Analyse de stabilité globale par des méthodes de différentiation automatique pour des applications industrielles.

Global stability method with automatic differentiation in industrial environment

• Auteur / Autrice : Alessandro Franchini
• Direction : Jean-Christophe Robinet
• Type : Projet de thèse
• Discipline(s) : Mécanique des fluides
• Date : Inscription en doctorat le 15/10/2021
• Etablissement(s) : Paris, HESAM
• Ecole(s) doctorale(s) : École doctorale Sciences des métiers de l'ingénieur
• Partenaire(s) de recherche : Laboratoire : DynFluid - Laboratoire de dynamique des fluides
• Partenaire(s) de recherche : Equipe de recherche : Instabilités, Transition & Contrôle
• Partenaire(s) de recherche : établissement de préparation de la thèse : École nationale supérieure d'arts et métiers (1780-....)

Mots clés

Mots clés libres

Stabilité

Differentiation automatique

Jets sous-détendus

Calculs hautes performances

Stability

Automatic differentiation

Over expand jets

High performance computing

Résumé

Recent advances in high-performance computing have enabled full-scale physics-based numerical simulations and optimization in academia and industry. Computational fluid dynamics (CFD) tools and numerical optimization techniques have been widely adopted to shorten the design cycle times and to explore the design space more efficiently. High-fidelity methods enable engineers to perform detailed designs earlier in the design process, allowing them to understand the design trade-offs better and make more informed decisions. In addition, advances in sensitivity analysis via the adjoint method dramatically improve aerodynamic shape optimization effectiveness and computational time. However, due to the complexity of the CFD solvers, deployment of the adjoint method in Reynolds-averaged Navier-Stokes (RANS) solvers remains a challenging task. In order to go in this direction and to be able to approach multi-physical flow configurations, during this thesis, a first step will be carried out by the linearization of the equations of motion. This stage is essential if one seeks to (i) compute the linear stability of a flow, (ii) optimize the latter with respect to an objective function, (iii) compute the receptivity or the sensitivity of the flow with respect to quantities of interest (QoI). There are several ways to do it. The first is to write the linearized equations analytically then to discretize them. This approach is qualified as differentiate-then-discretise approach". This is practicable when the equations are relatively simple (eq. incompressible), but for more complex systems of equations, problems of consistency and boundary conditions appear { making such an approach difficult. The alternative approach consists of discretizing, then linearizing. This approach is called discretise-then-differentiate approach". This amounts to linearizing equations that are already discretized and applying differentiation operations to a solver (to discrete instructions). There are different ways to do this. In this thesis, we have chosen to use an automatic differentiation (AD) method.