We consider in this paper the problem of finding appropriate models for Large Eddy Simulations of turbulent incompressible flows from a mathematical point of view. The Smagorinsky model is analyzed and the vorticity formulation of the Navier-Stokes equations is used to explore more efficient subgrid-scale models as minimal regularizations of these equations. Two classes of variants of the Smagorinsky model emerge from this approach: a model based on anisotropic turbulent viscosity and a selective model based on vorticity angles. The efficiency of these models is demonstrated by comparisons with reference results on decaying turbulence experiments.
Mots-clés : Navier-Stokes equations, large eddy simulation, subgrid-scale modeling, Smagorinsky model, selective anisotropic model
@article{M2AN_2003__37_1_187_0,
author = {Cottet, Georges-Henri and Jiroveanu, Delia and Michaux, Bertrand},
title = {Vorticity dynamics and turbulence models for {large-Eddy} simulations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {187--207},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
doi = {10.1051/m2an:2003013},
mrnumber = {1972658},
zbl = {1044.35051},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003013/}
}
TY - JOUR AU - Cottet, Georges-Henri AU - Jiroveanu, Delia AU - Michaux, Bertrand TI - Vorticity dynamics and turbulence models for large-Eddy simulations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 187 EP - 207 VL - 37 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003013/ DO - 10.1051/m2an:2003013 LA - en ID - M2AN_2003__37_1_187_0 ER -
%0 Journal Article %A Cottet, Georges-Henri %A Jiroveanu, Delia %A Michaux, Bertrand %T Vorticity dynamics and turbulence models for large-Eddy simulations %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 187-207 %V 37 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003013/ %R 10.1051/m2an:2003013 %G en %F M2AN_2003__37_1_187_0
Cottet, Georges-Henri; Jiroveanu, Delia; Michaux, Bertrand. Vorticity dynamics and turbulence models for large-Eddy simulations. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 1, pp. 187-207. doi : 10.1051/m2an:2003013. http://www.numdam.org/articles/10.1051/m2an:2003013/
[1] AGARD, A selection of test cases for the evaluation of large-eddy simulations of turbulent flows. Advisory report no. 345 (1998).
[2] , and, Remarks on the Breakdown of Smooth Solutions for the 3D Euler Equations. Springer-Verlag, Comm. Math. Phys. 94 (1984). | MR | Zbl
[3] and, On the regularizing effect of the vorticity direction in incompressible viscous flows. Differential Integral Equations 15 (2002). | MR | Zbl
[4] and, Local energy flux and subgrid-scale statistics in three dimensional turbulence. J. Fluid Mech. 366 (1998). | MR | Zbl
[5] ,, and, Spectral Methods in Fluid Dynamics. Springer-Verlag (1988). | MR | Zbl
[6] , Vorticity and Turbulence. Springer Verlag, Appl. Math. Sci. 103 (1994). | MR | Zbl
[7] , and, Evaluation of subgrid scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91 (1979). | Zbl
[8] and, Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated isotropic turbulence. J. Fluid Mech. 48 (1971).
[9] , Geometric Statistic in turbulence. SIAM Rev. 36 (1994). | MR | Zbl
[10] , Navier-Stokes Equations and Fluid Turbulence. Preprint arXiv:math.AP/0003235 (2000). | Zbl
[11] and, Direction of Vorticity and the Problem of Global Regularity for The Navier-Stokes Equations. Indiana Univ. Math. J. 42 (1993). | Zbl
[12] , and, Geometric Constraints on Potentially Singular Solutions for the 3-D Euler Equations. Comm. Partial Differential Equations 21 (1996). | MR | Zbl
[13] and, Navier-Stokes Equations. Univ. of Chicago Press, Chicago, Chicago Lectures in Math. (1989). | Zbl
[14] , Anisotropic Subgrid-Scale Numerical Schemes for Large Eddy Simulation of Turbulent Flows. Unpublished report (1997).
[15] , and, Simulation des grandes échelles : aspects mathématiques et numériques. ESAIM Proc. 11 (2002) 85-95. | Zbl
[16] and, Comparison of Dynamic Smagorinsky and Anisotropic Subgrid-Scale Models, in Proceedings of the Summer Program, Center for Turbulence Research (1998).
