Modeling error of \(\alpha\)-models of turbulence on a two-dimensional torus
type: Item
instance of: scholarly article
title: Modeling error of \(\alpha\)-models of turbulence on a two-dimensional torus
zbMATH Open document ID: 1473.35395
author: Luigi C. Berselli
author: Argus Adrian Dunca
author: Roger Lewandowski
author: Dinh Duong Nguyen
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2021-06-18T00:00:00Z
review text: The article focuses on different turbulence models in a two-dimensional periodic domain: the Leray-\(\alpha\) model, the simplified Bardina model, and the modified Leray-\(\alpha\) model, which are obtained from the Navier--Stokes equations by certain regularizations of the nonlinear term. Denoting by \(u_\alpha\) the solution to the respective \(\alpha\)-regularized model and by \(u\) the solution to the Navier--Stokes equations, the authors derive rates of convergence of \(u_\alpha\) to \(u\) as \(\alpha\to0\) in the norm of both \(L^\infty(0,T;L^2(\Omega))\cap L^2(0,T;H^1(\Omega))\) and \(H^1(0,T;L^2(\Omega))\cap L^2(0,T;H^2(\Omega))\), which improve known convergence rates for these models. Convergence rates for the corresponding pressure fields are also deduced, and the authors explain how to transfer their results to the more technical case of a bounded domain with zero Dirichlet conditions. The paper concludes with additional remarks on the difficulties that occur if one may derive analogous estimates in the case of three dimensions or the Euler equations.
reviewed by: Thomas Eiter
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76F65
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 7360946
zbMATH Keywords: rate of convergence
zbMATH Keywords: \(\alpha\)-turbulence models
zbMATH Keywords: Navier-Stokes equations
MaRDI profile type: Publication
full work available at URL: dcdsb.2020305
OpenAlex ID: W3005826029
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DOI: 10.3934/DCDSB.2020305
description: scientific article; zbMATH DE number 7360946