Évaluation et développement de modèles sous-maille pour la simulation des grandes échelles du mélange turbulent basés sur l’estimation optimale et l’apprentissage supervisé
ury members
M. Guillaume Balarac (LEGI)
M. Christophe Corre (LMFA)
M. Georgs-Henri Cottet (LJK)
M. Emmanuel Lévêque (LMFA)
M. Luc Vervisch (CORIA)
Abstract
This work develops subgrid model techniques and proposes methods of diagnosis for Large Eddy Simulation (LES) of turbulent mixing. Several models from these strategies are thus presented to illustrate these methods.
The principle of LES is to solve the largest scales of the turbulent flow responsible for major transfers and to model the action of small scales of flow on the resolved scales. Formally, this operation leads to filter equations describing turbulent mixing. Subgrid terms then appear and must be modeled to close the equations. In this work, we rely on the classification of subgrid models into two categories. "Functional" models which reproduces the energy transfers between the resolved scales and modeled scales and "Structural" models that seek to reproduce the exact subgrid term itself. The first major challenge is to evaluate the performance of subgrid models taking into account their functional behavior (ability to reproduce the energy transfers) and structural behaviour (ability to reproduce the term subgrid exactly). Diagnostics of subgrid models have been enabled with the use of the optimal estimator theory which allows the potential of structural improvement of the model to be evaluated. These methods were initially involved for the development of a first family of models called algebraic subgrid DRGM for "Dynamic Regularized Gradient Model". This family of models is based on the structural diagnostic of terms given by the regularization of the gradient model family. According to the tests performed, this new structural model’s family has better functional and structural performance than original model’s family of the gradient. The improved functional performance is due to the vanishing of inverse energy transfer (backscatter) observed in models of the gradient family. This allows the removal of the unstable behavior typically observed for this family of models.
In this work, we then propose the use of the optimal estimator directly as a subgrid scale model. Since the optimal estimator provides the model with the best structural performance for a given set of variables, we looked for the set of variables which optimize that performance. Since this set of variables is large, we use surrogate functions of artificial neural networks type to estimate the optimal estimator. This leads to the "Artificial Neural Network Model" (ANNM). These alternative functions are built from databases in order to emulate the exact terms needed to determine the optimal estimator. The tests of this model show that he it has very good performance for simulation configurations not very far from its database used for learning, so these findings may fail the test of universality.
To overcome this difficulty, we propose a hybrid method using an algebraic model and a surrogate model based on artificial neural networks. The basis of this new model family ACM for "Adaptive Coefficient Model" is based on vector and tensor decomposition of the exact subgrid terms. These decompositions require the calculation of dynamic coefficients which are modeled by artificial neural networks. These networks have a learning method designed to directlyoptimize the structural and functional performances of ACM. These hybrids models combine the universality of algebraic model with high performance but very specialized performance of surrogate models. The result give models which are more universal than ANNM.
Key words :
Turbulence, Mixing, Large Eddy Simulation, Optimal estimator, Artificial neural network, Subgrid scale models.