During situations of high incidence, high curvature of aero-engine intake lips can locally accelerate flow to supersonic speeds, producing undesirable shock wave boundary layer interactions (SWBLIs). The present work describes simulations of a novel experimental model resembling a lower intake lip at incidence. RANS, LES and hybrid RANS-LES are carried out at two angles of attack, α = 23° and α = 25°, with α = 25° possessing a high degree of shock oscillation. Modifications to the Spalart-Allmaras (SA) RANS turbulence model are proposed to account for re-laminarisation and curvature. These provide an improvement in prediction compared standard SA model. However, RANS models fail to reproduce post shock interaction flow, giving incorrect shape of the flow distortion. LES and hybrid RANS-LES perform well here, with downstream flow distortion in very good agreement with experimental measurements. LES and hybrid RANS-LES also capture the time averaged smearing of the shock which RANS cannot. However, low frequency shock oscillations in the α = 25° case are costly for LES, requiring long simulation time to obtain time averaged flow statistics. Hybrid RANS-LES offers a significant saving in computational cost, costing approximately 20% of LES.