The team is located in Montpellier.

Coastal zones are the theatre for numerous interfaces. The main elements that come to mind are the sea/earth interface, saline/brackish/fresh water interfaces and sediment/biological world interfaces. These elements cause most of the phenomena met within coastal zones to be in fragile equilibrium or more often, in constant evolution. This is due to the evolving external pressures, such as anthropic activity or physical forces (tectonic features, tide, precipitations, storms, sea level rise, sediment transport, etc.). In order to illustrate the considerable importance of such a research project, let us underline the following figures:

**60 % of the world population lives in a 100km wide coastal strip** (80% within 30km in Brittany),

**current sea level rise** has occurred at a mean rate of 1.8 mm per year for the past century, and more recently at rates
estimated near

It results that **coastal management** requires the
development of theoretical and applied models to facilitate the **decision
process**. For example, a city that wants to develop a harbour needs
to anticipate the time-evolution of urban floods. The construction of
defense barriers to protect buildings and houses from natural hazards
relies on the knowledge of potential submersion events, in a period
where the impact of global climatic and anthropic changes on the coastal
zone is expected to generate increased coastal risks (IPCC 2007 and 2013).
One also needs to analyze *"what if"* scenarios
for proposed changes in land use or land cover in coastal regions
(such as French Mont Saint-Michel).

As a matter of fact, the software
packages available for engineering applications are usually not satisfactory. More specifically, some modeling hypotheses (such as the hydrostatic approximation) should be weakened, and more appropriate numerical schemes should be implemented.
What is proposed with LEMON is to **increase the quality of
coastal engineering numerical tools**, thanks to better designed mathematical
and numerical models.

The mathematical modeling of the phenomena occurring within coastal zones and their interactions is currently a major scientific issue. If we want to model coastal zones, we have to consider the fact that they cover a very wide range of situations and that they are the result of several complex interacting phenomena (see Figure ). More specifically, many time scales and space scales are involved and many physical and biological phenomena are in action. Moreover, within each zone, specific interactions between those phenomena make it an almost unique situation. Hence, we are far from having a database aggregating every possible situation. Modeling complex phenomena with the objective of building and improving management/decision tools requires the interaction of several models, each of them being dedicated to the simulation of a specific process. Such (mathematical and numerical) models usually exist but scarcely interact: therefore there is a need to understand how these bricks can be modified (forcing terms, boundary conditions) in order to be assembled. It will require a dialog with specialists of the application domain (geophysics, mechanical engineering, biology, hydrology, etc.) to help to develop new mathematical and numerical models for coastal engineering.

Developing more accurate and/or less CPU demanding models and coupling them together, LEMON will have a strong impact in the applications targeted and in coastal management.

Shallow Water (SW) wave dynamics and dissipation represent an important research field. This is because shallow water flows are the most common flows in geophysics. In shallow water regions, dispersive effects (non-hydrostatic pressure effects related to strong curvature in the flow streamlines) can become significant and affect wave transformations. The shoaling of the wave (the “steepening” that happens before the breaking) cannot be described with the usual Saint-Venant equations. To model such various evolutions, one has to use more sophisticated models (Boussinesq, Green-Naghdi...). Nowadays, the classical Saint-Venant equations can be solved numerically in an accurate way, allowing the generation of bores and the shoreline motion to be handled, using recent finite-volume or discontinuous-Galerkin schemes. In contrast, very few advanced works regarding the derivation and modern numerical solution of dispersive equations , , are available in one dimensions, let alone in the multidimensional case. We can refer to , for some linear dispersive equations, treated with finite-element methods, or to for the first use of advanced high-order compact finite-volume methods for the Serre equations. Recent work undertaken during the ANR MathOCEAN lead to some new 1D fully nonlinear and weakly dispersive models (Green-Naghdi like models) that allow to accurately handle the nonlinear waves transformations. High order accuracy numerical methods (based on a second-order splitting strategy) have been developed and implemented, raising a new and promising 1D numerical model. However, there is still a lack of new development regarding the multidimensional case.

In shallow water regions, depending on the complex balance between non-linear effects, dispersive effects and energy dissipation due to wave breaking, wave fronts can evolve into a large range of bore types, from purely breaking to purely undular bore. Boussinesq or Green-Naghdi models can handle these phenomena . However, these models neglect the wave overturning and the associated dissipation, and the dispersive terms are not justified in the vicinity of the singularity. Previous numerical studies concerning bore dynamics using depth-averaged models have been devoted to either purely broken bores using NSW models , or undular bores using Boussinesq-type models . Let us also mention for tsunami modeling and , for the dam-break problem. A model able to reproduce the various bore shapes, as well as the transition from one type of bore to another, is required. A first step has been made with the one-dimensional code , . The SWASH project led by Zijlema at Delft addresses the same issues.

