Rotational forms of Large Eddy Simulation turbulence models: modeling and mathematical theory

Luigi C. Berselli (1) , Roger Lewandowski (2, 3) , Dinh Duong Nguyen (2)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

In this paper we present a derivation of a back-scatter rotational Large Eddy Simulation model, which is the extension of the Baldwin and Lomax model to non-equilibrium problems. The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary. After the derivation of the model, we prove some of the mathematical properties coming from the weighted energy estimates and which allow to prove existence and uniqueness of a class of regular weak solutions.

Mots clés: Fluid mechanics; Turbulence models; Rotational Large Eddy Simulation models; Navier-Stokes Equations

Domaines: Physique mathématique [math-ph]

Luigi C. Berselli, Roger Lewandowski, Dinh Duong Nguyen. Rotational forms of Large Eddy Simulation turbulence models: modeling and mathematical theory. Chinese Annals of Mathematics - Series B, 2021, 42 (1), pp.1-24. ⟨10.1007/s11401-021-0243-z⟩. ⟨hal-02569244⟩