Keywords
 A6. Modeling, simulation and control
 A6.1. Methods in mathematical modeling
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.4. Multiscale modeling
 A6.1.5. Multiphysics modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.6. Optimization
 A6.3. Computationdata interaction
 A6.3.2. Data assimilation
 A6.3.4. Model reduction
 A6.3.5. Uncertainty Quantification
 B3. Environment and planet
 B3.3. Geosciences
 B3.3.2. Water: sea & ocean, lake & river
 B3.3.3. Nearshore
 B3.4. Risks
 B3.4.1. Natural risks
 B3.4.3. Pollution
 B4. Energy
 B4.3. Renewable energy production
 B4.3.1. Biofuels
 B4.3.2. Hydroenergy
1 Team members, visitors, external collaborators
Research Scientist
 Julien Salomon [Team leader, INRIA, Senior Researcher, HDR]
Faculty Members
 Nina Aguillon [SORBONNE UNIVERSITE, Associate Professor]
 Bernard Di Martino [UNIV CORSE, Associate Professor, HDR]
 Cindy Guichard [SORBONNE UNIVERSITE, Associate Professor]
 Julien Guillod [SORBONNE UNIVERSITE, Associate Professor]
PostDoctoral Fellow
 Liudi Lu [UNIV GENEVE]
PhD Students
 Nelly Boulos Al Makary [UNIV PARIS XIII]
 Juliette Dubois [INRIA]
 Chourouk El Hassanieh [UNIV LIBANAISE]
 Léon Migus [SORBONNE UNIVERSITE]
 Luca Perrin [INRIA]
 Djahou Norbert Tognon [INRIA]
Technical Staff
 Sibylle Techene [CNRS, Engineer]
Interns and Apprentices
 Mael Karembe [INRIA, from Jun 2022]
 Dylan Machado [INRIA, from Jun 2022]
Administrative Assistants
 Laurence Bourcier [INRIA]
 Julien Guieu [INRIA]
Visiting Scientists
 Gabriele Ciaramella [ECOLE POLYT. MILAN, from Feb 2022]
 Marco Gambarini [ECOLE POLYT. MILAN, from Feb 2022]
 John Ringwood [UNIV MAYNOOTH, from May 2022 until Jun 2022]
External Collaborators
 MarieOdile Bristeau [Retired]
 Anne Mangeney [IPGP, HDR]
2 Overall objectives
2.1 Presentation
Among all aspects of geosciences, we mainly focus on gravity driven flows arising in many situations such as
 hazardous flows (flooding, rogue waves, landslides...),
 sustainable energies (hydrodynamicsbiology coupling, biofuel production, marine energies...),
 risk management and landuse planning (morphodynamic evolutions, early warning systems...)
There exists a strong demand from scientists and engineers in fluid mechanics for models and numerical tools able to simulate not only the water depth and the velocity field but also the distribution and evolution of external quantities such as pollutants or biological species and the interaction between flows and structures (seashores, erosion processes...). The key point of the researches carried out within ANGE is to answer this demand by the development of efficient, robust and validated models and numerical tools.
2.2 Scientific challenges
Due to the variety of applications with a wide range of spatial scales, reducedsize models like the shallow water equations are generally required. From the modelling point of view, the main issue is to describe the behaviour of the flow with a reducedsize model taking into account several physical processes such as nonhydrostatic terms, biological species evolution, topography and structure interactions within the flow. The mathematical analysis of the resulting model do not enter the field of hyperbolic equations anymore and new strategies have to be proposed. Moreover, efficient numerical resolutions of reducedsize models require particular attention due to the different time scales of the processes and in order to recover physical properties such as positivity, conservativity, entropy dissipation and equilibria.
The models can remain subject to uncertainties that originate from incomplete description of the physical processes and from uncertain parameters. Further development of the models may rely on the assimilation of observational data and the uncertainty quantification of the resulting analyses or forecasts.
3 Research program
3.1 Overview
The research activities carried out within the ANGE team strongly couple the development of methodological tools with applications to real–life problems and the transfer of numerical codes. The main purpose is to obtain new models adapted to the physical phenomena at stake, identify the main properties that reflect the physical meaning of the models (uniqueness, conservativity, entropy dissipation, ...), propose effective numerical methods to approximate their solution in complex configurations (multidimensional, unstructured meshes, wellbalanced, ...) and to assess the results with data in the purpose of potentially correcting the models.
The difficulties arising in gravity driven flow studies are threefold.
 Models and equations encountered in fluid mechanics (typically the free surface NavierStokes equations) are complex to analyze and solve.
 The underlying phenomena often take place over large domains with very heterogeneous length scales (size of the domain, mean depth, wave length, ...) and distinct time scales, e.g. coastal erosion, propagation of a tsunami, ...
 These problems are multiphysics with strong couplings and nonlinearities.
3.2 Modelling and analysis
Hazardous flows are complex physical phenomena that can hardly be represented by shallow water type systems of partial differential equations (PDEs). In this domain, the research program is devoted to the derivation and analysis of reduced complexity models compared to the NavierStokes equations, but relaxing the shallow water assumptions. The main purpose is then to obtain models welladapted to the physical phenomena at stake.
Even if the resulting models do not strictly belong to the family of hyperbolic systems, they exhibit hyperbolic features: the analysis and discretisation techniques we intend to develop have connections with those used for hyperbolic conservation laws. It is worth noticing that the need for robust and efficient numerical procedures is reinforced by the smallness of dissipative effects in geophysical models which therefore generate singular solutions and instabilities.
On the one hand, the derivation of the SaintVenant system from the NavierStokes equations is based on two approximations (the socalled shallow water assumptions), namely
 the horisontal fluid velocity is well approximated by its mean value along the vertical direction,
 the pressure is hydrostatic or equivalently the vertical acceleration of the fluid can be neglected compared to the gravitational effects.
As a consequence the objective is to get rid of these two assumptions, one after the other, in order to obtain models accurately approximating the incompressible Euler or NavierStokes equations.
On the other hand, many applications require the coupling with nonhydrodynamic equations, as in the case of microalgae production or erosion processes. These new equations comprise nonhyperbolic features and a special analysis is needed.
Multilayer approach
As for the first shallow water assumption, multilayer systems were proposed to describe the flow as a superposition of SaintVenant type systems 20, 24, 25. Even if this approach has provided interesting results, layers are considered separate and nonmiscible fluids, which implies strong limitations. That is why we proposed a slightly different approach 21, 22 based on a Galerkin type decomposition along the vertical axis of all variables and leading, both for the model and its discretisation, to more accurate results.
A kinetic representation of our multilayer model allows to derive robust numerical schemes endowed with crucial properties such as: consistency, conservativity, positivity, preservation of equilibria, ... It is one of the major achievements of the team but it needs to be analyzed and extended in several directions namely:
 The convergence of the multilayer system towards the hydrostatic Euler system as the number of layers goes to infinity is a critical point. It is not fully satisfactory to have only formal estimates of the convergence and sharp estimates would provide an optimal number of layers.
 The introduction of several source terms due for instance to the Coriolis force or extra terms from changes of coordinates seems necessary. Their inclusion should lead to substantial modifications of the numerical scheme.
 Its hyperbolicity has not yet been proven and conversely the possible loss of hyperbolicity cannot be characterised. Similarly, the hyperbolic feature is essential in the propagation and generation of waves.
Nonhydrostatic models
The hydrostatic assumption consists in neglecting the vertical acceleration of the fluid. It is considered valid for a large class of geophysical flows but is restrictive in various situations where the dispersive effects (like wave propagation) cannot be neglected. For instance, when a wave reaches the coast, bathymetry variations give a vertical acceleration to the fluid that strongly modifies the wave characteristics and especially its height.
Processing an asymptotic expansion (w.r.t. the aspect ratio for shallow water flows) into the NavierStokes equations, we obtain at the leading order the SaintVenant system. Going one step further leads to a vertically averaged version of the Euler/NavierStokes equations involving some nonhydrostatic terms. This model has several advantages:
 it admits an energy balance law (that is not the case for most dispersive models available in the literature),
 it reduces to the SaintVenant system when the nonhydrostatic pressure term vanishes,
 it consists in a set of conservation laws with source terms,
 it does not contain high order derivatives.
Multiphysics modelling
The coupling of hydrodynamic equations with other equations in order to model interactions between complex systems represents an important part of the team research. More precisely, three multiphysics systems are investigated. More details about the industrial impact of these studies are presented in the following section.
 To estimate the risk for infrastructures in coastal zones or close to a river, the resolution of the shallow water equations with moving bathymetry is necessary. The first step consisted in the study of an additional equation largely used in engineering science: The Exner equation. The analysis enabled to exhibit drawbacks of the coupled model such as the lack of energy conservation or the strong variations of the solution from small perturbations. A new formulation is proposed to avoid these drawbacks. The new model consists in a coupling between conservation laws and an elliptic equation, like the Euler/Poisson system, suggesting to use wellknown strategies for the analysis and the numerical resolution. In addition, the new formulation is derived from classical complex rheology models and allowed physical phenomena like threshold laws.
 Interaction between flows and floating structures is the challenge at the scale of the shallow water equations. This study requires a better understanding of the energy exchanges between the flow and the structure. The mathematical model of floating structures is very hard to solve numerically due to the nonpenetration condition at the interface between the flow and the structure. It leads to infinite potential wave speeds that could not be solved with classical free surface numerical schemes. A relaxation model was derived to overcome this difficulty. It represents the interaction with the floating structure with a free surface modeltype.
 If the interactions between hydrodynamics and biology phenomena are known through laboratory experiments, it is more difficult to predict the evolution, especially for the biological quantities, in a real and heterogeneous system. The objective is to model and reproduce the hydrodynamics modifications due to forcing term variations (in time and space). We are typically interested in phenomena such as eutrophication, development of harmful bacteria (cyanobacteria) and upwelling phenomena.
Data assimilation and inverse modelling
In environmental applications, the most accurate numerical models remain subject to uncertainties that originate from their parameters and shortcomings in their physical formulations. It is often desirable to quantify the resulting uncertainties in a model forecast. The propagation of the uncertainties may require the generation of ensembles of simulations that ideally sample from the probability density function of the forecast variables. Classical approaches rely on multiple models and on Monte Carlo simulations. The applied perturbations need to be calibrated for the ensemble of simulations to properly sample the uncertainties. Calibrations involve ensemble scores that compare the consistency between the ensemble simulations and the observational data. The computational requirements are so high that designing fast surrogate models or metamodels is often required.
In order to reduce the uncertainties, the fixed or mobile observations of various origins and accuracies can be merged with the simulation results. The uncertainties in the observations and their representativeness also need to be quantified in the process. The assimilation strategy can be formulated in terms of state estimation or parameter estimation (also called inverse modelling). Different algorithms are employed for static and dynamic models, for analyses and forecasts. A challenging question lies in the optimization of the observational network for the assimilation to be the most efficient at a given observational cost.
3.3 Numerical analysis
Nonhydrostatic scheme
The main challenge in the study of the nonhydrostatic model is to design a robust and efficient numerical scheme endowed with properties such as: positivity, wet/dry interfaces treatment, consistency. It must be noticed that even if the nonhydrostatic model looks like an extension of the SaintVenant system, most of the known techniques used in the hydrostatic case are not efficient as we recover strong difficulties encountered in incompressible fluid mechanics due to the extra pressure term. These difficulties are reinforced by the absence of viscous/dissipative terms.
Space decomposition and adaptive scheme
