Analysis of a Reduced-Order Approximate Deconvolution Model and its interpretation as a Navier-Stokes-Voigt regularization

TL;DR

This paper explores the mathematical properties of reduced-order approximate deconvolution models, revealing their connection to Navier-Stokes-Voigt regularization, and analyzes their energy, spectra, and turbulent flow behavior.

Contribution

It establishes a link between approximate deconvolution models and NS-Voigt regularization, providing theoretical insights and computational results.

Findings

NS-Voigt can be derived from approximate deconvolution models.

Energy spectra of the model align with turbulent flow characteristics.

Global attractor analysis offers insights into long-term behavior.

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 NS-Voigt model, and that NS-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.