Computational studies of transverse sonic injection of ethylene into a Mach 1.98 cross-flow and Mach 5 flow of air into a subscale inlet/isolator configuration are presented. A hybrid large-eddy simulation/Reynolds-averaged Navier-Stokes (LES/RANS) turbulence model is used, with the two-equation Menter-BSL closure for the RANS part of the flow and a Smagorinsky-type model for the LES part of the flow. A time-dependent blending function, dependent on modeled turbulence variables, is used to shift the closure from RANS to LES. Turbulent structures are sustained through the use of a 'random-walk' recycling/rescaling technique. The ethylene injection results using the hybrid model shows very good agreement with the Raman scattering data collected at the Air Force Research Laboratory. The LES/RANS database is used to examine the validity of the commonly-used assumption of a constant Schmidt number in the intense mixing zone downstream of the injection location. Predictions of Mach 5 flow into the inlet/isolator are compared with particle imaging velocimetry (PIV) and wall pressure data obtained at the University of Texas. Preliminary computational results are presented for two cases involving shock-train propagation within the isolator, one of which leads to inlet unstart. Here, the computational method appears to predict more flow separation than indicated in the experiment, leading to stronger shock trains that are not stabilized at the correct position.