In the quest for a better balance between accuracy and efficiency, a strategy consists in the adaptation of models. Indeed, the systems of partial differential equations we consider result from a hierarchy of simplifying assumptions. However, some of these hypotheses may turn out to be irrelevant locally. The adaptation of models thus consists in determining areas where a simplified model (e.g. shallow water type) is valid and where it is not. In the latter case, we may go back to the “parent” model (e.g. Euler) in the corresponding area. This implies to know how to handle the coupling between the aforementioned models from both theoretical and numerical points of view. In particular, the numerical treatment of transmission conditions is a key point. It requires the estimation of characteristic values (Riemann invariant) which have to be determined according to the regime (torrential or fluvial).
AsymptoticPreserving scheme for source terms
Hydrodynamic models comprise advection and sources terms. The conservation of the balance between source terms, typically viscosity and friction, has a significant impact since the overall flow is generally a perturbation around an equilibrium. The design of numerical schemes able to preserve such balances is a challenge from both theoretical and industrial points of view. The concept of AsymptoticPreserving (AP) methods is of great interest in order to overcome these issues.
Another difficulty occurs when a term, typically related to the pressure, becomes very large compared to the order of magnitude of the velocity. At this regime, namely the socalled low Froude (shallow water) or low Mach (Euler) regimes, the difference between the speed of the gravity waves and the physical velocity makes classical numerical schemes inefficient: firstly because of the error of truncation which is inversely proportional to the small parameters, secondly because of the time step governed by the largest speed of the gravity wave. AP methods made a breakthrough in the numerical resolution of asymptotic perturbations of partialdifferential equations concerning the first point. The second one can be fixed using partially implicit scheme.
Multiphysics models
Coupling problems also arise within the fluid when it contains pollutants, density variations or biological species. For most situations, the interactions are small enough to use a splitting strategy and the classical numerical scheme for each submodel, whether it be hydrodynamic or nonhydrodynamic.
The sediment transport raises interesting issues from a numerical aspect. This is an example of coupling between the flow and another phenomenon, namely the deformation of the bottom of the basin that can be carried out either by bed load where the sediment has its own velocity or suspended load in which the particles are mostly driven by the flow. This phenomenon involves different time scales and nonlinear retroactions; hence the need for accurate mechanical models and very robust numerical methods. In collaboration with industrial partners (EDF–LNHE), the team already works on the improvement of numerical methods for existing (mostly empirical) models but our aim is also to propose new (quite) simple models that contain important features and satisfy some basic mechanical requirements. The extension of our 3D models to the transport of weighted particles can also be here of great interest.
Optimisation
Numerical simulations are a very useful tool for the design of new processes, for instance in renewable energy or water decontamination. The optimisation of the process according to a welldefined objective such as the production of energy or the evaluation of a pollutant concentration is the logical upcoming challenge in order to propose competitive solutions in industrial context. First of all, the set of parameters that have a significant impact on the result and on which we can act in practice is identified. Then the optimal parameters can be obtained using the numerical codes produced by the team to estimate the performance for a given set of parameters with an additional loop such as gradient descent or Monte Carlo method. The optimisation is used in practice to determine the best profile for turbine pales, the best location for water turbine implantation, in particular for a farm.
4 Application domains
4.1 Overview
Sustainable development and environment preservation have a growing importance and scientists have to address difficult issues such as: management of water resources, renewable energy production, bio/geochemistry of oceans, resilience of society w.r.t. hazardous flows, urban pollutions, ...
As mentioned above, the main issue is to propose models of reduced complexity, suitable for scientific computing and endowed with stability properties (continuous and/or discrete). In addition, models and their numerical approximations have to be confronted with experimental data, as analytical solutions are hardly accessible for these problems/models. A. Mangeney (IPGP) and N. Goutal (EDF) may provide useful data.
4.2 Geophysical flows
Reduced models like the shallow water equations are particularly welladapted to the modelling of geophysical flows since there are characterized by large time or/and space scales. For long time simulations, the preservation of equilibria is essential as global solutions are a perturbation around them. The analysis and the numerical preservation of nontrivial equilibria, more precisely when the velocity does not vanish, are still a challenge. In the fields of oceanography and meteorology, the numerical preservation of the socalled geostrophic state, which is the balance between the gravity field and the Coriolis force, can significantly improve the forecasts. In addition, data assimilation is required to improve the simulations and correct the dissipative effect of the numerical scheme.
The sediment transport modelling is of major interest in terms of applications, in particular to estimate the sustainability of facilities with silt or scour, such as canals and bridges. Dredging or fillingup operations are expensive and generally not efficient in the long term. The objective is to determine a configuration almost stable for the facilities. In addition, it is also important to determine the impact of major events like emptying dam which is aimed at evacuating the sediments in the dam reservoir and requires a large discharge. However, the downstream impact should be measured in terms of turbidity, river morphology and flood.
4.3 Hydrological disasters
It is a violent, sudden and destructive flow. Between 1996 and 2005, nearly 80% of natural disasters in the world have meteorological or hydrological origines. The main interest of their study is to predict the areas in which they may occur most probably and to prevent damages by means of suitable amenities. In France, floods are the most recurring natural disasters and produce the worst damages. For example, it can be a cause or a consequence of a dam break. The large surface they cover and the long period they can last require the use of reduced models like the shallow water equations. In urban areas, the flow can be largely impacted by the debris, in particular cars, and this requires fluid/structure interactions be well understood. Moreover, underground flows, in particular in sewers, can accelerate and amplify the flow. To take them into account, the model and the numerical resolution should be able to treat the transition between free surface and underground flows.
Tsunamis are another hydrological disaster largely studied. Even if the propagation of the wave is globally well described by the shallow water model in oceans, it is no longer the case close to the epicenter and in the coastal zone where the bathymetry leads to vertical accretions and produces substantial dispersive effects. The nonhydrostatic terms have to be considered and an efficient numerical resolution should be induced.
While viscous effects can often be neglected in water flows, they have to be taken into account in situations such as avalanches, debris flows, pyroclastic flows, erosion processes, ...i.e. when the fluid rheology becomes more complex. Gravity driven granular flows consist of solid particles commonly mixed with an interstitial lighter fluid (liquid or gas) that may interact with the grains and decrease the intensity of their contacts, thus reducing energy dissipation and favoring propagation. Examples include subaerial or subaqueous rock avalanches (e.g. landslides).
4.4 Biodiversity and culture
Nowadays, simulations of the hydrodynamic regime of a river, a lake or an estuary, are not restricted to the determination of the water depth and the fluid velocity. They have to predict the distribution and evolution of external quantities such as pollutants, biological species or sediment concentration.
The potential of microalgae as a source of biofuel and as a technological solution for CO2 fixation is the subject of intense academic and industrial research. Largescale production of microalgae has potential for biofuel applications owing to the high productivity that can be attained in highrate raceway ponds. One of the key challenges in the production of microalgae is to maximize algae growth with respect to the exogenous energy that must be used (paddlewheel, pumps, ...). There is a large number of parameters that need to be optimized (characteristics of the biological species, raceway shape, stirring provided by the paddlewheel). Consequently our strategy is to develop efficient models and numerical tools to reproduce the flow induced by the paddlewheel and the evolution of the biological species within this flow. Here, mathematical models can greatly help us reduce experimental costs. Owing to the high heterogeneity of raceways due to gradients of temperature, light intensity and nutrient availability through water height, we cannot use depthaveraged models. We adopt instead more accurate multilayer models that have recently been proposed. However, it is clear that many complex physical phenomena have to be added to our model, such as the effect of sunlight on water temperature and density, evaporation and external forcing.
Many problems previously mentioned also arise in larger scale systems like lakes. Hydrodynamics of lakes is mainly governed by geophysical forcing terms: wind, temperature variations, ...
4.5 Sustainable energy
One of the booming lines of business is the field of renewable and decarbonated energies. In particular in the marine realm, several processes have been proposed in order to produce electricity thanks to the recovering of wave, tidal and current energies. We may mention waterturbines, buoys turning variations of the water height into electricity or turbines motioned by currents. Although these processes produce an amount of energy which is less substantial than in thermal or nuclear power plants, they have smaller dimensions and can be set up more easily.
The fluid energy has kinetic and potential parts. The buoys use the potential energy whereas the waterturbines are activated by currents. To become economically relevant, these systems need to be optimized in order to improve their productivity. While for the construction of a harbour, the goal is to minimize swell, in our framework we intend to maximize the wave energy.
This is a complex and original issue which requires a fine model of energy exchanges and efficient numerical tools. In a second step, the optimisation of parameters that can be changed in reallife, such as bottom bathymetry and buoy shape, must be studied. Eventually, physical experiments will be necessary for the validation.
4.6 Urban environment
The urban environment is essentially studied for air and noise pollutions. Air pollution levels and noise pollution levels vary a lot from one street to next. The simulations are therefore carried out at street resolution and take into account the city geometry. The associated numerical models are subject to large uncertainties. Their input parameters, e.g. pollution emissions from road traffic, are also uncertain. Quantifying the simulation uncertainties is challenging because of the high computational costs of the numerical models. An appealing approach in this context is the use of metamodels, from which ensembles of simulations can be generated for uncertainty quantification.
The simulation uncertainties can be reduced by the assimilation of fixed and mobile sensors. Highquality fixed monitoring sensors are deployed in cities, and an increasing number of mobile sensors are added to the observational networks. Even smartphones can be used as noise sensors and dramatically increase the spatial coverage of the observations. The processing and assimilation of the observations raises many questions regarding the quality of the measurements and the design of the network of sensors.
4.7 SmartCity
There is a growing interest for environmental problems at city scale, where a large part of the population is concentrated and where major pollutions can occur. Numerical simulation is well established to study the urban environment, e.g. for road traffic modelling. As part of the smartcity movement, an increasing number of sensors collect measurements, at traditional fixed observation stations, but also on mobile devices, like smartphones. They must properly be taken into account given their number but also their potential low quality.
Pratical applications include air pollution and noise pollution. These directly relate to road traffic. Data assimilation and uncertainty propagation are key topics in these applications.
5 Social and environmental responsibility
5.1 Footprint of research activities
Only few travels were done last year (including one flight) as a consequence of a will of the team to avoid this type of transportation.
5.2 Impact of research results
Part of ANGE activity is devoted to research on renewable energy. In this way, the team took part to the organization of the EMRSim 22 conference, which devoted to Marine Energy Techniques and Simulation.
6 New software and platforms
One ongoing work in collaboration with geographers (ISTEP Sorbonne Université) and statisticians (LPSM Sorbonne Université) consists of the study of tsunamigenic landslides. We are interested in the effects on the Morocco coast of a tsunami in the Alboran Sea caused by a landslide. A numerical procedure has been developed to couple Freshkiss3d (used for the wave propagation 26 see web page) with Shaltop 23 to model the landslide with a complex rheology of Bingham type 19.
6.1 New software
6.1.1 Freshkiss

