DC8: Adjoint-based Optimisation for Flows exhibiting Chaotic Dynamics

This is much more than just a PhD position!

Within the FairCFD Doctoral Network, you will benefit from a unique three-fold experience:

– Contribute to technological innovation in the field of automotive, in direct collaboration with an industrial partner (Toyota Gazoo Racing), by developing, programming, testing and implementing advanced and efficient CFD strategies, in the field of shape optimisation.

– Take part in a network-wide interdisciplinary effort to define and promote numerical sustainability in scientific research.

– Join a vibrant network of 15 doctoral candidates, across 9 European countries, with access to cutting-edge network events, high-level training to technical and transverse skills, and secondments in both academic and industrial environments.

See our website for more details on the network’s philosophy and actions, along with description of the other PhD positions (https://www.imft.fr/faircfd/project-presentation/).

Scientific program

Background

For industrial applications, once an evaluation tool (such as a CFD code, in fluid mechanics) is deemed satisfactory, the natural next step is optimisation (such as shape optimisation). Brute-force approaches are highly inefficient, particularly for problems with many design parameters. The most widely used alternative is gradient-based optimisation, typically supported by the adjoint method, as this may compute the derivatives of quantities of interest with respect to all design parameters at a cost independent of their number. Adjoint-based optimisation has proven highly effective in industries such as aeronautics and automotive. However, it becomes inefficient – or even inapplicable – when the systems under consideration exhibit chaotic dynamics. A well-established remedy is the Least Squares Shadowing (LSS) method, though its use is limited since it requires the storage of data fields, continuously over long-time horizons, making it computationally expensive. To overcome this, this PhD will integrate LSS with advanced data compression techniques (already developed in the host organization), significantly reducing storage requirements and computational costs, and thereby making the method practical for industrial applications.

Selected references:

[1]    A. Margetis, E. Papoutsis-Kiachagias and K. Giannakoglou. On the Aerodynamic Shape Optimization of Cars using Steady & Compression-assisted Unsteady Adjoint.  Engineering Optimization 2025; https://doi.org/10.1080/0305215X.2025.2457487

[2]    A. Margetis, E. Papoutsis-Kiachagias, K. Giannakoglou. Reducing memory requirements of unsteady adjoint by synergistically using check-pointing and compression. International Journal for Numerical Methods in Fluids 2023; 95(1):23-43.

[3]    A. Margetis, E. Papoutsis-Kiachagias, K. Giannakoglou. Lossy Compression Techniques Supporting Unsteady Adjoint on 2D/3D Unstructured Grids. Computer Methods in Applied Mechanics and Engineering 2021; 387:114152.

[4]    Q. Wang, R. Hui, P. Blonigan. Least squares shadowing sensitivity analysis of chaotic limit cycle oscillations. Journal of Computational Physics 2014; 267:210–224.

Your research program

The first objective of this research project is to reformulate the LSS problem for a flow around a bluff body (e.g. car geometry) by avoiding its conversion to a boundary value problem through the introduction and solution of extra adjoint equations that refer to the initial value problem. Backward and forward in time solutions of the corresponding PDEs will be tested and comparisons will be made. Then, an iterative solver will be introduced, the cost of which will be offset against the use of relaxation schemes and, in particular, compression techniques. Thus, an important part of this PhD will be dealing with compression techniques and specifically with the extensive use of CFS and 3CP in order to reduce the storage footprint and computational cost. The effect of the resulting smoothing on the chaotic behaviour of the flow solution as well as the break-down of standard adjoint methods will be investigated. The developed methods will be used in academic and industrial problems. The latter include, among others, automotive applications. All work and developments of this project will be done in the OpenFOAM environment; thus, good skills in programming in C++ and some knowledge of the OpenFOAM environment are required (see below)

The expected results include: (1) an improved gradient computation for unsteady, chaotic flows due to the reformulation of the LSS problem, (2) a new adjoint solver for the LSS problem and (3) use of the above methods and tools in aerodynamic optimisation problems of academic interest and real-world industrial (automotive) cases.

Where you will work

For the main part of your work, you will be hosted by PCOpt/NTUA at the Zografou Campus of NTUA in Athens, Greece. The PCOpt/NTUA group consists of about 12 people, including 3 experienced researchers, among which the developers of the open-source, publicly available adjointOptimisationFoam library (to be extended in this project). Apart from the PhD thesis supervisor (Prof. K. Giannakoglou), researchers of the PCOpt/NTUA Unit with previous experience in similar tasks (OpenFOAM, adjoint methods, compression techniques, chaotic flows; all of them experienced developers of the same or similar s/w to the one that will be used in this project) will support you. The PCOpt/NTUA Unit possesses a powerful multiprocessor platform, including both CPU and GPU clusters, which is expected to be upgraded during the project life; this will support your research.

