Chebyshev Optimized Approximate Deconvolution Models of Turbulence

Iuliana Stanculescu; William Layton

doi:10.1016/j.amc.2008.11.022

Chebyshev Optimized Approximate Deconvolution Models of Turbulence

Iuliana Stanculescu, William Layton

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ&lowast;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), <a title="Turn MathJax on"> Turn MathJaxon </a> where δδ is the filter width and α&ges;2α&ges;2. Using a deconvolution operator as an approximate filter inverse, yields the closure uu¯¯¯¯=D(u¯¯)D(u¯¯)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯+O(δα). <a title="Turn MathJax on"> Turn MathJaxon </a> 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.

Original language	American English
Journal	Applied Mathematics and Computation
Volume	208
DOIs	https://doi.org/10.1016/j.amc.2008.11.022
State	Published - Feb 1 2009

Keywords

Deconvolution
LES
Turbulence model

Disciplines

Mathematics

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@article{9e1d0264228548a6828f91c588416486,

title = "Chebyshev Optimized Approximate Deconvolution Models of Turbulence",

abstract = " If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ&lowast;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&ges;2α&ges;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. ",

keywords = "Deconvolution, LES, Turbulence model",

author = "Iuliana Stanculescu and William Layton",

year = "2009",

month = feb,

day = "1",

doi = "10.1016/j.amc.2008.11.022",

language = "American English",

volume = "208",

journal = "Applied Mathematics and Computation",

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T1 - Chebyshev Optimized Approximate Deconvolution Models of Turbulence

AU - Stanculescu, Iuliana

AU - Layton, William

PY - 2009/2/1

Y1 - 2009/2/1

N2 - If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ&lowast;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&ges;2α&ges;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.

AB - If the Navier–Stokes equations are averaged with a local, spacial convolution type filter,ϕ¯¯¯=gδ&lowast;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&ges;2α&ges;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.

KW - Deconvolution

KW - LES

KW - Turbulence model

UR - https://nsuworks.nova.edu/math_facarticles/39

U2 - 10.1016/j.amc.2008.11.022

DO - 10.1016/j.amc.2008.11.022

M3 - Article

SN - 0096-3003

VL - 208

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Chebyshev Optimized Approximate Deconvolution Models of Turbulence

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Keywords

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