Publications

2019

• Theoretical and numerical analysis of invariant measures of viscous stochastic scalar conservation laws
  
  • Martel Sofiane
  , 2019. This devoted to the theoretical and numerical analysis of a certain class of stochastic partial differential equations (SPDEs), namely scalar conservation laws with viscosity and with a stochastic forcing which is an additive white noise in time. A particular case of interest is the stochastic Burgers equation, which is motivated by turbulence theory. We focus on the long time behaviour of the solutions of these equations through a study of the invariant measures. The theoretical part of the thesis constitutes the second chapter. In this chapter, we prove the existence and uniqueness of a solution in a strong sense. To this end, estimates on Sobolev norms up to the second order are established. In the second part of Chapter~2, we show that the solution of the SPDE admits a unique invariant measure. In the third chapter, we aim to approximate numerically this invariant measure. For this purpose, we introduce a numerical scheme whose spatial discretisation is of the finite volume type and whose temporal discretisation is a split-step backward Euler method. It is shown that this kind of scheme preserves some fundamental properties of the SPDE such as energy dissipation and L^1-contraction. Those properties ensure the existence and uniqueness of an invariant measure for the numerical scheme. Thanks to a few regularity estimates, we show that this discrete invariant measure converges, as the space and time steps tend to zero, towards the unique invariant measure for the SPDE in the sense of the second order Wasserstein distance. Finally, numerical experiments are performed on the Burgers equation in order to illustrate this convergence as well as some small-scale properties related to turbulence
• Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach
  
  • Simon Bruno
  • Papoutsellis Christos
  • Benoit Michel
  • Yates Marissa L.
  Journal of Ocean Engineering and Marine Energy, Springer, 2019. The modeling of wave breaking dissipation in coastal areas is investigated with a fully nonlinear and dispersive wave model. The wave propagation model is based on potential flow theory, which initially assumes non-overturning waves. Including the impacts of wave breaking dissipation is however possible by implementing a wave breaking initiation criterion and dissipation mechanism. Three criteria from the literature, including a geometric, kinematic, and dynamic-type criterion, are tested to determine the optimal criterion predicting the onset of wave breaking. Three wave breaking energy dissipation methods are also tested: the first two are based on the analogy of a breaking wave with a hydraulic jump, and the third one applies an eddy viscosity dissipative term. Numerical simulations are performed using combinations of the three breaking onset criteria and three dissipation methods. The simulation results are compared to observations from four laboratory experiments of regular and irregular waves breaking over a submerged bar, irregular waves breaking on a beach, and irregular waves breaking over a submerged slope. The different breaking approaches provide similar results after proper calibration. The wave transformation observed in the experiments is reproduced well, with better results for the case of regular waves than irregular waves. Moreover, the wave statistics and wave spectra are predicted well in general, and in particular for regular waves. Some differences are observed for irregular wave cases, in particular in the low-frequency range. This is attributed to incomplete absorption of the long waves in the numerical model. Otherwise, the wave spectra in the range [0.5fp, 5fp] are reproduced well, before, inside, and after the breaking zone for the three irregular wave experiments. (10.1007/s40722-019-00154-7)
  DOI : 10.1007/s40722-019-00154-7
• Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model
  
  • Papoutsellis Christos
  • Yates Marissa L.
  • Simon Bruno
  • Benoit Michel
  Coastal Engineering, Elsevier, 2019, 154, pp.103579. (10.1016/j.coastaleng.2019.103579)
  DOI : 10.1016/j.coastaleng.2019.103579
• Quantifying forcing uncertainties in the hydrodynamics of the Gironde estuary
  
  • Laborie Vanessya
  • Ricci Sophie
  • de Lozzo Matthias
  • Goutal Nicole
  • Audouin Yoann
  • Sergent Philippe
  Computational Geosciences, Springer Verlag, 2019, 24 (1), pp.181-202. High tide combined with high meteorological surge levels and discharges in the Garonne and Dor-dogne rivers in the Gironde estuary (south-west France), may lead to high water levels and flooding near the Blayais nuclear power plant and the city of Bordeaux, with significant economic and social impacts. A global sensitivity analysis (GSA) was performed with a Telemac2D numerical model currently used for operational water level forecasts. The major sources of uncertainties were identified by computing the Sobol' indices for uncertain inputs with an analysis of variance (ANOVA) approach for a 7-day storm event in 2003. The generation of the GSA ensemble of simulations consists of sampling scalar and field random variables: constant and uniform friction coefficients, as well as time-varying hydrological and maritime forcings. The temporal perturbation of time-dependent upstream hydrological and down-Vanessya LABORIE Saint-Venant Hydraulics laboratory, Cerema, 134, route de Beauvais, CS 60039, 60280 Margny Lès Philippe SERGENT Cerema, 134, route de Beauvais, CS 60039, 60280 Margny Lès Compiègne, France stream maritime forcings is assumed to be represented by a Gaussian Process characterized by a correlation time scale calculated from observations. A Karhunen-Loève decomposition was then applied to retain a limited number of eigenmodes. The GSA is performed for 20 random variables using GENCI HPC computational resources for task parallelism and domain decomposition. This requires the use of 250 000 runs for an elapsed simulation time of 101 days on 32768 cores. The performance of the ensemble was assessed with a rank diagram and a reliability curve in comparison to a set of measured water levels at 12 observing stations along the estuary. It was shown that, for this event, the maritime boundary conditions and the Strickler coefficients have a predominant role along the length of the estuary with an influence driven by the tidal cycle. In the upstream fluvial areas, the friction coefficient and hydrological inputs are predominant. (10.1007/s10596-019-09907-7)
  DOI : 10.1007/s10596-019-09907-7
• Soils, Structures and Hydraulics: Expertise and Applied Research (SSHEAR) Project
  
