AACE-AFM-152: Sparsity-promoting reduced order modelling techniques for separated turbulent flows

Flows of interest in many disciplines, from aviation to energy production and atmospheric sciences, are turbulent. In such applications, the Reynolds number (Re) is high and the dynamics are characterized by a wide range of scales, with the separation between large and small length eddies growing as Re3/4. Hence, high fidelity numerical simulation of these flows become prohibitive for design studies.

A promising approach consists in reduced order modelling whereby complex flow dynamics are distilled into a reduced order model (ROM), a system that reproduces the main features of the original problem with a greatly reduced number of degrees of freedom, hence enabling large reductions of the computational costs associated to simulation of the problem.
At large enough Reynolds numbers, a key feature of the resulting ROMs is that the energy transfers between the modes of the model are sparse. This sparsity is physically determined by the inherent multi-scale nature of the turbulent flow and because the dynamics at a certain length scale are determined by the dynamics of scales of commensurate lengths and much less by significantly larger or smaller scales. Current state-of-the-art model order reduction techniques do not exploit this property and produce densely-connected ROMs. These become computationally inefficient when a large number of modes is required to describe a large number of energy–containing scales. Exploiting this sparsity is the key to retain computational efficiency in these scenarios, and can lead to increased physical understanding.

The main objective of this PhD project is to develop a novel model sparsification technique that produces sparsely-connected ROMs incorporating the key features of high Reynolds number turbulence. In a sparsely-connected ROM only the dynamically relevant energy transfers are retained, hence the computational cost associated to simulation can be significantly reduced. The focus of the research will be on 1) developing data-driven methods to unravel the sparsity, using well-established statistical and machine learning techniques, 2) correlate these methods to the underlying physics of the problem and 3) perform an extensive parametric investigation on the interaction between Reynolds number, sparsity and computational costs. The modelling technique will be demonstrated in a test case involving a representative turbulent separated flow, for which fully-resolved numerical simulations will be performed on IRIDIS, the high performance computing facility of the University of Southampton.

We are looking for an applicant with a background in physics, engineering or applied mathematics. Inclination towards software development, numerical modelling and a good knowledge of fluid mechanics and turbulence will be instrumental. One full three-year studentship is available at EU/UK level. The stipend is at the standard EPSRC levels.

If you wish to discuss any details of the project informally, please contact Dr Davide Lasagna (email: [Email Address Removed]) or Dr Andrea Da Ronch (email: [Email Address Removed]).