5.1.1 2DLayeredMotion

• Name: Estimation of 2D independent mesoscale layered atmospheric motion fields
• Functional Description: This software enables to estimate a stack of 2D horizontal wind fields corresponding to a mesoscale dynamics of atmospheric pressure layers. This estimator is formulated as the minimization of a global energy function. It relies on a vertical decomposition of the atmosphere into pressure layers. This estimator uses pressure data and classification clouds maps and top of clouds pressure maps (or infra-red images). All these images are routinely supplied by the EUMETSAT consortium which handles the Meteosat and MSG satellite data distribution. The energy function relies on a data model built from the integration of the mass conservation on each layer. The estimator also includes a simplified and filtered shallow water dynamical model as temporal smoother and second-order div-curl spatial regularizer. The estimator may also incorporate correlation-based vector fields as additional observations. These correlation vectors are also routinely provided by the Eumetsat consortium.
• URL: http://fluid.irisa.fr/index.html
• Contact: Étienne Mémin
• Participant: Étienne Mémin

5.1.2 3DLayeredMotion

• Name: Estimation of 3D interconnected layered atmospheric motion fields
• Functional Description: This software extends the previous 2D version. It allows (for the first time to our knowledge) the recovery of 3D wind fields from satellite image sequences. As with the previous techniques, the atmosphere is decomposed into a stack of pressure layers. The estimation relies also on pressure data and classification clouds maps and top of clouds pressure maps. In order to recover the 3D missing velocity information, physical knowledge on 3D mass exchanges between layers has been introduced in the data model. The corresponding data model appears to be a generalization of the previous data model constructed from a vertical integration of the continuity equation.
• URL: http://fluid.irisa.fr
• Contact: Étienne Mémin

5.1.3 DenseMotion

• Name: Estimation of 2D dense motion fields
• Functional Description: This code allows the computation from two consecutive images of a dense motion field. The estimator is expressed as a global energy function minimization. The code enables the choice of different data models and different regularization functionals depending on the targeted application. Generic motion estimators for video sequences or fluid flows dedicated estimators can be set up. This software allows in addition the users to specify additional correlation based matching measurements. It enables also the inclusion of a temporal smoothing prior relying on a velocity vorticity formulation of the Navier-Stoke equation for Fluid motion analysis applications.
• URL: http://fluid.irisa.fr/index.html
• Contact: Étienne Mémin
• Participant: Étienne Mémin

5.1.4 Low-Order-Motion

• Name: Estimation of low order representation of fluid motion
• Functional Description: This code enables the estimation of a low order representation of a fluid motion field from two consecutive images.The fluid motion representation is obtained using a discretization of the vorticity and divergence maps through regularized Dirac measure. The irrotational and solenoidal components of the motion fields are expressed as linear combinations of basis functions obtained through the Biot-Savart law. The coefficient values and the basis function parameters are formalized as the minimizer of a functional relying on an intensity variation model obtained from an integrated version of the mass conservation principle of fluid mechanics.
• URL: http://fluid.irisa.fr
• Contact: Étienne Mémin
• Participants: Anne Cuzol, Étienne Mémin

5.1.5 TYPHOON

• Keyword: Fluid mechanics
• Functional Description: Typhoon is a fluid motion estimator from image sequences. It is almost real-time dedicated to the measurement of LIDAR sequences, multi-scale, fast and precise to make a fine scale analysis of fluid flows with applications in the fields of energy, transport and environment.
• URL: https://phys.csuchico.edu/lidar/typhoon/
• Authors: Pierre Dérian, Christopher Mauzey, Étienne Mémin
• Contact: Étienne Mémin
• Participants: Christopher Mauzey, Étienne Mémin, Pierre Dérian
• Partner: CSU Chico

5.1.6 H2OLab

• Keywords: Simulation, Energy, Contamination, Groundwater, Hydrogeology, Heterogeneity, Uncertainly, Multiscale
• Scientific Description: The software platform contains a database which is interfaced through the web portal H2OWeb. It contains also software modules which can be used through the interface H2OGuilde. The platform H2OLab is an essential tool for the dissemination of scientific results. Currently, software and database are shared by the partners of the h2mno4 project.
• Functional Description:

  The software platform H2OLab is devoted to stochastic simulations of groundwater flow and contaminant transport in highly heterogeneous porous and fractured geological media.

  -Modeling and numerical simulation of aquifers -Porous and fractured heterogeneous media -Flow with mixed finite elements -Solute transport with a Lagrangian method -Stochastic modeling for data uncertainty.

