Analysis of commutation errors for functions with low regularity

Commutation errors arise in the derivation of the space averaged Navier–Stokes equations, the basic equations for the large eddy simulation of turbulent flows, if the filter is non-uniform or asymmetric (skewed) with non-constant skewness. These errors need to be analyzed for turbulent flow fields,...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-09, Vol.206 (2), p.1027-1045
Main Authors: Berselli, Luigi C., Grisanti, Carlo R., John, Volker
Format: Article
Language:English
Subjects:
Commutation errors
Error analysis
Exact sciences and technology
Gaussian and box filter
Mathematical analysis
Mathematics
Non-smooth functions
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Real functions
Sciences and techniques of general use
Space averaged Navier–Stokes equations
Special functions
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Summary:Commutation errors arise in the derivation of the space averaged Navier–Stokes equations, the basic equations for the large eddy simulation of turbulent flows, if the filter is non-uniform or asymmetric (skewed) with non-constant skewness. These errors need to be analyzed for turbulent flow fields, where one expects a limited regularity of the solution. This paper studies the order of convergence of commutation errors, as the filter width tends to zero, for functions with low regularity. Several convergence results are proved and it is also shown that convergence may fail (or its order decreases) if the functions become less smooth. The main results are those dealing with Hölder–continuous functions and with functions having singularities. The sharpness of the analytic results is confirmed with numerical illustrations.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.09.011