Chebychev optimized approximate deconvolution models of 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), 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). The residual stress of this model (and related models) depends directly on the deconvolution error, u − D(u). This report derives deconvolution operators satisfying the necessary conditions of [24] yielding an effective turbulence model, which minimize the deconvolution error for velocity fields with finite kinetic energy. We also give a convergence theory of deconvolution as δ → 0, an ergodic theorem as the deconvolution order N → ∞, and estimate the increase in accuracy obtained by parameter optimization. The report concludes with numerical illustrations.