• URL: http://h2olab.inria.fr/
• Contact: Jocelyne Erhel
• Participants: Géraldine Pichot, Grégoire Lecourt, Jean-Raynald De Dreuzy, Jocelyne Erhel
• Partners: Université de Rennes 1, CNRS, Université de Lyon, Université de Poitiers

5.1.7 PALMTREE

• Keyword: Monte-Clarlo
• Functional Description:

  We present an easy-to-use package for the parallelization of Lagrangian methods for partial differential equations. In addition to the reduction of computation time, the code aims at satisfying three properties:

  simplicity: the user just has to add the algorithm governing the behaviour of the particles. portability: the possibility to use the package with any compiler and OS. action-replay: the ability of the package to replay a selected batch of particles.

  The last property allows the user to replay and capture the whole sample path for selected particles of a batch. This feature is very useful for debugging and catching some relevant information.

• Authors: Lionel Lenôtre, Géraldine Pichot, Lionel Lenôtre, Lionel Lenôtre
• Contacts: Jocelyne Erhel, Géraldine Pichot

5.1.8 GRT3D

• Name: Global Reactive Transport in 3D
• Keywords: Geochemistry, Dispersion, Scientific calculation, Simulation, Advection
• Scientific Description:

  Participants : Édouard Canot, Jocelyne Erhel [correspondant] .

  Version: version 2.0, April 2014

  APP: registered

  Programming language: C

  Abstract: Reactive transport modeling has become an essential tool for understanding complex environmental problems. It is an important issue for MoMaS and C2S@EXA partners (see sections 8.2.5 , 8.2.3 ), in particular Andra. We have developed a method coupling transport and chemistry, based on a method of lines such that spatial discretization leads to a semi-discrete system of algebraic differential equations (DAE system). The main advantage is to use a complex DAE solver, which controls simultaneously the timestep and the convergence of Newton algorithm. The approach SIA uses a fixed-point method to solve the nonlinear system at each timestep, whereas the approach SNIA uses an explicit scheme.

  The software suite GRT3D has four executable modules:

  SIA1D: Sequential Iterative Approach for 1D domains,

  GDAE1D: Global DAE approach for 1D domains,

  SNIA3D: Sequential Non Iterative Approach for 1D, 2D or 3D domains.

  GDAE3D: Global DAE approach for 1D, 2D or 3D domains. This module has three variants: the original one with logarithms, an optimized one still with logarithms, an optimized one which does not use logarithms.

  Current work: extension of the chemistry module and parallelization.

• Functional Description:

  Reactive transport modeling has become an essential tool for understanding complex environmental problems. It is an important issue for MoMaS and C2S@EXA partners, in particular Andra. We have developed a method coupling transport and chemistry, based on a method of lines such that spatial discretization leads to a semi-discrete system of algebraic differential equations (DAE system). The main advantage is to use a complex DAE solver, which controls simultaneously the timestep and the convergence of Newton algorithm. The approach SIA uses a fixed-point method to solve the nonlinear system at each timestep, whereas the approach SNIA uses an explicit scheme.

  The software suite GRT3D has four executable modules:

  SIA1D: Sequential Iterative Approach for 1D domains,

  GDAE1D: Global DAE approach for 1D domains,

  SNIA3D: Sequential Non Iterative Approach for 1D, 2D or 3D domains.

  GDAE3D: Global DAE approach for 1D, 2D or 3D domains. This module has three variants: the original one with logarithms, an optimized one still with logarithms, an optimized one which does not use logarithms.

• Authors: Caroline De Dieuleveult, Jocelyne Erhel, Souhila Sabit, Nadir Soualem
• Contact: Jocelyne Erhel
• Participants: Caroline De Dieuleveult, Édouard Canot, Jocelyne Erhel, Nadir Soualem, Souhila Sabit
• Partner: ANDRA

6.1.1 Monocular 3D reconstruction for image-based velocity estimation

Participants: Etienne Mémin.

6.1.2 Development of an image-based measurement method for large-scale characterization of indoor airflows

Participants: Dominique Heitz, Etienne Mémin, Romain Schuster.

6.1.3 3D flows reconstruction from image data

Participants: Dominique Heitz, Etienne Mémin.

6.2.1 Optimal control techniques for the coupling of large scale dynamical systems and image data

Participants: Mohamed Yacine Ben Ali, Pranav Chandramouli, Dominique Heitz, Etienne Mémin, Gilles Tissot.