Name:
FREe Surface Hydrodynamics using KInetic SchemeS

Keywords:
Finite volume methods, Hydrostatic NavierStokes equations, Free surface flows

Functional Description:
Freshkiss3D is a numerical code solving the 3D hydrostatic and incompressible NavierStokes equations with variable density.

Contact:
Jacques Sainte Marie

Participants:
Fabien Souillé, Emmanuel Audusse, Jacques Sainte Marie, MarieOdile Bristeau

Partners:
UPMC, CEREMA
6.1.2 TSUNAMATHS

Keywords:
Modeling, Tsunamis

Functional Description:
Tsunamaths is an educational platform aiming at simulating historical tsunamis. Real data and mathematical explanations are provided to enable people to better understand the overall process of tsunamis.
 URL:

Contact:
Jacques Sainte Marie

Participants:
Emmanuel Audusse, Jacques Sainte Marie, Raouf Hamouda
6.1.3 Verdandi

Keywords:
HPC, Model, Software Components, Partial differential equation

Functional Description:
Verdandi is a free and opensource (LGPL) library for data assimilation. It includes various such methods for coupling one or several numerical models and observational data. Mainly targeted at large systems arising from the discretization of partial differential equations, the library is devised as generic, which allows for applications in a wide range of problems (biology and medicine, environment, image processing, etc.). Verdandi also includes tools to ease the application of data assimilation, in particular in the management of observations or for a priori uncertainty quantification. Implemented in C++, the library may be used with models implemented in Fortran, C, C++ or Python.
 URL:

Contact:
Vivien Mallet

Participants:
Dominique Chapelle, Gautier Bureau, Nicolas Claude, Philippe Moireau, Vivien Mallet
6.1.4 Polyphemus

Keyword:
Simulation

Functional Description:
Polyphemus is a modeling system for air quality. As such, it is designed to yield uptodate simulations in a reliable framework: data assimilation, ensemble forecast and daily forecasts. Its completeness makes it suitable for use in many applications: photochemistry, aerosols, radionuclides, etc. It is able to handle simulations from local to continental scales, with several physical models. It is divided into three main parts:
libraries that gather data processing tools (SeldonData), physical parameterizations (AtmoData) and postprocessing abilities (AtmoPy),
programs for physical preprocessing and chemistrytransport models (Polair3D, Castor, two Gaussian models, a Lagrangian model),
model drivers and observation modules for model coupling, ensemble forecasting and data assimilation.
 URL:

Contact:
Vivien Mallet

Participants:
Sylvain Doré, Vivien Mallet
6.1.5 Urban noise analysis

Keyword:
Environment perception

Functional Description:
This software processes mobile observations collected by the application Ambiciti (previously known as SoundCity). It can merge simulated noise maps with the mobile observations.

Authors:
Raphaël Ventura, Vivien Mallet, Guillaume Chérel

Contact:
Vivien Mallet
6.1.6 Freshkiss3D

Keywords:
Python, Cython, NavierStokes

Functional Description:
Tool for the numerical solution of free surface NavierStokes equations
 Publication:

Contact:
Jacques Sainte Marie

Participants:
Cedric Doucet, Apolline El Baz, Jacques Sainte Marie

Partner:
UPMC
7 New results
7.1 Numerical methods
7.1.1 Optimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.
Participants: LiuDi Lu, Julien Salomon.
Coll. with Olivier Bernard In 8, we focus on a periodic resource allocation problem applied to a dynamical system which comes from a biological system. More precisely, we consider a system with $N$ resources and $N$ activities, each activity use the allocated resource to evolve up to a given time $T>0$ where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimization of a mixing strategy to enhance the growth rate in a microalgal raceway system. A mixing device, such as a paddle wheel, is considered to control the rearrangement of the depth of the algae cultures, hence the light perceived at each lap. We prove that if the dynamics of the system is periodic, then the period corresponds to one reallocation whatever the order of the involved permutation matrix is. A nonlinear optimization problem for one reallocation process is then introduced. Since $N!$ permutations need to be tested in the general case, it can be numerically solved only for a limited number of $N$. To overcome this difficulty, we introduce a second optimization problem which provides a suboptimal solution of the initial problem, but whose solution can be determined explicitly. A sufficient condition to characterize cases where the two problems have the same solution is given. Some numerical experiments are performed to assess the benefit of optimal strategies in various settings.7.2 Modelling
7.2.1 Optimal optical conditions for Microalgal production in photobioreactors.
Participants: LiuDi Lu.
Coll. with Olivier Bernard The potential of industrial applications for microalgae has motivated their recent fast development. Their growth dynamics depends on different factors that must be optimized. Since they get their energy from photosynthesis, light is a key factor that strongly influences their productivity. Light is absorbed and scattered in the liquid medium, and irradiance exponentially decreases towards the darkest part of the photobioreactor at a rate nonlinearly depending on the biomass concentration. Maximizing productivity is then a tricky problem, especially when the growth rate is inhibited by an excess of light. Productivity optimization turns out to be highly dependent on how light is distributed along the reactor, and is therefore related to the extinction rate and the background turbidity. We propose in 7 a theoretical analysis of this problem, by introducing the concept of optical depth productivity for systems where background turbidity must be accounted for. A global optimum maximizing productivity is proposed, extending the concept of the compensation condition, consisting in compensating the algal growth rate at the bottom of the reactor by the respiration. This condition can drive the optimization of the surface biomass productivity depending on the minimum reachable depth. We develop a nonlinear controller and prove the global asymptotic stability of the biomass concentration towards the desired optimal value.7.2.2 LowMach type approximation of the NavierStokes system with temperature and salinity for free surface flows.
Participants: Léa Boittin, MarieOdile Bristeau, Anne Mangeney, Jacques SainteMarie, Fabien Souillé.
Coll. with François Bouchut In 9, we are interested in free surface flows where density variations coming e.g. from temperature or salinity differences play a significant role in the hydrodynamic regime. In water, acoustic waves travel much faster than gravity and internal waves, hence the study of models arising from compressible fluid mechanics often requires a decoupling between these waves. Starting from the compressible NavierStokes system, we derive the socalled NavierStokesFourier system in an "incompressible" regime using the lowMach scaling, hence filtering the acoustic waves, neglecting the density dependency on the fluid pressure but keeping its variations in terms of temperature and salinity. A slightly modified lowMach asymptotics is proposed to obtain a model with thermomechanical compatibility. The case when the density depends only on the temperature is studied first. Then the variations of the fluid density with respect to temperature and salinity are considered, and it seems to be the first time that salinity dependency is considered in this low Mach limit. We give a layeraveraged formulation of the obtained models in an hydrostatic context, allowing to derive numerical schemes endowed with strong stability properties that are presented in a companion paper. Several stability properties of the layeraveraged NavierStokesFourier system are proved.7.2.3 A bed pressure correction of the friction term for depthaveraged granular flow models.
Participants: Anne Mangeney.
Coll. with François Bouchut, Juan Manuel DelgadoSánchez, Enrique Domingo FernándezNieto, Gladys NarbonaReina Depthaveraged models, such as the SavageHutter model with Coulomb or Pouliquen friction laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose in 10 an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Secondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the staticflowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of motion because it is based on a second order correction of the pressure valid for slow granular flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Several numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation.7.2.4 Existence and Uniqueness for Plane Stationary Navier–Stokes Flows with Compactly Supported Force.
Participants: Julien Guillod.
Coll. with Mikhail Korobkov, Xiao Ren In 11, we study the stationary Navier–Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existence of solutions to this problem was only known under special symmetry and smallness assumptions. In the paper we solve the key difficulties in applying Leray’s invading domains method and, as a consequence, prove the existence of Dsolutions in the whole plane for arbitrary compactly supported force. The boundary condition at infinity are verified in two different scenarios: (I) the limiting velocity is sufficiently large with respect to the external force, (II) both the total integral of force and the limiting velocity vanish. Hence, our method produces large class of new solutions with prescribed spatial limits. Moreover, we show the uniqueness of Dsolutions to this problem in a perturbative regime. The main tools here are two new estimates for general Navier–Stokes solutions, which have rather simple forms. They control the difference between mean values of the velocity over two concentric circles in terms of the Dirichlet integral in the annulus between them.7.2.5 Wellposedness of the Stokestransport system in bounded domains and in the infinite strip.
Participants: Antoine Leblond.
In 12, we consider the Stokestransport system, a model for the evolution of an incompressible viscous fluid with inhomogeneous density. This equation was already known to be globally wellposed for any initial density with finite first moment in . We show that similar results hold on different domain types. We prove that the system is globally wellposed for initial data in bounded domains of and as well as in the infinite strip . These results contrast with the illposedness of a similar problem, the incompressible porous medium equation, for which uniqueness is known to fail for such a density regularity.7.3 Assessments of models by means of experimental data and assimilation
7.3.1 Simulationbased high resolution fire danger mapping using deep learning.
Participants: Frédéric Allaire, Vivien Mallet.
Coll. with JeanBaptiste Filippi, Florence Vaysse Wildfire occurrence and behavior are difficult to predict very locally for the next day. In 6, we use an artificial neural network emulator called DeepFire, trained on the basis of simulated fire sizes, and study its application to fire danger mapping using actual weather fore1 casts. Experimental analysis is based on DeepFire forecasts for 13 relatively big fires that occurred in Corsica and corresponding forecasts based on a fire danger index used in operational conditions. A comparative analysis of both indices is presented, highlighting the differences in terms of precision and expected results of such predictions. Forcing weather forecasts used as input have high spatial resolution and high frequency, which also applies to the fire danger predictions. Additionally, input uncertainty is propagated through DeepFire, resulting in ensembles of emulated fire size. Eventually, several approaches are proposed to analyze the results and help in investing assessment of nextday fire danger using this new simulationbased prediction system.8 Bilateral contracts and grants with industry
Participants: Yohan Penel.
Yohan Penel supervises the PhD thesis of Giuseppe Parasiliti about the Physical, mathematical and numerical modelling of a gas flow for the transportation of liquified natural gas. This work is the result of a close collaboration with the corporation GTT, which has already collaborated with ANGE in the last years, through the Carnot institute SMILE.Participants: Jacques SainteMarie.
Jacques SainteMarie has a contract with Eaux de Paris about Hydraulic modeling, calibration and diagnosis. (20202023, with S. Labbé, Laboratoire D'Alembert and LPSM)9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Associate Teams in the framework of an Inria International Lab or in the framework of an Inria International Program
OCEANIA
 Title: Intelligence Artificielle, Données et Modèles pour Comprendre les Océans et le Changement Climatique
