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International audience; Homogeneous turbulence and turbulence in scale-by-scale equilibrium, played a leading role in the turbulence research of the second half of the twentieth century, and Jack Herring was an important contributor to these developments. The research activity which has followed these developments over the past ten to fifteen years concerns turbulence, which is out of scale-by-scale equilibrium either because it is non-stationary or because it is non-homogeneous or both. This paper is a short review of recent progress in this relatively new direction of turbulence research.

International audience; This paper presents an improved immersed boundary method (IBM) with new wall model-ing assumptions for the simulation of compressible flows on Cartesian grids. This methodrelies on an adaptive positioning of both target and image points, in accordance with theReynolds number. It primarily ensures that the mesh is fine enough at the first computedcells to correctly capture the strong variations of the tangential velocity in the wall nor-mal direction, and ultimately prevents the appearance of spurious oscillations at the wall.In the present work, we take into consideration normal pressure gradient information,interpolated at a new set of image points positioned farther away from the geometry, inorder to extend the validity domain of our wall modeling. This significantly improvesthe prediction of the skin friction and the skin pressure coefficients, and also results in abetter estimation of both the drag and lift coefficients through the near-field integrationof all aerodynamic forces at the wall. The latest developments essentially consist in asecond-order extraction of the pressure at the wall during the post-processing step and amodification of Musker’s algebraic wall function to reconstruct the velocities and frictionat the target points at each iteration of the flow solver. This new methodology has beenvalidated through the study of subsonic flow simulations around a NACA0012 profile anda 3.5:1 prolate spheroid, where good agreements between the wall-modeled IBM solutionsand the body fitted wall-resolved references have been observed.

The motion of small non- spherical particles suspended in a turbulent flow is relevant for a large variety of natural and industrial applications such as aerosol dynamics in respiration, red blood cells motion, plankton dynamics, ice in clouds, combustion, to name a few. Anisotropic particles react on turbulent flows in complex ways, which depend on a wide range of parameters (shape, inertia, fluid shear). Inertia-free particles, with size smaller than the Kolmogorov length, follow the fluid motion with an orientation generally defined by the local turbulent velocity gradient. Therefore, this thesis is focused on the dynamics of these objects in turbulence exploiting stochastic Lagrangian methods. The development of a model that can be used as predictive tool in industrial computational fluid dynamics (CFD) is highly valuable for practical applications in engineering. Models that reach an acceptable compromise between simplicity and accuracy are needed for progressing in the field of medical, environmental and industrial processes. The formulation of a stochastic orientation model is studied in two-dimensional turbulent flow with homogeneous shear, where results are compared with direct numerical simulations (DNS). Finding analytical results, scrutinising the effect of the anisotropies when they are included in the model, and extending the notion of rotational dynamics in the stochastic framework, are subjects addressed in our work. Analytical results give a reasonable qualitative response, even if the diffusion model is not designed to reproduce the non-Gaussian features of the DNS experiments. The extension to the three-dimensional case showed that the implementation of efficient numerical schemes in 3D models is far from straightforward. The introduction of a numerical scheme with the capability to preserve the dynamics at reasonable computational costs has been devised and the convergence analysed. A scheme of splitting decomposition of the stochastic differential equations (SDE) has been developed to overcome the typical instability problems of the Euler–Maruyama method, obtaining a mean-square convergence of order 1/2 and a weakly convergence of order 1, as expected. Finally, model and numerical scheme have been implemented in an industrial CFD code (Code_Saturne) and used to study the orientational and rotational behaviour of anisotropic inertia-free particles in an applicative prototype of inhomogeneous turbulence, i.e. a turbulent channel flow. This real application has faced two issues of the modelling: the numerical implementation in an industrial code, and whether and to which extent the model is able to reproduce the DNS experiments. The stochastic Lagrangian model for the orientation in the CFD code reproduces with some limits the orientation and rotation statistics of the DNS. The results of this study allows to predict the orientation and rotation of aspherical particles, giving new insight into the prediction of large scale motions both, in two-dimensional space, of interest for geophysical flows, and in three-dimensional industrial applications., Le mouvement de petites particules non-sphériques en suspension dans un écoulement turbulent a lieu dans une grande variété d’applications naturelles et industrielles. Par exemple, ces phénomènes impactent la dynamique des aérosols dans l’atmosphère et dans les voies respiratoires, le mouvement des globules rouges dans le sang, la dynamique du plancton dans l’océan, la glace dans les nuages ou bien la combustion. Les particules anisotropes réagissent aux écoulements turbulents de manière complexe. Leur dynamique dépend ainsi d’un large éventail de para- mètres (forme, inertie, cisaillement du fluide). Les particules sans inertie, dont la taille est inférieure à la longueur de Kolmogorov, suivent le mouvement du fluide avec une orientation généralement gouvernée par le gradient local de vitesse turbulente. Cette thèse est axée sur la dynamique de tels objets en turbulence en ayant recours à des méthodes Lagrangienes stochastiques. Le développement d’un modèle qui peut être utilisé comme outil prédictif dans le cadre de la dynamique de fluides numérique (CFD) au niveau industriel est d’un grand intérêt pour les applications concrètes en ingénierie. Par ailleurs, pour progresser dans le domaine de la médecine, de l’environnement et des procédés industriels, il est nécessaire que ces modèles atteignent un compromis acceptable entre simplicité et précision. La formulation d’un modèle stochastique pour l’orientation de telles particules est tout d’abord présentée dans le cadre d’un écoulement turbulent bidimensionnel avec un cisaillement homogène. Des simulations numériques directes (DNS) sont produites pour guider et évaluer la proposition de modèle. Les questions abordés dans ce travail portent sur la représentation de formes analytiques du modèle, sur les effets des anisotropies inclues dans le modèle, et sur l’extension de la notion de dynamique rotationnelle dans le cadre de cette approche stochastique. Les résultats obtenus avec le modèle, comparés avec la DNS, produisent une réponse qualitative acceptable, même si ce modèle diffusif n’est pas conçu pour reproduire les caractéristiques non-gaussiennes des expériences numériques (DNS). L’extension au cas tridimensionnel du modèle d’orientation pose le problème de son implé- mentation numérique efficace. Dans ce travail, un schéma numérique capable de simuler la dynamique d’orientation de telles particules, à un coût de calcul raisonnable, est introduit. La convergence de ce schéma est également analysée. Pour ce faire, un schéma fondé sur la décomposition de la dynamique a été développé pour résoudre les équations différen- tielles stochastiques (EDS) de rotation de ces particules. Cette décomposition permet de surmonter les problèmes d’instabilité typiques de la méthode Euler–Maruyama; on a ainsi obtenu une convergence en norme L2 d’ordre 1/2 et une convergence faible d’ordre 1, comme classiquement attendu. Enfin, le schéma numérique a été implémenté dans un code CFD industriel (Code_Saturne). Ce modèle a ensuite été utilisé pour étudier l’orientation et la rotation de particules anisotropes sans inertie dans le cas d’un écoulement turbulent inhomogène, à savoir un écoulement de canal plan turbulent. Cette application dans un cas pratique a permis de mettre en evidence deux difficultés liées au modèle : d’abord, l’implémentation numérique dans un code industriel, ensuite la capacité du modèle à reproduire les expériences numériques obtenues par DNS. Ainsi, le modèle stochastique Lagrangien pour l’orientation de sphéroïdes implémenté dans Code_Saturne permet de reproduire, avec certaines limites, les statistiques d’orientation et de rotation de sphéroïdes mesurées dans la DNS.

International audience; The transition from regular to apparently chaotic motions is often observed in nonlinear flows. The purpose of this article is to describe a deterministic mechanism by which several smaller scales (or higher frequencies) and new phases can arise suddenly in a nonlinear flow under the impact of forcing terms. This phenomenon is illustrated in the context of Hamilton-Jacobi equations. It is derived from a multiscale and multiphase analysis of nonlinear differential equations involving stiff oscillating source terms. We introduce an original method allowing to get the existence of solutions during long times, as well as asymptotic descriptions and reduced models. This is achieved by implementing three main tools: a blow-up procedure (extending the normal form method), a Wentzel-Kramers-Brillouin approximation (of super-critical type) and the Hadamard's global inverse function theorem which can be applied here due to transparency conditions (coming from a complete integrability condition).

International audience; In order to study the unsteady flows occurring in the wake of space launchers, numerical models have to provide an accurate description of both the turbulent behaviour of base flows and the thermodynamic properties of the multi-species and reactive propulsive jets. As the complexity of models dedicated to each of these objectives can have a significant impact on computational cost, especially for reusable designs including several nozzles, authors have often to establish a compromise between an accurate treatment of turbulence and the taking into account of chemistry effects. To contribute to the improvement of launcher base flow predictions, this paper presents the study of a four-nozzle space launcher configuration with a dedicated numerical workflow focusing on the treatment of turbulence. Indeed, such a case has only been studied with RANS approaches so far, and is treated here with the automatic mode of the Zonal Detached Eddy Simulation (ZDES Mode 2 2020) and hybrid numerical methods, based on Ducros' sensor and allowing to resolve well the turbulent fluctuations of the base flow while capturing the strong normal shock structures inside the jets. The computations are furthermore performed thanks to inert bi-species numerical methods enabling to take into account some thermodynamic properties of the jets with an acceptable computational cost. The bi-species scale resolving numerical workflow is able to reproduce the main features of multi-jets afterbody flows and provides a satisfying agreement with experimental pressure measurements. Compared with RANS calculations, the use of ZDES not only gives access to additional information regarding the unsteadiness of the flow but also provides distinct predictions of the mean aerodynamic field.

