This paper presents results from a computational analysis of a series of experiments conducted in the CUBRC 48" reflected shock tunnel for the purpose of studying the transition of afterbody wake flows. The experiments examined the flow over a spherically-blunted capsule, roughly chosen to be a scale representation of the new Orion crew module currently being designed by NASA. In this study, we have focused on three test runs for analysis, corresponding to low, medium, and high Reynolds number conditions. Each case has been examined with the intent of understanding the influence of turbulence modeling, time accuracy, and flux discretization on solution accuracy. Numerically, we find a standard first order in time, second order in space (with modified Steger-Warming fluxes) to be adequate for the external, reentry type flows of interest. For the low Reynolds number case (ReD ≤ 10 6), a laminar Navier-Stokes simulation is sufficient to accurately capture the statistical character of the flowfield. At the medium Reynolds number (ReD = 6.3×106), the analysis indicates a possibly transitional wake where heat transfer predictions are bounded by laminar and turbulent simulations. At the high Reynolds number (ReD = 10.8×106), the experimental data are best matched by a fully turbulent calculation using the Detached Eddy Simulation (DES) form of the Spalart-Allmaras turbulence model. Additionally, comparisons between Reynolds-averaged Navier-Stokes (RANS) and DES calculations reveal the inability of RANS models to correctly capture either the rapidly fluctuating flow transients or mean field. Repeating the DES calculation with an alternative second order in time, low-dissipation flux scheme shows a substantial improvement in the simulation's ability to capture flow transients and may prove crucial for applications in which this is a priority. It is observed that the improvements seen in moving from RANS to DES and from Steger-Warming to the low-dissipation scheme are related in that both ultimately reduce the level of unnecessary dissipation present in the simulation.