Maxime STAUFFERT
Pendant presque 10 ans, dont 4 en tant qu’ingénieur-chercheur au CEA, je me suis intéressé aux schémas numériques dans le domaine de la mécanique des fluides : implicites-explicites, ordres élevés de type Galerkin discontinus, raffinements de maillages, multi-physiques.
Depuis 2024, je fais partie de l’équipe de visualisation au CEA, qui développe l’outil Themys, une application open-source basée sur ParaView / VTK. Mes centres d’intérêts dans la thématique de la visualisation sont les représentations de données complexes : sur des maillages ordres élevés (courbes de Bézier, NURBS), avec des techniques de raffinements de maillages (basés sur des patchs ou des arbres), ordres élevés de type Galerkin discontinus.
SIAM Journal on Scientific Computing, 2021
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Abstract
The sensitivity equation method aims at estimating the derivative of the solution of partial differential equations with respect to a parameter of interest. The objective of this work is to investigate the ability of an isogeometric discontinuous Galerkin (DG) method to evaluate accurately sensitivities with respect to shape parameters originating from computer-aided design (CAD) in the context of compressible aerodynamics. The isogeometric DG method relies on nonuniform rational B-spline representations, which allows us to define a high-order numerical scheme for Euler/Navier--Stokes equations, fully consistent with CAD geometries. We detail how this formulation can be exploited to construct an efficient and accurate approach to evaluate shape sensitivities. A particular attention is paid to the treatment of boundary conditions for sensitivities, which are more tedious in the case of geometrical parameters. The proposed methodology is first verified on a test-case with an analytical solution and then applied to two more demanding problems that concern the inviscid flow around an airfoil with its camber as a shape parameter and the unsteady viscous flow around a three-element airfoil with the positions of slat and flap as parameters.
Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020
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We are interested in the numerical approximation of the shallow water equations in two space dimensions. We propose a well-balanced, all-regime, and positive scheme. Our approach is based on a Lagrange-projection decomposition which allows to naturally decouple the acoustic and transport terms.
The Astrophysical Journal, Volume 876, Number 2 (144), 2019
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By generalizing the theory of convection to any type of thermal and compositional source terms (diabatic processes), we show that thermohaline convection in Earth's oceans, fingering convection in stellar atmospheres, and moist convection in Earth's atmosphere are derived from the same general diabatic convective instability. We also show that "radiative convection" triggered by the CO/CH4 transition with radiative transfer in the atmospheres of brown dwarfs is analogous to moist and thermohaline convection. We derive a generalization of the mixing-length theory to include the effect of source terms in 1D codes. We show that CO/CH4 "radiative" convection could significantly reduce the temperature gradient in the atmospheres of brown dwarfs similarly to moist convection in Earth's atmosphere, thus possibly explaining the reddening in brown dwarf spectra. By using idealized 2D hydrodynamic simulations in the Ledoux unstable regime, we show that compositional source terms can indeed provoke a reduction of the temperature gradient. The L/T transition could be explained by a bifurcation between the adiabatic and diabatic convective transports and seen as a giant cooling crisis: an analog of the boiling crisis in liquid/steam-water convective flows. This mechanism, with other chemical transitions, could be present in many giant and Earth-like exoplanets. The study of the impact of different parameters (effective temperature, compositional changes) on CO/CH4 radiative convection and the analogy with Earth moist and thermohaline convection is opening the possibility of using brown dwarfs to better understand some aspects of the physics at play in the climate of our own planet.
Thèse de Doctorat de l'Université Paris-Saclay, 2018
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On étudie dans le cadre de la thèse une famille de schémas numériques permettant de résoudre les équations de Saint-Venant. Ces schémas utilisent une décomposition d'opérateur de type Lagrange-projection afin de séparer les ondes de gravité et les ondes de transport. Un traitement implicite du système acoustique (relié aux ondes de gravité) permet aux schémas de rester stable avec de grands pas de temps. La correction des flux de pression rend possible l'obtention d'une solution approchée précise quel que soit le régime d'écoulement vis-à-vis du nombre de Froude. Une attention toute particulière est portée sur le traitement du terme source qui permet la prise en compte de l'influence de la topographie. On obtient notamment la propriété dite équilibre permettant de conserver exactement certains états stationnaires, appelés état du "lac au repos". Des versions 1D et 2D sur maillages non-structurés de ces méthodes ont été étudiées et implémentées dans un cadre volumes finis. Enfin, une extension vers des méthodes ordres élevés Galerkin discontinue a été proposée en 1D avec des limiteurs classiques ainsi que combinée avec une boucle MOOD de limitation a posteriori.
Communications in Mathematical Sciences, Volume 15, Number 3, 2017
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Abstract
This work focuses on the numerical approximation of the shallow water equations (SWE) using a Lagrange-projection type approach. We propose to extend to this context the recent implicit-explicit schemes developed in [C. Chalons, M. Girardin, and S. Kokh, SIAM J. Sci. Comput., 35(6):a2874–a2902, 2013], [C. Chalons, M. Girardin, and S. Kokh, Commun. Comput. Phys., to appear, 20(1):188–233, 2016] in the framework of compressible flows, with or without stiff source terms. These methods enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, and maintain accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms in SWE and more specifically to the wellknown well-balanced property. We prove that the proposed numerical strategy enjoys important non linear stability properties and we illustrate its behaviour past several relevant test cases.
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, 2017
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This work considers the barotropic Euler equations and proposes a high-order conservative scheme based on a Lagrange-Projection decomposition. The high-order in space and time are achieved using Discontinuous Galerkin (DG) and Runge-Kutta (RK) strategies. The use of a Lagrange-Projection decomposition enables the use of time steps that are not constrained by the sound speed thanks to an implicit treatment of the acoustic waves (Lagrange step), while the transport waves (Projection step) are treated explicitly. We compare our DG discretization with the recent one (Renac in Numer Math 1-27, 2016, [7]) and state that it satisfies important non linear stability properties. The behaviour of our scheme is illustrated by several test cases.