International audience; Most widely used Reynolds-averaged Navier-Stokes (RANS) models employ the Boussinesq approximation, which assumes a linear relationship between the turbulent Reynolds stresses and the mean-velocity gradient tensor. This assumption, which can be very stringent, is more suited for simple shear-flows and is regarded as an important shortcoming for the improvement of the representation of turbulence in complex geometries. Correction of the local turbulence length scales, as achieved, for example, by the introduction of a correction term in the eddy-viscosity equation of a Spalart-Allmaras model, then indeed only allows relatively small corrections to the base-line model and may not be sufficiently flexible to adapt to common situations where the Reynolds stresses are not aligned with the velocity gradient tensor. For the variational data-assimilation step, we consider a vectorial source correction term in the momentum equations (output quantity) together with the Spalart-Allmaras model, which allows full flexibility to adapt to any mean-flow topology. We show how the machine-learning framework should be adapted, in particular with respect to the vectorial nature of the correction term and given invariance properties. As for the input quantities, we discuss the impact of considering either local quantities for the nondimensionalization or global ones that characterize the configuration. We showcase the procedure on the periodic hill configuration, for which a rich direct numerical simulation database is available in the literature: in particular, the availability of the full mean-flow solution for a range of Reynolds numbers and geometries ensures identification of “physical” correction terms and allows learning of turbulence models that accurately extrapolate to new Reynolds numbers and geometries.

International audience; In this paper, we present recent improvements of an Immersed Boundary Method (IBM) for the simulation of turbulent compressible flows on Cartesian grids. The proposed approach enables to remove spurious oscillations at the wall on skin pressure and friction coefficients. Results are compared to a body-fitted approach using the same wall function, showing that the stair-step immersed boundary provides a smooth solution compared to the body-fitted one. The immersed boundary method has been modified to adapt the location of forced and forcing points involved in the immersed boundary reconstruction to the Reynolds number. This method has been validated either for subsonic and transonic flow regimes, through the simulation of the subsonic turbulent flow around a NACA0012 profile and the transonic flow around a RAE2822 profile and the three-dimensional ONERA M6 wing.; Dans ce papier, nous présentons les améliorations récentes relatives à une méthode de frontières immergées (IBM) pour la simulation des écoulements turbulents compressibles sur maillages cartésiens. La méthode proposée permet de supprimer les oscillations parasites apparaissant sur les coefficients de pression et de frottement à la paroi. Les résultats sont comparés à une méthode de maillages conformes aux obstacles, où la couche limite est résolue par le maillage ou modélisée par un modèle de paroi, permettant de justifier que l'approche IBM sur maillages en escaliers permet d'obtenir une solution régulière comparable à la solution sur maillage curviligne. La méthode de frontières immergées a été modifiée pour adapter au nombre de Reynolds du cas d'écoulement la localisation des points de forçage ou de référence et des points corrigés ou points cibles utilisés dans la reconstruction IBM. Cette méthode a été validée sur des simulations d'écoulements en régime subsonique et transsonique, respectivement autour d'un profil NACA0012 et d'un profil RAE2822. Enfin une simulation de l'écoulement transsonique autour de l'aile ONERA M6 est effectuée pour valider l'approche sur un cas tridimensionnel.

We report an idealized numerical study of a melting and freezing solid adjacent to a turbulent, buoyancy-affected shear flow, in order to improve our understanding of topography generation by phase changes in the environment. We use the phase-field method to dynamically couple the heat equation for the solid with the Navier-Stokes equations for the fluid. We investigate the evolution of an initially-flat and horizontal solid boundary overlying a pressure-driven turbulent flow. We assume a linear equation of state for the fluid and change the sign of the thermal expansion coefficient, such that the background density stratification is either stable, neutral or unstable. We find that channels aligned with the direction of the mean flow are generated spontaneously by phase changes at the fluid-solid interface. Streamwise vortices in the fluid, the interface topography and the temperature field in the solid influence each other and adjust until a statistical steady state is obtained. The crest-to-trough amplitude of the channels are larger than about 10$\delta_{\nu}$ in all cases, with $\delta_{\nu}$ the viscous length scale, but are much larger and more persistent for an unstable stratification than for a neutral or stable stratification. This happens because a stable stratification makes the cool melt fluid buoyant such that it shields the channel from further melting, whereas an unstable stratification makes the cool melt fluid sink, inducing further melting by rising hot plumes. The statistics of flow velocities and melt rates are investigated, and we find that channels and keels emerging in our simulations do not significantly change the mean drag coefficient., Comment: 35 pages, 15 figures

In turbulent rough-walled flows, the 2D friction-roughness relation differs from its 3D counterpart., The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f − r relation may be expressed by the Strickler empirical scaling f ∝ r1/3. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f ∝ r and the f − r relation is not the same in 2D as in 3D. Our findings are beyond the purview of the standard theory of friction but consistent with a competing theory in which f is linked to the turbulent spectrum via the spectral exponent α: In 3D, α = 5/3 and the theory yields f ∝ r1/3; in 2D, α = 3 and the theory yields f ∝ r.

International audience; In this paper, we present simulations of turbulent thermal convection driven by free-surface evaporation above and by a heated wall below. A novel algorithm is proposed for predicting evaporation rates at a free surface, which we then validate against experimental data. At the top of a cuboidal domain, a shear-free boundary condition acts as an approximation of the free surface. We first focus on a domain of aspect ratio Γ = 1, where a fully resolved direct numerical simulation is carried out at a moderate Rayleigh number, Ra = 1.2 × 107, and we compare flow statistics with a Large-Eddy Simulation (LES) on a coarse grid. Both the fully resolved simulation and the LES predict well the time- and area-averaged evaporation rate and free surface temperature when compared with the experimental data. Next, we carry out a series of LES with an increasing lower wall temperature and, consequently, Ra. We then validate the evaporation model by comparing LES predictions of the time- and area-averaged mass flux and temperature at the upper boundary against the experimental measurements. The aspect ratio of the domain is then reduced, and we show, for the first time, the transition to a dual-roll state of the large-scale circulation (LSC) at the aspect ratio of Γ = 1/4 in a cuboidal domain. The temperature and velocity distributions at the free surface are impacted by the state of the LSC. However, we find that the water-side turbulence and aspect ratio play a negligible role on the evaporation rate above, in accordance with experimental observations.

This thesis aims at studying the main mechanisms involved in transitional and turbulent channel flows. Concerning the transitional channel flow, there is a range of Reynolds numbers for which turbulent oblique bands plunged in the laminar flow are observed. In this thesis, the main mechanisms involved in the origin and growth of these turbulent bands are investigated using linear and nonlinear optimization techniques. First, in a large-sized channel, it is shown that the minimal-energy perturbation able to generate turbulent bands has a spot-like structure characterized by small- and large-scale structures. Depending on the Reynolds number, this minimal seed evolves in time with two different mechanisms: for Re < 1200 an isolated oblique band is created; whereas, for Re > 1200, a quasi spanwise-symmetric evolution is observed, giving rise to two distinct bands. Then, reducing the problem complexity to a tilted domain, it is found that two main elements are necessary to induce transition towards turbulent bands: i) a linear energy growth mechanism such as the lift-up for generating streaks inside the turbulent bands; ii) large-scale vortices ensuring spatial localisation.In the last part of this thesis, in order to investigate the coherent structures usually observed in turbulent flows, the nonlinear optimization technique is extended to the turbulent channel flow and a 'new' mathematical framework for the computation of statistically-invariant coherent solutions is proposed. In both techniques, the unsteady Reynolds-Averaged Navier-Stokes equations written in a perturbative form with respect to the turbulent mean flow are used and solutions with structures at multiple turbulent scales are found., Cette thèse vise à étudier les principaux mécanismes impliqués dans les écoulements de type canal autour de la transition vers la turbulence. Plus particulièrement, il existe une gamme de nombres de Reynolds pour laquelle la turbulence reste localisée sous la forme de bandes obliques turbulentes plongées dans un écoulement laminaire. Dans cette thèse, les principaux mécanismes à l’origine et responsables de l’évolution de ces bandes turbulentes sont étudiés au travers de techniques d’optimisation linéaires et non linéaires. Tout d’abord, dans un canal de grande dimension, il a été démontré que la perturbation d’énergie minimale capable de générer des bandes turbulentes est localisée et caractérisée par des structures à petite et grande échelles. Selon le nombre de Reynolds, ce minimal seed évolue dans le temps avec deux mécanismes différents : pour Re 1200, une évolution symétrique dans la direction transverse est observée, donnant lieu à deux bandes distinctes. Ensuite, en réduisant la complexité du problème à un domaine incliné, on constate que deux éléments principaux sont nécessaires pour induire la transition vers des bandes turbulentes : i) un mécanisme linéaire de type lift-up est nécessaire à la génération des streaks à l’intérieur des bandes turbulentes ; ii) des tourbillons à grande échelle assurant la localisation spatiale.Dans la dernière partie de cette thèse, afin d’étudier les structures cohérentes habituellement observées dans les écoulements turbulents, la méthode d’optimisation non linéaire est étendue aux écoulements de canal turbulent et une ’nouvelle’ méthode mathématique pour le calcul des solutions cohérentes invariantes est proposées. Dans ces deux méthodes, les équations instationnaires de Navier-Stokes sont écrites en moyenne de Reynolds et sous une forme perturbative autour du champ moyen turbulent ; des solutions en termes de structures à différentes échelles turbulentes sont trouvées.

