Machine-Learning for Stress Tensor Modelling in Large Eddy Simulation

Abstract

The accurate modelling of the unresolved stress tensor is particularly important for Large Eddy Simulations (LES) of turbulent flows. This term affects the transfer of energy from the largest to the smallest scales and vice versa, thus controlling the evolution of the flow field-in reacting flows, the flow field transports scalar fields such as mass fractions and temperature both of which control the species production and destruction rates. A large number of models have been developed in past years for the stress tensor in incompressible and non-reacting flows. A common characteristic of the majority of the classical models is that simplifying assumptions are typically involved in their derivation which limits their predictive ability. At the same time, various tunable parameters appear in the relevant closures whose value depends on the flow geometry/configuration/spatial location, and which require careful regularisation. Data-driven methods for the stress tensor is an emerging alternative modelling approach which may help to circumvent the above issues, and in recent studies several such models were developed and evaluated. This chapter discusses the modelling problem, presents some of the most popular algebraic models, and reviews some recent advances on data-driven methods.