A Machine Learning Approach to Unresolved-Scale Modeling for Burgers’ Equation

This thesis is part of a greater effort to use machine learning for the development of flexible and universal unresolved-scale models in large eddy simulation (LES). The novelty in the current work is that a neural network learns to predict the integral forms of the unresolved-scale terms directly without a priori assumptions on the underlying...

Finite element discretization of the Spalart-Allmaras turbulence model

The Reynolds-averaged Navier-Stokes equations are numerically solved in a segregated manner, along with the Spalart-Allmaras turbulence model. The Galerkin as well as multiple stabilized finite element formulations are derived for the Spalart-Allmaras turbulence model, and tested for robustness. For a turbulent channel flow and a backward facing...

Multiscale failure modelling of quasi-brittle materials

The conventional multiscale homogenization theory, which has mainly been applied to determine constitutive laws for bulk materials, suffers from two drawbacks when applied to softening materials. Firstly, the coarse scale response is sensitive to the finite element mesh used to discretize the coarse scale domain. Secondly, increasing the size of...

On finite element variational multiscale methods for incompressible turbulent flows

Two realizations of finite element variational multiscale (VMS) methods for the simulation of incompressible turbulent flows are studied. The difference between the two approaches consists in the way the spaces for the large scales and the resolved small scales are chosen. The paper addresses issues of the implementation of these methods, the...

Space-time multiscale methods for Large Eddy Simulation

The Variational Multiscale (VMS) method has appeared as a promising new approach to the Large Eddy Simulation (LES) of turbulent flows. The key advantage of the VMS approach is that it allows different subgrid-scale (SGS) modeling assumptions to be made at different ranges of the resolved scales. Typically, in the VMS method, SGS modeling is...