For every model set in a bounded domain, there is a need to consider
boundary conditions. When the boundaries correspond to a modeling
choice rather than to a physical reality, the corresponding boundary
conditions should not create spurious oscillations or other unphysical
behaviour at the artificial boundary. Such conditions are called **open
boundary conditions** (OBC). They have been widely studied by applied
mathematicians since the pionneering work of on transparent
boundary conditions. Deep studies of these operators have been performed
in the case of linear equations, , , .
Unfortunately, in the case of geophysical fluid dynamics, this theory leads
to nonlocal conditions (even in linear cases) that are not usable in numerical models. Most
of current models (including high quality operational ones) modestly
use a *no flux* condition (namely an homogeneous Neumann boundary
condition) when a free boundary condition is required. But in many
cases, Neumann homogeneous conditions are a very poor approximation
of the exact transparent conditions. Hence the need to build higher
order approximations of these conditions that remain numerically tractable.

Numerous physical processes are involved in coastal modeling, each
of them depending on others (surface winds for coastal oceanography,
sea currents for sandbars dynamics, etc.). Connecting two (or more)
model solutions at their interface is a difficult task, that
is often addressed in a simplified way from the mathematical viewpoint:
this can be viewed as the one and only iteration of an iterative process.
This results with a low quality coupled system, which could be improved
either with additional iterations, and/or thanks to the improvement
of interface boundary conditions and the use of OBC (see above). Promising
results have been obtained in the framework of **ocean-atmosphere
coupling** (in a simplified modeling context) in ,
where the use of advanced coupling techniques (based on domain decomposition
algorithm) are introduced.

The mathematical modeling of **fluid-biology** coupled systems
in lagoon ecosystems requires one or several water models. It is of
course not necessary (and not numerically feasible) to use accurate
non-hydrostatic turbulent models to force the biological
processes over very long periods of time. There is a compromise to
be reached between accurate (but untractable) fluid models such as
the Navier-Stokes equations and simple (but imprecise) models such
as .

In urbanized coastal zones, upscaling is also a key issue. This stems not only from the multi-scale aspects dealt with in the previous subsection, but also from modeling efficiency considerations.

The typical size of the relevant hydraulic feature in an urban area
is between 0.1 m and 1.0 m, while the size of an urban area usually
ranges from

Upscaling provides an answer to this problem by allowing macroscopic equations to be derived from the small-scale governing equations. The powerful, multiple scale expansion-based homogeneization technique , , has been applied successfully to flow and transport upscaling in porous media, but its use is subordinated to the stringent assumptions of (i) the existence of a Representative Elementary Volume (REV), (ii) the scale separation principle, and (iii) the process is not purely hyperbolic at the microscopic scale, otherwise precluding the study of transient solutions . Unfortunately, the REV has been shown recently not to exist in urban areas . Besides, the scale separation principle is violated in the case of sharp transients (such as tsunami waves) impacting urban areas because the typical wavelength is of the same order of magnitude as the microscopic detail (the street/block size). Moreover, 2D shallow water equations are essentially hyperbolic, thus violating the third assumption.

These hurdles are overcome by averaging approaches. Single porosity-based, macroscopic shallow water models have been proposed , , and applied successfully to urban flood modeling scale experiments , , . They allow the CPU time to be divided by 10 to 100 compared to classical 2D shallow water models. Recent extensions of these models have been proposed in the form of integral porosity and multiple porosity shallow water models.

**Our main challenge is:
build and couple elementary models in coastal areas to improve their
capacity to simulate complex dynamics.** This challenge consists of
three principal scientific objectives. First of all, each of the elementary
models has to be consistently developed (regardless of boundary conditions
and interactions with other processes). Then open boundary conditions
(for the simulation of physical processes in bounded domains) and
links between the models (interface conditions) have to be identified
and formalized. Finally, models and boundary conditions (*i.e.*
coupled systems) should be proposed, analyzed and implemented in a
common platform.

The time-evolution of a water flow in a three-dimensional computational
domain is classically modeled by Navier-Stokes equations for incompressible
fluids.
Depending on the physical description of the considered domain, these
equations can be simplified or enriched. Consequently, there are **numerous
water dynamics models** that are derived from the original Navier-Stokes
equations, such as primitive equations, shallow water equations (see
), Boussinesq-type dispersive models ),
etc. The aforementioned models have **very different mathematical
natures**: hyperbolic *vs* parabolic, hydrostatic *vs*
non-hydrostatic, inviscid *vs* viscous, etc. They all carry
nonlinearities that make their mathematical study (existence, uniqueness
and regularity of weak and/or strong solutions) highly challenging
(not to speak about the $1M Clay competition for the 3D Navier Stokes
equations, which may remain open for some time).

