Turbulent flows as generalized Kelvin-Voigt materials: Modeling and analysis

被引:17
作者
Amrouche, Cherif [1 ]
Berselli, Luigi C. [2 ]
Lewandowski, Roger [3 ,4 ]
Dinh Duong Nguyen [3 ,4 ]
机构
[1] Univ Pau & Pays Adour, Lab Math & Leurs Applicat, UMR CNRS 5142, Pau, France
[2] Univ Pisa, Dipartimento Matemat, Via Buonarroti 1-c, I-56127 Pisa, Italy
[3] Univ Rennes 1, IRMAR, UMR CNRS 6625, Rennes, France
[4] INRIA Rennes, FLUMINANCE Team, Rennes, France
关键词
Fluid mechanics; Turbulence models; Degenerate operators; Navier-Stokes equations; Turbulent kinetic energy; EQUATIONS;
D O I
10.1016/j.na.2020.111790
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We perform a new modeling procedure for a 3D turbulent fluid, evolving towards a statistical equilibrium. This will result to add to the equations for the mean field (v, p) the term -alpha del . (l(x)Dv(t)), which is of the Kelvin-Voigt form, where the Prandtl mixing length l = l(x) is not constant and vanishes at the solid walls. We get estimates for mean velocity v in L-t(infinity) H-x(1) boolean AND W-t(1,2) H-x(1/2), that allow us to prove the existence and uniqueness of regular-weak solutions (v, p) to the resulting system, for a given fixed eddy viscosity. We then prove a structural compactness result that highlights the robustness of the model. This allows us to consider Reynolds averaged equations and pass to the limit in the quadratic source term, in the equation for the turbulent kinetic energy k. This yields the existence of a weak solution to the corresponding Navier-Stokes Turbulent Kinetic Energy system satisfied by (v, p, k). (C) 2020 Elsevier Ltd. All rights reserved.
引用
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页数:24
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