 Partner Institution(s):
 ANGE, BIOCORE, TAU Inria teams, France
 Universidad de Chile (Center of Mathematical Modeling), Chile
 Pontificia Universidad Catól ica de Chile, Chile
 Fondation TARA Océan, France,
 GOSEE CNRS Federation, France
 Université de Nantes (ComBi team), France
 Date/Duration: 11.2020–10.2024
 Additionnal info/keywords: Artificial Intelligence and Modeling for Understanding Oceans and Climate Change
There is strong scientific evidence of the negative effects of climate change on the ocean. These changes will have a drastic impact on nearly all life forms in the ocean, as well as additional consequences for food security and ecosystems in coastal communities as well as inland. Despite these impacts, scientific data and infrastructure are still lacking to better understand and quantify the consequences of these disturbances on the marine ecosystem. There is a need not only to collect more data, but also to develop and apply stateoftheart mechanisms capable of transforming this data into real knowledge, policy, and action. This is where artificial intelligence, machine learning and modeling tools are needed. OceanIA, this ambitious interdisciplinary Inria Challenge, aims to develop new artificial intelligence and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the Ocean and its role in regulating and sustaining the biosphere and fighting climate change. OceanIA is also an opportunity to structure Inria's contributions around a global scientific challenge in the convergence of artificial intelligence, biodiversity and climate change.
9.2 International research visitors
 69 June 2022: visit of F. Kwok (Université Laval, Canada). Work on time parallelization of assimilation techniques.
 613 Feb. 2022: visit of G. Ciaramella and M. Gambarini (MOX, Polytechnico de Milano). Work about optimization of wave energy converters.
 G. Barennechea (U. Strathclyde, Scotland) has been invited (1 month) for a work about Free Surface NavierStokes equations.
9.3 National initiatives
Projet Emergence ALARM (20182022)
Participants: Jacques SainteMarie, Apolline ElBaz.
 Project acronym: ALARM
 Project title: Alboran sea submarine landslides
 Coordinator: Sara Lafuerza (ISTeP  UMR 7193 Institut des Sciences de la Terre de Paris)
 Funding: 55 00 euros.
Simulation et étude de glissements de terrain et tsunami dans la mer d'Alboran
équipe junior ISCD (20192022)
Participants: Jacques SainteMarie, Nina Aguillon, Sybille Téchène, Julien Guillod.
 Project acronym: Andiamo
 Project title: Andiamo
 Coordinator: N. Aguillon, S. Téchène, J. Deshayes (SU)
 Funding: 70 000 euros.
The ANDIAMO project brings together mathematicians and oceanographers from SU around long term global ocean models. The main challenge is that the mesh size and time step are large, yielding nonnegligible truncation errors and schemes dominated by numerical diffusion. Importantly, solutions for regional simulations do not transfer to our needs, as small errors in water mass characteristics have large impact on long term simulations. Thus “nonconverged” methods and numerical analysis on coarse mesh are needed.
Another important part of the project is to establish a dialogue and to build further collaborations between mathematicians and oceanographers, around questions arising in climatology that require new numerical methods (interactions with continental ice, quantification of uncertainties…).
Projet Emergence (20212023)
Participants: Julien Guillod.
 Project acronym: Emergence
 Project title: Etudes numériques d'équations fluides
 Coordinator: Julien Guillod (SU)
 Funding: 28 000 euros.
ANR ALLOWAPP (20192023)
Participants: Julien Salomon.
 Project acronym: ALLOWAPP
 Project title: Algorithmes pour l'optimisation à grande échelle de problèmes de propagation d'ondes
 Coordinator: Laurence Halpern (Université ParisNord)
 Funding: 317 891 euros.
The goal of the ALLOWAPP project is the design of spacetime parallel algorithms for largescale optimization problems associated with wave propagation phenomena. Such problems appear in seismology, geophysics, but also in various applications from data assimilation. The large amount of data and the volume of computations required for the accurate numerical solution of wave propagation problems, within an optimization loop, requires the use of massively parallel computers. Timeparallel methods have experienced a great development in the last ten years, and for parabolic problems an almost perfect efficiency for a large number of processors has been achieved (scalability). It is quite different for wave propagation problems. In this project, we propose to develop robust, efficient and scalable methods for spacetime parallelization of these optimization problems.
ANR GeoFun (20202024)
Participants: Nina Aguillon.
 Project acronym: GeoFun
 Project title: Ecoulements géophysiques avec des modèles unifiés
 Coordinator: Martin Parisot (INRIA Bordeaux SudOuest)
 Funding: 524 880 euros.
The GeoFun project aims to improve the modeling and simulation of geophysical flows involving at least two different processes. Numerical simulation of watersheds and estimation of water resources is the main application of the project's achievements. In this context, a free surface flow (rivers, lakes) is the upper part of a groundwater flow (water table). Our vision of river transport is often naive, because we think first of rivers, lakes and floods, but in reality, 80 % of the water of the continents is underground. Sometimes, the porous substratum is covered by an impermeable rock stratum, which confines the flow as in pipes, except for some points where springs and resurgences appear.
ANR SingFlows (20192023)
Participants: Julien Guillod.
 Project acronym: SingFlows
 Project title: Ecoulements avec singularités : couches limites, filaments de vortex, interaction vaguestructure
 Coordinator: David GerardVaret (Institut de mathématiques de Jussieu  Paris Rive Gauche)
 Funding: 263 628 euros.
The objective of SingFlows is to develop mathematical and numerical tools for the analysis of three problems in fluid dynamics: the behaviour of anisotropic flows (boundary layers, shallow water flows), the dynamics of vortical structures, and the evolution of fixed or floating structures in water waves. Our will to unify these different problems is natural, because they share many mathematical features. The underlying keypoint is that they are described by singular solutions of Euler or NavierStokes equations. The word singular refers here:  either to a lack of smoothness: it applies for instance to vortex filaments, which are Dirac masses along curves, or to the contact line between water and the floating structure,  or to a singular dependence of the solution with respect to a parameter, typically the Reynolds number (like in boundary layers). The connection between the two points of view is usually made by viscous regularization of the nonsmooth structure, or conversely by taking the vanishing limit of the parameter. More generally, the three problems considered in SingFlows involve flows with very small scales. A relevant description then requires the derivation of reduced models.
ANR Topup (20212024)
Participants: Cindy Guichard.
 Project acronym: Topup
 Project title: Highresolution topography upscaling for overland flows
 Coordinator: Konstantin Brenner (UNIVERSITE COTE D'AZUR  Laboratoire JeanAlexandre Dieudonné)
 Funding: 248 335 euros.
The objective of the project is to design efficient DD and Ms methods adapted to multiscale freesurface flow problems, to implement them in the form of an HPC code, and finally to validate them on a set of tests based on realistic highresolution topographic data. The last objective will be achieved through a close collaboration with the Nice Côte d'Azur Metropolis
ANR Saphir (20222024)
Participants: Jacques SainteMarie, Bernard Di Martino.
 Project acronym: Saphir
 Project title: Sensor Augmented weather Prediction at high Resolution
 Coordinator: JF. Muzy (Université de Toulouse Paul Sabatier)
 Funding: 296 000 euros.
ANR DEEPNUM (20222026)
Participants: Julien Salomon.
 Project acronym: DEEPNUM
 Project title: Algorithmes pour l'optimisation à grande échelle de problèmes de propagation d'ondes
 Coordinator: Julien Salomon
 Funding: 493 799,20 euros.
The project aims at developing the interplay between Deep Neural Networks (DNNs) and Differential Equations (DEs), with the goal of modeling complex dynamical systems arising from the observation of natural phenomena. Two application domains are targeted, environment and healthcare. We address three fundamental questions: how to adapt and apply numerical analysis theory to DNNs for analyzing them, providing theoretical guaranties and improving their robustness, how to combine simulation and data based models into hybrid systems, how could DNNs help solving DEs and complement numerical solvers. In addition, we evaluate our methods on simulation and real world data in the environment and health domains. DeepNuM gathers partners with complementary skills: DEs and Environment (INRIAANGE), Machine Learning and DNNs (Sorbonne – MLIA), DEs and Biophysics (INRIAEPIONE).
GdR MathGeoPhy (2022–2027)
Participants: Emmanuel Audusse, Bernard di Martino, Nicole Goutal, Cindy Guichard, Anne Mangeney, Martin Parisot, Jacques SainteMarie.
The MathGeoPhy interdisciplinary research group was created in January 2022, for five years. It is funded by the French National Center for Scientific Research (CNRS), with the mission of animating the French scientific community around the theme of mathematics in interaction with the geophysics of fluid and solid envelopes. The members of the GdR are interested in mathematical modeling, scientific computing and the development of new numerical methods applied in particular to : offshore and coastal ocean dynamics, gravity waves, coastal erosion problems