International audience; The paper gives the main results of an experimental test campaign aimed at quantifying the effects of very low roughness levels on the flat plate turbulent drag in transonic conditions. This work, in a field not completely understood yet, the one of the transitionally rough regime, has revealed its importance by showing that some surfaces considered as hydrodynamically smooth in past studies might not have been. That issue can be strongly critical in the delicate exercise of experimental / numerical comparisons, and more specifically, when it comes to absolute drag predictions, if the fluid dynamics computations use only, as they almost always do, infinitely smooth surfaces. The experiments carried out in the S8Ch wind tunnel have involved high-level measurement techniques, such as micro-drag evaluation with a three-component balance and near-wall laser Doppler velocimetry, for Mach numbers from 0.55 to 0.8 and maximum Reynolds numbers based on the sample length and boundary layer thickness of about 2.6 million and 0.13 million respectively, the greatest friction Reynolds number being close to 5,000. A dozen surface samples were tested, with average roughness values from less than 0.25 µm (mirror-polished aluminum) to more than 10 µm (commercial sandpapers), and in between standard-machined or painted samples (including pressure sensitive paintings). A pragmatic computational fluid dynamics study reproducing this test campaign was completed. It is based on the well-known equivalent sand grain roughness height approach and also on the Musker correlation, which was adapted. The results and validity of such Reynolds-averaged Navier-Stokes simulations in that particular regime are discussed. Anyway, both experimental and numerical outcomes of this 2 work are in agreement to indicate that drag can be significantly impacted even for roughness Reynolds numbers potentially below the usual threshold values often considered in the engineering world (i.e. about 3.5 to 5). And the cross-analysis of surface drag production and roughness characteristics has allowed the decisive role played by the rms (or average) roughness height, the skewness and kurtosis coefficients and more especially the slope parameter to be confirmed.

Unsteady simulations of turbulent flows (LES : Large Eddy Simulation, for instance) still present an important computational cost. Improvement of numerical time integration methods could reduce the computational effort needed by these simulations. Explicit time integration methods present attractive properties such that accuracy and good compatibility with HPC (parallelization, vectorization…). Nevertheless, the time step used by these methods is strongly restricted : it is chosen to respect the most severe CFL condition over the mesh. This makes explicit time integration methods very expensive in terms of computational cost. Explicit local time stepping methods use a non uniform time step to satisfy several local CFL conditions over the mesh. The time step is more optimal over the mesh, which leads to a reduction of computational cost with respect to an explicit time integration method with a uniform time step. Most of the local time stepping schemes proposed in the literature are applied to academical test cases, and very few applications are performed in CFD. This thesis's goal is to show the ability of explicit local time stepping schemes to carry out efficient and accurate simulations of turbulent flows. To reach this goal, two new explicit local time stepping schemes have been developed. Then, two LES have been carried out with our most efficient local time stepping scheme. Both cases have demonstrated the accuracy and the efficiency of our local time stepping scheme for the computations of turbulent flows.; La simulation instationnaire d'écoulements turbulents (LES : Large Eddy Simulation, par exemple) reste à l'heure actuelle coûteuse en terme de temps de calcul. Un travail sur les méthodes numériques d'intégration temporelle des équations de la mécanique des fluides peut rendre de type de simulation plus accessible. Les méthodes d'intégration temporelle explicites présentent des propriétés intéressantes telles qu'une bonne précision et une bonne compatibilité avec les techniques HPC (parallélisation, vectorisation...). Néanmoins, le pas de temps de ces méthodes est fortement limité : il est choisi de manière à respecter la contrainte CFL la plus restrictive sur le maillage. Ceci rend ces méthodes généralement très coûteuses. Dans le cas des méthodes explicites à pas de temps local, le pas de temps varie sur le maillage en s'adaptant à différentes contraintes CFL locales. Le pas de temps est plus optimal sur l'ensemble du maillage, ce qui réduit les temps de simulation par rapport à une méthode explicite à pas de temps global (uniforme). Les schémas à pas de temps local de la littérature sont essentiellement utilisés sur des cas-test académiques, et on recense peu d'applications de ces schémas en CFD. L'objectif de cette thèse est de montrer que ce type de schéma peut être utilisé de manière efficace pour la LES. Pour atteindre cet objectif, deux nouveaux schémas à pas de temps local ont d'abord été mis en place. Deux simulations LES ont ensuite été réalisées à l'aide de notre schéma à pas de temps local le plus performant. Ces deux simulations ont démontré la bonne précision et l'efficacité de notre schéma à pas de temps local pour la simulation d'écoulements turbulents.

In a forced three-dimensional turbulent flow the scales larger than the forcing scale have been conjectured to reach a thermal equilibrium state forming a $k^{2}$ energy spectrum, where $k$ is the wavenumber. In this work we examine the properties of these large scales in turbulent flows with the use of numerical simulations. We show that the choice of forcing can strongly affect the behaviour of the large scales. A spectrally dense forcing (a forcing that acts on all modes inside a finite-width spherical shell) with long correlation times may lead to strong deviations from the $k^{2}$ energy spectrum, while a spectrally sparse forcing (a forcing that acts only on a few modes) with short correlated time scale can reproduce the thermal spectrum. The origin of these deviations is analysed and the involved mechanisms is unravelled by examining: (i) the number of triadic interactions taking place, (ii) the spectrum of the nonlinear term, (iii) the amplitude of interactions and the fluxes due to different scales and (iv) the transfer function between different shells of wavenumbers. It is shown that the spectrally dense forcing allows for numerous triadic interactions that couple one large-scale mode with two forced modes and this leads to an excess of energy input at the large scales. This excess of energy is then moved back to the small scales by self-interactions of the large-scale modes and by interactions with the turbulent small scales. The overall picture that arises from the present analysis is that the large scales in a turbulent flow resemble a reservoir that is in (non-local) contact with a second out-of-equilibrium reservoir consisting of the smaller (forced, turbulent and dissipative) scales. If the injection of energy at the large scales from the forced modes is relative weak (as is the case for the spectrally sparse forcing) then the large-scale spectrum remains close to a thermal equilibrium and the role of long-range interactions is to set the global energy (temperature) of the equilibrium state. If, on the other hand, the long-range interactions are dominant (as is the case for the spectrally dense forcing), the large-scale self-interactions cannot respond fast enough to bring the system into equilibrium. Then the large scales deviate from the equilibrium state with energy spectrum that may display exponents different from the $k^{2}$ spectrum.

The aim of this paper is the direct numerical simulation of the shock wave boundary layer interaction (SWBLI). For these interactions, the separation bubble bubble, as well as the subsequent reflected shock wave, are known to oscillate in a low-frequency streamwise motion. The origin of those oscillations, however still unclear, has been related either to the shedding of vortices in the mixing layer downstream of the separation, or to the turbulent structures in the incoming boundary layer. An in-house parallel (MPI) Finite-Volume DNS/LES solver base on a high order finite volume scheme with shock capturing procedure is used to study this phenomenon. As a first step, by simulating the interaction between a laminar boundary layer and an incident shock wave, we suppress the suspected influence of the large turbulent structures of the boun- dary layer on the SWBLI unsteadiness. In this configuration, no unsteadiness of the SWBLI has been observed. Only the unsteadiness of the reattachement point have been observed. This result tends to suggest the importance of the turbulent structures of the incoming boundary layer in the low frequency oscillations of the SWBLI system. A Synthetic Eddy Method that we adapted to compressible flow, have been developed to achieve this objective without a prohibitive additional computational cost. The Synthetic Eddy Method is used to perform the DNS of a shock wave turbulent boundary layer interaction. This simulation allowed to observe the unsteadiness of the reattachement point but also of the separation point. The unsteadiness of the the whole SWBLI system has then been reproduced in this simulation.

International audience; In this paper, two local time stepping schemes of order two and three in time are proposed. By construction, they are not mass conservative but a correction stage is added to make them conservative. These schemes are compared with some local time stepping schemes existing in the literature (schemes of Constantinescu and Sandu). The comparisons are carried out on various test cases. They prove that our schemes are efficient and our third order local time stepping has a higher time accuracy than the schemes based on the strategy of Constantinescu and Sandu. Our third order local time stepping scheme is used to perform an industrial-like test case: a 3D Large-Eddy Simulation over an airfoil.; Dans ce papier, deux schémas à pas de temps local d'ordre deux et trois en temps sont proposés. Par construction, ils ne sont pas conservatifs mais une étape de correction est ajoutée pour les rendre conservatifs. Ces schémas sont comparés à des schémas à pas de temps local de la littérature (schémas de Constantinescu et Sandu). Les comparaisons sont réalisées sur des cas-test variés, et montrent que nos schémas sont efficaces. Notre schéma à pas de temps local d'ordre trois se révèle plus précis que les schémas de Constantinescu et Sandu. Il est utilisé pour réaliser un cas-test de type industriel : une simulation LES, 3D, d'un écoulement autour d'un profil d'aile.

International audience; In this paper, two local time stepping schemes of order two and three in time are proposed. By construction, they are not mass conservative but a correction stage is added to make them conservative. These schemes are compared with some local time stepping schemes existing in the literature (schemes of Constantinescu and Sandu). The comparisons are carried out on various test cases. They prove that our schemes are efficient and our third order local time stepping has a higher time accuracy than the schemes based on the strategy of Constantinescu and Sandu. Our third order local time stepping scheme is used to perform an industrial-like test case: a 3D Large-Eddy Simulation over an airfoil.; Dans ce papier, deux schémas à pas de temps local d'ordre deux et trois en temps sont proposés. Par construction, ils ne sont pas conservatifs mais une étape de correction est ajoutée pour les rendre conservatifs. Ces schémas sont comparés à des schémas à pas de temps local de la littérature (schémas de Constantinescu et Sandu). Les comparaisons sont réalisées sur des cas-test variés, et montrent que nos schémas sont efficaces. Notre schéma à pas de temps local d'ordre trois se révèle plus précis que les schémas de Constantinescu et Sandu. Il est utilisé pour réaliser un cas-test de type industriel : une simulation LES, 3D, d'un écoulement autour d'un profil d'aile.

