Transverse injection at sonic speed from a rectangular slot into a supersonic crossflow is numerically explored with an indigenously developed parallel three-dimensional (3D) Reynold-averaged Navier–Stokes (RANS) solver for unstructured grids. The RANS models used for turbulence closure are the one-equation Spalart–Allmaras (SA) model and the two-equation shear stress transport (SST) model. For each model, the influence of compressibility corrections is assessed. Due to the presence of shock-turbulent boundary layer interaction (STBLI) in the flow, various STBLI corrections are assessed for both the models. Most of the simulations are two-dimensional (2D), but three-dimensional simulations are also performed to investigate the mismatch between the experimental dataset and the numerical results. The SA model is less sensitive to STBLI corrections, but some improvement in its prediction of the separation distance is found with the compressibility corrections. The SST model results are insensitive to the compressibility corrections, but the STBLI correction improves its results. Improved agreement with the experimental dataset is found when simulations are done in 3D, suggesting that the experiments were not so close to 2D as previously believed.