International Journal of Computing Science and Mathematics
Navier-Stokes equations, Large eddy simulation, Approximate deconvolution model, Turbulence
If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, φ = gδ ∗ φ , the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies
u = D(u) + O(δ α ),
where δ is the filter width and α ≥ 2. Using a deconvolution operator as an approximate filter inverse yields the closure
uu = D(u)D(u) + O(δ α ).
We derive optimal approximate deconvolution models for 3D turbulence. Specifically, we find the optimal parameters that minimize the time averaged consistency error of approximate deconvolution operators and models for time averaged, fully developed, homogeneous, isotropic turbulence.
We answer important questions of How to adapt deconvolution procedures to velocities from homogeneous, isotropic turbulent flows? and What is the increase in accuracy that results?
Layton, William and Stanculescu, Iuliana, "K-41 Optimized Approximate Deconvolution Models" (2007). Mathematics Faculty Articles. 69.