Dynamical behavior of the turbulent channel flow separation induced by a wall-mounted two-dimensional bump is studied, with an emphasis on unsteadiness characteristics of vortical motions evolving in the separated flow. The present investigations are based on an experimental approach and Direct Numerical Simulation ( Dns ). The main interests are devoted to give further insight on mean flow properties, characteristic scales and physical mechanisms of low-frequencies unsteadiness. The study also aims to clarify the Reynolds number effects. Results are presented for turbulent flows at moderate Reynolds-number R e τ ranging from 125 to 730 where R e τ is based on friction velocity and channel half-height. A large database of time-resolved two-dimensional Piv measurements is used to obtain the velocity distributions in a region covering the entire shear layer and the flow surrounding the bump. An examination of both high resolved velocity and wall-shear stress measurements showed that for moderate Reynolds numbers, a separated region exists until a critical value. Under this conditions, a thin region of reverse flow is formed above the bump and a large-scale vortical activity is clearly observed and analyzed. Three distinct self-sustained oscillations are identified in the separated zone. The investigation showed that the flow exhibits the shear-layer instability and vortex-shedding type instability of the bubble. A low-frequency self-sustained oscillation associated with a flapping phenomenon is also identified. The experimental results are further emphasized using post-processed data from Direct Numerical Simulations, such as flow statistics and Dynamic Mode Decomposition. Physical mechanisms associated with observed self-sustained oscillations are then suggested and results are discussed in the light of instabilities observed in a laminar regime for the same flow configuration.

International audience; The lattice kinetic scheme (LKS), a modified version of the classical single relaxation time (SRT) lattice Boltzmann (LB) method, was initially developed as a suitable numerical approach for non-Newtonian flow simulations and a way to reduce memory consumption of the original SRT approach. The better performances observed for non-Newtonian flows are mainly due to the additional degree of freedom allowing an independent control over the relaxation of higher-order moments, independently from the fluid viscosity. Although widely applied to fluid flow simulations, yet no theoretical analysis of LKS has been performed. The present work focuses on a systematic von Neumann analysis of the linearized collision operator. Thanks to this analysis, the effect of the modified collision operator on the stability domain and spectral behavior of the scheme are clarified. Results obtained in this study show that correct choices of the "second relaxation coefficient" lead, to a certain extent, to more consistent dispersion and dissipation for large values of the first relaxation coefficient. Furthermore, appropriate values of this parameter can lead to a larger linear stability domain. At moderate and low values of the viscosity, larger values of the free parameter are observed to increase dissipation of kinetic modes, while leaving the acoustic modes untouched and having a less pronounced effect on the convective mode. This increased dissipation leads in general to less pronounced sources of non-linear instability, thus improving the stability of the LKS.

International audience; Direct numerical simulation data obtained from two statistically stationary, one-dimensional, planar, weakly turbulent, premixed flames are analyzed in order to examine the influence of flame-generated vorticity on the surface area of the reaction zone. The two flames are associated with the flamelet combustion regime and are characterized by two significantly different density ratios σ = 7.53 and 2.5, with all other things being roughly equal. The obtained results indicate that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling of the reaction surface, reduce its area, and, hence, decrease the burning rate. Thus, these results call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence. In particular, in the case of σ = 7.53, the local stretch rate, which quantifies the local rate of increase or decrease in the surface area, is predominantly negative in regions characterized by a large magnitude of enstrophy or a large magnitude of the baroclinic torque term in the enstrophy transport equation, with the effect being more pronounced at larger values of the mean combustion progress variable. If the density ratio is low, e.g., σ = 2.5, the baroclinic torque weakly affects the vorticity field within the mean flame brush and the aforementioned effect is not pronounced.

International audience; Recent studies have pointed out the potential of several coastal or river areas to provide significant energy resources in the near future. However, technological processes for extracting energy using Marine Current Energy Converters (MCEC) are not generically "field-ready" and still require significant research to be set up. The present work comes within this framework: we develop the numerical model OceaPoS, useful to carry out a comprehensive description of turbulent flow patterns past MCEC and forward optimize the turbine arrays configurations and evaluate their environmental effects. The OceaPos model consists in describing the fluid as an ensemble of Lagrangian particles ruled by a Stochastic process. OceaPos follows the same methodology than SDM-WindPoS model for wind farm simulations and adapts the Lagrangian stochastic downscaling method (SDM) of Bossy et al. (2016, 2018) to the tidal and oceanic boundary layer. We also introduce a Lagrangian version of actuator discs to take account of one or several MCEC's devices and their effects on the flow dynamics. Several benchmarks are presented, and numerical predictions are compared to experimental results.

This paper investigates the effect of a finite Reynolds number (FRN) on the flatness factor ($F$) of the velocity derivative in decaying homogeneous isotropic turbulence by applying the eddy damped quasi-normal Markovian (EDQNM) method to calculate all terms in an analytic expression for $F$ (Djenidi et al., Phys. Fluids, vol. 29 (5), 2017b, 051702). These terms and hence $F$ become constant when the Taylor microscale Reynolds number, $Re_{\unicode[STIX]{x1D706}}$ exceeds approximately $10^{4}$. For smaller values of $Re_{\unicode[STIX]{x1D706}}$, $F$, like the skewness $-S$, increases with $Re_{\unicode[STIX]{x1D706}}$; this behaviour is in quantitative agreement with experimental and direct numerical simulation data. These results indicate that one must first ensure that $Re_{\unicode[STIX]{x1D706}}$ is large enough for the FRN effect to be negligibly small before the hypotheses of Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk SSSR, vol. 32, 1941b, pp. 16–18; J. Fluid Mech., vol. 13, 1962, pp. 82–85) can be assessed unambiguously. An obvious implication is that results from experiments and direct numerical simulations for which $Re_{\unicode[STIX]{x1D706}}$ is well below $10^{4}$ may not be immune from the FRN effect. Another implication is that a power-law increase of $F$ with respect to $Re_{\unicode[STIX]{x1D706}}$, as suggested by the Kolmogorov 1962 theory, is not tenable when $Re_{\unicode[STIX]{x1D706}}$ is large enough.

Since the recent discovery of asymmetric modes in the wake of a simplified vehicle geometry, reminiscent from a bifurcation at low Reynolds numbers, some questions related to the aerodynamic development of ground vehicles such as the influence of lateral wind, pitch and afterbody boat-tail classically used during shape optimization remain unanswered. Our work is devoted to assess those questions experimentally for simplified but also real geometries. The tests are conducted in an industrial wind-tunnel, at the 2/5-scale for the academic body and at the full scale for the minivans. We show that the vehicle's misalignment only modifies the asymmetric mode's orientation without affecting its intensity. We build a model predicting not only this orientation but also the consequences on the cross-flow aerodynamic loading. The contribution of the instability to the lift or side force coefficients is of the order of 0,02 independently of lateral wind or of the vehicle's pitch. Afterbody boat-tails also impact the wake dynamics and its orientation but the instability is never suppressed. These results are retrieved for real vehicles such as minivans, whose wake is then subjected to the same asymmetric mode as well, revealed unambiguously with pitch sensitivity experiments. Our results indicate that, for all considered vehicles, the asymmetric wake mode is systematically present in the driving envelope. The control or the suppression of this mode should offer new optimization's perspectives for blunt based vehicles such as minivans or SUVs., Depuis la découverte des modes asymétriques dans le sillage d'un corps simplifié d'automobile, réminiscents d'une bifurcation à bas nombre de Reynolds, se posent des questions propres au développement aérodynamique des véhicules terrestres telles que l'influence du vent latéral, de l'assiette et du rétreint d'arrière-corps couramment utilisé en phase d'optimisation. Notre travail s'attache à répondre expérimentalement à ces questions pour des géométries simplifiées mais aussi réelles. Les essais sont réalisés en soufflerie industrielle à l'échelle 2/5 pour le corps académique et en pleine échelle pour les monospaces. Nous montrons que le désalignement du véhicule par rapport à l'écoulement incident n'a pour effet que de modifier l'orientation du mode asymétrique sans en changer l'intensité. Nous construisons un modèle simple prédisant non seulement cette orientation mais aussi les conséquences sur les efforts aérodynamiques transverses. La contribution de l'instabilité sur les coefficients aérodynamiques de portance ou d'effort latéral est de l'ordre de 0,02 indépendamment du vent de travers et de l'assiette du véhicule. Les rétreints d'arrière-corps affectent également la dynamique du sillage et son orientation, mais l'instabilité n'est jamais supprimée. Ces résultats sont retrouvés pour des véhicules réels de type monospace dont le sillage est donc également soumis au même mode asymétrique, révélé sans ambigüité par des expériences de sensibilité en assiette. Nos résultats indiquent que, pour tous les véhicules considérés, le mode asymétrique de sillage est systématiquement présent dans l'enveloppe de conduite. Le contrôle ou la suppression de ce mode devrait offrir de nouvelles perspectives d'optimisation des véhicules à culot droit de type monospaces ou SUV.

International audience; High-Reynolds-number experiments are conducted in the roughness sublayer of a turbulent boundary-layer developing over a cubical canopy. Stereoscopic particle image velocimetry is performed in a wall-parallel plane to evidence a high degree of spatial modulation of the small-scale turbulence around the footprint of large-scale motions, despite the suppression of the inner layer by the high roughness elements. Both Fourier and wavelets analyses show that the near-wall cycle observed in smooth-wall-bounded flows is severely disrupted by the canopy, whose wake in the roughness sublayer generates a new range of scales, closer to that of the outer-layer large-scale motions. This restricts significantly scale separation, hence a diagnostic method is developed to divide carefully and rationally the fluctuating velocity fields into large- and small-scale components. Our analysis across all turbulent kinetic energy terms sheds light on the spatial imprint of the modulation mechanism, revealing a very different signature on each velocity component. The roughness sublayer shows a preferential arrangement of the modulated scales similar to what is observed in the outer-layer of smooth-wall-bounded flows – small-scale turbulence is enhanced near the front of high momentum regions and damped at the front of low-momentum regions. More importantly, accessing spanwise correlations reveals that modulation intensifies the most along the flanks of the large-scale motions.

