A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.
Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate
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Carlson, JR, & Gatski, TB. "Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate." Proceedings of the ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. Volume 1: Fora, Parts A and B. Montreal, Quebec, Canada. July 14–18, 2002. pp. 533-538. ASME. https://doi.org/10.1115/FEDSM2002-31259
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