Simulations of combustion in high-speed and supersonic flows need to account for autoignition phenomena, compressibility,andtheeffectsofintenseturbulence.Inthepresentwork,theevolution-variablemanifoldframework of Cymbalist and Dimotakis ("On Autoignition-Dominated Supersonic Combustion," AIAA Paper 2015-2315, June 2015) is implemented in a computational fluid dynamics method, and Reynolds-averaged Navier-Stokes and wall-modeled large-eddy simulations are performed for a hydrogen-air combustion test case. As implemented here, the evolution-variable manifold approach solves a scalar conservation equation for a reaction-evolution variable that represents both the induction and subsequent oxidation phases of combustion. The detailed thermochemical state of thereactingfluidistabulatedasalow-dimensionalmanifoldasafunctionofdensity,energy,mixturefraction,andthe evolution variable. A numerical flux function consistent with local thermodynamic processes is developed, and the approach for coupling the computational fluid dynamics to the evolution-variable manifold table is discussed. Wall-modeled large-eddy simulations incorporating the evolution-variable manifold framework are found to be in good agreement with full chemical kinetics model simulations and the jet in supersonic crossflow hydrogen-air experimentsofGambaandMungal("Ignition,FlameStructureandNear-WallBurninginTransverseHydrogenJets in Supersonic Crossflow," Journal of Fluid Mechanics, Vol. 780, Oct. 2015, pp. 226-273). In particular, the evolutionvariable manifold approach captures both thin reaction fronts and distributed reaction-zone combustion that dominate high-speed turbulent combustion flows.