This thesis concerns two dimensional simulations of high speed viscous gas flow. A high resolution numerical scheme has been developed for the solution of the Navier-Stokes equations for chemical non-equilibrium reacting flow on a parallel computer platform. A convection-diffusion-reaction operator split method is employed so that appropriately efficient independent numerical schemes can be used for the separate operator split PDEs. The convection solver uses a Riemann problem based Godunov types scheme. The solution to the diffusion terms is based on the directional dominance of diffusion, with a line implicit scheme for the dominant terms and explicit treatment for the less dominant terms. A point implicit scheme is used in the reaction solver to maintain numerical stability in the solution of chemically stiff systems. Test cases concerning the flow past sharp leading edge flat plates and compression ramps have been considered. Flat plate test cases include supersonic flow of an oxygen-argon mixture over a plate with a downstream catalytic section and hypersonic flow of air over a plate made of steel. Compression ramp test cases include hypersonic perfect gas flow of nitrogen over ramps up to a maximum ramp angle of 35° and hypersonic air flow over steel ramps up to a maximum of 24°. There is a poor prediction of peak heating rates in the compression ramp test cases. This may be due to a number of reasons which include a poor prediction of the reattachment length, turbulent transition and three-dimensional effects. The catalytic effects of steel give rise to changes in the chemical composition close to the surface, but there is no significant change in the surface heat transfer rate or wall shear stress solutions, i.e. for engineering purposes, the flow is effectively frozen.