For combustion occurring in high-speed flows, radical-formation time scales and ignition delay times may be similar to, or dominate, relevant flow time scales. Accurate modeling of induction and autoignition processes is critical to the prediction of combustor performance. The evolution-variable manifold (EVM) approach of Cymbalist and Dimotakis1 uses a transported scalar to explicitly track the evolution of induction leading to autoignition and subsequent robust combustion in its representation of autoignition-dominated combustion. In the present work, the EVM method is implemented in a computational fluid dynamics code and wall-modeled large-eddy simulations are performed for two ethylene-air high-speed combustion test cases. The detailed thermochemical state of the reacting fluid is tabulated as a function of a reduced number of state variables that include density, energy, mixture fraction, and a reaction-evolution variable. A thermodynamically consistent numerical flux function is developed and the approach for coupling the CFD to the EVM table is discussed. It is found that particular attention must be given to the solution of the energy equation to obtain accurate and computationally stable results. The results show that the LES-EVM approach shows promise for the simulation of turbulent combustion of hydrocarbons in high-speed flows that are dominated by ignition delay and have regions of thin reaction fronts as well as distributed reaction zones.