  • Chevalier Christophe
  • Schmidt Franziska
  • Larrarte Frédérique
  • Cheetham Mark
  • Durand Edouard
  • Sergent Philippe
  • Gondret Philippe
  • de La Roque Sidoine
  , 2019, pp.6p. The phenomenon of scouring represents a significant contributing factor in the destabilizing and destruction of civil structures (bridges, earth embankments and buildings) during major flood events, yet our understanding of the mechanisms involved remains highly empirical. These erosive processes are complex and involve many disciplines including soil, fluid and structural mechanics. To overcome the reliance on empiricism, while building general knowledge and proposing optimized methods aimed at diagnostics, advanced warning procedures and infrastructure management, a consortium comprising six complementary partners has been formed within the project SSHEAR (?Soils, Structures and Hydraulics: Expertise and Applied Research?) financially supported by the French National Research Agency (ANR). After a presentation of the project, a first assessment of the achieved results is proposed: experimental developments; numerical modelling; feedback in the field.
• Modélisation de l’entraînement d’air dans l'eau avec la méthode SPH
  
  • Fonty Thomas
  , 2019. Les écoulements au sein d'ouvrages hydrauliques – déversement au-dessus d'un barrage, déferlement d'une vague sur une digue, etc. – sont le siège de forts mélanges d'eau et d'air qui se traduisent visuellement par la formation d'eaux blanches à la dynamique complexe. Représenter fidèlement le phénomène d'entraînement/capture des bulles d'air dans l'eau revêt donc un aspect stratégique important pour le dimensionnement de ces ouvrages. La modélisation tant physique que numérique de tels cas s'avère délicate à cause du fort rapport de densité entre les phases et de la nature multi-échelle de ces écoulements impliquant des effets de turbulence et de tension de surface. La méthode numérique SPH (Smoothed Particle Hydrodynamics), approche totalement lagrangienne qui représente l'écoulement comme un ensemble de particules en mouvement sans recours à un maillage, est particulièrement adaptée à la simulation de tels écoulements fortement déformés. Néanmoins, les limites actuelles de puissance de calcul empêchent encore de simuler finement des cas d'application industriels à large emprise en hydraulique. On se propose donc dans cette thèse de modéliser ces écoulements de manière macroscopique via un modèle de mélange qui consiste à voir chaque particule SPH comme un volume de mélange d'eau et d'air en mouvement. On détaille d'abord la dérivation des équations continues de ce modèle de mélange, puis on présente un état de l'art des simulations multiphasiques SPH. A partir du modèle continu et des outils actuels de discrétisation, un modèle de mélange diphasique SPH est ensuite mis en place en vue de son implémentation sur GPU (Graphics Processing Unit). Un accent tout particulier est mis sur les éléments originaux de discrétisation développés, notamment la dérivation d'un schéma aux bonnes propriétés numériques pour le suivi de l'évolution des volumes par phase et l'écriture d'un formalisme de frontières ouvertes pour un mélange. La turbulence, centrale dans le phénomène d'entraînement d’air, est modélisée via un modèle k-ϵ incluant un terme de flottabilité. Ce modèle de mélange est validé sur des cas académiques bidimensionnels de complexité croissante tels que la séparation d'un mélange eau-huile, un écoulement de Poiseuille diphasique, l'instabilité de Rayleigh–Taylor et un lâché de sédiments, illustrant sa polyvalence. La phénoménologie de l'entraînement d'air est ensuite décrite, et le modèle appliqué à des structures communément rencontrées en hydraulique, comme des jets plongeants et des coursiers en marches d'escalier, en introduisant une fermeture spécifique de la vitesse relative entre les phases. Enfin, on présente des premiers cas d'application industriels aux géométries et dynamiques complexes
• Sensitivity Analysis of the Mascaret model on the Odet River
  
