed to solve the resulting coupled system of algebraic equations. The method is consistently capable of reducing the maximum normalized residual by 5 orders of magnitude in 50 to 80 work units.

The capability of the aforementioned discretizations and solution method to resolve turbulent flow has been demonstrated by performing large eddy simulations of the bypass transition of a flat plate boundary layer induced by periodically passing wakes, and the turbulent buoyancy-driven flow in square and cubical cavities.