K-41 optimised approximate deconvolution models
by William Layton, Iuliana Stanculescu
International Journal of Computing Science and Mathematics (IJCSM), Vol. 1, No. 2/3/4, 2007

Abstract: Average the Navier–Stokes equations, with a local, spatial convolution type filter.
The result system is not closed due to __
The result system is not closed due to uu.
Let D be a bounded linear operator which satisfies u = D(ū) + O(δ^α) where δ is the filter width and α ≥ 2. Using D as an approximate filter inverse yields the closure
___._________
uu = D(ū)D(ū)+O(δ^α)

The residual stress of this model (and related models) depends directly on the deconvolution error u − D(ū). We find deconvolution parameters that minimise the deconvolution error for homogeneous, isotropic turbulence. This work addresses: How to adapt deconvolution to homogeneous, isotropic turbulent flows? and What is the increase in accuracy?

Online publication date: Thu, 10-Jan-2008

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