  • Tiberi-Wadier Anne-Laure
  • Goutal Nicole
  • Ricci Sophie
  • Sergent Philippe
  • Monteil Céline
  , 2019. A Global Sensitivity Analysis (GSA) is carried out on the Mascaret model of the Odet river (France, Brittany) to identify and rank the major sources of uncertainty at observing stations on the network for the simulated water level, considering the upstream and downstream boundary conditions and the area distributed friction coefficients values. Upstream, ensemble hydrologic forcings are forecasted with the rainfall-runoff distributed model MORDOR-TS, using uncertain hydrologic model parameters drawn from uniform distributions. The downstream maritime boundary condition is perturbed taking into account the temporal correlation of the errors in storm surge. The Sobol' indices are computed at Kervir, Moulin-Vert and Justice stations given hypothesis on the statistical distribution of the aleatory variables. The study focuses on the 23 to the 26 December 2013 event. GSA highlights that the simulated water level at the three stations is mainly controlled by the immediate downstream friction coefficient when the boundary conditions are not perturbed. The flood plain friction coefficients only become important around the peak of the event. However, when the boundary conditions are also taken into account, they become predominant for the simulated water level and the value of the friction coefficients has less influence.
• Telemac3D for aquatic ecological modelling: calibration of the coupled ecological library AED2
  
  • Piccioni Francesco
  • Vinçon-Leite Brigitte
  • Le Minh-Hoang
  • Lemaire Bruno J.
  • Casenave Céline
  • Hong Yi
  • Jodeau Magali
  • Pham Chi-Tuan ;
  • Vidal Javier
  • Goutal Nicole
  , 2019. The monitoring and preservation of water quality is one of the main challenges in modern society. Anthropogenic stressors originated from urbanization and industrialization can have a strong impact on water resources in terms of pollutant release and nutrient enrichment. Together with the ongoing climate change, they can lead to the proliferation of primary producers and the eutrophication of the water bodies. Harmful algal blooms, and in particular cyanobacteria blooms, are an ever increasing concern worldwide as their occurrence strongly increases, expanding to higher latitudes due to warmer water temperature. Cyanobacteria are able to produce toxins that are dangerous to human health and represent a serious threat not only for the balances of an ecosystem but to human society as well. Aquatic ecological models are useful tools that can be used to simulate the biogeochemical cycle in a water body identifying the factors triggering events such as harmful algal blooms, in order to provide stakeholders with reliable projections for decision making. However, their calibration and validation often remains a challenging task: biological and chemical data deriving from field surveys are often sparse in space and time and, due to the complexity of the biogeochemical cycle, these models generally involve a high number of parameters to adjust. Aquatic ecological models need to rely on a robust hydrodynamic simulator, upon which the biogeochemical cycle is simulated. Telemac3D has recently been coupled by EDF R&D with the well-known ecological library Aquatic EcoDynamics (AED2). In this context, we aim to test the performance of Telemac3D coupled with AED2 on a full scale experimental site by comparison with high-frequency in situ data. The study site is a small and shallow urban lake located in the east of Great Paris metropolitan area. The lake suffers from repeated and severe harmful algal blooms in summer and autumn. Aside from the traditional monitoring via field campaigns and water sampling, the study site is equipped with specific sensors recording data at high-frequency (every 10 minutes) for water temperature, pH, dissolved oxygen and for the concentration of specific pigments to monitor phytoplankton growth (chlorophyll-a and phycocyanin, considered as proxies for total biomass and cyanobacteria biomass, respectively). The use of high-frequency data allows on the first hand to test the capability of the model to reproduce daily cycles and rapid blooms events spanning only a few days, and on the other hand to gain in computational time while calibrating the model on a short time periods of two to three weeks. Model results are compared with water temperature data at different depths to test the ability of the coupled hydrodynamic model to reproduce thermal stratification in the water column. The ecological module AED2 is set up to simulate two main algal groups present in the study site, green algae and cyanobacteria. High-frequency observations of chlorophyll-a and phycocyanin are used to calibrate the ecological model AED2 and to test its outcomes. Model results show that Telemac3D coupled with AED2 is able to correctly reproduce biomass growth in a water body over short bloom events spanning roughly three weeks. Even though a feedback originated from strong biomass growth can be detected in water temperature results, the model is also able to correctly reproduce thermal water column stratification. These possible feedbacks need to be taken into account when calibrating the heat-exchange budget at the water-air interface.
• Three-dimensional Modelling of Radionuclides Dispersion in a Marine Environment with Application to the Fukushima Dai-ichi Case
  