Network activities

Integration within the FairCFD Network

Within the FairCFD network, you will contribute mainly to WP4: Efficient optimization for complex problems. You will regularly exchange with other DCs of the network applying similar approaches to other problems, and/or applying different numerical methods to similar problems.
One secondment (short research stays in other partners of the network) is planned during the PhD at TGRe for 6 months where you will apply the developed methods to automotive cases.

Interdisciplinary task: co-designing numerical frugality 

Beyond your individual research program described above, you will contribute along with all other FairCFD doctoral candidates to a network-wide multidisciplinary effort (WP5) addressing the environmental and societal dimensions of numerical simulation.
Each DC will participate in the definition of practical metrics for numerical frugality (computational cost, energy use, resource impact) and contribute data from their simulations to a collective meta-analysis. This initiative will be supported by interdisciplinary experts and accompanied by a dedicated DC in social sciences, who will lead a qualitative study on evolving practices in simulation across the network. Together, we aim to build concrete, informed recommendations for sustainable scientific computing.

Network Training Program — More Than Just a PhD

As a Doctoral Network funded by Marie Sklodowska-Curie Actions (MSCA-DN), FairCFD will offer to you a rich and engaging training experience, including

–       Four one-week training events; (i) an induction week devoted to team-building, open-science practices and sustainability issues, (ii) an Essential Skills Accelerator event combining aiming to to equip DCs with essential technical and transferable skills, (iii) a Hackathon event where DCs will collaborate in teams to solve complex physics problem and compare various simulation strategies in terms of precision and sobriety, and (iv) a Career and Leadership Development Forum Aiming to equip DCs with transferable skills essential for their future careers.

–       Five On-line courses combining technical training to state-of-the art simulation methods ranging from physics-based approaches to data-driven ones, exposition to industrial applications, along with Social, ethical and environmental aspects of decision-making in modelling practices.

–       Involvement in the organisation of scientific events, including a mini-symposium as part of a large-audience scientific conference, a scientific symposium allowing to share the output in terms of new methods, innovation, and applications to industrial processes, and a Societal colloquium to deliver the outputs of the multidisciplinary tasks of the network.

This programme is designed to support your growth as a researcher, innovator, and engaged citizen, fully equipped to lead the next generation of responsible simulation science. See our website for more details (https://www.imft.fr/faircfd/project-presentation/)

Where to apply

The application process will be officially opened on April 1, 2026, till May 31.

The candidates should send a CV, cover letter, BSc and MSc degrees (certified copies plus translation in English) and two letters of recommendation. Copies of publications could be sent later on, upon request. Personal interviews might be asked.

All applications must be mailed here with subject: “FairCFD, application to DC8”.

Requirements

Research Field

Engineering » Mechanical engineering

Computational Physics

Computational Mathematics

Education Level

Master Degree or equivalent

Skills/Qualifications

  • Master’s degree (or equivalent) in fluid mechanics, applied mathematics or physics, scientific computing, or related fields.
  • Strong background in fluid mechanics, mathematics, numerical methods, PDEs, and/or data-driven modeling.
  • Very good programming skills in C++ and experience in the OpenFOAM environment.
  • Experience in using/developing adjoint-based optimisation methods is welcome.
  • Interest in interdisciplinary research and open science.
  • Excellent knowledge of written and spoken English (working language).

Practical Informations

Benefits

The successful candidates will receive an attractive salary in accordance with the MSCA regulations for Doctoral Researchers. The exact (net) salary will be confirmed upon appointment and is dependent on local tax regulations and on the country correction factor (to allow for the difference in cost of living in different EU Member States). The salary includes a living allowance, a mobility allowance, and a family allowance (if applicable). The guaranteed PhD funding is for 36 months (i.e., EC funding, additional funding is possible, depending on the local Supervisor, and in accordance with the regular PhD time in the country of origin).

Eligibility critria

According to the international mobility rules of the MSCA-DN program, the candidates must not have spent more than 12 months in the hosting country (Greece), during the 36 months preceding the starting of the PhD. Apart from this rule, worldwide applications are expected and encouraged.

Selection process

The application process will be officially opened on April 1, 2026, till May 31. Meanwhile, additional information can be obtained by contacting the supervisors along with the DN coordinating team. For this sake, please contact us by e-mail here, mentioning “FairCFD, application to DC8” in the subject of the e-mail.

Additional comments

A start date will be negotiated with the successful candidate. Ideally start dates would be september 2026.