The objective is to focus on the mathematical and numerical modeling
of models adapted to **nearshore dynamics**, accounting
for complicated wave processes. There exists a large range of models, from the shallow water equations (eventually weakly dispersive) to some fully dispersive deeper models. All these models can be obtained from a suitable asymptotic analysis of the water wave equations (Zakharov formulation) and if the theoretical study of these equations has been recently investigated , there is still some serious numerical challenges. So we plan to focus on the derivation and implementation of robust and high order discretization methods for suitable two dimensional models, including enhanced fully nonlinear dispersive models and fully dispersive models, like the Matsuno-generalized approach proposed in . Another objective is to study the shallow water dispersive models without any irrotational flow assumption. Such a study would be of great interest for the study of nearshore circulation (wave induced rip currents).

For obvious physical and/or computational reasons, our models are
set in bounded domains. Two types
of boundaries are considered: physical and mathematical. Physical boundaries are materialized
by an existing interface (atmosphere/ocean, ocean/sand, shoreline,
etc.) whereas mathematical boundaries appear with the truncation of
the domain of interest. In the
latter
case, **open boundary conditions** are mandatory in order not to create
spurious reflexions at the boundaries. Such
boundary conditions being nonlocal and impossible to use in practice,
we shall look for approximations. We shall obtain them thanks to the
asymptotic analysis of the (pseudo-differential) boundary operators
with respect to small parameters (viscosity, domain aspect ratio,
Rossby number, etc.). Naturally, we **will seek
the boundary conditions leading
to the best compromise** between mathematical well-posedness
and physical consistency. This will make extensive use
of the mathematical theory of **absorbing operators** and their
approximations .

The Green-Naghdi equations provide a correct description of the waves
up to the breaking point while the Saint-Venant equations are more
suitable for the description of the surf zone (i.e. after the breaking). Therefore, the challenge here is first to **design a coupling strategy** between these two systems of equations, first in a simplified one-dimensional case, then to
the two-dimensional case both on cartesian and unstructured grids. High order accuracy should be achieved through the use of flexible Discontinuous-Galerkin methods.

Additionally, we will couple our weakly dispersive shallow water models to other fully dispersive deeper water models. We plan to mathematically analyze the coupling between these models. In a first step, we have to understand well the mixed problem (initial and boundary conditions) for these systems. In a second step, these new mathematical development have to be embedded within a numerically efficient strong coupling approach. The deep water model should be fully dispersive (solved using spectral methods, for instance) and the shallow-water model will be, in a first approach, the Saint-Venant equations. Then, when the 2D extension of the currently developped Green-Naghdi numerical code will be available, the improved coupling with a weakly dispersive shallow water model should be considered.

In the context of Schwarz relaxation methods, usual techniques can be seen as the first iteration
(not converged) of an iterative algorithm. Thanks to the work performed
on efficient boundary conditions, we shall **improve the quality
of current coupling algorithms**, allowing for qualitatively satisfying
solutions **with a reduced computational cost** (small number
of iterations).

We are also willing to explore the role of geophysical processes on some biological ones. For example, the design of optimal shellfish farms relies on confinement maps and plankton dynamics, which strongly depend on long-time averaged currents. Equations that model the time evolution of species in a coastal ecosystem are relatively simple from a modeling viewpoint: they mainly consist of ODEs, and possibly advection-diffusion equations. The issue we want to tackle is the choice of the fluid model that should be coupled to them, accounting for the important time scales discrepancy between biological (evolution) processes and coastal fluid dynamics. Discrimination criteria between refined models (such as turbulent Navier-Stokes) and cheap ones (see ) will be proposed.

**Coastal processes evolve at very different time scales**: atmosphere
(seconds/minutes), ocean (hours), sediment (months/years) and species
evolution (years/decades). Their coupling can be seen as a *slow-fast*
dynamical system, and a naïve way to couple them would be to
pick the smallest time-step and run the two models together: but the
computational cost would then be way too large. Consequently **homogenization
techniques or other upscaling methods**
should be used in order to account for these various time scales at
an affordable computational cost. The research objectives are the following:

So far, the proposed upscaled models have been validated against theoretical results obtained from refined 2D shallow water models and/or very limited data sets from scale model experiments. The various approaches proposed in the literature , , , , , , , , have not been compared over the same data sets. Part of the research effort will focus on the extensive validation of the models on the basis of scale model experiments. Active cooperation will be sought with a number of national and international Academic partners involved in urban hydraulics (UCL Louvain-la-Neuve, IMFS Strasbourg, Irvine University California) with operational experimental facilities.

