Doctorant anisotropic mesh adaptation for aerothermal simulations h/f

A propos d'Inria

Inria est l'institut national de recherche dédié aux sciences et technologies du numérique. Il emploie 2600 personnes. Ses 215 équipes-projets agiles, en général communes avec des partenaires académiques, impliquent plus de 3900 scientifiques pour relever les défis du numérique, souvent à l'interface d'autres disciplines. L'institut fait appel à de nombreux talents dans plus d'une quarantaine de métiers différents. 900 personnels d'appui à la recherche et à l'innovation contribuent à faire émerger et grandir des projets scientifiques ou entrepreneuriaux qui impactent le monde. Inria travaille avec de nombreuses entreprises et a accompagné la création de plus de 200 start-up. L'institut s'eorce ainsi de répondre aux enjeux de la transformation numérique de la science, de la société et de l'économie. Doctorant F/H Anisotropic Mesh Adaptation for Aerothermal Simulations

Type de contrat : CDD

Niveau de diplôme exigé : Bac +5 ou équivalent

Fonction : Doctorant

Niveau d'expérience souhaité : Jeune diplômé

A propos du centre ou de la direction fonctionnelle

Le centre de recherche Inria de Saclay a été créé en 2008. Sa dynamique s'inscrit dans le développement du plateau de Saclay, en partenariat étroit d'une part avec le pôle de l'Université Paris-Saclay et d'autre part avec le pôle de l'Institut Polytechnique de Paris. Afin de construire une politique de site ambitieuse, le centre Inria de Saclaya signé en 2021 des accords stratégiques avec ces deux partenaires territoriaux privilégiés.

Le centre compte, dont 27 sont communes avec l'Université Paris-Saclay ou l'Institut Polytechnique de Paris. Son action mobilise plus de 600 personnes, scientifiques et personnels d'appui à la recherche et à l'innovation, issues de 54 nationalités.

Le centre Inria Saclay - Île-de-France est un acteur essentiel de la recherche en sciences du numérique sur le plateau de Saclay. Il porte les valeurs et les projets qui font l'originalité d'Inria dans le paysage de la recherche : l'excellence scientifique, le transfert technologique, les partenariats pluridisciplinaires avec des établissements aux compétences complémentaires aux nôtres, afin de maximiser l'impact scientifique, économique et sociétal d'Inria.

Contexte et atouts du poste

Numerical simulation has been booming over the last thirty years, thanks to increasingly powerful numerical methods, computer-aided design (CAD), the mesh generation for complex 3D geometries, and the coming of supercomputers (HPC). The discipline is now mature and has become an integral part of design in science and engineering applications. This new status has led scientists and engineers to consider numerical simulation of problems with ever increasing geometrical and physical complexities. A simple observation of this chart

CAD --> Mesh --> Solver --> Visualization / Analysis

shows: no mesh = no simulation along with "bad" mesh = wrong simulation. We have concluded that the mesh is at the core of the classical computational pipeline and a key component to significant improvements. Therefore, the requirements on meshing methods are an ever increasing need, with increased difficulty, to produce high quality meshes to enable reliable solution output predictions in an automated manner.

Mesh adaptation is an innovative method for controlling errors in numerical simulations by generating meshes that are adapted to the geometry and physics of the problem being studied. It results in a powerful methodology that reduces significantly the size of the mesh required to reach the desired accuracy. Thus, it impacts favorably the simulation CPU time and memory requirement. Moreover, as the generated adapted mesh is in agreement with the physics of the flow, for some applications, this is the only way to obtain an accurate prediction. In fact, mesh adaptation enables a full control of discretization errors on the geometric model and the solution. Thus, it is a first step in the certification of numerical solutions by the obtention of mesh converged solutions, i.e., providing high-fidelity numerical simulations.

Nowadays, mesh adaptation is a mature tool which is well-posed mathematically. And, as it is fully automatic, it has started to be used in {industrial R&D departments} (Safran, Airbus, MBDA, Boeing, NASA,). Indeed, it has already proved, throughout many publications and applications, its superiority with respect to fixed mesh. However, its domain of application is in majority restricted to inviscid steady or unsteady flows. It has been recently extended to turbulent flows for steady problems.

The goal of this thesis is to develop this breakthrough numerical technology for aerothermal simulations in the turbomachinery community. This thesis will be done in collaboration with Safran Tech.

Mission confiée

The high pressure turbines, immediately after the combustion chamber, are subjected to a huge thermal stress that risk to reduce the life cycle of the component. In this context, conjugated heat transfer (CHT) is a fundamental topic to correctly model the entire fluid-solid system. In this sense, wall temperature, heat flux and heat transfer coefficient should be correctly predicted to correctly design the components. Given the complexity of the problem, we should find some simple cases able to mimic the real-world conditions. In the scientific community, the most studied configuration is the convective heat transfer in a boundary-layer flow over a flat plate of finite thickness with two-dimensional thermal conduction in the solid plate. Given the complexity and high cost of conducting experimental investigations, a fully three-dimensional numerical approach was employed to simulate the problem. It is important to note that usually the thermal and aerodynamic communities rely on different type of tools and methods to approximate the equations that govern their physics. Aerodynamic designs relies on the Reynolds Averaged Navier Stokes (RANS) simulations that are nowadays the most widely used for performance prediction of gas turbines and aerodynamic components in turbomachinery community. The thermal community are relying on the discretization of the heat equation and on Finite Element Solvers. On top of this poses the method of coupling the two solvers. An interesting modal analysis was posed by Giles and extended with a direct application to high pressure turbine. These analysis highlighted three different coupling methodologies and the dependence of the stability of the coupling on the material conductivity (both solid and fluid) and on the discretization of the domain. It is possible to find some optimization of the coupling condition where the characteristic of the materials and the discretization have been linked to an optimal relaxation parameter in a Robin boundary condition in the coupling.

