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PhD Studentship: Recursive reduced order modelling of large scale dynamical systems.

Aerodynamics & Flight Mechanics Group

Location:  Highfield Campus
Closing Date:  Saturday 01 September 2018
Reference:  962518AK

Project Reference: CDT-NGCM-422

Numerical modelling of complex engineering problems has become one of the most important steps in efficient design and analysis of aerospace systems. An example of such systems is the analysis of aerodynamic flows around complete aircraft. With recent advancements in computational resources, computational fluid dynamics has become an attractive approach for modelling these complex flows. However, due to the complexity of the physics and the computational modelling of these large scale dynamical systems, computational costs may be prohibitive. Consequently, predictive models and control schemes that cannot account for or take advantage of efficient algorithms have very limited success. Therefore, the central question posed in this research project is: Can we develop reduced order modelling techniques of large scale dynamical systems, and investigate high Reynolds-number turbulent flows around a flexible airframe?

The aim of the project is to establish a technique to reduce the size and complexity of a reduced order model, producing what can be thought of as a “recursive reduced order model”. The first step consists of enhancing the projection technique [1] developed by the supervisor. This strategy manipulates the nonlinear governing equations to extract a reduced-order model of a prescribed form. The assumption is that the original large scale model can be approximated by a reduced order model expanded in Taylor’s series for the perturbation variable, and whose dynamics is restricted within a space described by appropriate basis vectors. The method has proved successful but two fundamental research questions are still open for discussion. To this goal, the project will explore the use of proper orthogonal decomposition for the automated selection of basis vectors and automatic differentiation for higher order derivatives calculations. The second step involves the deployment of a sparsification technique to filter out those terms of the reduced order model that have a negligible contribution to the accuracy of the resulting recursive reduced order model. The knowledge of the exact structure of the reduced order model originating from Taylor’s series expansion promises a straightforward application of the sparsification technique.

The successful applicant has a background in physics, engineering or applied mathematics. Experience with programming is essential. One full three-year studentship is available for UK/EU students only. The stipend is at the standard EPSRC-level.

[1] A Da Ronch et al; 2012; “Nonlinear model reduction for flexible aircraft control design”; AIAA Atmospheric Flight Mechanics Conference; AIAA Paper 2012-4404

If you wish to discuss any details of the project informally, please contact Andrea Da Ronch, Aerodynamics and Flight Mechanics research group, Email:

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling ( For details of our 4 Year PhD programme, please see 

For a details of available projects click here

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The closing date for this job opportunity has now passed, and applications are no longer being accepted for this position

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