  • Bacchi Vito
  • Tassi Pablo
  Environmental Modeling and Assessment, 2019, 24 (5), pp.457-477. In this work, we present the implementation, verification and validation of a three-dimensional model able to reproduce the propagation of 137Cs radionuclide in coastal waters and its interaction with suspended sediments, in the framework of the open-source TELEMAC-MASCARET modelling system. The validation of the model was realized by comparing numerical results with field measurements of radionuclides concentration in the Japan Sea nearby the Fukushima Dai-ichi nuclear power plant (NPP). The developed model uses as external forcing the data available immediately after or during the accident, as, e.g. weather conditions (wind, pressure, temperature) and/or the harmonic components of tides. In contrast with previous models implemented in the study area, the model presented here is limited to the coastal area near Fukushima and refined in the coastal area close to the NPP. Numerical results show that the model is able to reproduce the propagation and diffusion of the released 137Cs in the vicinity of the Fukushima Dai-ichi NPP. Consequently, we show that the numerical results obtained with a small-scale model with a simple forcing are consistent, at a coastal scale, with models which employed a general circulation model based on data assimilation techniques or variation method for hydrodynamics. Therefore, this model could be employed in an emergency situation, when the dissolved radioactivity is considered. © 2018, Springer International Publishing AG, part of Springer Nature. (10.1007/s10666-018-9614-6)
  DOI : 10.1007/s10666-018-9614-6
• A French experience of Structural Health Monitoring of scour affecting river infrastructures
  
  • Larrarte Frédérique
  • Schmidt Franziska
  • Durand Edouard
  • Bontemps Arnaud
  • Della Longa Yannick
  • Cheetham Mark
  • de La Roque Sidoine
  • Hosseingholian Mohsen
  • Chevalier Christophe
  , 2019, pp.3p.. This paper presents a French experience of SHM of structures affected by scour
• 3D Numerical Simulation of Scour Erosion Around An Obstacle
  
  • Zhang Wei
  , 2019. The foundations of offshore wind turbines and bridge piers have an impact on the surrounding flow and the sediment transport around the obstacles, which will then cause structural instability. To better understand this phenomenon, this work presents a newly developed code (NSMP3D) using unstructured finite volume method (UFVM) to simulate the flow and the scour process around a circular cylinder. A sigma-coordinate system is employed in order to obtain an accurate representation of the evolution of free surface or the interface between fluid and sediment. To avoid the checkerboard problem caused by the collocated grid, a momentum interpolation scheme is used by introducing face-normal velocities at the mid-points of cell faces. Required by Large Eddy Simulation (LES), a central scheme combined with semi-implicit Adams-Bashforth scheme are proposed in this model to get second-order accuracy in time and in space. Pressure-correction projection method is employed to decouple the velocity and pressure fields. First, this work validates second-order accuracy, numerical stability and computational efficiency and capacity of the numerical model using several benchmark test-cases. The proposed model has been used for simulating 3D turbulent open-channel flows, 2D and 3D lid-cavity flows, a standing wave in a closed basin, and 3D turbulent flows around a vertical cylinder. The proposed model is able to correctly reproduce the characteristic flow features in all test-cases. Second, the simulation of channel flow driven by suspended sediment is conducted to study the interaction of sediments and turbulence. With increasing the settling velocity, flow turbulence is less able to keep the sediments in suspension, and the flow in the channel tends towards the laminar solution. Finally, large eddy simulations of the flow around a vertical cylinder for free-slip bed, rigid bed and live-bed cases are carried out, respectively. Bed erosion is simulated by solving the sediment continuity equation using a mass-conservative sand-slide algorithm and a bedload transport rate, which is based on a description of physical processes (Engelund & Fredsøe, 1976). The mean velocity profile and shear stress validate the accuracy of this model. Horseshoe vortex and lee-wake vortex shedding structure are simulated and compared with the reference. The formation and the temporal development of the scour hole and other topographic bed features are successfully reproduced
• A French experience of continuous scour monitoring on real sites
  
  • Larrarte Frédérique
  • Chollet Hugues
  • Battist Louis
  • Dela Longua Yannick
  • Chevalier Christophe
  , 2019, pp.7p. Controlling the risk of scouring of structures, beds or banks due to natural hazards (floods, floods, extreme hydraulic regimes, dam failures) is a major challenge for sustainable development and land use planning. These processes are the main cause of destruction of buildings (civil engineering structures, earthworks, buildings) during major floods. The SSHEAR project, "Soils, Structures and Hydraulics: Expertise and Applied Research? has been set up to improve scour mechanisms knowledge, to develop innovative experimental and observational tools and hydraulic numerical models at both laboratory and full-scale, and then to build optimized diagnostic, warning and management methods for bridges operators. This paper reports on the ?field approach? task of SSHEAR project.. Among the work carried out, we have investigated whether relatively inexpensive methods using commercial sensors can be implemented. After a shot remembering of the scour parameters to be monitored, the benchmark study and the choice of monitoring devices available on the market have been detailed. The preliminary results presented here show that the challenge is being met. (10.3850/38WC092019-0410)
  DOI : 10.3850/38WC092019-0410
• Some elements about scale effect on scour studies
  
