Analysis of a reduced-order approximate deconvolution model and  its interpretation as a Navier-Stokes-Voigt regularization

Luigi C.  Berselli; Tae-Yeon  Kim; Leo G.  Rebholz

doi:10.3934/dcdsb.2016.21.1027

Article Contents

2016, Volume 21, Issue 4: 1027-1050. Doi: 10.3934/dcdsb.2016.21.1027

This issue Previous Article Next Article Irreducibility and strong Feller property for stochastic evolution equations in Banach spaces

Analysis of a reduced-order approximate deconvolution model and its interpretation as a Navier-Stokes-Voigt regularization

1.
Dipartimento di Matematica, Università di Pisa, I-56127 Pisa
2.
Department of Civil Infrastructure and Environmental Engineering, Khalifa University of Science, Technology & Research (KUSTAR), Abu Dhabi
3.
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634

Received: April 30, 2015

Revised: December 31, 2015

Published: May 2016

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Abstract

We study mathematical and physical properties of a family of recently introduced, reduced-order approximate deconvolution models. We first show a connection between these models and the Navier-Stokes-Voigt model, and also that Navier-Stokes-Voigt can be re-derived in the approximate deconvolution framework. We then study the energy balance and spectra of the model, and provide results of some turbulent-flow computations that backs up the theory. Analysis of global attractors for the model is also provided, as is a detailed analysis of the Voigt model's treatment of pulsatile flow.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76F65, 76D03.

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