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.