Subgrid-Scale model using Artificial Neural Networks for Wall-bounded Turbulent flows

Abstract

The chaotic nature of turbulent flows combined with the diverse scales present within turbulent flows makes these flows very challenging to accurately simulate. Since turbulence is a phenomenon that cannot be avoided in real flows, a good understanding and accurate representation of turbulent flows would help to advance in the technical front in a sustainable manner. Over the years, LES and DNS have come up as different methods by which this problem of turbulence could be solved, to an extent. DNS resolves all the relevant scales thereby providing the most accurate option. However, it can only be used for flows with low Reynolds number. LES is a less costly option but it requires a wall model in order to represent the wall-bounded flow with practical computing costs. An attempt was made by Thijs Durieux as well as Matthijs Beekman to create such a model for the 1D burgers equations, with the help of Artificial Neural Networks(ANN). In both cases, the ANN was used to find unresolved scale model coefficients that are the closest fit so that the results of the LES are close to the ones obtained by a DNS. In order to do this efficiently, a training error measure(TEM) was developed which was used by the ANN to obtain the correct model coefficients. This worked well, but only one form of unresolved scale model (algebraic Variational multiscale model) was used and the cases considered were easily handled by that particular model.

The aim of this thesis is therefore to examine the effectiveness of the procedures used so far for alternative subgrid scale forms of the unresolved scale model and more challenging test problems. In particular, the ANN calibration of the Orthogonal subgrid-scale model and the Dynamic Orthogonal subgrid-scale model are considered using test cases of constant forcing, periodic forcing, and a Stochastic forcing. The stochastic forcing case would provide an initial idea of how the results for Navier stokes would look like. Response surfaces for both the training error measure(TEM) as well as the simulation error measure (SEM) were also plotted to further investigate the performance of the ANN.

It is shown from this thesis that the ANN model is able to work with different forms of the unresolved scale model and different forcing functions. Additionally, the potential gains resulting from spatially varying coefficients are demonstrated. It was also found that the training error measure(TEM) used to train the ANN is able to work efficiently only if there exist model coefficients that would fit the reference data correctly. In a scenario where these coefficients do not exist, the training error measure(TEM) can behave very differently from the simulation error measure(SEM) which results in the ANN producing results that are very different from what is required. A major conclusion is therefore that while the TEM is a good measure to qualitatively analyze the situation, in challenging cases it would be worthwhile to consider a slightly different approach.