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Unified turbulence models for LES and RANS, FDF and PDF simulations. (English) Zbl 1161.76496

Summary: A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier-Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76F55 Statistical turbulence modeling
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
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