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The objective of this study is to develop a robust framework to model shock-turbulence interactions that happen in many engineering applications dealing with compressible flows. The model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a co-located finite volume scheme with minimum aliasing errors is implemented to model the turbulent region in the combination of a semi-discrete, central scheme to capture the discontinuities with sufficiently low dissipation to minimize the effect of large eddy simulation (LES) for turbulent flows. To evaluate the effectiveness of the model, LESs are conducted to study the interaction of stationary shocks with turbulent flows. The simulations of the shock-turbulence interaction show the same physical trends as previously published results for high-fidelity DNS and LES.