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Article Dans Une Revue Communications in Mathematical Sciences Année : 2014

Modeling error in Approximate Deconvolution Models

Résumé

We investigate the assymptotic behaviour of the modeling error in approximate deconvolution model in the 3D periodic case, when the order $N$ of deconvolution goes to $\infty$. We consider successively the generalised Helmholz filters of order $p$ and the Gaussian filter. For Helmholz filters, we estimate the rate of convergence to zero thanks to energy budgets, Gronwall's Lemma and sharp inequalities about Fouriers coefficients of the residual stress. We next show why the same analysis does not allow to conclude convergence to zero of the error modeling in the case of Gaussian filter, leaving open issues.

Dates et versions

hal-00833238 , version 1 (12-06-2013)

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Argus Adrian Dunca, Roger Lewandowski. Modeling error in Approximate Deconvolution Models. Communications in Mathematical Sciences, 2014, 12 (4), pp.757-778. ⟨10.4310/CMS.2014.v12.n4.a8⟩. ⟨hal-00833238⟩
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