DESCRIPTION :
The postdoctoral project fits in the ongoing Inria-CWI Associate Team SPADES https://team.inria.fr/memphis/spades-associate-team/ . The project SPADES (Structure-Preserving Approximations of Dynamical systems in Engineering and Science) focuses on the development and the analysis of structure-preserving model reduction techniques for conservation laws. Long research stays at CWI Amsterdam will be encouraged.
The postdoctoral project will focus on the development of space-time structure-preserving model reduction of parametric compressible flows, with emphasis on the compressible Euler and the Navier-Stokes equations.
Reduced order models introduce a further layer of approximation compared to the corresponding high-fidelity models, being designed to enable fast and efficient simulations while maintaining an acceptable level of accuracy. This is particularly important in parametric problems, when simulations need to be repeated many times under different input parameters. To allow for further reduction, we consider space-time techniques [1,2] as they enable model reduction of temporal degrees of freedom as well, as opposed to more traditional time-marching high-fidelity methods. Thus, space-time techniques have the potential to achieve much more significant speedups for parametric problems.
However, the development of reduced models with a low computational cost, which at the same time retain the physical properties and structures of high-fidelity models, remains a major challenge. In this project, we shall focus on the development of energy- and entropy-stable numerical methods, to ensure nonlinear stability and accuracy of the numerical scheme, as well as consistency with the physics of the problem [3]. Such a property is also compelling in the case of discontinuities as it allows the method to capture the correct weak solution.
We also plan to address the development of effective deterministic and/or stochastic closure terms to model the effect of the truncated modes on the dominant dynamics (truncation error). Since we use standard (time-marching) high-fidelity models for snapshot generation, while using fully-implicit space-time methods for the construction of the reduced-order model, the closure model should also account for the discrepancy between the high-fidelity model and the reduced-order model (model error).
A tentative program of the project is as follows.
* Review of entropy- and energy-stable high-order methods and projection-based model reduction techniques for conservation laws.
* Design and implementation of space-time model reduction techniques for subsonic inviscid and viscous flows. We shall focus on the development of provably semi- and fully-discrete entropy- and energy-stable reduced models. We shall develop a space-time method for both high-fidelity and reduced-order computations, to facilitate the assessment of the model reduction procedure.
* Extension to shock-dominated (transonic, supersonic, all-Mach) flows. Such an extension requires to introduce limiting strategies to prevent oscillatory behaviors; it also probably requires the use of nonlinear data compression techniques.
Code d'emploi : Chargé de Recherches (h/f)
Domaine professionnel actuel : Scientifiques
Niveau de formation : Bac+8
Temps partiel / Temps plein : Plein temps
Type de contrat : Contrat à durée indéterminée (CDI)
Compétences : Computational Fluid Dynamics, Compression des Données, Programmation Informatique, Systèmes Dynamiques, Informatique Scientifique, Aérodynamique, Travaux de Construction, Analyse Numérique, Oscillation, Équation Différentielle Partielle, Sciences Physiques, Recherche Post-Doctorale, Simulations, Vitesse Supersonique, Publication / Edition
Courriel :
tommaso.taddei@inria.fr
Téléphone :
0524574000
Type d'annonceur : Employeur direct
