Communications in Mathematical Sciences

Volume 12 (2014)

Number 4

Modeling error in approximate deconvolution models

Pages: 757 – 778



Argus A. Dunca (Faculty of Mathematics and Computer Science, Spiru Haret University, Bucharest, Romania)

Roger Lewandowski (IRMAR, UMR 6625, Université Rennes 1, Rennes, France)


We investigate the asymptotic behavior of the modeling error in 3D periodic Approximate Deconvolution Models, when the order $N$ of deconvolution goes to $\infty$. We consider generalized Helmholtz filters of order $p$, then the Gaussian filter. For Helmholtz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall’s Lemma, and sharp inequalities applied to the Fourier coefficients of the residual stress. We next explain why the same analysis does not imply convergence to zero of the modeling error in the case of the Gaussian filter, leaving open issues.


Navier-Stokes equations, large eddy simulation, deconvolution models

2010 Mathematics Subject Classification

35Q30, 76D03, 76D05, 76F65

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