The maturation of high-performance computer architectures and computational algorithms has prompted the development of a new generation of models that attempt to combine the robustness and ef ciency offered by the Reynolds averaged Navier-Stokes equations with the higher level of modeling offered by the equations developed for large eddy simulation. The application of a new hybrid approach is discussed, where the transition between these equation sets is controlled by a blending function that depends on local turbulent ow properties, as well as the local mesh spacing. The utilization of local turbulence properties provides added control in specifying the regions of the ow intended for each equation set, removing much of the burden from the grid-generation process. Moreover, the model framework allows for the combination of existing closure model equations, avoiding the dif culty of formulating a single set of closure coef cients that perform well in both Reynolds averaged and large eddy simulation modes. Simple modi cations to common second-order accurate Reynolds averaged Navier-Stokes algorithmsare proposed to enhance the capturing of large eddy motions. Incompressible Poiseuille ow, supersonic base ow, and supersonic ow over recessed cavities were considered to evaluate various aspects of the proposed model and computational framework. Calculations using another hybrid approach (detached eddy simulation) were also performed for comparison. Nomenclature a i j = matrix of normalized velocity variances and covariances b = law of the wall intercept C D k! = cross-diffusion term for the speci c turbulent dissipation rate C d = constant for the destruction term of k C DES = constant for the detached eddy simulation (DES) length scale C p = pressure coef cient C s = constant for the Smagorinsky viscosity coef cient C ¹ = constant for the turbulent viscosity coef cient C ! p = constant for the production term of ! c = constant for the gradient sensor D = cavity depth d = distance to the nearest solid surface F = blending function F c ; F d ; F u = central, dissipative, and upwind contributions to the inviscid uxes f = joint normal distribution function h = channel height k = turbulent kinetic energỳ = turbulent length scale m = normalized cavity mass n;¯= constants for the latency parameter of Speziale 6 P = pressure P k = production term for the turbulent kinetic energy P ! = production term for the speci c turbulent dissipation rate q = MUSCL extrapolated variable R = sting base radius r = numerical dissipation reduction factor r; µ = polar coordinates t = time u i = velocity u ¿ = friction velocity V = turbulent velocity scale v i = velocity normalized with the rms of its uctuation x; y; z = Cartesian coordinates 1 = subgrid length scale ± i j = Kronecker delta ± C ; ± ¡ = nite difference operators (forward, backward) ² = turbulent dissipation rate or generic small numbeŕ = blending function argument · = MUSCL interpolation constant or law of the wall slope ¹ = viscosity coef cient º = speci c viscosity coef cient ...

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