Upscaling of source terms. Two types of source terms play a key role
in shallow water models: geometry-induced source terms (arising from
the irregular bathymetry) and friction/turbulence-induced energy loss
terms. In all the upscaled shallow water models presented so far,
only the large scale effects of topographical variations have been
upscaled. In the case of wetting/drying phenomena and small depths
(e.g. the *Camargue* tidal flats), however, it is forseen that
subgrid-scale topographic variations may play a predominant role.
Research on the integration of subgrid-scale topography into macrosocopic
shallow water models is thus needed. Upscaling of friction/turbulence-induced
head loss terms is also a subject for research, with a number of competing
approaches available from the literature , , , .

Upscaling of transport processes. The upscaling of surface pollutant transport processes in the urban environment has not been addressed so far in the literature. Free surface flows in urban areas are characterized by strongly variable (in both time and space) flow fields. Dead/swirling zones have been shown to play a predominant role in the upscaling of the flow equations , . Their role is expected to be even stronger in the upscaling of contaminant transport. While numerical experiments indicate that the microscopic hydrodynamic time scales are small compared to the macroscopic time scales, theoretical considerations indicate that this may not be the case with scalar transport. Trapping phenomena at the microscopic scale are well-known to be upscaled in the form of fractional dynamics models in the long time limit , . The difficulty in the present research is that upscaling is not sought only for the long time limit but also for all time scales. Fractional dynamics will thus probably not suffice to a proper upscaling of the transport equations at all time scales.

As a long term objective, the team shall create a common architecture for existing codes, and
also the future codes developed by the project members, to offer a
simplified management of various evolutions and a single and well
documented tool for our partners. It will aim to be self-contained
including pre and post-processing tools (efficient meshing approaches,
GMT and VTK libraries), but must of course also be opened to user's
suggestions, and account for existing tools inside and outside Inria.
This numerical platform will be dedicated to the simulation
of all the phenomena of interest, including flow propagation, sediment
evolution, model coupling on large scales, from deep water to the
shoreline, including swell propagation, shoaling, breaking and run-up.
This numerical platform clearly aims at becoming a reference software
in the community. It should be used to **develop a specific
test case** around Montpellier which embeds many processes and their
mutual interactions: from the *Camargue* (where the Rhône river
flows into the Mediterranean sea) to the *Étang de Thau* (a
wide lagoon where shellfishes are plentiful), **all the processes
studied in the project occur in a 100km wide region**, including of
course the various hydrodynamics regimes (from the deep sea to the
shoaling, surf and swash zones) and crucial morphodynamic issues (*e.g.*
in the town of Sete).

Saint-Venant and Boussinesq equations have been widely applied until recently to model and simulate the propagation and transformations of waves in the nearshore area, over rapidly varying topography. However, the first equations do not include dispersive effects, and consequently have a domain of validity limited to the surf zone. The second set of equations overcome the limitations of the SV equations but relies on a “small amplitude assumption” and is therefore unable to model the whole range of waves transformations. This is the reason why they are usually called “weakly nonlinear Boussinesq equations”. A better suited set of equations is known as the Green-Naghdi equations, but until recently, they have received far less attention, both from the theoretical and numerical point of view. In particular, there is no available numerical method of arbitrary ordre for 2d simulations on unstructured meshes. Additionally, the construction of rigorous positive preserving schemes is a paramount for the study of waves run-up.

Floods have been identified by the National Accounting Authority (Cour des Comptes) to represent up to 1% of the GNP in terms of damage cost. For crisis management purposes, modeling urban floods at the scale of the conurbation is highly desirable. This however cannot be achieved in the current state of technology because of the meshing and computational cost (up to one billion cells being needed to mesh an entire urban area). This can be overcome by upscaling the shallow water equations so as to obtain large scale models that can operate three orders of magnitude faster than refined 2D models. Various upscaled versions of the upscaled 2D Shallow Water Equations have been proposed in the literature, some of which by members of the Lemon team. Further developments are being carried out, including the subgrid-scale description of topography variations and a better representation of energy dissipation terms. Laboratory experiments are also needed to discriminate between the various existing models.

Shallow Water (SW) models are widely used for the numerical modeling of river flows. Depending on the geometry of the domain, of the flow regime, and of required accuracy, either 1D or 2D SW models are implemented. It is thus necessary to couple 1D models with 2D models when both models are used to represent different portions of the same river. Moreover, when a river flows into the sea/ocean (e.g. the Rhône river in the Mediterranean), one may need to couple a 2D SW with a full 3D model (such as the Navier-Stokes equations) of the estuary. These issues have been widely addressed by the river-engineering community, but often with somehow crude approaches in terms of coupling algorithms. This may be improved thanks to more advanced boundary conditions, and with the use of Schwarz iterative methods for example.

