Adjoint-based Optimisation for Flows exhibiting Chaotic Dynamics (MSCA-DN FairCF
National Technical University of Athens, Greece, NY, United States
Organisation/Company National Technical University of Athens Department School of Mechanical Engineering Research Field Engineering › Mechanical engineering Engineering › Aerospace engineering Mathematics › Computational mathematics Physics › Computational physics Physics › Mathematical physics Researcher Profile First Stage Researcher (R1) Positions PhD Positions Application Deadline 31 May 2026 - 23:59 (Europe/Athens) Country Greece Type of Contract Not Applicable Job Status Full-time Hours Per Week 40 Offer Starting Date 1 Sep 2026 Is the job funded through the EU Research Framework Programme? Horizon Europe - MSCA Marie Curie Grant Agreement Number 101226482 Is the Job related to staff position within a Research Infrastructure? No
Offer Description 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 adjoint-based 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.
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 aerodynamic 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. The hosting organization has developed and made publicly available the adjoint method in the OpenFOAM CFD toolbox; the same method has been developed and adequately assessed in the in-house GPU-accelerated PUMA code. 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 issue, 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
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
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.
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.
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 compression techniques. Thus, an important part of this PhD will be dealing with compression techniques and, specifically, with the extensive use of two methods (CFS and 3CP; developed in a previous PhD; see references) 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 C++ (either working in OpenFOAM or the PUMA code); thus, a very good knowledge of programming in C++ is 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 shape optimisation problems of academic interest and real-world industrial (automotive) cases.
Where you will work
For the main part of your work (excluding secondement), you will be hosted by the Parallel CFD & Optimization Unit of the Fluids Dept. of the School of Mechanical Engineering of the National Technical University of Athens (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 adjoint/CFD code(s) as well as the compression techniques to be used; it is beneficial that all these experienced researchers and code developers will support your PhD. 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.
Integration within the FairCFD Network
Within the FairCFD network, you will contribute mainly to its fourth Work-Package (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 (Toyota Gazoo Racing) 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/ )
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++; experience in the OpenFOAM environment or programming in CUDA/C++ is welcome. Experience in using commercial CFD s/w is welcome but insufficient for the needs of the DC8 project.
Experience in developing adjoint-based optimisation methods is welcome.
Interest in interdisciplinary research and open science.
Excellent knowledge of written and spoken English (working language).
Languages ENGLISH Level Excellent
Additional Information The successful candidate will receive an attractive gross salary of 4,720.00 € per month 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 and a mobility allowance. An additional family allowance (if applicable*) is foreseen. 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).
* Family is defined as persons linked to the researcher by (a) marriage, or (b) a relationship with equivalent status to a marriage recognized by the national legislation of the country of the beneficiary or of nationality of the researcher, or (c) dependent children who are actually being maintained by the researcher.
Eligibility criteria
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 recruitment process will adhere to the principles of equal opportunities, transparency and non-discrimination, in line with the European Charter for Researchers, and will actively promote diversity and gender balance. In particular, applications from female candidates are strongly encouraged, as women remain underrepresented in engineering disciplines.
To apply, 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. All applications must be mailed here with subject: “FairCFD, application to DC8”. Personal interviews might be asked.
The application process will be officially opened on
April 1 , 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.
If you are interested in more than one position belonging to the FairCFD network, please apply to 2 positions at most and precise the second choice in your cover letter. Extra applications not respecting this rule will be discarded.
Additional comments
A starting date will be negotiated with the successful candidate. The ideal starting date will be September, 1 2026.
#J-18808-Ljbffr
Offer Description 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 adjoint-based 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.
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 aerodynamic 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. The hosting organization has developed and made publicly available the adjoint method in the OpenFOAM CFD toolbox; the same method has been developed and adequately assessed in the in-house GPU-accelerated PUMA code. 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 issue, 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
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
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.
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.
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 compression techniques. Thus, an important part of this PhD will be dealing with compression techniques and, specifically, with the extensive use of two methods (CFS and 3CP; developed in a previous PhD; see references) 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 C++ (either working in OpenFOAM or the PUMA code); thus, a very good knowledge of programming in C++ is 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 shape optimisation problems of academic interest and real-world industrial (automotive) cases.
Where you will work
For the main part of your work (excluding secondement), you will be hosted by the Parallel CFD & Optimization Unit of the Fluids Dept. of the School of Mechanical Engineering of the National Technical University of Athens (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 adjoint/CFD code(s) as well as the compression techniques to be used; it is beneficial that all these experienced researchers and code developers will support your PhD. 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.
Integration within the FairCFD Network
Within the FairCFD network, you will contribute mainly to its fourth Work-Package (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 (Toyota Gazoo Racing) 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/ )
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++; experience in the OpenFOAM environment or programming in CUDA/C++ is welcome. Experience in using commercial CFD s/w is welcome but insufficient for the needs of the DC8 project.
Experience in developing adjoint-based optimisation methods is welcome.
Interest in interdisciplinary research and open science.
Excellent knowledge of written and spoken English (working language).
Languages ENGLISH Level Excellent
Additional Information The successful candidate will receive an attractive gross salary of 4,720.00 € per month 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 and a mobility allowance. An additional family allowance (if applicable*) is foreseen. 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).
* Family is defined as persons linked to the researcher by (a) marriage, or (b) a relationship with equivalent status to a marriage recognized by the national legislation of the country of the beneficiary or of nationality of the researcher, or (c) dependent children who are actually being maintained by the researcher.
Eligibility criteria
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 recruitment process will adhere to the principles of equal opportunities, transparency and non-discrimination, in line with the European Charter for Researchers, and will actively promote diversity and gender balance. In particular, applications from female candidates are strongly encouraged, as women remain underrepresented in engineering disciplines.
To apply, 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. All applications must be mailed here with subject: “FairCFD, application to DC8”. Personal interviews might be asked.
The application process will be officially opened on
April 1 , 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.
If you are interested in more than one position belonging to the FairCFD network, please apply to 2 positions at most and precise the second choice in your cover letter. Extra applications not respecting this rule will be discarded.
Additional comments
A starting date will be negotiated with the successful candidate. The ideal starting date will be September, 1 2026.
#J-18808-Ljbffr