Applied Mathematics and Computation
Turbulence model, LES, Deconvolution
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 termuu¯¯¯¯. An approximate deconvolution operator DD is a bounded linear operator which satisfies
u=D(u¯¯)+O(δα), Turn MathJaxon
where δδ is the filter width and α⩾2α⩾2. Using a deconvolution operator as an approximate filter inverse, yields the closure
uu¯¯¯¯=D(u¯¯)D(u¯¯)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+O(δα). Turn MathJaxon
The residual stress of this model (and related models) depends directly on the deconvolution error,u−D(u¯¯). This report derives deconvolution operators 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→0δ→0, an ergodic theorem as the deconvolution order N→∞N→∞, and estimate the increase in accuracy obtained by parameter optimization. The report concludes with numerical illustrations.
Stanculescu, Iuliana and Layton, William, "Chebyshev Optimized Approximate Deconvolution Models of Turbulence" (2009). Mathematics Faculty Articles. 39.