Antoine ROUSSEAU spent 9 months in the office of Inria Chile (Santiago, Chile) from February to October 2016 to collaborate on the new project on *Marine Energies Research International Center* (MERIC) in Chile. Antoine is the scientific coordinator of the research line “Advanced modeling for marine energy”, and several members of LEMON, CARDAMOM and TOSCA research teams will be involved in this 8 years project in partnership with DCNS and Enel.

Tsunami-Lab is an educational platform enabling simulation and visualization of tsunami effects in real time, with several historical scenarios and the possibility to build your own one. The target of this project is to provide students as well as general audience with an educational tool, intended to reduce tsunamis impact in Chile and help sparing human lives.

Tsunami-Lab was initated by José Galaz, engineer in mathematics and civil ingeneering, when he was working at the National Research Center for Integrated Gestion of Natural Hazards (CIGIDEN). The app is born with the match of a need - teach general audience more efficient methods to decrease tsunamis impact and spare human lives - and the use of new technologies. Later, a collaboration came up between CIGIDEN, Inria Chile and Inria (team LEMON) in order to optimize this project development.

Participant: Antoine Rousseau

Contact: José Galaz, jdgalazm@gmail.com

Urban floods are usually simulated using two-dimensional shallow water models. A correct representation of the urban geometry and hydraulics would require that the average computational cell size be between 0.1 m and 1 m. The meshing and computation costs make the simulation of entire districts/conurbations impracticable in the current state of computer technology.

An alternative approach consists in upscaling the shallow water equations using averaging techniques. This leads to introducing storage and conveyance porosities, as well as additional source terms, in the mass and momentum balance equations. Various versions of porosity-based shallow water models have been proposed in the literature. The Shallow Water 2 Dimensions (SW2D) computational code embeds various finite volume discretizations of these models. Ituses fully unstructured meshes with arbitrary numbers of edges. The key features of the models and numerical techniques embedded in SW2D are

specific momentum/energy dissipation models that are active only under transient conditions. Such models, that are not present in classical shallow water models, stem from the upscaling of the shallow water equations and prove essential in modeling the features of fast urban flow transients accurately

three different closure relationships between the averaged flow variables and porosity-based fluxes

modified HLLC solvers for an improved discretization of the momentum source terms stemming from porosity gradients

higher-order reconstruction techniques that allow for faster and more stable calculations in the presence of wetting/drying fronts.

Contact: Vincent Guinot

The computation of the wind at small scale and the estimation of its uncertainties is of particular importance for applications such as wind energy resource estimation. To this aim, starting in 2005, we have developed a new method based on the combination of an existing Numerical Weather Prediction model providing a coarse prediction, and a Lagrangian Stochastic Model for turbulent flows. This Stochastic Downscaling Method (SDM) requires a specific modeling of the turbulence closure, and involves various simulation techniques whose combination is totally original (such as Poisson solvers, optimal transportation mass algorithm, original Euler scheme for confined Langevin stochastic processes, and stochastic particle methods).

In 2013, WindPoS became the kernel of the wind farm modeling of the Fundacion Inria Chile. In France, its development is going on through the collaborative Modéol project on the evaluation of wind potential.

This is a joint work with Mireille Bossy from the team TOSCA.

Contact: Mireille Bossy, mireille.bossy@inria.fr

In , we work on nontraditional models where the so-called traditional approximation on the Coriolis force is removed. In the derivation of the quasi-geostrophic equations, we obtain new terms in δ/ε, where the domain aspect ratio and the Rossby number are both small numbers. We provide here some rigorous crossed-asymptotics with regards to these parameters , prove some mathematical and physical results on the nontraditional models, and situate them among traditional ones. This was also published as lecture notes given by Antoine ROUSSEAU in 2014: see .

In 2015, Sélim Cornet developed a numerical model for the hydrodynamics of Vaccares system in Camargue. The data and reference simulations (made with TELEMAC-2D) were provided by Tour du Valat (contact O. Boutron). Sélim's work consisted in the implementation and validation of the porosity shallow water model developped by Vincent GUINOT , in order to obtain accurate but inexpensive simulations of the Vaccares hydrosystem. In 2016, we identified inconsistencies in the porosity closure model. These modeling issues have been analysed and a new theoretical approach, including new energy principles in the derivation of the porosity model, are under investigation.