 micromacro approaches, granular and complex flows
 fluvial and torrential hydrodynamics, extreme events and environmental risks, landslides, avalanches, volcanic eruptions, glaciology, etc.
GdR EOLEMR (2021–2026)
Participants: Julien Salomon, Jacques SainteMarie.
OBJECTIVES : To promote the dissemination of existing knowledge and expertise within and across disciplines. The GDR EMR is a forum for the exchange of expertise and knowhow within and across disciplines. To promote the implementation of collaborations, between partners of the GDR and with the industrial fabric. The GDR is an entry and orientation point. It provides a forum for the exchange of information concerning industrial needs and the skills of the academic community; and enables the bringing together of players. Valuing the national scientific community The GDR EMR gives visibility to the community, in particular through the development of a mapping of the actors and themes available on the web platform
10 Dissemination
10.1 Promoting scientific activities
We use the following acronyms : NAg (Nina Aguillon), JS (Julien Salomon), JG (Julien Guillod), BM (Bernard di Martino), JSM (Jacques SainteMarie), NAy (Nathalie Ayi), CG (Cindy Guichard), AL (Antoine Leblond), NT (Norbert Tognon), LP (Lucas Perrin), MR (MAthieu Rigal), EA (Emmanuel Audusse), LM (Léon Migus), JD (Juliette Dubois) etc.
10.1.1 Scientific events: organisation
Member of the organizing committees
 JS took part of the organization of the conference EMRSim 22 at Roscoff,
 JG took part of the organization of the conference FoCM 2023 at Paris,
 JS coorganizes the bimonthly seminar "Rencontres INRIAJLL en analyse numérique et calcul scientifique"
 JG coorganizes the monthly seminar "Analyse nonlinéaire et EDP"
 JG coorganizes the monthly seminar "InfoMath"
 NAg coorganizes the yearly "Journée interne du Laboratoire JL. Lions"
 BM coorganized the "Journées du GDR Analyse Fonctionnelle, Harmonique et Probabilité 2022"
10.1.2 Journal
Member of the editorial boards
JS is editor in chief of MATAPLI (national journal of the applied maths community). EA is responsible for its section "Du côté des écoles d'ingénieurs".
Reviewer  reviewing activities
The team members were referee for the following journals
 JS: SIAM SISC, AIMS Maths, JSSC
 JG: Philosophical Transactions of the Royal Society A, European Physical Journal Plus, Zeitschrift für Angewandte Mathematik und Mechanik, Journal of Differential Equations
 BM: Journal of Fluid Mechanics, Scientific Reports
 CG: Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM)
 Nay: Journal of Differential Equations EA Computer & Fluids, Calcolo, CMS
10.1.3 Invited talks
 JS: PinT 2022: 11th Conference on ParallelinTime Integration CIRM Marseille 1115.07.22
 JS: JeanMorlet Chair 2022: Research School  Domain Decomposition for Optimal Control Problems CIRM Marseille 59.09.22
 JS: 27th International Conference on Domain Decomposition Methods. Prague 1115.07.22
 JG: Séminaire du Laboratoire de Mathématiques de Versailles Versaille, Paris 24/03
 JG: Conference in honor of J.P. Eckmann Genève 0710.06.2022
 JG: Workshop On Fluid Structure Interaction Problems Bruxelles 1012.10.2022
 JG: Journée interne du LJLL Paris 8/11
 JG: Infomath: construre un site web Paris 01/12
 JSM: Digital Tech Conference Rennes 06/12
 JSM: Green Tech Forum Paris 01/12
 LM: ICLR Workshop on Geometrical and Topological Representation Learning A distance 29/04/22
 LM: GDR ISIS Apprentissage et modélisation physique Paris 14/06/22
 LM: SCAI PhD Workshop on Artificial Intelligence Paris 10/10/22
 LP: emrsim2022 : Simulation et Optimisation pour les Énergies Marines Renouvelables Roscoff 30.052.06.2022
 LP: 45ème congrès d'Analyse Numérique (CANUM 2020) EvianLesBains 1317.06.2022
 NT: 45ème congrès d'Analyse Numérique (CANUM 2020) EvianLesBains 1317.06.2022
 NT: 27th International Conference on Domain Decomposition Methods. Prague 2529.07.2022
 NAy: Conférence de clôture de l’ANR MoHyCon Pornichet 10/03/22
 NAy: Working group of QuAMProcs ANR Inria Paris 08/03/22
 NAy: Frontiers in the interplay between probability and kinetic theory Edimburgh (online) 04/04/22
 NAy: GDR ANGE Paris 19/05/22
 NAy: 45ème congrès d'Analyse Numérique (CANUM 2020) EvianLesBains 1317.06.2022
 NAy: Round Meanfield : crowdopinioncells Rome 29/09/22
 NAy: Séminaire du LMAC UTC Compiègne 04/10/22
 NAy: Kinetic and hydrodynamic descriptions in collective behavior Grenade (Espagne) 08/11/22
 NAy: Séminaire Bourbaki du Vendredi IHP, Paris 18/11/22
 JD: GDR ANGE Inria Paris 29/03/22
 JD: Séminaire des doctorants de l'UMA ENSTA Paris 04/11/22
 NAg: séminaire de mathématiques appliqués du laboratoire Jean Leray Nantes 22/11/22
 NAg: Séminaire ÉDP, Modélisation et Calcul Scientifique de LyonSaint Etienne Lyon 24/05/22
 NAg: Séminaire EDP Strasbourg 12/05/22
 NAg: GDR ANGE Inria Paris 10/10/22
 NAg: Semaine pour le Climat Inria Paris 29/09/22
 MR: CANUM 2022 Evianlesbains 15/06/22
 MR: Séminaire d’analyse appliquée A3 (laboratoire LAMFA) Amiens 10/10/22
 EA: Séminaire ASCIOM Montpellier 22/03/22
 EA: Séminaire INRIALJLL Paris 16/05/22
 EA: Séminaire LAMFA Amiens 04/04/22
 EA: Journée Modélisation en hydrodynamique Toulon 27/04/22
 EA: Séminaire Calcul Scientifique et Modélisation Bordeaux 24/11/22
 EA: Séminaire LJLL Paris 9/12/22
 AL: Conférence Singflows Bordeaux Bordeaux 12/04/22
 AL: CIRM Conférences écoulements Luminy 09/05/22
 AL: EMSRIM 2022 Roscoff 30/05/22
 AL: Séminaire des doctorantes de l'IRMAR Rennes 13/06/22
 AL: Summer School fluids Lyon 27/06/22
 AL: Mathflows CIRM Luminy 04/12/22
10.1.4 Leadership within the scientific community
 EA is adjoint director of GDR MathGeoPhy (2022)
 JS is member of the board of AMIES (2018)
10.1.5 Research administration
 JS is Membre du CES of INRIA (2018).
 JSM is directeur scientifique adjoint (2019).
 JG is Member of the admin. board of IHP (2021).
 JSM belongs to the External advisory board  ERC Synergy (20202024).
 JSM belongs to the board of the PEPR 'agroécologie et numérique' (20222028).
 JSM is responsible for the program 'Numérique et environnement' (2022).
 NAy belongs to the council of laboratoire LJLL (2020).
 NAy belongs to the scientific comittee of UFR 929 (2020).
 JG belongs to the council of Licence mathématiques de Sorbonne Université (2019).
 NAy and JG is in jury of Prime RIPEC (2022).
 EA is member of the Commission Recherche and CAC of USPN (20202024).
 NAg belongs to the administration council of UFR 929, SU (2022).
 EA and JS were in the specialists comittee for the recruitment of an assistant prof. at IUT Bobigny.
 JG and NAy were in the specialists comittee for the recruitment of an assistant prof. at LJLL.
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
EG is the president of commission française pour l'enseignement des mathématiques (CFEM)
Teaching activities of ANGE are summarized in the following.
 Julien Salomon
 Méthodes numériques pour des modèles incluants des EDP, 45,M2,Université d'AbomeyCalavi, Bénin, CM
 Méthodes numériques pour des modèles incluants des EDP, 45H, M2, Univ. ParisDauphine, CM
 Cindy Guichard
 Analyse numérique 48H, L3, Sorbonne Université TD+TP
 Méthodes numériques 31H, M2, Sorbonne Université CM+TD
 Co responsable de la majeure Ingénierie Mathématiques pour l'Entreprise M2 Sorbonne Université
 Jacques SainteMarie
 Modélisation des écoulements gravitaires, 40 H, M1, Univ. ParisDiderot et IPGP
 Méthodes numériques en géosciences, 50 H, M2, Univ. ParisDiderot et IPGP,
 Hyperbolic models for complex flows, 25 H, M2, Sorbonne Université
 Nelly Boulos Al Makary
 Analyse2, 36 H, L1, Université Sorbonne Paris Nord, TD
 Mathématiques pour les études scientifiques, 36H, L1, Sorbonne Université
 Nathalie Ayi
 Probabilités, 38H, L3, Sorbonne Université, TD
 Approximation des EDPs, 36H, M1, Sorbonne Université CM
 Algèbre linéaire, 60H, L2, Sorbonne Université CMTD
 Bernard Di Martino
 Outils Mathématiques, 45H, L1, Université de Corse
 Pratique d'analyse, 18H, L2, Université de Corse TP
 Pratique d'algèbre, 18H, L2, Université de Corse TP
 Emmanuel Audusse
 EDO, 30H, ING1, USPN, TDTP
 Optimisation, 30H, ING2, USPN,TDTP
 Optimisation, 45H, M1, USPN,TDTP
 Calcul scientifique, 30H, L2, USPN, CMTDTP
 analyse numérique avec Matlab, 30H, L3, USPN, TP
 Léon Migus
 Informatique 2 (fortran), 40H, M1, Polytech Sorbonne, TP
 Julien Guillod
 Méthodes numériques pour les EDP instationnaires 18H, M2 Sorbonne Université TD/TP
 Programmation Python pour les mathématiques 45H, L2 Sorbonne Université TP/TD
 Nina Aguillon
 Directrice des études de L2 mathématiques, 64H, L2, Sorbonne Université
 Mathématiques pour les études scientifiques 2, 42H, L1, Sorbonne Université CMTD
 Topologie et calcul différentiel 1, 36H, L2, Sorbonne Université TD
 Modèles hyperboliques d'écoulements complexes dans le domaine de l'environnement, 10H, M2, Sorbonne Université, CM
 Mathieu Rigal
 Topologie, analyse hilbertienne et intégration, 36H, L3, (ING1) Polytech Sorbonne
 TP d'introduction à Matlab 4, 4H, L1, Polytech Sorbonne
 Chourouk El Hassanieh
 Mathématiques pour les études scientifiques 1 & 2, 46 + 102H, L1, Sorbonne Université
 Antoine Leblond
 Analyse numérique, 72H, L3, Sorbonne Université, TP, TD+TP
 Juliette Dubois
 Analyse mathématique, 16H, L3, Polytech Sorbonne, TP
 Lucas Perrin
 Méthodesng the second a numériques : algèbre matricielle et fonctions d'une variable réelle, 40H, L2, Univ. ParisDauphine, TP+TD
 Analyse de Fourier, 28H, L3, Polytech Sorbonne, TD
10.2.2 Supervision