  • Larrarte Frédérique
  • Schmidt Franziska
  • Boujia Nisrine
  • Vidal Vincent
  • Bontemps Arnaud
  • de La Roque Sidoine
  • Chevalier Christophe
  , 2019, pp.7p. To study the effect of scour on bridge structures, it is necessary to take into account the scale of the problem. To understand the vibrations of a structure, as for example a bridge pier affected by scour phenomenon, several experiments are in complementarity: first the behavior of reduced scale bridge piers can be studied in a hydraulic flume, where all conditions are taken so that the soil is scoured, second, the real-scale dynamical behaviour of bridge piers can be monitored and analyzed. Both approaches are presented here, and the complementary aspect of the results is shown. (10.3850/38WC092019-0748)
  DOI : 10.3850/38WC092019-0748
• Calculating the smoothing error in SPH
  
  • Violeau Damien
  • Fonty Thomas
  Computers and Fluids, Elsevier, 2019, 191, pp.104240. (10.1016/j.compfluid.2019.104240)
  DOI : 10.1016/j.compfluid.2019.104240
• Viscoelastic flows with conservation laws
  
  • Boyaval Sébastien
  , 2019. We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluids with memory that are characterized by one relaxation-time parameter. Precisely, the system of quasilinear PDEs is detailed for the shallow- water regime, i.e. for hydrostatic incompressible 2D flows with free surface under gravity. It generalizes Saint-Venant system to viscoelastic flows of Maxwell fluids, and encompasses previous works with F. Bouchut. It also generalizes the (thin-layer) elastodynamics of hyperelastic materials to viscous fluids, and to various rheologies between solid and liquid states that can be formulated using our new variable as material parameter. The new viscoelastic flow model has many potential applications, additionally to falling into the theoretical framework of (symmetric hyper- bolic) systems of conservation laws. In computational rheology, it offers a new approach to the High-Weissenberg Number Problem (HWNP). For transient geophysical flows, it offers perspectives of thermodynamically-compatible numerical simulations, with a Finite-Volume (FV) discretization say. Besides, one FV discretization of the new continuum model is proposed herein to precise our ideas incl. the physical meaning of the solutions. Perspectives are finally listed after some numerical simulations.
• High frequency monitoring of biogeochemical processes in a small and shallow lake
  
  • Calabro Souza Guilherme
  • Piccioni Francesco
  • Hong Yi
  • Dubois Philippe
  • Saad Mohamed
  • Casenave Céline
  • Jodeau Magali
  • Moilleron Régis
  • Lemaire Bruno J.
  • Brigitte Vinçon-Leite
  , 2019. Small and shallow inland water bodies are important providers of ecosystem services, e.g. in metropolitan areas. Their presence is massive in most landscapes, and they contribute substantially to global biogeochemical cycles. The dynamics of their ecological functioning is fast (e.g., algal blooms can appear and recede within a few days) and its spatial variability can be high. Understanding these processes requires high-frequency measurements. Within the ANR ANSWER and the AquaREA project, biogeochemical processes are monitored and modelled in a small and shallow lake, both in the water column and at the sediment-water interface. The study site is a 0.12 km2 and 2.3 m deep lake in the Greater Paris. Physical-chemical variables (water temperature, conductivity, pH, dissolved oxygen), chlorophyll-a fluorescence, a proxy of total phytoplankton biomass, and phycocyanin fluorescence, a proxy of cyanobacteria biomass, have been monitored since 2015 at high frequency (every 10 min) at three different points and two depths. Nitrate concentration is also continuously monitored by UV and visible light spectroscopy. An innovative system, based on the atmospheric technique Relaxed Eddy Accumulation, is under development and will enable to quantify the fluxes of nutrients and greenhouse gases at the water-sediment interface. This continuous monitoring dataset is used for phytoplankton modelling and bloom forecast.
• Étude expérimentale et numérique des écoulements à surface libre en présence d'obstacles émergés et faiblement submergés
  