Solute dispersion in porous media is usually modelled using Fick's law or fractional variations of the solute dispersion equation. The Fickian model, however, is known to exhibit a number of drawbacks, such as poor scaling properties. This is also true for its fractional counterparts, that perform with limited success when compared to experimental data sets. In , a high-quality experimental device is built in the form of periodic heterogeneities (Model Heterogeneous Porous Medium) of length 15 cm. Placing up to 10 MHPM in series allows the scaling properties of the dispersion model to be analyzed. Besides providing a high quality experimental database, the results in indicate that (i) previously identified scaling trends for the dispersion coefficient may easily be explained by experiment variability, (ii) there exists a linear transport model that allows the experimental behaviour to be reproduced at all scales, (iii) this model is not the advection-dispersion model (even fractional). More experiments have been performed this year with a different connexion between each MHPM. More experiments have been performed this year with a different connexion between each MHPM. The benchmarking of various numerical models is currently under process; it includes classical models such as Advection-Diffusion, Mobile-Immobile, Multi Rate … as well as a proposed Purely Advective Multi Region model.

In collaboration with Mohsen Chebbi (ENIT, Tunis) and Salwa Toumi (ENIT, Tunis), we propose stochastic models of anaerobic membrane bioreactors . These biotechnology processes are usually described as differential equations valid at large population scale. We propose model at different scales. At the microscopic scale, we consider a pure jump stochastic model that can be exactly simulated. However, when the size of the population is large that type of exact simulation is not feasible, hence we propose approximated simulation methods in discrete time, of the Poisson type or of the diffusive type. We establish the law of large numbers and the central limit theorem of the functional type.

We also consider different problems of simultaneous filtering and parameter estimation for hidden Markov models: in collaboration with Samuel Nyobe Som (University of Yaoundé 1) we study natural ressources examples; in collaboration with Oussama Hadj-Abdelkader (University of Tlemcen) we study applications in biotechnology. In both cases the fact that the frequency of data acquisition is slow enough to improve classical techniques.

Hydrodynamic models in two dimensions require a precise knowledge of the domain topography, but data acquisition (field surveys, RADAR, etc.) remains difficult to set up at a large scale. Progress in remote sensing data now allows the automatic monitoring of water surfaces delineation from areal or satellite images (e.g. ); and flood dynamics from remote sensing data are known to be informative on floodplain topography for long. The idea is thus to combine sparse punctual information (obtained from ground survey) with continuous contour lines (obtained from image treatment) to better assess the domain topography. Two different approaches have been tested during Mathieu Dartevelle’s internship (3 months): the first one is based on geostatistical considerations (kriging and conditional simulations) and the second one, deterministic, uses spline functions obtained from a minimisation process. The main challenge stands in the fact that, if the contour line is known to be an isovalue curve, its elevation is not known. First results have been presented in but work is still needed especially to retrieve a precise estimation of curve elevation from very few data points. This work is done in collaboration with Jean-Stéphane Bailly (Lisah, AgroParisTech Montpellier).

In collaboration with Coralie Fritsch (Inria Nancy) and Otso Ovaskainen (University of Helsinki), we propose a numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds . Though the method is general, we illustrate this method with a mass-structured individual-based chemostat model. We assume that the mutations are rare and that the resident population is large, in which case the mutant population can be viewed, on a short time scale, as evolving in a constant environment. Both deterministic and stochastic models can be proposed to describe such a problem. We exploit a previously derived mathematical relationship between these models to derive a general method for analyzing the invasion fitness of stochastic models.

In collaboration with Nicolas Champagnat and Coralie Fritsch (Inria Nancy), we studied the variations of the principal eigenvalue associated to a growth-fragmentation-death equation with respect to a parameter . We use the probabilistic individual-based interpretation of the model. We study the variations of the survival probability of the stochastic model, using a generation by generation approach. Then, making use of the link between the survival probability and the principal eigenvalue established in a previous work, we deduce the variations of the eigenvalue with respect to the parameter of the model.

The finite volume-based, SW2D computational code (see Software section) is used by Cereg Ingénierie and Enveo (Montpellier Lavérune location) on a regular basis to carry out flood risk assessment studies. The code is constantly being developed on a work-for-hire basis depending on the company needs. The developments mostly concern pre- and post-processing functionalities, as well as specific hydraulic modules.

A two-dimensional shallow water with depth-variable porosity has been developed. The depth-variable porosity allows the subgrid-scale variations of the topography and hydraulic connectivity to be accounted for. The governing equations are written in conservation form and solved using a finite volume scheme. This allows the CPU time of the computational code to be divided by 2 to 3 orders of magnitude. The model is currently being tested against in situ measurements in the Vaccarès system in collaboration with Tour du Valat.

Antoine ROUSSEAU collaborates with ARTELIA in the framework of M-P Daou's PhD thesis (CIFRE).

