One of the current goals of research in hypersonic, airbreathing propulsion is access to higher Mach numbers. A strong driver of this goal is the desire to integrate a scramjet engine into a transatmospheric vehicle airframe in order to improve performance to low Earth orbit (LEO) or the performance of a semi-global transport. An engine concept designed to access hypervelocity speeds in excess of Mach 10 is the shock-induced combustion ramjet (i.e. shcramjet). This dissertation presents numerical studies simulating the physics of a shcramjet vehicle traveling at hypervelocity speeds with the goal of understanding the physics of fuel injection, wall autoignition mitigation, and combustion instability in this flow regime. This research presents several unique contributions to the literature. First, different classes of injection are compared at the same flow conditions to evaluate their suitability for forebody injection. A novel comparison methodology is presented that allows for a technically defensible means of identifying outperforming concepts. Second, potential wall cooling schemes are identified and simulated in a parametric manner in order to identify promising autoignition mitigation methods. Finally, the presence of instabilities in the shock-induced combustion zone of the flowpath are assessed and the analysis of fundamental physics of blunt-body premixed, shock-induced combustion is accelerated through the reformulation of the Navier Stokes equations into a rapid analysis framework. The usefulness of such a framework for conducting parametric studies is demonstrated.