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The concept of optimal estimators, recently introduced by Moreau et al. [Phys. Fluids 18, 1 (2006)] is used as an a priori tool to discuss the accuracy of subfilter models. Placed in the framework of large-eddy simulation of combustion problems, this work focuses on the subfilter models used to evaluate the subfilter variance of a conserved scalar, the mixture fraction. The a priori tests are performed using 5123 direct numerical simulation data of forced homogeneous isotropic turbulence. First, the performance of the most commonly used models for the subfilter variance is studied. Using optimal estimators, the Smagorinsky-type model [Pierce and Moin, Phys. Fluids 10, 3041 (1998)] is shown to have the best set of parameters. However, the conventional dynamic formulation of the model leads to large errors in the variance prediction. It was found that assumptions used in the model formulation are not verified. A new dynamic procedure based on a Taylor series expansion is then proposed to improve the predictive accuracy. The a priori tests show that the new model substantially improves predictive accuracy.

International audienceNew procedures are explored for the development of models in the context of large eddy simulation (LES) of a passive scalar. They rely on the combination of the optimal estimator theory with machine-learning algorithms. The concept of optimal estimator allows to identify the most accurate set of parameters to be used when deriving a model. The model itself can then be defined by training an artificial neural network (ANN) on a database derived from the filtering of direct numerical simulation (DNS) results. This procedure leads to a subgrid scale model displaying good structural performance, which allows to perform LESs very close to the filtered DNS results. However, this first procedure does not control the functional performance so that the model can fail when the flow configuration differs from the training database. Another procedure is then proposed, where the model functional form is imposed and the ANN used only to define the model coefficients. The training step is a bi-objective optimisation in order to control both structural and functional performances. The model derived from this second procedure proves to be more robust. It also provides stable LESs for a turbulent plane jet flow configuration very far from the training database but over-estimates the mixing process in that case

International audienceIn this work, modeling of the near-wall region in turbulent flows is addressed. A new wall-layer model is proposed with the goal to perform high-Reynolds number large-eddy simulations of wall bounded flows in the presence of a streamwise pressure gradient. The model applies both in the viscous sublayer and in the inertial region, without any parameter to switch from one region to the other. An analytical expression for the velocity field as a function of the distance from the wall is derived from the simplified thin-boundary equations and by using a turbulent eddy coefficient with a damping function. This damping function relies on a modified van Driest formula to define the mixing-length taking into account the presence of a streamwise pressure gradient. The model is first validated by a priori comparisons with direct numerical simulation data of various flows with and without streamwise pressure gradient and with eventual flow separation. Large-eddy simulations are then performed using the present wall model as wall boundary condition. A plane channel flow and the flow over a periodic arrangement of hills are successively considered. The present model predictions are compared with those obtained using the wall models previously proposed by Spalding, Trans. ASME, J. Appl. Mech 28, 243 (2008) and Manhart et al., Theor. Comput. Fluid Dyn. 22, 243 (2008) . It is shown that the new wall model allows for a good prediction of the mean velocity profile both with and without streamwise pressure gradient. It is shown than, conversely to the previous models, the present model is able to predict flow separation even when a very coarse grid is used