**Cart'Eaux** project (European Regional Development Fund (ERDF)): in partnership with colleagues of LIRMM and HSM (Montpellier) and with Berger-Levrault company, Carole DELENNE and Benjamin COMMANDRE are developing a methodology that will collect and merge multi-sources data in the aim of mapping urban drainage networks for hydraulic modeling purpose. This chain of treatment includes: i) detection of manhole covers from remote sensing data (aerial images, numerical elevation models…), 2) development of an algorithm to retrieve the network from the detected points and other information such as roads or topography, 3) data manning to extract useful characteristics for the hydraulic model, from various databases available or from documents automatically gathered from the web. A confidence index will be given to each characteristic assessed and a sensitivity analysis will enable the software to propose a hydraulic model together with an associated uncertainty.

The GeRIMU project (Gestion du Risque d'Inondation en Milieu Urbain) counts 3 partners: Cerec Ingénierie, HSM and Predict Services. In this porject, the upscaled shallow water model with porosity SW2D developed at HSM is embedded in a software chain that will allow fast uran flood computations from forecasted precisiptation fields. The project is funded under the Feder scheme. It has earned a distinction from the local Scientific Advisory Committee ("Coup de coeur du COSTI").

Fabien MARCHE is member of the ANR project BonD (PI Sylvie Benzoni), 2013-2017

Fabien MARCHE is member of the ANR project ACHYLLES (PI Rodolphe Turpault), 2014-2017

Fabien CAMPILLO is member of the ANR project Slofadybio, 2015-2016

Antoine ROUSSEAU is member of the ANR project ANSWER (PI Céline Casenave), 2016-2019

Vincent GUINOT was the main investigator of an International Training Network (ITN) proposal in 2016. The proposal was not accepted and will be submitted again in 2017, accounting for the remarks made by the reviewers.

Antoine ROUSSEAU spent 9 months at Inria Chile from January to October 2016.

In 2015, the *Marine Energies Research International Center* (MERIC) was launched in Chile by CORFO. Antoine ROUSSEAU will be the scientific coordinator for Inria, and several members of LEMON, CARDAMOM and TOSCA research teams will be involved in this 8 years project driven by DCNS. Antoine ROUSSEAU and Fabien MARCHE are involved in the research line *advanced modeling for marine energy*.

Vincent GUINOT collaborates with B.F. Sanders (Irvine University, Californie, USA)

Carole DELENNE and Vincent GUINOT collaborates with S. Soares-Frazao (Unité de Génie Civil, Université catholique de Louvain, Belgium)

Antoine ROUSSEAU continues to collaborate with H. Ramirez (CMM, Santiago) and P. Gajardo (UTFSM, Valparaiso) after the end of the Inria associated team Dymecos (2015).

Antoine ROUSSEAU spent 9 months at Inria Chile from January to October 2016. He co-advised 2 master students and 1 research engineer in the framework of the MERIC project in Chile. Antoine ROUSSEAU also participated to the Tsunamilab project between Inria Chile and CIGIDEN.

Vincent GUINOT : Journal of Hydroinformatics.

Antoine ROUSSEAU : Discrete and Continuous Dynamical Systems, Series S.

Fabien MARCHE : Advances in Applied Mathematics and Mechanics, International Journal for Numerical Methods in Fluids, Journal of Applied and Computational Mathematics, Journal of Computational Physics, Journal of Scientific Computing and SIAM Journal on Scientific Computing.

Vincent GUINOT : Journal of Hydrology and Journal of Hydroinformatics.

Antoine ROUSSEAU : Applied Numerical Mathematics, International Journal for Numerical Methods in Fluids.

Carole DELENNE workshop « Modelling the flood peril » Paris, May 30th and 31st, Université Pierre et Marie Curie

Antoine ROUSSEAU : Café Scientifique (Institut Français de Santiago, Ambassade de France), August 6th, 2016

Antoine ROUSSEAU : 4th French-Chilean workshop on Bioprocess Modeling, Santiago, Sept. 2016

Antoine ROUSSEAU belongs to the workgroup dedicated to the development of SELECT, an Inria internal software to manage scientific recruitment. Carole DELENNE responsable d’année EGC3, direction des études EGC et tutorat de 5 apprentis (je sais pas où ca se met…)

F. Campillo, Stochastic modelling of ecosystems, 20 h, M2R Biostatistics, Univ. Montpellier

F. Campillo, Object oriented programming: probabilistic modeling and statistical numerics for biology, 20 h, Doctoral lectures, Univ. Montpellier