International audience; Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A Variational MultiScale stabilized finite element method is employed to solve the incompressible Navier-Stokes equations. Finally, the Spalart-Allmaras turbulence model is solved using the Streamline Upwind Petrov-Galerkin (SUPG) method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases. This article is protected by copyright. All rights reserved.

Direct Numerical Simulation (DNS) of high Reynolds number compressible flows involving shock waves is a challenging task since one must use a numerical scheme that can both represent small scale structures with the minimum of numerical dissipation, and capture discontinuities with the robustness that is common to Godunov-type methods without spoiling the accuracy in the vicinity of the discontinuity. In this context, a high order One-Step Monotonicity-Preserving (OSMP) scheme has been developed by following a Lax-Wendroff approach. The objective of this work is to check the ability of the unlimited OS scheme and its limited version (OSMP) to accurately predict turbulent and shocked flows.

This thesis aims at unraveling the main mechanisms involved in transitional and turbulent flows. The central idea is that of using a nonlinear optimization technique to investigate the origin and role of coherent structures usually observed in these flows. This method has been used in three different contexts. First, a linearly stable laminar flow has been considered and the optimization has been used to compute the most amplified perturbations among all disturbances able to trigger transition to turbulence. Once turbulence is well established, a fully 3D nonlinear optimization maximizing the turbulent kinetic energy is used to study coherent structures populating turbulent shear flow as well as investigate the mechanisms responsible for the energy (optimally) growth and exchange. Then, a dynamical system approach is applied to fluid flow equations. The geometry of the state space is investigated by using transient growth theory to reveal the importance of the stable and unstable manifold. In the same framework, a nonlinear minimization algorithm is used to compute heteroclinic connections among invariant solutions of the Navier-Stokes equations., Cette thèse vise à démêler les principaux mécanismes impliqués dans les écoulements transitoires et turbulents. L’idée centrale est d'utiliser une technique d’optimisation non linéaire pour étudier l’origine et le rôle des structures cohérentes habituellement observées dans ces écoulements. Cette méthode a été utilisée dans trois contextes différents. Tout d’abord, un écoulement laminaire linéairement stable a été considéré et l'optimisation a été utilisée pour calculer les perturbations les plus amplifiées parmi toutes les perturbations capables de déclencher une transition vers la turbulence. Une fois que la turbulence est bien établie, une optimisation non linéaire entièrement 3D maximisant l'énergie cinétique turbulente est utilisée pour étudier les structures cohérentes qui peuplent l’écoulement turbulent et les mécanismes responsables de la croissance et de l’échange d’énergie (optimale) sont étudiés. Ensuite, une approche de type système dynamique est appliquée aux équations du mouvement. La géométrie de l’espace des phases est étudiée en utilisant la théorie de la croissance transitoire pour évaluer l’importance des variétés stable et instable dans la dynamique. Dans le même cadre, un algorithme de minimisation non linéaire est utilisé pour calculer les connexions hétérocliniques parmi les solutions invariantes des équations de Navier-Stokes.

International audience; Direct numerical simulations (DNSs) have been performed to examine the inertia, shape, and gravity field effects on the dynamics of ellipsoidal particles within a vertical turbulent channel flow. To investigate the effects induced by the particle inertia and shape, computations have been conducted for three aspect ratios and two response times. The influence of gravity has been examined through a comparison with DNS data provided in earlier studies without gravity. The originality of this study is that the prediction of the hydrodynamic force and pitching torque acting on the non-spherical particles has been carried out with recent expressions valid outside the Stokes flow regime. With the data extracted from the DNS, a statistical analysis of the particle spatial distribution, orientation, and translational and angular velocities is carried out. Results show that the presence of a significant mean relative velocity between the dispersed and continuous phases greatly modifies the dynamics of non-spherical particles. Without gravity, the dynamics of ellipsoids is close to that of spheres, whereas it becomes strongly dependent on the particle shape with gravity.

International audience; A high-order Vorticity Confinement (VC) method is applied to the calculation of compressible vortical flows. High-order extensions of the VC methodology have been developed for the Navier-Stokes equations using a methodology that remains independent of the baseline numerical scheme, as the original VC formulation of Steinhoff. The VC method is primarily oriented towards the accurate calculation of cases involving the advection of vortical structures (e.g. wakes), allowing their propagation over long distances with low numerical dissipation. The present work however mainly investigates their applicability to the simulation of turbulent flows, where the improvement in the preservation of vortical structures shows great interest. High-order VC schemes were found to be consistent with complex vortical flow dynamics without the need of special treatment to accommodate the vortex interaction mechanisms characteristic of turbulent flows. Furthermore, they were found to consistently improve the resolvability of baseline FE-MUSCL schemes for reasonable values of the confinement parameter ε, close to the value of the high-order artificial dissipation coefficient. Last, the dependence of the solution on the confinement parameter µ was found to be moderate for the values and cases investigated in this paper.; Une méthode de confinement de vorticité (VC) d'ordre élevé est appliquée dans des calculs des écoulements tourbillonnaires compressibles. Les extensions de la méthode VC pour les ordres élevés ont été développées par une méthodologie qui reste indépendante du schéma numérique de base, comme la formulation VC originale de Steinhoff. Le VC est principalement orienté vers le calcul précis des cas impliquant l'advection de structures tourbillonnaires (p. ex. sillages), permettant leur propagation sur de longues distances avec une faible dissipation numérique. Cependant, le présent travail étudie principalement leur applicabilité dans la simulation des écoulements turbulents, où une meilleure préservation des structures tourbillonnaires présente un grand intérêt. Les schémas VC d'ordre élevé se sont révélés être consistants avec la dynamique des écoulements tourbillonnaires complexes sans besoin de traitement spécial pour accommoder les mécanismes d'interactions tourbillonnaires caractéristiques des écoulements turbulents. De plus, ils permettent d'améliorer la résolvabilité des schémas numériques FE-MUSCL de base pour des valeurs raisonnables du paramètre de confinement epsilon, proche de la valeur du coefficient de dissipation artificielle d'ordre élevé. Enfin, la dépendance de la solution à la valeur du paramètre de confinement mu reste modérée pour les valeurs et cas-tests étudiés dans cet article.

International audience; The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.

International audience; We report Particle Image Velocimetry of the Large Scale Circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-Bénard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow to consider a bi-dimensional mean flow. Lots of previous heat flux measurements have shown a Nusselt–Rayleigh regime transition corresponding to an increase of the heat flux in presence of roughness which is higher than the surface increase. Our velocity measurements show that if the mean velocity field is not clearly affected by the roughness, the velocity fluctuations rise dramatically. It is accompanied by a change of the longitudinal velocity structure functions scaling. Moreover, we show that the boundary layer becomes turbulent close to roughness, as it was observed recently in the air [Liot et al., JFM, vol. 786, pp. 275-293]. Finally we discuss the link between the change of the boundary layer structure and the ones observed on the Large Scale Circulation.

Ventilation plays a key role in thermal comfort of building's occupants in hot climates by refreshing air surrounding them. Mechanical or natural ventilation must be controlled for two reasons: do not disturb the bulding's occupants and comply with the regulations in force. Discomfort is linked to too high air velocities or turbulent intensity. Designers can use the numerical tools for a finer prediction of airflow. The simulation of configurations at the building scale can be done using averaged Navier-Stokes equations approach in addition to a turbulence model. These simulations are used by researchers as sizing tools or for the optimization of ventilation components. In addition, the shape of the ventilation nozzle can passively contributes to the optimization of some aeraulics phenomena. The improvement of these ventilation components can be achieved by the use of shape optimization methods. Topological optimization by addition of material makes it possible for the optimization of cost functions defined on the fluid or on its boundaries. The main objective of this manuscript is to propose a tool to control airflows in building by the search for optimal shape of ventilation nozzle. This work proposes a contribution to the topological optimization of turbulent flows in buildings. In a first step, topological optimization by adding material is applied to minimize pressure losses in a T-shaped pipe. The developed model is subjected to the hypothesis of the frozen turbulence. In a second step, the complete adjoint model is proposed for the standard turbulence model k-epsilon for the minimization of the total pressure losses on the one hand and the turbulent intensity on the other hand. Finally, these tools are applied to the shape optimization of ventilation nozzle. The results of topological optimization by adding virtual material show good potential for the orientation of the airflows but does not guarantee the control of the air velocities in the room. Moreover, the minimization of turbulent intensity through the complete approach contributed to the reduction of the dissatisfaction rate due to excessive turbulent intensity in the room., La ventilation joue un rôle important dans le confort thermique des occupants d'un bâtiment en climat chaud, en contribuant au rafraîchissement de l'air qui les entoure. Qu'elle soit mécanique ou naturelle, la ventilation doit être maîtrisée pour ne pas gêner l'occupant et respecter des normes ou réglementations en vigueur. Ces gênes sont liées à des vitesses d'air ou à une intensité turbulente trop élevée. Les concepteurs doivent alors faire appel à l'outil numérique pour une prédiction fine des écoulements d'air. La simulation de configurations à l'échelle du bâtiment peut se faire par une approche moyennée des équations de Navier-Stokes en complément d'un modèle de turbulence. Ces simulations sont utilisées par les chercheurs comme des outils de dimensionnement, ou encore, d'optimisation des composants de ventilation. De plus, la forme des bouches de ventilation peut contribuer passivement à l'optimisation de certains phénomènes aérauliques. L'amélioration de ces formes peut ainsi se faire par l'utilisation de méthodes d'optimisation de forme. L'optimisation topologique par ajout de matière permet de trouver des formes pour optimiser des fonctionnelles objectifs définies sur le fluide ou sur ses frontières. C'est sur cette méthode que ces travaux de thèse se concentrent pour proposer un outil de contrôle des écoulements d'air dans le bâtiment par la recherche de formes optimales de bouches de ventilation. Ces travaux de thèse proposent une contribution à l'optimisation topologique d'écoulements turbulents dans le bâtiment. Dans un premier temps, la méthode par ajout de matière est appliquée pour minimiser les pertes de charge dans une conduite d'aération en forme de Té. Le modèle adjoint développé est soumis à l'hypothèse de turbulence gelée. Dans un second temps le modèle adjoint complet est proposé pour le modèle de turbulence standard k-epsilon pour la réduction des pertes de charge d'une part et de l'intensité turbulente d'autre part. Enfin, ces outils sont appliqués à l'optimisation de forme de bouches de ventilation. Les résultats montrent ainsi un bon potentiel de l'optimisation topologique par ajout de matière pour l'orientation des écoulements d'air mais ne garantissent pas la maîtrise des vitesses d'air dans la pièce. De plus, la minimisation de l'intensité turbulente grâce à l'approche complète développée a contribué à la réduction du taux d'insatisfaction lié à une intensité turbulente trop élevée dans la pièce.

