Development of a symbolic regression method for the formulation of wall laws in CFD

Development of a symbolic regression method for the formulation of wall laws in CFD
The use of Artificial Intelligence in Computational Fluid Dynamics (CFD) is very promising to propose new physical models. Few studies have been done so far on the modeling of wall flows, for which the available physical models are facing great difficulties to be applicable and predictive. A recent PhD thesis at IFPEN has shown the ability of a neural network trained on high-fidelity wall-resolved data to reproduce the physics of a turbulent non-equilibrium boundary layer, accurately inferring wall friction from flow variables at a distance corresponding to the wall resolution of typical RANS coarse meshes. The present thesis aims at continuing this work to include the prediction of wall heat flux, a key element for many application areas at IFPEN involving thermal and cooling aspects. In particular, the objective is to formulate analytical thermal wall laws through the development of an adapted Gene Expression Programming (GEP) method. This symbolic regression approach allows to form interpretable analytical models, more regular and more robust than methods based on neural networks. This new approach will also have the advantage of being more easily implemented in any type of CFD code. In a first step, the PhD student will focus on the implementation of a GEP methodology with a first validation in terms of prediction of wall shear stress on single-phase turbulent canonical flows, and the results will be compared to those obtained with neural networks. The approach will then be extended to the prediction of wall heat flux from high-fidelity test cases representative of liquid cooling of electric drive train components. 
This research topic, at the crossroads of numerical fluid modeling and advanced machine learning techniques, will be supervised by a multidisciplinary team of researchers from IFPEN and LISN.

Keywords: CFD, machine learning, symbolic regression, heat transfer modeling

• Academic supervisor    Dr Christian ANGELBERGER (IFPEN), Dr Anne SERGENT (LISN) & Dr Lionel MATHELIN (LISN)  
• Doctoral School   ED579 - SMEMaG, Université Paris Saclay
• IFPEN supervisors    Dr Adèle POUBEAU & Dr Thibault FANEY
• PhD location    IFPEN, Rueil-Malmaison, France  
• Duration and start date    3 years, starting in the fourth quarter 2024 (Novembre 4)
• Employer    IFPEN
• Academic requirements    Master's degree or third year of engineering school, with a strong background either in CFD or mathematics & statistics, and the willingness to learn the other topic 
• Language requirements    English level B2 (CEFR)    
• Other requirements    Computational and programming skills (LINUX, Python)

To apply, please send your cover letter and CV to the IFPEN supervisor indicated below.