Modeling error in Approximate Deconvolution Models

2011/11/28 by Adrian Dunca, Dunca, Adrian, Roger Lewandowski +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1111.6362

openalex publication_date 2011/11/28 · arxiv created 2012/10/09 · arxiv updated 2012/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 ∞. 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.

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