Lattice Boltzmann (LB) based Large Eddy Simulation (LES), Reynolds-averaged Navier-Stokes (RANS) as well as hybrid RANS/LES methods within the Launch Ascent and Vehicle Aerodynamics (LAVA) solver framework are applied to NASA's wall-mounted hump. Computational results are compared with experiments performed by Greenblatt et al. A detailed comparison between the accuracy and resolution requirements of the two approaches for turbulence resolving simulations, as well as the suitability of different grid paradigms (body-fitted curvilinear and block structured Cartesian) are presented. This test case is part of NASA's Revolutionary Computational Aerosciences (RCA) sub-project which addresses the technical challenge of predicting flow separation and reattachment accurately. Improvements in predictive accuracy by as much as 90% are demonstrated using LB as well as hybrid RANS/LES approaches compared to state-of-the-art steady state RANS simulations.