Q : Florian, you are the recipient of the 2018 ONERA best PhD student award in the “Fluid Mechanics and Energetics” domain. Congratulations. Can you tell us about your PhD topic and the original contributions of your work ?
Broadly, my PhD is at the intersection of applied mathematics and aeroacoustics, an area of fluid mechanics concerned with the generation, propagation, and absorption of sound waves in a moving medium.
Due to the growth in air traffic during the last decades, the regulation on aircraft environmental impact has become increasingly stringent, and bodies such as ACARE set high goals for future noise reductions. At the certification level, the European Aviation Safety Agency issues noise level requirements, but even an already certified airliner can see its commercial viability threatened by the demands of individual airports. From the point of view of an aircraft or engine manufacturer, it is of paramount importance to deal with these operational threats as well as to improve future designs. Given the cost of testing, a lot of effort is being put into improving the reliability of computational aeroacoustics (CAA) to enable better noise level predictions.
To reduce the noise emitted by an aircraft, one practical solution consists in mounting passive sound absorbing materials, commonly known as acoustical liners. The problem at the heart of my thesis is the computation of the sound absorbed by such materials, which can be modeled using what is formally known as impedance boundary conditions (IBCs).
My PhD thesis focuses on time-domain IBCs in aeroacoustics, although most of my work could equally be applied to electromagnetics. The starting point of my thesis was the finding that IBCs had been studied separately by physical, computational, and mathematical communities, without many connections. I have considered all three aspects, starting from the physical literature, to address the following broad questions :
- What is the mathematical structure of physical impedance models ?
- How does the IBC affect the well-posedness and stability of the original problem ?
- What is the most computationally efficient way to discretize an IBC at high order ?
Q : You graduated from ISAE-SUPAERO as an engineer in 2015 and then decided to pursue on a PhD program. What were your expectations then about a PhD and, three years later, would you say they have been fulfilled ?
As a student fresh out of ISAE-SUPAERO, I had two main motivations to pursue a PhD. Firstly, I was looking forward to furthering my knowledge of applied mathematics and fluid mechanics. Secondly, I was attracted by the challenge that constitutes a PhD : would I be up to the task ? Another factor in my decision was the work experience that I acquired while at ISAE-SUPAERO, mainly during a gap year in the aeronautical industry : I was keen on discovering a new working environment, namely the “small world” of academic research.
In retrospect, I think it is difficult as a student to fully realize how wide the gap is between a PhD and a master’s degree or a work experience. Indeed, a PhD is much more than a mere scientific project : it is also a fast track to the mastery of soft skills such as communication, organization, as well as, and maybe most importantly, your ability to deal with failures, setbacks, or disappointments, which are bound to occur during such a long experience.
Overall, I feel that I have got more out of this PhD than I was expecting. I have grown scientifically, but also learnt valuable lessons that will surely help me a great deal.
Q : You mention communication skills. You have participated in conferences and taught classes in applied mathematics at ISAE-SUPAERO. How would you describe these experiences ?
Scientific conferences and classes are regular occurrences during a PhD and bring a welcome break to the daily grind. This combination of research, communication, and teaching is I think what makes the PhD experience so unique. Although the level of discourse obviously varies between conferences and classes, both require a significant amount of preparation and rely on the same pedagogic skills.
I have enjoyed the fundamental unpredictability of classes, or, more exactly, of students. For example, it is stunning to see the kind of out-of-the-box questions you can get ask ! As for conferences, they are a way of meeting and getting valuable feedback from other researchers in your field in a friendly atmosphere. I should also mention that they enable you to travel : another perk of being a PhD student !
Q : What are your plans for the future ?
I am going to INRIA for a post-doctoral position. In the longer term, I would like to work in an area where I can use the problem-solving skills I have learnt during my PhD. A position that combines teaching and research or an industry job related to scientific computing would suit me.
Absorption of a sound wave in an acoustically treated duct. (Top) Duct schematic : inlet on the left, outlet on the right, sound absorbing material mounted on the top wall between L1 and L2. (Bottom) Snapshot of a time-domain computation : pressure field. (4th order Discontinuous Galerkin on 552 triangles, 4th order 8-stage Runge-Kutta, CFL=0.85.)