The transport of particles by turbulent flows is ubiquitous in nature and industry. It occurs in planet formation, plankton dynamics and combustion in engines. For the dispersion of atmospheric pollutants, traditional predictive models based on eddy diffusivity cannot accurately reproduce high concentration fluctuations, which are of primal importance for ecological and health issues. The first part of this thesis relates to the dispersion by turbulence of tracers continuously emitted from a point source. Mass fluctuations are characterized as a function of the distance from the source and of the observation scale. The combination of various physical mixing processes limits the use of fractal geometric tools. An alternative approach is proposed, allowing to interpret mass fluctuations in terms of the various regimes of pair separation in turbulent flows. The second part concerns particles with a finite and possibly large inertia, whose dispersion in velocity requires developing efficient modelling techniques. A novel numerical method is proposed to express inertial particles distribution in the position-velocity phase space. Its convergence is validated by comparison to Lagrangian measurements. This method is then used to describe the modulation of two-dimensional turbulence by large-Stokes-number heavy particles. At high inertia, the effect is found to be analogous to an effective large-scale friction. At small Stokes numbers, kinetic energy spectrum and nonlinear transfers are shown to be modified in a non-trivial way which relates to the development of instabilities at vortices boundaries.; Le transport de particules par des écoulements turbulents est un phénomène présent dans de nombreux écoulements naturels et industriels, tels que la dispersion de polluants dans l'atmosphère ou du phytoplancton et plastiques dans et à la surface des océans. Les modèles prédictifs classiques ne peuvent prévoir avec précision la formation de larges fluctuations de concentrations. La première partie de cette thèse concerne une étude de la dispersion turbulente de traceurs émis à partir d'une source ponctuelle et continue. Les fluctuations spatiales de masse sont déterminées en fonction de la distance à la source et à l'échelle d'observation. La combinaison de plusieurs phénomènes physiques à l'origine du mélange limite la validité d'une caractérisation de géométrie fractale. Une approche alternative est proposée, permettant d'interpréter les fluctuations massiques en terme des différents régimes de séparation de pair dans des écoulements turbulents. La seconde partie concerne des particules ayant une inertie finie, dont la dispersion dans l'espace des vitesses requiert de développer des techniques de modélisation adaptées. Une méthode numérique originale est proposée pour exprimer la distribution des particules dans l'espace position-vitesse. Cette méthode est ensuite utilisée pour décrire la modulation de la turbulence bi- dimensionnelle par des particules inertielles. A grand nombres de Stokes, l'effet montré est analogue à celui d'une friction effective à grande échelle. Aux petits Stokes, le spectre de l'énergie cinétique du fluide et les transferts non-linéaires sont modifiées d'une manière non triviale.

Fluid mechanics is involved in many practical problems related to both environmental and industrial situations. On the one hand, the aim of fluid mechanics in civil engineering is to provide adequate water services such as the supply of potable water, sewerage, drainage, dams, irrigation, river and sea (flood) defences … On the other hand, a knowledge of fluid mechanics is essential in chemical engineering because most of chemical-processing operations are conducted in the fluid phase. Examples : biochemical, chemical, energy, fermentation, materials, petroleum, polymer, food, cosmetics, pharmaceuticals and waste-processing industries. We will present the following key issues of fluid mechanics related to both hydraulic and chemical engineering which are about accurate prediction of : (1) velocity profiles in turbulent flows, (2) concentration profiles in fluid-solid two phase flows. In both hydraulic and chemical engineering, we need accurate modeling of the flow in pipes, ducts and channels. The concept of boundary layer (Ludwig Prandtl, 1904) has allowed importnat theoretical progress in fluid mechanics. Turbulent flows are significantly affected by the presence of walls. Successful predictions of turbulence models used for wall-bounded turbulent flows depend on accurate description of the flow in the near-wall region. On the one hand, we will see how it is possible to improve the prediction of near-wall mean streamwise velocity profile U + by solving the momentum equation. An eddy viscosity formulation based on a near-wall turbulent kinetic energy function (Absi, 2008) and the van Driest mixing length equation (van Driest, 1956) is used (Absi 2009). On the other hand, an ordinary differential equation (ODE) for velocity distribution in open channel flows is presented based on an analysis of the Reynolds-averaged Navier–Stokes equations and a log-wake modified eddy viscosity distribution. This proposed equation allows to predict the velocity-dip-phenomenon, i.e. the maximum velocity below the free surface (Absi 2011) and shows therefore a potential interest for the prediction of flow rates in sewers. Fluid-solid two phase flows are involved in both hydraulic and chemical engineering, in sediment transport in rivers and channels (important since sediments reduce dams reservoir capacity), pneumatic conveying of raw materials involved in the manufacture of food, cosmetic or pharmaceutical products, fluidisation, … In particle-laden flows, the coefficient of turbulent diffusion of suspended particles is related to the eddy viscosity, through the turbulent Schmidt number. The classification is based on the volumetric particle concentration and Stokes number St which is the ratio between the particle timecale and the integral turbulence timescale or turnover time of large eddy. Therefore, a large value of St corresponds to a weak sedimentation process and therefore to a more uniform concentration profile. At the opposite, a small value of St corresponds to a strong concentration gradient. We will present an interesting case of suspended sediments over wave ripples where concentration profiles, in semi-log plots, are upward convex for fine sand and upward concave for coarse sand.

This work reports an experimental investigation of the flow through a random array of fixed solid spheres. The volume fraction of the spheres is 2 %, and the Reynolds number $Re$ based on the sphere diameter and the average flow velocity is varied from 120 to 1040. Using time and spatial averaging, the fluctuations have been decomposed into two contributions of different natures: a spatial fluctuation that accounts for the strong inhomogeneity of the flow around each sphere, and a time fluctuation that comes from the instability of the flow at large enough Reynolds numbers. The evolutions of these two contributions with the Reynolds number are different, so that their relative importance varies. However, when each is normalized by using its own variance and the integral length scales of the fluctuations, their spectra and probability density functions (PDFs) are almost independent of $Re$. The spatial fluctuation mostly comes from the velocity deficit in the wakes of the spheres, and is thus dominated by scales larger than one or two sphere diameters. It is found to be responsible for the asymmetry of the PDFs of the vertical fluctuations and of the major part of the anisotropy level between the vertical and the horizontal components of the fluctuations. The time fluctuation dominates at scales smaller than the integral length scale. It is isotropic and its PDFs, well described by an exponential distribution, are non-Gaussian. The spectra of the spatial and the time fluctuations both show an evolution as the power $-3$ of the wavenumber, but not exactly in the same subrange. All these properties are found in remarkable agreement with the results of both experimental investigations and large eddy simulations (LES) of a homogeneous bubble swarm. This confirms that the main mechanism responsible for the production of bubble-induced fluctuations is the interaction of the velocity disturbances caused by obstacles immersed in a flow and that the structure of this agitation is weakly dependent on the precise nature of the obstacles. The understanding and the modelling of the agitation generated by the motion of a dispersed phase, such as the bubble-induced agitation, therefore require one to distinguish between the roles of these two contributions.