[17] and, Anisotropic grid-based formulas for subgrid-scale models, in Annual Research Brief, Center for Turbulence Research, Stanford University and NASA Ames Research Center (1997).
[18] , Modélisation des écoulements compressibles et hypersoniques : une approche instationnaire. Ph.D. thesis, INPG-LEGI Grenoble (1993).
[19] and, Subgrid-scale models based on incremental unknowns for large eddy simulations, in Annual Research Brief, Center for Turbulence Research, Stanford University and NASA Ames Research Center (1998).
[20] , Simulation numérique directe et des grandes échelles de couches limites compressibles. Ph.D. thesis, INPG-LEGI Grenoble (1995).
[21] , and, The three dimensional viscous Camassa-holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dynam. Differential Equations 14 (2002). | Zbl
[22] and, Approximating the larger eddies in fluid motion II: a model for space filtered flow. Math. Models Methods Appl. Sci. 10 (2000). | MR | Zbl
[23] ,, and, A Dynamic Subgrid-Scale Eddy Viscosity Model. Phys. Fluids A 3 (1991). | Zbl
[24] and, Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model. Preprint ANL/MCS-P932-0302 (2002).
[25] , Analyse mathématique et numérique de certains modèles de viscosité turbulente. Ph.D. thesis, University Joseph Fourier Grenoble I (2002).
[26] , The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30 (1941). | JFM | Zbl
[27] , The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breasch, New York (1969). | Zbl
[28] , On the Dynamical System Generated by the Navier-Stokes Equations. English translation in J. Sov. Math. 3 (1975). | Zbl
[29] , New equations for the description of the viscous incompressible fluids and solvability in the large of the boundary value problems for them, in Boundary Value Problems of Mathematical Physics V, Amer. Math. Soc., Providence, RI (1970). | Zbl
[30] , Energy cascade in large-eddy simulations of turbulent flows. Adv. Geophysics 18 (1974).
[31] , Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934). | JFM
[32] , Turbulence in Fluids. Kluwer Academic Publishers, Dordrecht (1997). | MR | Zbl
[33] and, New trends in large eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28 (1996) 45-82.
[34] , Quelques méthodes de résolution des problèmes aux limites non-linéaires. Dunod, Paris (1969). | MR | Zbl
[35] , and, On the properties of similarity subgrid-scales models as deduced from measurements in a turbulent jet. J. Fluids Mech. 275 (1994) 83-119.
[36] and, A Finite-Dimensional Attractor for Three-Dimensional Flow of Incompressible Fluids. J. Differential Equations 127 (1996). | MR | Zbl
[37] and, Global Well-posedness for the Lagrangian Averaged Navier-Stokes (LANS) Equations on Bounded Domains. Meeting of Royal Society London (2000).
[38] , and, The Geometry and Analysis of the Averaged Euler Equations and a New Diffeomorphism Group. Geom. Funct. Anal. 10 (2000). | MR | Zbl
[39] and, Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239 (1992) 157-194. | Zbl
[40] ,,,,, and, Numerical Simulations of Homogeneous Turbulence Using the Lagrangian Averaged Navier-Stokes Equations in Proc. CTR summer school (2000).
[41] , Uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids. Appl. Anal. 43 (1992). | MR | Zbl
[42] , and, Subgrid scale energy transfer and near-wall turbulence structure. Phys. Fluids 8 (1996) 215-224. | Zbl
[43] and, Numerical Simulation of Turbulent Flows. Annu. Rev. Fluid Mech. 16 (1984) 99-137. | Zbl
[44] , General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather Review 91 (1963).
[45] , Turbulence modeling for time-dependent RANS and VLES: A review. AIAA Journal 36 (1998). | Zbl
[46] and, An Approximative Deconvolution Procedure for Large-Eddy Simulation. Phys. Fluids 11 (1999).
[47] , Infinite Dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, Appl. Math. Sci. 68 (1988). | MR | Zbl
[48] , Direct and large-eddy simulation of the compressible turbulent mixing layer. Ph.D. thesis, University of Twente (1995).
[49] , Turbulence Modeling CFD. DCW Industries Inc. (1993).
[50] , Nonlinear Functional Analysis and its Applications. Springer-Verlag (1990). | Zbl
Cité par Sources :