JS, PhD, Lucas Perrin, SU, 20212024
Parallélisation en temps et assimilation de données.

JS, PhD, Léon Migus, SU, 20202023
Deep Neural Networks and Differential Equations.

NA, EA, Martin Parisot, PhD, Nelly BOULOS, Paris 13, 20182022
Modélisation et simulation numérique de la dynamique d'un acquifère érodable.

NA, JSM, NAy, PhD, Mathieu Rigal, UPMC, 20192022
Low Froude regime and dispersive effects in kinetic formulations.

BDM, JSM, JG, EG, Samer Israwi (Libanese university), PhD, Chourouk El Hassanieh, Inria, 20192023
Mathematical and numerical analysis of some dispersive models in fluids mechanics

JSM, Sébastien Impériale, PhD, Juliette Dubois, Inria 20202023,
Modélisation et approximation numérique de la propagation des ondes acoustique et des ondes de gravité dans les fluides à surface libre

YP, Nora Aissiouene, PierreYves Lagrée, PhD, Giuseppe Parasiliti, SU, 20202023
Physical, mathematical and numerical modelling of a gas flow for the transportation of liquified natural gas

JS, PhD, Norbert Tognon, SU, 20222025,
Analyse de l'algorithme ParaOpt.

JS, Intern M1, Dylan Machado, INRIA, 03.202207.22,
Etude de stratégies de mélanges pour la production d'algues?

