Supersonic Combustion Scramjet (supersonic combustion ramjet) engines offer tremendous potential for high-speed transport of missiles and aircraft. High speed air is compressed by the ram effect in the inlet of the scramjet. Fuel (typically hydrogen or some hydrocarbon) is injected into the supersonic airstream and, hopefully, mixes, ignites, and burns. Ejection of the high enthalpy gases through a nozzle produces the desired thrust. We say hopefully because all of the above must occur in less than several milliseconds of residence time within the engine. Hence, rapid mixing, ignition, and combustion is key and flameholding and stability become critical. Because of the difficulties in conducting flight, and even ground, testing, computational modeling plays a key role. Because of the time scales involved turbulent-chemistry interactions and the influence of complex shock structures is important. The focus on transient events suggest the use of large eddy simulation requiring accurate and efficient subgrid-scale turbulent combustion models capable of handling detailed finite-rate chemical kinetics. Numerical methods must simultaneously be able to capture broadband turbulence with minimal numerical dissipation and capture shocks with minimal spurious oscillations. We are exploring the use of both high-order ESWENO and hybrid central/upwind schemes for numerics with direct closures for SGS combustion. Below we show ESWENO simulation snapshots of OH and T from a 2D H2-Air reacting shear layer interacting with an oblique shock wave followed by a density snapshot from a hybrid central/upwind simulation of supersonic flow over a step. Also snapshots from 3D simulations of supersonic flow (air) with scalar (fuel) injection flowing over a cavity are shown.