In order to achieve important performance improvements, and reduce design iteration cost, the simulation process should be mastered and interactions between physics should be taken into account. In this context, the aerothermic coupled simulation is a cornerstone of the design process. In the context of this PhD, Safran Tech will study different solutions in order to couple RANS simulations with steady thermal solver. All of this is coupled with the anisotropic mesh adaptation technology in order to redistribute the discretization error and to achieve mesh-solution convergence at the end of a non-linear process.

This thesis will focus on three main topics:
- Design an optimal coupling techniques (strong or weak coupling) for the aerothermal problem that takes into account the unstructured nature of the anisotropic adapted meshes
- Extend the error estimate theory to coupled problem (here the RANS and the heat equations)
- Develop convergence boosting techniques, such as multigrid that have demonstrated to be optimal for elliptic problems (such as heat equation), for the coupled problem within the remeshing framework.

The PhD student will first learn all the concepts related to metric-based mesh adaptation. He/she will perform several steady adaptive simulations of turbulent flows (RANS) to become familiar with the mesh adaptive simulation platform involving a flow solver, an adaptive mesh generator, an error estimate code and an interpolation code. Simulations on turbomachinery applications will be considered.

In the first part of this thesis, he/she will focus on the coupling methodology between the Finite Volume RANS solver and the Finite Element heat solver. Two approaches will be evaluated. The weak coupling method (also called staggered approach) using local Robin conditions and non matching meshes for both physics. In particular, it required surface interpolation to set-up the Robin boundary conditions. The second approach is a strong coupling method (also named monolithic approach) where both the RANS and the heat equations are solved simultaneously. This monolithic method puts more stress on the linear system resolution but should converge more efficiently. For each of these methods, the adjoint problem will have to be formulated and solved in order to access the class of goal-oriented error estimates.

The second part of this thesis will focus developing feature-based and goal-oriented error estimates for the coupled problem. Error estimates exist for RANS equation and heat equation but they handle different scales in the considered sensors. The first step would be to make homogenous these two error estimates, and then to take into account Robin conditions. To these end, the new error estimate should equidistribute properly the error between the two domains. Finally, a global error estimate will be developed for the strong coupling method.

The last part of the thesis will focus on multigrid technics. First, he/she will implement the multigrid approach for the heat equation. This is well-know and demonstrated in the literature. Then, the multigrid approach will be developed for the RANS equations. Today, this is an open problem in the context of unstructured meshes but is is fundamental for an efficient and fast solution of the strong coupling problem.

In this work, the PhD student will be confronted to both {theoretical} issues (error estimate theory, numerical analysis, ) and {scientific computing} issues (numerical schemes, fast and efficient implementation of the numerical methods, parallel computing, ).

Principales activités

The following schedule is proposed for the 3 years of thesis:

[T0 + 6] Learn how to use the GammaO project software and environment by running steady RANS using the mesh adaptive solution platform.
Bibliography on aerothermal coupling problem for turbomachinery, error estimate theory and multigrid methods.

[T0 + 12] Development of weak-coupling method using Robin boundary conditions.
Multigrid method for the heat equation.
Validation of the coupled solver on several aerothermal turbomachinery configurations.

[T0 + 18] Development of staggered error estimate for the weak-coupling method.
Development of the mesh adaptive framework in this context.

[T0 + 24] Development of multigrid method for the RANS equation.
Validation of the multigrid coupled solver within the mesh adaptive solution platform on several aerothermal turbomachinery configurations.

[T0 + 30] Development of strong-coupling method and the monolithic error-estimate.
Comparison between the weak and strong coupling methodology.

[T0 + 36] Writing the thesis manuscript.

Compétences

Le candidat doit avoir suivi une formation en mathématiques appliquées ou une formation d'ingénieur. il serait très appréciable que le candidat ait suivi des cours en :
- langage de programmation en C et python
- analyse numérique (Eléments finis, Volumes finis)
- calcul matriciel
- calcul parallèle (MPI, multithread)
- mécanique des fluides.
Un bon niveau d'anglais est requis pour ce travail.

Avantages

- Restauration subventionnée
- Transports publics remboursés partiellement
- Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
- Possibilité de télétravail (après 6 mois d'ancienneté) et aménagement du temps de travail
- Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
- Prestations sociales, culturelles et sportives (Association de gestion des oeuvres sociales d'Inria)
- Accès à la formation professionnelle
- Sécurité sociale

Rémunération

Salaire mensuel brut : 2.300 euros