JS, Intern M2, Constanza Molina, INRIA Chile, 05.202210.2022
Holocene dust transport simulation using PINN

JG, AnneLaure Dalibard, PhD, Antoine Leblond, SU 09.2020,
Evolution de patches de densité dans des fluides incompressibles

JG, Tutorat FSMP, Kala Agbo Bidi, FSMP/SU 09.202106.2022
Tutorat d'un étudiant de M2 étranger lauréat d'une bourse PGSM de la FSMP

JSM, Etienne Mémin, Postdoc, PierreMarie Boulvard, Inria 20212022,
Location uncertainties in free surface flows models  Numerical analysis and implementation in Freshkiss3d

EA, F. Benkhaldoun, PhD Laila Baroukh, USPN 20212024,
Simulation numérique pour des écoulements partiellement congestionnés avec rhéologie complexe
 NA, EA, Stage L1, J. Baraka, SU juin 2022, Tsunamaths
10.2.3 Juries

JS, 01.06.2022, PhD Rapporteur, Raed Blel, Cermics,
"Analyse et le développement de méthodes de réduction de modèles dans des contextes stochastiques".

JS, 14.09.2022, PhD Jury (président), Ibrahim Ayed CIFRE SUThales SIX
"Réseaux de neurones profonds pour la modélisation de phénomènes physiques complexes incorporation de connaissances a priori".

JSM, 12.2022, PhD, Directeur de thèse, Mathieu Rigal, Sorbonne Université,
"Régime bas Froude et schémas cinétiques implicites pour les équations de SaintVenant".

NAy, 14.11.2022, PhD, Coencadrante Mathieu Rigal, Sorbonne Université
"Régime bas Froude et schémas cinétiques implicites pour les équations de SaintVenant".

NAg, 14.11.2022, PhD Coencadrante Mathieu Rigal, Sorbonne Université
"Régime bas Froude et schémas cinétiques implicites pour les équations de SaintVenant".

NAg, 13.12.2022, PhD Coencadrante, Nelly Boulos El Makary, Sorbonne Paris Nord
"Analyse d'un modèle hyperbolique de type Saint Venant à deux vitesses".

NAg, 07.12.2022, PhD, Examinatrice, Alice Masset, Université de Picardie,
"Équations de SaintVenant avec effets rotatifs et thermiques : aspects théoriques et schémas numériques".

EA, 13.12.2022, PhD Directeur de thèse, Nelly Boulos El Makary, Sorbonne Paris Nord,
"Analyse d'un modèle hyperbolique de type Saint Venant à deux vitesses".

EA 16.6.2022, PhD, Examinateur, Noémie Gaveau, Univ. Orléans,
"Résultats numériques et théoriques sur les équations de SaintVenant, couplées à un modèle d’érosion ou avec force de Coriolis".
10.3 Popularization
 JS, dec. 2022 Accueil de Collégiens
 NA, 2018, coorganization de Mathematic Park (Licence Level)
 JSM, oct. 2022, Ambassadeur for "la fête de la science 2022"
 JSM, 2022, MOOC "impact environnemental du numérique"
 NAy, Sept 2022 , Creation of the podcast "Têteàtête Chercheuse(s)"
 NAy, May 2022 , Participation to the exposition "Mathématiques, Informatique ... avec elles"
 NAy, jan. 2022, Interview of Laure SaintRaymond about her participation to ICM
 NAy, june 2022 Participation à la Master Class Lyceéennes organisée par l'association Seéphora Berrebi Scolarships for Women in Advanced Mathematics & Computer Science
 NAy, aug. 2022, Paneliste à la conférence Matrix x Imaginary coorganiseée by MoMaths (New York) and Imaginary
 NAy, oct. 2022, Intervention devant des lycéennes et lycéens, lycée Louis le Grand
 NAy, dec. 2022, Conférence dans le cadre d'une journée Filles et Maths à Tours
 NAy, dec. 2022, Intervention devant des lycéens et des lycéennes, Lycée Jean Zay, Orléans
 NAy, dec. 2022, Intervention devant des lycéens et des lycéennes, Lycée Charles Péguy, Orléans
 JD, dec. 2022, Intervention devant des lycéens et lycéennes, Lycée Racine Paris
 NAg, oct. 2022, Invitée pour une intervention fête de la sciences
 NAg, april 2022, Speed meeting métier, journée "filles, maths et info, une équation lumineuse" at polytechnique
 NAg, march 2022, Speed meeting métier, journée "filles, maths et info, une équation lumineuse" at IHP + video
 NAg, oct. 2022, cycle de Conférencesmétiers du Master Mathématiques de Sorbonne Université
11 Scientific production
11.1 Major publications
 1 articleApproximation of the hydrostatic NavierStokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation.J. Comput. Phys.2302011, 34533478URL: http://dx.doi.org/10.1016/j.jcp.2011.01.042
 2 articleA multilayer SaintVenant system with mass exchanges for Shallow Water flows. Derivation and numerical validation.ESAIM Math. Model. Numer. Anal.452011, 169200URL: http://dx.doi.org/10.1051/m2an/2010036
 3 articleAn energyconsistent depthaveraged Euler system: derivation and properties.Discrete and Continuous Dynamical Systems  Series B2042015, 28
 4 unpublishedAnalysis of the Blade Element Momentum Theory.April 2020, working paper or preprint
 5 articleVertically averaged models for the free surface Euler system. Derivation and kinetic interpretation.Math. Models Methods Appl. Sci. (M3AS)2132011, 459490URL: http://dx.doi.org/10.1142/S0218202511005118
11.2 Publications of the year
International journals
 6 articleSimulationbased high resolution fire danger mapping using deep learning.International Journal of Wildland Fire314April 2022, 379394
 7 articleOptimal optical conditions for Microalgal production in photobioreactors.Journal of Process Control1122022, 6977
 8 articleOptimal periodic resource allocation in reactive dynamical systems: Application to microalgal production.International Journal of Robust and Nonlinear ControlMay 2022
 9 articleLowMach type approximation of the NavierStokes system with temperature and salinity for free surface flows.Communications in Mathematical Sciences2022
 10 articleA bed pressure correction of the friction term for depthaveraged granular flow models.Applied Mathematical Modelling106February 2022, 627658
 11 articleExistence and Uniqueness for Plane Stationary Navier–Stokes Flows with Compactly Supported Force.Communications in Mathematical PhysicsNovember 2022
 12 articleWellposedness of the Stokestransport system in bounded domains and in the infinite strip.Journal de Mathématiques Pures et Appliquées158February 2022
Scientific books
 13 bookA twostep numerical scheme in time for surface quasi geostrophic equations under location uncertainty.2022, 110
Doctoral dissertations and habilitation theses
 14 thesisLow Froude regime and implicit kinetic schemes for the SaintVenant system.Sorbonne UniversiteNovember 2022
Reports & preprints
 15 miscHow to find a discrete entropy inequality when you don’t know if it exists.December 2022
 16 miscEnergy stable and linearly wellbalanced numerical schemes for the nonlinear Shallow Water equations with Coriolis force.January 2022
 17 miscAcoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation.December 2022
 18 miscTimeparallelization of sequential data assimilation problems.December 2022
11.3 Cited publications
 19 articleOn the rigidlid approximation of shallow water bingham model.DCDSB2622021, 875905
 20 articleA multilayer SaintVenant model~: Derivation and numerical validation.Discrete Contin. Dyn. Syst. Ser. B522005, 189214
 21 articleApproximation of the hydrostatic NavierStokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical validation.J. Comput. Phys.2302011, 34533478URL: http://dx.doi.org/10.1016/j.jcp.2011.01.042
 22 articleA multilayer SaintVenant system with mass exchanges for Shallow Water flows. Derivation and numerical validation.ESAIM Math. Model. Numer. Anal.452011, 169200URL: http://dx.doi.org/10.1051/m2an/2010036
 23 articleGravity driven shallow water models for arbitrary topography.Comm. in Math. Sci.22004, 359389
 24 article A robust wellbalanced scheme for multilayer shallow water equations.Discrete Contin. Dyn. Syst. Ser. B132010, 739758
 25 articleNumerical simulation of twolayer shallow water flows through channels with irregular geometry.J. Comput. Phys.19512004, 202235

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unpublishedhome page.2020,
https://freshkiss3d.gitlabpages.inria.fr/freshkiss3d/applications.html