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.
Highlights
Over the past several decades, many large eddy simulation (LES) models have been introduced and tested, with varying degrees of success; see e.g. [9, 42] for extensive overviews
Our results reveal that the reduced-order ADM (RADM) is more computable than the Navier-Stokes equations (NSE) and has spectral scaling similar to the Leray-α model [18], which matches that of true fluid flow on larger scales in the inertial range, but smaller scales are transferred more quickly to even smaller scales
We have presented a detailed mathematical analysis of several important aspects of the RADM
Summary
Over the past several decades, many large eddy simulation (LES) models have been introduced and tested, with varying degrees of success; see e.g. [9, 42] for extensive overviews. Two attractive models of the current generation are approximate deconvolution models (ADMs) [1, 2], and Voigt regularization models [13, 34], both of which have recently seen significant interest from both mathematicians and engineers These models are known to be well-posed [7, 10, 19, 34], have attractive physical properties (such as energy and helicity conservation and cascades [34, 35]), and have performed well in (at least some) numerical simulations [32, 45], including when applied to the Euler equations for ideal fluids [13]. Conclusions are drawn in the final section, and prospective future work is discussed
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