Dense gas turbulent flows, of great interest for a wide range of engineering applications, exhibit physical phenomena that are still poorly understood and difficult to reproduce experimentally. In this work, we study for the first time the influence of dense gas effects on the structure of compressible turbulence by means of numerical simulations. The fluid considered is PP11, a heavy fluorocarbon, whose thermodynamic behavior is described by means of different equations of state to quantify the sensitivity of solutions to modelling choices. First, we considered the decay of compressible homogeneous isotropic turbulence. Temperature fluctuations are found to be negligible, whereas those of the speed of sound are large because of the strong dependence on density. The peculiar behavior of the speed of sound significantly modifies the structure of the turbulence, leading to the occurrence of expansion shocklets. The analysis of the contribution of the different structures to energy dissipation and enstrophy generation shows that, for a dense gas, high expansion regions play a role similar to high compression ones, unlike perfect gases, in which the observed behaviour is highly asymmetric. Then, we carried out numerical simulations of a supersonic turbulent channel flow for several values of Mach and Reynolds numbers. The results confirm the validity of the Morkovin' hypothesis. The introduction of a semi-local scaling, taking into account density and viscosity variations across the channel, allow to compare the wall-normal profiles of turbulent quantities (Reynolds stresses, anisotropy, energy budgets) with those observed in ideal gases. Nevertheless, the thermodynamic variables exhibit a different evolution between perfect and dense gases, since the high specific heats of the latter lead to a decoupling of dynamic and thermal effects, and to a behavior close to that of variable property incompressible fluids.; Les écoulements turbulents de gaz denses, qui sont d’un grand intérêt pour un large éventail d'applications, sont le siège de phénomènes physiques encore peu connus et difficiles à étudier par des approches expérimentale. Dans ce travail, nous étudions pour la première fois l’influence des effets de gaz denses sur la structure de la turbulence compressible à l’aide de simulations numériques. Le fluide considéré est le PP11, un fluorocarbure lourd, dont le comportement thermodynamique a été représenté à l’aide de différentes lois d’état, afin de quantifier la sensibilité des solutions aux choix de modélisation. Nous avons considéré d’abord la décroissance d’une turbulence homogène isotrope compressible. Les fluctuations de température sont négligeables, alors que celles de la vitesse du son sont importantes à cause de leur forte dépendance de la densité. Le comportement particulier de la vitesse du son modifie de manière significative la structure de la turbulence, conduisant à la formation de shocklets de détente. L’analyse de la contribution des différentes structures à la dissipation d’énergie et à la génération d’enstrophie montre que, pour un gaz dense, les régions de forte dilatation jouent un rôle similaire à celles de forte compression, contrairement aux gaz parfaits, dans lesquels le comportement est fortement dissymétrique. Ensuite, nous avons mené des simulations numériques pour une configuration de canal plan en régime supersonique, pour plusieurs valeurs des nombres de Mach et de Reynolds. Les résultats confirment la validité de l’hypothèse de Morkovin. L’introduction d’une loi d’échelle semi-locale prenant en compte le variations de densité et viscosité, permet de comparer les profils des grandeurs turbulentes (contraintes de Reynolds, anisotropie, budgets d’énergie) avec ces observés en gaz parfait. Les variables thermodynamiques, quant à elles, présentent une évolution très différente pour un gaz parfait et pour un gaz dense, la chaleur spécifique élevée de ce dernier conduisant à un découplage des effets dynamiques et thermiques et à un comportement proche de celui d’un fluide incompressible avec des propriétés variables.

International audience; In the present work the quantification of the time-lasting effects of production mechanisms in homogeneous isotropic turbulence decay is addressed. The analysis is developed through the use of theoretical tools as well as numerical calculations based on the eddy damped quasinormal Markovian (EDQNM) model. In both cases a modified Lin equation is used, which accounts for production mechanisms as proposed by Meldi, Lejemble, and Sagaut [“On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence,” J. Fluid Mech. 756, 816–843 (2014)]. The approaches used show that an exponential decay law can be observed if the intensity of the forcing is strong enough to drive the turbulence dynamics, before a power-law decay is eventually attained. The EDQNM numerical results indicate that the exponential regime can persist for long evolution times, longer than the observation time in grid turbulence experiments. A rigorous investigation of the self-similar behavior of the pressure spectrum has been performed by a comprehensive comparison of EDQNM data with direct numerical simulation (DNS)/experiments in the literature. While DNS and free decay EDQNM simulations suggest the need of a very high Reλ threshold in order to observe a clear −7/3 slope of the pressure inertial range, experimental data and forced EDQNM calculations indicate a significantly lower value. This observation suggests that the time-lasting effects of production mechanisms, which cannot be excluded in experiments, play a role in the lack of general agreement with classical numerical approaches. These results reinforce the urge to evolve the numerical simulation state of the art towards the prediction of realistic physical states.

[Notes_IRSTEA]Article number 023118 [Departement_IRSTEA]Ecotechnologies [TR1_IRSTEA]SPEE; International audience; The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different spatial symmetries and temporal behaviors. Because large particles are less and less sensitive to flow fluctuations as their size increases, we observe the emergence of a slow dynamics corresponding to back-and-forth motions between two attractors, and a super-slow regime synchronized with flow reversals when they exist. Such dynamics is substantially reproduced by a one dimensional stochastic model of an over-damped particle trapped in a two-well potential, forced by a colored noise. An extended model is also proposed that reproduces observed dynamics and trapping without potential barrier: the key ingredient is the ratio between the time scales of the noise correlation and the particle dynamics. A total agreement with experiments requires the introduction of spatially inhomogeneous fluctuations and a suited confinement strength.

A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{\unicode[STIX]{x1D619}}_{ij}(\boldsymbol{k},t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\boldsymbol{k}$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.

The spectral model of Perry, Henbest & Chong (1986) predicts that the integral length-scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale's variation to be more realistic while keeping with the Townsend-Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high Reynolds number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high Reynolds number data by Hultmark, Vallikivi, Bailey & Smits (2012, 2013). The finding of Dallas, Vassilicos & Hewitt (2009) that it is the eddy turnover time and not the mean flow gradient which scales with distance to the wall and skin friction velocity in the intermediate layer implies, when combined with Townsend's (1976) production-dissipation balance, that the mean flow gradient has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmark, Vallikivi, Bailey & Smits (2012, 2013). The same approach also predicts that the mean flow gradient has a logarithmic decay at distances to the wall larger than the position of the outer peak, a qualitative prediction which the aforementioned data also support., 14 pages, 9 figures

The evolution of plankton in the ocean, the mixing and deposition of sediments in rivers or the manufacture of some food products imply the transport of finite-size, neutrally buoyant material particles by a turbulent flow. Despite the numerous natural and industrial processes where they appear, the dynamics of such particles is still not fully understood. In particular, there is no acceptable model either for their motion or for the manner with which they perturb the carrier flow. The numerical and experimental work of this thesis contribute to a better understanding of such aspects. A first part is dedicated to study numerically the dynamics of isolated spherical particles. I have developed analysis tools that allowed me to quantify their relative motion to the fluid and their local influence on the turbulent flow. A second part concerns the collective effects of a large number of particles onto turbulence. For that, I have performed experimental particle-tracking measurements in a von Kármán flow seeded with various particles volume fractions. The main result is a tendency for the particles to attenuate the amplitude of turbulent fluctuations. At variance, the particles have no influence on the fine statistical properties of the flow. Also, these measurements suggest the large scales of the flow undergo a phase transition at volume fractions above a critical threshold.; L’évolution du plancton dans les océans, le mélange et la déposition de sédiments dans les cours d’eau ou encore la fabrication de certains produits agroalimentaires impliquent le transport de particules matérielles de taille finie et de flottabilité nulle par un écoulement turbulent. Malgré les nombreux processus naturels et industriels où elles interviennent, la dynamique de telles particules reste à ce jour mal comprise. En particulier, il n’existe pas de modèle adéquat pour leur mouvement ou la façon dont elles perturbent le fluide porteur. Les travaux numériques et expérimentaux de cette thèse contribuent à une meilleure compréhension de tels aspects. Un premier volet est consacré à l’étude numérique de la dynamique de particules sphériques isolées. J’ai notamment développé des outils d’analyse qui m’ont permis de quantifier leur mouvement relatif au fluide ainsi que leur influence locale sur l’écoulement turbulent. Un second volet porte sur les effets collectifs d’un grand nombre de grosses particules sur la turbulence. Pour cela j’ai effectué des mesures expérimentales par suivi lagrangien dans un écoulement de von Kármán ensemencé avec différentes fractions volumiques de particules. Le résultat principal est que les particules ont tendance à atténuer l’amplitude des fluctuations turbulentes. En revanche, celles-ci n’ont pas d’influence sur les propriétés statistiques fines de l’écoulement. Aussi, ces mesures suggèrent l’existence d’une transition de phase dans les grandes échelles de l’écoulement pour des fractions volumiques de particules au delà d’un seuil critique.

International audience; Energy-conserving discretizations are widely regarded as a fundamental requirement for high-fidelity simulations of turbulent flows. The skew-symmetric splitting of the nonlinear term is a well-known approach to obtain semi-discrete conservation of energy in the inviscid limit. However, its computation is roughly twice as expensive as that of the divergence or advective forms alone. A novel time-advancement strategy that retains the conservation properties of skew-symmetric-based schemes at a reduced computational cost has been developed. This method is based on properly constructed Runge–Kutta schemes in which a different form (advective or divergence) for the convective term is adopted at each stage. A general framework is presented to derive schemes with prescribed accuracy on both solution and energy conservation. Simulations of homogeneous isotropic turbulence show that the new procedure is effective and can be considerably faster than skew-symmetric-based techniques.

International audience; This paper presents details of the solver Aghora for the simulation of unsteady compressible turbulent flows. Different modelling levels are used: Reynolds averaged Navier-Stokes equations coupled with turbulence transport equations, variational multi-scale formulation of large-eddy simulation, and direct numerical simulation. The space discretization is based on a high-order discontinuous Galerkin method with representation of curved boundaries. High-order explicit and implicit Runge-Kutta methods are used for the time integration. The performance of the solver will be assessed in various examples of compressible turbulent flow numerical simulation in three space dimensions.

