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Towards a physics-informed deep reinforcement learning framework for more accurate large-eddy simulation of turbulent flows

  • School: School of Science and Technology
  • Study mode(s): Full-time / Part-time
  • Starting: 2023
  • Funding: UK student / EU student (non-UK) / International student (non-EU) / Fully-funded


Project ID: SST2

Large-eddy simulation (LES) is the state-of-the-art computational fluid dynamics (CFD) technique to study environmental and industrial flows, turbomachinery, aerodynamics, atmospheric flows to name a few. It resolves the large energy-carrying flow scales and parameterises the small computationally-demanding scales. Therefore, it saves the computational cost by an order of magnitude compared to high-fidelity techniques, i.e direct numerical simulation (DNS). Additionally, unlike low-fidelity techniques, namely Reynolds-Averaged Navier Stokes (RANS), LES is a scale resolving technique, hence allowing to study flow physics in detail. Up until the early 2000s, due to the computational limitations, industry was mainly using RANS. However, since the first LES by Deardorff (1970), the computer power has increased by seven orders of magnitude and industry is transitioning from RANS to LES. Despite substantial advances in LES modelling, there remain challenges, among which is the complex interactions between numerical and modelling errors. This challenge was partially addressed in a new framework by Rouhi et al. (Phys. Rev. Fluids, 1, p.044401, 2016), which allowed to minimise the numerical error by decoupling the model from the simulation grid. However, the modelling error remains the outstanding challenge. This project aims towards building a novel deep reinforcement learning framework for minimisation of modelling error in LES.

The framework will harness the hierarchical multifractal nature of turbulence and treat it as a cascade-based ordinary differential equation system. The goal will be to train reinforcement learning policies with evolutionary strategies.  In order to train the nested neural ordinary differential equation architecture, we will leverage the mathematical field of matrix gradient flows on compact smooth manifolds (Lie groups) that are equipped with rich algebraic structure. Thus, the training process will become equivalent to the task of constructing expressive parameterised flows on the orthogonal group. Apart from the effectiveness and stability of the reinforcement learning training (due to constraining the matrix flow to develop on the compact manifold), this framework will also  introduce interpretability of the chosen optimal action in the search space.

The developed framework will be applied on complex benchmark turbulent flows (e.g. channel flow, backward facing step etc.). Upon success of these initial test cases, more challenging (and of a higher impact) scenarios from industrial partners / real world data will be considered (e.g. airfoil, ground vehicle etc.).

At national level, this project is aligned with UK’s Jet zero strategy for net zero emission by 2050, which aims to minimise the carbon emission in the aviation industry. The developed turbulence modelling framework for this project is suitable for aerodynamic optimisation of air transport systems. Further, this project is aligned with one of the objectives of NASA Computational Fluid Dynamic vision by 2030, which is towards more robust large-eddy simulation models for application to complex geometries.

Supervisory Team:

  • Dr Archontis Giannakidis (Director of Studies), Department of Mathematics, Nottingham Trent University
  • Dr Amirreza Rouhi (Early Career Researcher), Department of Engineering, Nottingham Trent University
  • Dr David Chappell, Department of Mathematics, Nottingham Trent University
  • Dr Saleh Rezaeiravesh, Department of Mechanical, Aerospace and Civil Engineering, University of Manchester

Entry qualifications

  • 1st class / 2:1 undergraduate degree, and / or equivalent
  • Completed masters level qualification and / or evidence of substantive published research works

How to apply

Please visit our how to apply page for a step-by-step guide and make an application and include the project ID in your application

Application deadline: Thursday 8 June 2023.

Interviews will take place in mid-June 2023

Fees and funding

This is a NTU studentship funded opportunity

Guidance and support

Further guidance and support on how to apply can be found on our apply page.

Still need help?

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