Numerical Analysis of Approximate Deconvolution Models of Turbulence
Iuliana Stanculescu · NSUWorks (Nova Southeastern University) · 2006
If the NSE are averaged with a local, spacial, convolution type filter the resulting system is not closed due to the term g ∗ (uu). A deconvolution operator GN is one which satisfies: u = GN (g ∗ u) + O(δ) (0.1) where δ is the filter width. This yields the closure method: g ∗ (uu) = g ∗ (GN (g ∗ u)GN (g ∗ u)) + O(δ) (0.2) We will review several solutions to the ill-possed deconvolution problem, present an ”optimal” deconvolution procedure and present numerical analysis and numerical experiments with it. ∗Department of Mathematics, University of Pittsburgh, Pittsburgh, PA,15260, U.S.A.; email: [email protected], www.math.pitt.edu/ wjl †Department of Mathematics, University of Pittsburgh, Pittsburgh, PA,15260, U.S.A.; email: [email protected], www.math.pitt.edu/ ius1