The Magnetoplasmadynamic (MPD) thruster is an electromagnetic thruster that produces a higher specific impulse than conventional chemical rockets and greater thrust densities than electrostatic thrusters, but the well-known operational limit---referred to as ``onset"---imposes a severe limitation efficiency and lifetime. This phenomenon is associated with large fluctuations in operating voltage, high rates of electrode erosion, and three-dimensional instabilities in the plasma flow-field which cannot be adequately represented by two-dimensional, axisymmetric models. Simulations of the Princeton Benchmark Thruster (PBT) were conducted using the three-dimensional version of the magnetohydrodynamic (MHD) code, MACH. Validation of the numerical model is partially achieved by comparison to equivalent simulations conducted using the well-established two-dimensional, axisymmetric version of MACH. Comparisons with available experimental data was subsequently performed to further validate the model and gain insights into the physical processes of MPD acceleration. Thrust, plasma voltage, and plasma flow-field predictions were calculated for the PBT operating with applied currents in the range $6.5kA < J < 23.25kA$ and mass-flow rates of $1g/s$, $3g/s$, and $6g/s$. Comparisons of performance characteristics between the two versions of the code show excellent agreement, indicating that MACH3 can be expected to be as predictive as MACH2 has demonstrated over multiple applications to MPD thrusters. Predicted thrust for operating conditions within the range which exhibited no symptoms of the onset phenomenon experimentally also showed agreement between MACH3 and experiment well within the experimental uncertainty. At operating conditions beyond such values , however, there is a discrepancy---up to $\sim20\%$---which implies that certain significant physical processes associated with onset are not currently being modeled. Such processes are also evident in the experimental total voltage data, as is evident by the characteristic ``voltage hash", but not present in predicted plasma voltage. Additionally, analysis of the predicted plasma flow-field shows no breakdown in azimuthal symmetry, which is expected to be associated with onset. This implies that perhaps certain physical processes are modeled by neither MACH2 nor MACH3; the latter indicating that such phenomenon may not be inherently three dimensional and related to the plasma---as suggested by other efforts---but rather a consequence of electrode material processes which have not been incorporated into the current models.

Passive flow control achieved by surface dimpling can be an effective strategy for reducing drag around bluff bodies - an example of substantial popular interest being the flow around a golf ball. While the general effect of dimples causing a delay of boundary layer separation is well known, the mechanisms contributing to this phenomena are subtle and not thoroughly understood. Numerical models offer a powerful approach for studying drag reduction, however simulation strategies are challenged by complex geometries, and in applications the introduction of ad hoc turbulence models which introduce additional uncertainty. These and other factors provide much of the motivation for the current study, which focused on the numerical simulations of the flow over a simplified configuration consisting of a dimpled flat plate. The principal goals of the work are to understand the performance of the numerical methodology, and gain insight into the underlying physics of the flow. Direct numerical simulation of the incompressible Navier-Stokes equations using a fractional step method was employed, with the dimpled flat plate represented using an immersed boundary method. The dimple geometry utilizes a fixed dimple aspect ratio, with dimples arranged in a single spanwise row. The grid sizes considered ranged from approximately 3 to 99 million grid points. Reynolds numbers of 3000 and 4000 based on the inlet laminar boundary layer thickness were simulated. A turbulent boundary layer was induced downstream of the dimples for Reynolds numbers which did not transition for the flow over an undimpled flat plate. First and second order statistics of the boundary layer that develops agree reasonably well with those for turbulent channel flow and flat plate boundary layers in the sublayer and buffer layers, but differ in the outer layer. Inspection of flow visualizations suggest that early transition is promoted by thinning of the boundary layer, initiation of shear layer instabilities over the dimples, flow separation and reattachment, and tripping of the boundary layer at the trailing edge of the dimples.