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Near-wall treatment for LES models

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The most basic form of wall modeling for LES simply imposes some additional constraints upon the eddy viscosity. The standard Smagorinsky model eddy viscosity is nonzero at solid boundaries, which is contrary to the notion that the eddy viscosity should be zero where there is no turbulence. The easy fix for this situation is to add a Van Driest-style damping function into the length scale:

D(y^+;A^+,m,n)=[1 - \exp(-{y^+}^n/{A^+}^n)]^m.

Various different values for A^+, m, and n have been used. The use of this formulation requires the accurate computation of wall shear (in order to compute y^+), which has generally been accomplished by high grid resolution in near-wall regions. The legitimacy of terming such simulations as true LES's has been debated, as in the opinion of some the additional resolution is transitioning the simulation into a DNS in near-wall regions. At the very least, it is probably a violation of the "spirit" of LES, so models that do not require ad hoc damping have been sought.

Add some text here about approximate boundary conditions, etc. Add references, too.

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