This paper describes the application of a Finite Volume Godunov method to hypersonic flows with thermally perfect gas equation of state. The HyShot-II scramjet project has been used for this purpose. The HyShot-II configuration was tested in the High Enthalpy Shock Tunnel Goettingen (HEG) of the German Aerospace Center, DLR, and a Computational Fluid Dynamics (CFD) analysis was presented by Karl et al10 using unstructured and Hybrid grids. The LES approach used in this paper employs a new fifth-order accurate method in space with modified variable extrapolation on a structured grid at a flow of Mach 7.4 and altitude of 27 km. Two dimensional CFD analysis is presented on the complete geometry of the Hyshot-II scramjet and separately on the combustion chamber at fuel-off conditions using air as thermally perfect gas as a precursor to the future three dimensional studies. Two test cases for high Mach number thermally perfect gas flow, normal and oblique shocks, are also presented and the results are compared with NASA TPG (Thermally Perfect Gas) code results.