In this work, we investigate the implementation of hybrid methods on heterogeneous computers in order to achieve numerical simulations of multi-scale problems. The hybrid numerical method consists of coupling methods of different natures to solve the physical and numerical characteristics of the problem. It is based on a remeshed particle method that combines the advantages of Lagrangian and Eulerian methods. Particles are pushed by local velocities and remeshed at every time-step on a grid using high order interpolation formulas. This forward semi-lagrangian method takes advantage of the regular mesh on which particles are reinitialized but is not limited by CFL conditions.We derive a class of high order methods for which we are able to prove convergence results under the sole stability constraint that particle trajectories do not intersect.In the context of high performance computing, a strong portability constraint is applied to the code development in order to handle the rapid evolution of architectures and their heterogeneous nature. An analysis of the numerical efficiency of the GPU implementation of the method is performed and extended to multi-GPU platforms. The hybrid method is applied to the simulation of the transport of a passive scalar in a 3D turbulent flow. The two sub-problems of the flow and the scalar calculations are solved simultaneously on multi-CPU and multi-GPU architectures.; Dans cette thèse nous explorons les possibilités offertes par l'implémentation de méthodes hybrides sur des machines de calcul hétérogènes dans le but de réaliser des simulations numériques de problèmes multiéchelles. La méthode hybride consiste à coupler des méthodes de diverses natures pour résoudre les différents aspects physiques et numériques des problèmes considérés. Elle repose sur une méthode particulaire avec remaillage qui combine les avantages des méthodes Lagrangiennes et Eulériennes. Les particules sont déplacées selon le champ de vitesse puis remaillées à chaque itération sur une grille en utilisant des formules de remaillage d'ordre élevés. Cette méthode semi-Lagrangienne bénéficie des avantages du maillage régulier mais n'est pas contrainte par une condition de CFL.Nous construisons une classe de méthodes d'ordre élevé pour lesquelles les preuves de convergence sont obtenues sous la seule contrainte de stabilité telle que les trajectoires des particules ne se croisent pas.Dans un contexte de calcul à haute performances, le développement du code de calcul a été axé sur la portabilité afin de supporter l'évolution rapide des architectures et leur nature hétérogène. Une étude des performances numériques de l'implémentation GPU de la méthode pour la résolution d'équations de transport est réalisée puis étendue au cas multi-GPU. La méthode hybride est appliquée à la simulation du transport d'un scalaire passif dans un écoulement turbulent 3D. Les deux sous-problèmes que sont l'écoulement turbulent et le transport du scalaire sont résolus simultanément sur des architectures multi-CPU et multi-GPU.

International audience; Turbulent flows in aeronautical applications typically have a very wide range of length and time scales characterized by their high Reynolds numbers. Traditionally, the prohibitively large computational cost implied by a high Reynolds number has made physical modelling rather than direct computation of turbulent scales a more popular approach in the industry. While well-calibrated turbulence models can provide good accuracy at reasonable computational costs, they tend to have a very limited range of applicability. In particular, flows with inhomogeneous features sensitive to small errors, such as flow with detachment, cannot be accurately predicted by conventional models and require computing a greater range of turbulent scales. Large-eddy simulation (LES) aims to resolve all relevant turbulent scales while employing more fundamental models to account for the influence of the unresolved scales. Therefore, it has great potential for a more universal turbulence simulation methodology that is valid for any configuration. In order to make LES a tool of engineering practice, it is necessary to address issues of computational cost, handling of complex geometries and compatibility of the employed models with the used numerical method. In this work, we propose a residual- based variational multiscale discontinuous Galerkin method to address these issues and to ultimately improve efficiency by exploiting its flexibility in local refinement. The variational multiscale (VMS) [1] approach is a framework for designing numerical methods and associated models for multiscale phenomena. In this approach, the scales not resolved by the numerical scheme are modelled by a fine scale model. This apprach is particularly well-suited for higher order methods, since the model term does not add any low order consistency errors. In the context of LES, many VMS variants have been proposed, with implicit [2] and explicit [3] fine scale models. The implicit models have the disadvantage of introducing additional degrees of freedom for the fine scales, leading to a three-level decomposition of scales. In this work we concentrate on extending the cheaper explicit residual- based fine scale model developed in the framework of continuous finite element methods [3] to discontinuous Galerkin (DG) [4] methods to benefit from their excellent scalability properties in simulating unsteady phenomena on parallel computers. DG methods have been successfully used in the variational multiscale setting for the large-eddy simulation of turbulence [5, 6] with implicit fine scale models. In this work we propose a cheaper explicit fine scale model based on a scaling of the cell and face residuals of the resolved scales. We numerically explore various options for constructing residual-based fine scale models for DG discretizations. These methods differ in how (or whether) the jump residuals are taken into account for the fine scale model. We compare these options using the viscous Burgers’ equation in 1D to note that residual-based VMS DG with even the simplest fine scale model that disregards interface jumps gives results that are better than the plain DG method for underresoved simulations. In the second part of this study, we apply the proposed methodology to the compressible Navier-Stokes equations. We perform LES of wall-bounded turbulence based on the proposed residual-based VMS DG method and compare our results to the results obtained through implicit LES and LES based on the three-level VMS DG method in terms of accuracy and computational cost. We conclude that the proposed residual-based VMS DG method is competitive with the three-level VMS DG in terms of accuracy while retaining only the coarse scale degrees of freedom. In terms of computational cost, the proposed method is better than the three-level VMS and competitive with implicit LES.

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.

International audience; In this paper, a multiphysics numerical approach for predicting the ionization level in solid rocket engine plumes is presented. Ionization takes place in the rocket combustion chamber and in the exhaust plume. A low-temperature, high-density plasma is created, with small Debye length in most of the plume region. Ambipolar diffusion is therefore assumed for ions and electrons in the plume, and a set of conservation equations is derived to be solved by the numerical model. A number of numerical strategies to resolve this system is derived, as well as a novel scheme that enforces charge neutrality. This approach is integrated into a complex code for compressible, multispecies, turbulent flow simulations. The model is then coupled with a Maxwell's equations solver in order to simulate the radar cross section of rocket plumes. Finally, computations of ionization levels and radar cross section of a Black Brant rocket plume are presented.

In this work, we investigate the implementation of hybrid methods on heterogeneous computers in order to achieve numerical simulations of multi-scale problems. The hybrid numerical method consists of coupling methods of different natures to solve the physical and numerical characteristics of the problem. It is based on a remeshed particle method that combines the advantages of Lagrangian and Eulerian methods. Particles are pushed by local velocities and remeshed at every time-step on a grid using high order interpolation formulas. This forward semi-lagrangian method takes advantage of the regular mesh on which particles are reinitialized but is not limited by CFL conditions.We derive a class of high order methods for which we are able to prove convergence results under the sole stability constraint that particle trajectories do not intersect.In the context of high performance computing, a strong portability constraint is applied to the code development in order to handle the rapid evolution of architectures and their heterogeneous nature. An analysis of the numerical efficiency of the GPU implementation of the method is performed and extended to multi-GPU platforms. The hybrid method is applied to the simulation of the transport of a passive scalar in a 3D turbulent flow. The two sub-problems of the flow and the scalar calculations are solved simultaneously on multi-CPU and multi-GPU architectures., Dans cette thèse nous explorons les possibilités offertes par l'implémentation de méthodes hybrides sur des machines de calcul hétérogènes dans le but de réaliser des simulations numériques de problèmes multiéchelles. La méthode hybride consiste à coupler des méthodes de diverses natures pour résoudre les différents aspects physiques et numériques des problèmes considérés. Elle repose sur une méthode particulaire avec remaillage qui combine les avantages des méthodes Lagrangiennes et Eulériennes. Les particules sont déplacées selon le champ de vitesse puis remaillées à chaque itération sur une grille en utilisant des formules de remaillage d'ordre élevés. Cette méthode semi-Lagrangienne bénéficie des avantages du maillage régulier mais n'est pas contrainte par une condition de CFL.Nous construisons une classe de méthodes d'ordre élevé pour lesquelles les preuves de convergence sont obtenues sous la seule contrainte de stabilité telle que les trajectoires des particules ne se croisent pas.Dans un contexte de calcul à haute performances, le développement du code de calcul a été axé sur la portabilité afin de supporter l'évolution rapide des architectures et leur nature hétérogène. Une étude des performances numériques de l'implémentation GPU de la méthode pour la résolution d'équations de transport est réalisée puis étendue au cas multi-GPU. La méthode hybride est appliquée à la simulation du transport d'un scalaire passif dans un écoulement turbulent 3D. Les deux sous-problèmes que sont l'écoulement turbulent et le transport du scalaire sont résolus simultanément sur des architectures multi-CPU et multi-GPU.

This work focuses on the development of the Discontinuous Galerkin (DG) method for the large-eddy simulation (LES) of turbulents flows. The DG method shows some interesting properties for LES : high-order of accuracy, compact stencil, unstructured meshes and amodal polynomial basis which can be used to implement multiscale turbulence models. We consider in this work the Variational Multiscale approach (VMS), which consists in splitting the resolved scales into two components using the modal basis in order to restrict the action of the model to a given range of small scales. The models have been tuned using the transfer functions of the DG hp-discretizations. The accuracy of the DG method for the representation of turbulent phenomena has been assessed through DNS of free and wall-bounded canonical flows. Finally, the VMS/DG approach has been assessed for simple configurations at high Reynolds numbers. We have shown that this particular approach allows for an accurate representation of turbulent flows for coarse discretizations.; Cette thèse vise à développer et évaluer la méthode de Galerkin discontinue (DG) pour la simulationdes grandes échelles (LES) des écoulements turbulents. L’approche DG présente un nombre d’avantages intéressants pour la LES : ordre élevé, stencil compact, prise en compte des maillages non structurés et expression de la solution numérique dans une base de polynômes permettant l’utilisation de modèles de turbulence multi-échelle. Parmi ce type de modèles, nous nous sommes intéressés ici à la méthode Variational Multiscale (VMS) qui consiste à séparer les échelles résolues dans la base de polynômes pour restreindre l’influence du modèle à une gamme réduite d’échelles. Les modèles considérés ont été paramétrés en prenant en compte les fonctions de transfert spécifiques aux discrétisations DG. La précision de la méthode pour la représentation de phénomènes turbulents variés a été évaluée à travers la réalisation de DNS de configurations académiques. Enfin, l’approche VMS/DGa été éprouvée sur des configurations simples à haut nombre de Reynolds. Il apparaît que cette méthodologie permet la représentation précise des phénomènes turbulents pour un coût réduit en terme de degrés de liberté.