  • Oukacine Marina
  , 2019. Selon le Ministère de la Transition Écologique et Solidaire, les inondations sont le principal risque naturel en France. Du fait du dérèglement climatique, les inondations extrêmes deviendront plus fréquentes. Les personnes et les biens, i.e. habitations, installations industrielles, doivent donc être protégés contre ces crues pour lesquelles les données sont très rares voire inexistantes. Lorsque l’on passe d’une crue faible à une crue extrême, l’extension spatiale de l’inondation en lit majeur varie fortement. La nature des obstacles rencontrés varie : végétation basse, arbres, habitations... Ces obstacles ou macro-rugosités hydrauliques peuvent être émergés, ou faiblement immergés.Le but de ce travail de thèse est d’analyser les processus physiques dominants associés à des écoulements de crues extrêmes en présence d’obstacles émergés ou faiblement submergés. Cette thèse s’organise en deux parties : une partie expérimentale et une partie numérique.La partie expérimentale porte sur l’exploration, dans un canal de laboratoire, de la structure verticale du profil de vitesse et des effets géométriques liés à la configuration étudiée représentant une plaine d’inondation urbanisée avec des taux d’immersion de (symbole dollar) D/h = à 0,42 ; 0,93 ; 0,98(symbole dollar) et (symbole dollar)1,48(symbole dollar) ((symbole dollar) D(symbole dollar) étant la hauteur d’eau et (symbole dollar) h(symbole dollar) la hauteur de l’obstacle). Des mesures ADV et PIV des vitesses moyennes et des fluctuations turbulentes ont montré que les propriétés de l’écoulement changent notablement selon que les écoulements sont émergés ou faiblement submergés. Les interactions entre le détachement tourbillonnaire, la surface libre, les obstacles et la rugosité de fond sont étudiées.La partie numérique analyse différents types de modélisation classiquement utilisés pour simuler des événements de crue. Le cas expérimental de la première partie de thèse sert de référence.D'abord, un modèle analytique basé sur l’écriture du bilan de quantité de mouvement au niveau d’un volume hydraulique élémentaire permet de considérer différentes modélisations de la résistance globale à l’écoulement d'obstacles en régime uniforme. Un premier modèle simple intègre la résistance à l’écoulement du au frottement de fond et aux obstacles dans un même terme de type « frottement~». Un second modèle décompose en deux parties la résistance à l’écoulement~: un frottement de fond et une résistance due aux obstacles représentée par un terme de traînée. L’obstruction à l’écoulement sera alors représentée par un terme de porosité.L’analyse porte sur la pertinence d’utiliser les coefficients de frottement ou de traînée calibrés pour l’écoulement avec le plus faible débit pour simuler des écoulements à fort débit et en particulier la transition de l’émergence à la submergence des obstacles.Ensuite, les obstacles seront représentés explicitement dans le cadre d’un modèle « Saint-Venant » bidimensionnel. La convergence en maillage est étudiée et une analyse comparative des résultats expérimentaux et simulés est menée. De plus,L’influence de la répartition géométrique des obstacles sur le profil vertical de la vitesse moyenne longitudinale est étudiée avec une modélisation 3D-LES utilisant Code_Saturne. Les résultats expérimentaux serviront de cas de référence pour la validation.Au terme de cette seconde partie de thèse, des recommandations seront émises pour modéliser de façon pertinente ces écoulements au regard d’objectifs opérationnels
• Viscous scalar conservation law with stochastic forcing: strong solution and invariant measure
  
  • Martel Sofiane
  • Reygner Julien
  , 2019. We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally Lipschitz continuous and have at most polynomial growth. Neither the flux nor the noise need to be non-degenerate. In a first part, we show the existence and uniqueness of a global solution in a strong sense. In a second part, we establish the existence and uniqueness of an invariant measure for this strong solution.
• Stabilisation de systèmes hyperboliques non-linéaires en dimension un d’espace
  
  • Hayat Amaury
  , 2019. Cette thèse est consacrée à l'étude de la stabilisation des systèmes d'équations aux dérivées partielles hyperboliques non-linéaires. L'objectif principal est de trouver des conditions de bords garantissant la stabilité exponentielle du système. Dans une première partie on s'intéresse à des systèmes généraux qu'on cherche à stabiliser en norme C^1 en introduisant un certain type de fonctions de Lyapunov, puis on regarde plus précisément les systèmes de deux équations pour lesquels on peut comparer nos résultats avec la stabilisation en norme H^{2}. On s'intéresse ensuite à quelques équations physiques: l'équation de Burgers et les systèmes densité-vélocité, dont font partie les équations de Saint-Venant et les équations d'Euler isentropiques. A l'aide d'une entropie locale dissipative, on montre qu'on peut stabiliser les systèmes densité-vélocité par des contrôles aux bords simples et, étonnement, ces contrôles ne dépendent pas explicitement des paramètres du système, pourvu qu'ils soient physiquement admissibles. Par ailleurs, on développe une méthode pour stabiliser les états-stationnaires avec un choc dans le cas de l'équation de Burgers et des équations de Saint-Venant. Enfin, dans une troisième partie on s'intéresse aux contrôles proportionnels-intégraux (PI), très utilisés en pratique mais mal compris mathématiquement dans le cas des systèmes non-linéaires de dimension infinie. Pour les systèmes d'une seule équation on introduit une méthode d'extraction pour trouver des conditions optimales de stabilité sur les paramètres du contrôle. Finalement on traite le cas des équations de Saint-Venant avec un unique contrôle PI.
• Flow and detailed 3D morphodynamic data from laboratory experiments of fluvial dike breaching
  
