Predictions of the flow over a wall-mounted hump are obtained using solutions of the Reynolds-averaged Navier-Stokes (RANS) equations and Detached-Eddy Simulation (DES). The upstream solution is characterized by a two-dimensional turbulent boundary layer with a thickness approximately half of the maximum hump thickness measured at a location about two chord lengths upstream of the leading edge. The Reynolds number based on the hump chord length is 9.75 × 106. A slot at approximately 65% chord (C) is used for flow control via a spatially uniform (with respect to the spanwise coordinate) steady suction, and with alternating suction/blowing. Solutions of the two- and three-dimensional RANS equations are obtained using the Spalart-Allmaras and SST turbulence models. DES is applied to a three-dimensional geometry corresponding to an extruded section of the hump. DES predictions of the baseline case exhibit a three-dimensional chaotic structure in the wake, with a mean reverse-flow region that is 20% shorter than predicted by the two-dimensional RANS computations. DES predictions of the pressure coefficient in the separated-flow region for the baseline case exhibit good agreement with measurements and are more accurate than either the S-A or SST RANS results. The simulations also show that blockage effects in the experiments used to assess the predictions are important - 3D RANS predictions more accurately predict the pressure distribution upstream and over the front portion of the hump. Predictions of the steady suction case show a reduction in the length of the reverse-flow region, though are less accurate compared to the baseline configuration. Unsteady 2D RANS predictions of the sinusoidal suction/blowing case are used to investigate impedance affects associated with increases in the driving velocity. The simulations show that a factor of four increase in the cavity driving velocity increases the average velocity through the slot by only a factor of 2.7.