Large Eddy Simulations

LES for turbulent flows stem from the observation that, although one is often only interested in large scale coherent structures, small scales cannot just be ignored because they contribute, though non-linear effects, to large scale dynamics. They need to be parametrized through so-called sub-grid models.

Our work has followed three directions
    • the mathematical analysis of original and selective Smagorinsky models [1,2]
    • the definition and validation of dissipative anisotropic gradient models [3,4]
    • the definition and use of robust variants of the dynamic model [5]
    • the understanding of implicit sub-grid scale modeling in particle methods [6].
Our current project is to use particle methods at a sub-grid resolution in combination with classical flows solvers and LES models to study anomalous spectral behavior in scalar transport [7,8,9].

Coherent structures in a plane jet

[1] G.-H. Cottet, D. Jiroveanu and B. Michaux, Vorticity dynamics and turbulence models for large-eddy simulations, M2AN, 37, 187-207, 2003. pdf file

[2] G.-H. Cottet, D. Jiroveanu, and B. Michaux, Simulations des grandes échelles: aspects mathématiques et numériques,  In 32e Congres National d'Analyse Numérique, Port d'Albret, Juin 2000,  ESAIM: Proceedings, 11, 85-95, 2002. pdf file

[3] G.-H. Cottet, Anisotropic subgrid-scale numerical schemes for Large Eddy Simulations of turbulent flows, preprint, 1997. pdf file

[4] G.-H. Cottet and A.A Wray,  Anisotropic grid-based formulas for subgrid-scale models, in Annual Research Briefs, Center for Turbulence Research, Stanford, 1997. pdf file

[5] G.-H. Cottet and O.V. Vasilyev,  Comparison of dynamic Smagorinsky and anisotropic subgrid-scale models, Center for Turbulence Research, Proceedings of the Summer Program 1998, pp 389-397. pdf file

[6] G-H. Cottet,  Artificial viscosity models for vortex and particle methods, J. Comp. Phys.,  127, 1996. pdf file

[7] G.-H. Cottet, G. Balarac and M. Coquerelle, Sub-grid particle resolution for the turbulent transport of a passive scalar, 12th Euromech Conference, Marburg, September 7-10, 2009.pdf file

[8] J.-B. Lagaert, G. Balarac and G.-H. Cottet, Numerical evidence of universal scaling for the scalar variance spectrum in forced homogeneous turbulence, submitted, 2012.pdf file

[9] J.-B. Lagaert, G. Balarac and G.-H. Cottet,  Hybrid spectral particle method for turbulent transport of passive scalar J. Comp. Phys., 260, 127-142, 2014. pdf file