  • Rifai Ismail
  • El Kadi Abderrezzak Kamal
  • Erpicum Sébastien
  • Archambeau Pierre
  • Violeau Damien
  • Pirotton Michel
  • Dewals Benjamin
  Scientific Data, Nature Publishing Group, 2019, 6 (1), pp.53. This paper presents a dataset obtained from fifty four laboratory experiments of the breaching of fluvial dikes due to flow overtopping. Data were collected on two complementary experimental setups, each consisting of a main channel representing the river, an erodible lateral dike and a floodplain. The dataset covers seven test series, involving varying hydraulic boundary conditions ( e . g . inflow discharge, downstream boundary conditions), main channel dimensions, as well as bottom and dike material. The following experimental data were produced: time series of water levels in the main channel, time series of flow discharges in the main channel and through the breach, as well as high resolution 3D reconstructions of the breach geometry during its expansion. The latter measurements were performed using a novel non-intrusive laser profilometry technique developed for this research. Reuse of the collected data will support efforts to improve our understanding of the physical processes underpinning fluvial dike breaching. It will also enable benchmarking the accuracy of conceptual or detailed numerical models for the prediction of dike breaching, which is central to flood risk management. (10.1038/s41597-019-0057-y)
  DOI : 10.1038/s41597-019-0057-y
• Numerical Study of Alternate Bars in Alluvial Channels With Nonuniform Sediment
  
  • Cordier F.
  • Tassi Pablo
  • Claude N.
  • Crosato A.
  • Rodrigues S.
  • Pham van Bang D.
  Water Resources Research, American Geophysical Union, 2019, 55 (4), pp.2976-3003. Abstract Rivers typically present heterogeneous bed material, but the effects of sediment nonuniformity on river bar characteristics are still unclear. This work investigates the impact of sediment size heterogeneity on alternate bars with a morphodynamic numerical model. The model is first used to reproduce a laboratory experiment showing alternate bar formation with nonuniform bed material. Subsequently, the influence of sediment size heterogeneity on alternate bars is investigated distinguishing hybrid from free bars, definition based on the presence/absence of morphodynamic forcing, considering the results of nine scenarios. In four of them, a transverse obstacle is used to generate forcing. The computations are carried out with the Telemac‐Mascaret system solving the two‐dimensional shallow‐water equations with a finite element approach, accounting for horizontal and vertical sediment sorting processes. The results show that sediment heterogeneity affects free migrating and hybrid bars in a different way. The difference lies in the presence/absence of a migration front, so that distinct relations between bed topography, bed shear stress, and sediment sorting are obtained. Sediment sorting and associated planform redistribution of bed roughness only slightly modify free migrating bar morphodynamics, whereas hybrid bars are greatly impacted, with decreased amplitude and increased wavelength. Increased sediment size heterogeneity increases the degree of sediment sorting, while the sorting pattern remains the same for both free and hybrid bars. Moreover, it produces averagely higher, longer, and faster free bars, while in the case of hybrid bars their wavelength is increased but no general trend can be determined for their amplitude. (10.1029/2017WR022420)
  DOI : 10.1029/2017WR022420
• Mixture model for two-phase flows with high density ratios: A conservative and realizable SPH formulation
  
  • Fonty Thomas
  • Ferrand Martin
  • Leroy Agnès
  • Joly Antoine
  • Violeau Damien
  International Journal of Multiphase Flow, Elsevier, 2019, 111, pp.158-174. The numerical modelling of two-phase mixture flows with high density ratios (e.g. water/air) is challenging. Multiphase averaged models with volume fraction representation encompass a simple way of simulating such flows: mixture models with relative velocity between phases. Such approaches were implemented in SPH (Smoothed Particle Hydrodynamics) using a mass-weighted definition of the mixture velocity, but with limited validation. Instead, to handle high density ratios, a mixture model with a volumetric mixture velocity is developed in this work. To avoid conservation issues raised by the discretization of the relative material displacement contribution in the volume fraction equation, a formulation on phase volumes is derived following a finite volume reasoning. Conservativity, realizability, limit behaviour for single-phase flow are the leading principles of this derivation. Volume diffusion is added to prevent development of instabilities due to the colocated nature of SPH. This model is adapted to the semi-analytical SPH wall boundary conditions. Running on GPU, this approach is successfully applied to the separation of phases in a settling tank with low to high density ratios. An analytical solution on a two-phase mixture Poiseuille flow is also used to check the accuracy of the numerical implementation. Then, a Rayleigh-Taylor instability test case is performed to compare with multi-fluid SPH. Finally, a comparison with experimental and numerical data is made on a sand dumping case; this highlights some limits of this mixture model. (10.1016/j.ijmultiphaseflow.2018.11.007)
  DOI : 10.1016/j.ijmultiphaseflow.2018.11.007
• Development and validation of a 3D RBF-spectral model for coastal wave simulation
  
