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arXiv · 1608.02655

Damping Functions correct over-dissipation of the Smagorinsky Model

Ali Pakzad
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Abstract

This paper studies the time-averaged energy dissipation rate $\langle \varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over-damp. One common correction is to include damping functions that reduce the effects of model viscosity near walls. Mathematical analysis is given here that allows evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function. Moreover, the analysis motivates a modified van Driest damping. It is proven that the combination of the Smagorinsky with this modified damping function does not over dissipate and is also consistent with Kolmogorov phenomenology.

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Ali Pakzad. 2017-07-30. Damping Functions correct over-dissipation of the Smagorinsky Model. https://doi.org/10.1002/mma.4444

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