Communications in Mathematical Sciences
Volume 12 (2014)
Modeling error in approximate deconvolution models
Pages: 757 – 778
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