  • Raoult Cécile
  • Benoit Michel
  • Yates Marissa L.
  Journal of Computational Physics, Elsevier, 2019, 378, pp.278-302. With the objective of simulating wave propagation in the nearshore zone for engineering-scale applications, a two dimensional (2DV) model based on the Euler-Zakharov equations (Yates and Benoit, 2015; Raoult et al., 2016) is extended to three dimensions (3D). To maintain the flexibility of the approach with the goal of applying the model to irregularly shaped domains, the horizontal plane is discretized with scattered nodes. The horizontal derivatives are then estimated using the Radial Basis Function-Finite Difference (RBF-FD) method, while a spectral approach is used in the vertical dimension. A sensitivity analysis examined the robustness of the RBF-FD approach as a function of RBF parameters when estimating the derivatives of a representative function. For a targeted stencil size between 20 and 30 nodes, Piecewise-Smooth (PS) polyharmonic spline (PHS) functions are recommended, avoiding the use of Infinitely-Smooth (IS) RBFs, which are less appropriate for the desired applications because of their dependence on a shape parameter. Comparisons of simulation results to observations from two wave basin experiments show that nonlinear effects induced by complex bottom bathymetries (10.1016/j.jcp.2018.11.002)
  DOI : 10.1016/j.jcp.2018.11.002
• Mixture model for two-phase flows with high density ratios: A conservative and realizable SPH formulation
  
  • Fonty Thomas
  • Ferrand Martin
  • Leroy Agnès
  • Joly Antoine
  • Violeau Damien
  International Journal of Multiphase Flow, Elsevier, 2019, 111, pp.158-174. (10.1016/j.ijmultiphaseflow.2018.11.007)
  DOI : 10.1016/j.ijmultiphaseflow.2018.11.007
• Coastal Wave Hydrodynamics and Morphological Evolution
  
  • Yates Marissa L.
  , 2019. Ce manuscrit présente un résumé de mes travaux de recherche qui sont focalisés sur deux thèmes principaux : l’évolution morphologique des plages et l’hydrodynamique de vagues en zone côtière. Ces deux thèmes sont fortement liés, avec l’objectif commun d’améliorer, à la fois la connaissance des processus physiques qui contrôlent la dynamique en zone côtière, et aussi les modèles numériques capables de reproduire l’hydrodynamique et l’évolution morphologique dans cet environnement complexe. Le premier chapitre présente succinctement ces deux thèmes, mes projets de recherche, les collaborations que j’ai développées et l’évolution de mes travaux de recherche pendant les 10 dernières années depuis la n ma thèse. Pendant cette période, j’ai suivi une gamme d’approches diérentes pour aborder ces thèmes, allant de l’analyse des observations in situ et des expériences en laboratoire, à la modélisation empirique et numérique des processus observés. Ces approches complémentaires m’ont d’abord permis d’étudier les processus physiques qui contrôlent la dynamique en zone côtière à plusieurs échelles d’espace et de temps pour développer une vision globale de cet environnement complexe. Ces travaux ont de plus contribué à mon deuxième objectif, à savoir le développement des modèles empiriques et numériques pour une variété d’applications, allant de l’évaluation des risques côtiers et l’estimation de la ressource des énergies marines renouvelables, au dimensionnement et à la gestion des structures marines et côtières. Le deuxième chapitre est dédié au thème de la morphodynamique en zone côtière, avec deux grands axes de travail : (1) l’analyse de l’évolution morphologique des plages, basée sur des observations morphologiques de plusieurs sites d’étude et sur des mesures expérimentales eectuées en laboratoire, pour améliorer la compréhension des variations spatiales et temporelles observées, et (2) la modélisation empirique et numérique de l’évolution des prols de plage, validés avec les observations, pour améliorer les outils de prédiction. Ses travaux m’ont permis d’identier des questions fondamentales qui continuent de structurer mes thèmes de recherche, en particulier une amélioration de la compréhension des processus d’érosion et d’accrétion, et notamment des variations en espace et en temps à une variété d’échelles. Ces connaissances me permettent de valider des modèles numériques basés sur des processus physiques et de les appliquer aux échelles spatiales locales et aux échelles temporelles des événements, mais aussi de proposer des modèles simpliés, de type empirique, applicables aux échelles spatiales d’une plage ou d’un secteur du littoral et aux échelles temporelles des saisons, des années, des décennies. Mes travaux en cours explorent diérents axes d’amélioration de ces types de modélisation, notamment pour améliorer la prise en compte des processus physiques dans un modèle empirique d’équilibre, incluant le transport longshore, les interactions entre les vagues et le niveau de l’eau et les impacts du changement climatique.