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A generalized re-normalization group (RNG) turbulence model based on the local "dimensionality" of the flow field is proposed. In this modeling approach the model coefficients C₁, C₂, and C₃ are all constructed as functions of flow strain rate. In order to further validate the proposed turbulence model, the generalized RNG closure model was applied to model the backward facing step flow (a classic test case for turbulence models). The results indicated that the modeling of C₂ in the generalized RNG closure model is reasonable, and furthermore, the predictions of the generalized RNG model were in better agreement with experimental data than the standard RNG turbulence model. As a second step, the performance of the generalized RNG closure was investigated for a complex engine flow.