Optimal estimation for Large-Eddy Simulation of turbulence and application to the analysis of subgrid models

The tools of optimal estimation are applied to the study of subgrid models for Large-Eddy Simulation of turbulence. The concept of optimal estimator is introduced and its properties are analyzed in the context of applications to a priori tests of subgrid models. Attention is focused on the Cook and Riley model in the case of a scalar field in isotropic turbulence. Using DNS data, the relevance of the beta assumption is estimated by computing (i) generalized optimal estimators and (ii) the error brought by this assumption alone. Optimal estimators are computed for the subgrid variance using various sets of variables and various techniques (histograms and neural networks). It is shown that optimal estimators allow a thorough exploration of models. Neural networks are proved to be relevant and very efficient in this framework, and further usages are suggested.

[1]  F. Girosi,et al.  Nonlinear prediction of chaotic time series using support vector machines , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[2]  J. Riley,et al.  A subgrid model for equilibrium chemistry in turbulent flows , 1994 .

[3]  R. Moser,et al.  Optimal LES formulations for isotropic turbulence , 1999, Journal of Fluid Mechanics.

[4]  Stefan Volker,et al.  Optimal Large -Eddy Simulation of Turbulent Channel Flow , 2000 .

[5]  U. Schumann.  Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli , 1975 .

[6]  Hossam Eldin Ali,et al.  Neuronet-Based Approach for Assessing Liquefaction Potential of Soils , 1998 .

[7]  C. J. Stone,et al.  Consistent Nonparametric Regression , 1977 .

[8]  Johan A. K. Suykens,et al.  Least Squares Support Vector Machines , 2002 .

[9]  Jean-Michel Friedt,et al.  Simultaneous amplitude and Frequency Noise Analysis in Chua's Circuit , 2003, Int. J. Bifurc. Chaos.

[10]  C. J. Stone,et al.  Optimal Rates of Convergence for Nonparametric Estimators , 1980 .

[11]  O. Teytaud,et al.  LEARNING FROM NOISE IN CHUA'S OSCILLATOR , 2001 .

[12]  P. Moin,et al.  A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar , 1998 .

[13]  Ingo Steinwart,et al.  Consistency of support vector machines and other regularized kernel classifiers , 2005, IEEE Transactions on Information Theory.

[14]  George Papanicolaou,et al.  Macroscopic Modelling of Turbulent Flows , 1985 .

[15]  Simon Haykin,et al.  Making sense of a complex world , 1998 .

[16]  Chenning Tong,et al.  Measurements of conserved scalar filtered density function in a turbulent jet , 2001 .

[17]  Feng Gao,et al.  A large‐eddy simulation scheme for turbulent reacting flows , 1993 .

[18]  Parviz Moin,et al.  An evaluation of the assumed beta probability density function subgrid-scale model for large eddy simulation of nonpremixed, turbulent combustion with heat release , 2000 .

[19]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[20]  M. Rogers,et al.  A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows , 1997, Journal of Fluid Mechanics.

[21]  A. Moreau,et al.  Mixing in Isotropic Turbulence with Scalar Injection and Applications to Subgrid Modeling , 2000, Proceeding of First Symposium on Turbulence and Shear Flow Phenomena.

[22]  R. Olshen,et al.  Asymptotically Efficient Solutions to the Classification Problem , 1978 .

[23]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[24]  Jean-Pierre Bertoglio,et al.  A stochastic subgrid model for sheared turbulence , 1985 .

[25]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[26]  H. Pitsch.  LARGE-EDDY SIMULATION OF TURBULENT COMBUSTION , 2006 .

[27]  R. Goodman,et al.  Application of neural networks to turbulence control for drag reduction , 1997 .

[28]  S. Pope,et al.  Filtered density function for large eddy simulation of turbulent reacting flows , 1998 .

[29]  T. H. Davies,et al.  The Electrical Charge of 18‐Min. Br80 from Isomeric Transition , 1950 .

[30]  Halbert White,et al.  Connectionist nonparametric regression: Multilayer feedforward networks can learn arbitrary mappings , 1990, Neural Networks.