Data-driven subgrid-closure models for simulating turbulent multi-phase flow

Turbulence is the most prevalent state of fluid motion; most of the flows in nature and in technical applications are turbulent. What makes these types of flows so interesting and at the same time challenging from a scientific perspective is their multiscale nature, which means that effects are coupled across all occurring scales. This also causes turbulent flows to be highly sensitive to minute changes in the surroundings - small scale influences may eventually cause large scale changes, a feature of a (quasi)chaotic system which is also known as the butterfly effect. This mandates simulations based on coarse scale models of turbulence like Large Eddy Simulation (LES), which make the computational costs manageable; however, this approach introduces the added challenge of modelling the subscale effects. Although considerable research effort based on mathematical and physical reasoning have been invested in finding such a closure model, an agreed-upon best model remains elusive. The primary objective of this research project is to develop strategies for devising adaptive closure models which are extracted from existing turbulence data through machine learning methods. Based on coarse grid data only, we propose to train subgrid models that predict suitable closure terms based on the current surrounding flow state. Artificial neural networks are particularly attractive candidate algorithms for this task, as they have been shown to be universal function approximators for a finite amount of neurons under very mild assumptions. This expressivenes of neural networks explains their recent success across many machine learning tasks and motivates their choice for this project. In addition, convolutional neural networks allow a natural incorporation of neighbouring information and spatial structures. Incorporating physical constraints into the surrogate model is still an active area of research for neural networks. We therefore rely on novel multilayer kernel methods to guarantee stable model terms. While the main focus of our work is on supervised learning, other learning paradigms will also be investigated. Based on preliminary models for incompressible flow, we will extend the work towards compressible multicomponent flows.