C. Delenne, Méthodes mathématiques pour l’ingénieur, 10.5H CM, 22.5hTD, L3, Polytech Montpellier

C. Delenne, Hydraulique, 60hTP, M1, Polytech Montpellier

C. Delenne, Hydraulic transients, 27hTD, M1, Polytech Montpellier

C. Delenne, Modélisation hydraulique à surface libre 2D, 6h TD, M2, Polytech Montpellier

C. Delenne, Tutorat de stages et projets, 77hETD, L3-M2, Polytech Montpellier

C. Delenne, Mathématiques, 15h CM, 15hTD, L3 (apprentissage), Polytech Montpellier

C. Delenne, Hydraulique, 28hTD, L1, IUT Génie Civil, Nîmes

V. Guinot, Mécanique des fluides, 72h ETD, L3, Polytech'Montpellier

V. Guinot, Hydraulique à surface libre, 60h ETD, L3, Polytech'Montpellier

V. Guinot, Méthodes Mathématiques pour l'Ingénieur, 18h ETD, M1, Polytech'Montpellier

V. Guinot, Hydraulique des Réseaux, 30h ETD, M1, Polytech'Montpellier

V. Guinot, Mécanique des Fluides, Master SPAE, 36h ETD, M1, UMontpellier

V. Guinot, Transitoires hydrauliques, 54 h ETD, M1, Polytech'Montpellier

V. Guinot, tutorat de stages ingénieur, 15h ETD, M1, Polytech'Montpellier

V. Guinot, Modélisation hydraulique à surface libre 2D, 6h ETD, M2, Polytech'Montpellier

V. Guinot, Projet Industriel de Fin d'Etudes (PIFE), 30h ETD, M2, Polytech'Montpellier

V. Guinot, Tutorat de Stage de fin d'études ingénieur, 18h ETD, M2, Polytech'Montpellier

F. Marche, Biomaths, 72h TD., L1, Université Montpellier

F. Marche, Analyse numérique des EDP, 24H CM, 12H TD, 15H TP., M1, Université Montpellier

F. Marche, Calcul scientifique avancé, 26H CM, M2R, Université Montpellier

A. Rousseau, Towards Coupling Coastal and Large Ocean Models, 6h, Master, PUC, Santiago, Chile

A. Rousseau, Introduction to numerical methods in CFD, 6h, Master, Inria Chile, Santiago, Chile

A. Rousseau, Introduction to ROMS, 12h, Master, Inria Chile and CIGIDEN, Santiago, Chile

PhD: Mehdi Pierre Daou, *Développement d'une méthodologie de couplage multi-modèles avec changements de dimension. Validation sur un cas-test réaliste en dynamique littorale*, Univ. Grenoble, Sept. 2016, Eric Blayo (EPI MOISE) and Antoine Rousseau

PhD in progress: Mohsen Chebbi, Modélisation stochastique de procédés membranaires de traitement des eaux usées. September 2014, S. Toumi (ENIT, Tunis) and F. Campillo

PhD in progress: Oussama Hadj-Abdelkader, Filtrage particulaire pour le chemostat. September 2014, A. Hadj-Abdelkader (Univ. Tlemcen) and F. Campillo

Carole DELENNE : Jury member: Andriarimina Daniel Rakotonirina, *Fluid-solid interactions in a non-convex granular media: application to rotating drums and packed bed reactors*, december 2016, ENS Lyon

Antoine ROUSSEAU : Referee and jury member: Mrs Souad Khiari, *Problèmes Inverses de Points Sources dans les Modèles de Transport Dispersif de Contaminants
Identifiabilité et Observabilité*, October 2016, Université de Technologie de Compiègne & Université de Tunis El-Manar / ENIT

Antoine ROUSSEAU : Jury member: M. Mehdi Pierre Daou, *Développement d'une méthodologie de couplage multi-modèles avec changements de dimension. Validation sur un cas-test réaliste en dynamique littorale*, September 2016, Univ. Grenoble

Antoine ROUSSEAU : Jury member: M. Victor Riquelme, *Problemas de control óptimo para la bioremediación de recursos acuíferos*, September 2016, Univ. de Chile, Santiago & Univ. Montpellier

Fabien MARCHE : Jury member: Mrs Nora Aissiouene, *Analyse numérique et approximation discrète d’un modèle dispersif en eau peu profonde*, December 2016, Univ. Pierre et Marie Curie, Paris

Antoine ROUSSEAU : Jury member: Mrs Carine Lucas, *Modélisation de problèmes de mécanique des fluides : approches théoriques et numériques*, December 2016, Université d'Orléans

Teaching manager of the department "Water and Civil Engineering", Polytech Montpellier, in charge of the first year of the training. Academic supervisor of 5 apprentices.

Antoine ROUSSEAU gave several conferences for highschool students and their teachers in France and Chile, on the topics of mathematical modeling for environmental sciences:

*Fête de la Science*, Oct. 2016, Genopolys Montpellier

*Café Cientificó*, Aug. 2016, Instituto Francés, Santiago, Chile

Antoine ROUSSEAU is member of the national Inria network for scientific outreach *Médiation scientifique*

Antoine ROUSSEAU is member of the editorial board of Interstices

Antoine ROUSSEAU co-authored the Calendrier Mathématique 2017