In another axis of research, in collaboration with the CSTB Nantes centre and within the PhD of Yacine Ben Ali we will explore the definition of efficient data assimilation schemes for wind engineering. The goal is here to couple Reynolds average model to pressure data at the surface of buildings. Several techniques have been proposed to that end. We show in particular that optimisation conducted in Sobolev space is highly beneficial as it brings natural smoothing to the sought solutions and avoid the use of regularization penalty. The techniques proposed consists in correcting the equations related to turbulent kinetic energy and dissipation 43.

6.2.2 Ensemble data assimilation of large-scale dynamics with uncertainty

Participants: Benjamin Dufée, Etienne Mémin.

6.2.3 Reduced-order models for flows representation from image data

Participants: Dominique Heitz, Etienne Mémin, Gilles Tissot.

6.2.4 Learning of the dynamics of large scale geophysical systems using semi-group theory for data assimilation

Participants: Berenger Hug, Etienne Mémin, Gilles Tissot.

6.2.5 Estimation and control of amplifier flows

Participants: Gilles Tissot.

A class of flows, denoted "oscillator flows", are characterised by unstable modes of the linearised operator. A consequence is the dominance of relatively regular oscillations associated with a nonlinear saturation. Despite the non-linear behaviour, associated structures and dynamical evolution are relatively easy to predict. Canonical configurations are the cylinder wake flow or the flow over an open cavity.

By opposition to that, "amplifier flows" are linearly stable with regard to the linearised operator. However, due to their convective nature, a wide range of perturbations are amplified in time and convected away such that it vanishes at long time. The consequence is the high sensitivity to perturbations and the broad band response that forbid a low rank representation. Jets and mixing layers show this behaviour and a wide range of industrial applications are affected by these broad band perturbations. It constitutes then a class of problems that are worth to treat separately since it is one of the scientific locks that render hard the transfer of methodologies existing in flow control and estimation to industrial applications.

There exists a type of models, that we will denote as "parabolised", that are able to efficiently represent amplifier flows. These models, such as parabolised stability equations and one-way Navier-Stokes propagate, in the frequency domain, hydrodynamic instability waves over a given turbulent mean flow. We can note that these models, by their structure, give access to a natural experimental implementation. They are an ingredient adapted to represent the system, but have a mathematical structure strongly different from the dynamical models classically used in control and data assimilation. It is then important to develop new methodologies of control, estimation and data assimilation with these models to reach our objectives. Moreover, inventing new models by introducing the modelling under location uncertainties in these parabolised models will be perfectly adapted to represent the evolution and the variability of an instability propagating within a turbulent flow.

6.3.1 Ocean internal tide dynamics and modelling

Participants: Noé Lahaye, Gilles Tissot, Etienne Mémin.

This reseach effort addresses the dynamics of internal tides in the ocean, which are high-frequency internal waves that propagate in the oceans. These internal waves are a driver of small-scale mixing and energy dissipation in the ocean, and are key for the accuracy of ocean climate models that cannot resolve it explicitly. Some work, based on analysis of high-resolution idealized and realistic numerical simulations, has been undertaken to understand how internal tides are affected by the background currents in the ocean. A method based on linearization around the background-flow and vertical mode decomposition is implemented to study the dynamics and derive a reduced-complexity, reduced-dimension models of the propagation of the internal tides 25. Forthcoming work will extend the model through explicit dealing of uncertainties by means of stochastic calculus. We will then use this model to construct an ensemble-based data assimilation system using satellite altimeter observations and surface drifter trajectories. This aims at radically improving the estimates of the distribution of the internal tide in the ocean, which is poorly constrained to date.

6.3.2 Reduced dynamical models for geophysical flows

Participants: Noé Lahaye.

In this task, the dynamics of coherent structures in a reduced model of the ocean mixed layer was addressed. This model, the thermal rotating shallow water (TRSW) equations, is a vertically averaged model of the hydrostatic navier-stokes equations under the Boussinesq approximation and with Coriolis term, and retains the horizontal variations of density (or temperature). In the strong rotation regime, a low Rossby number asymptotic model can be derived : the Thermal Quasi-Geostrohic model. This work, in collaboration with V. Zeitlin and T. Dubos (LMD, Paris), investigated the dynamics of the coherent dipolar analytical solution in this model and the parent TRSW model. It exhibited a surprising small sale instability, leading to mixing of the thermal anomaly carried by the dipole 26. This research activity is pursued to better understand the dynamics of these models, in connexion with the STUOD project, which involve such models.

6.3.3 Geophysical flows modeling under location uncertainty

Participants: Werner Bauer, Pranav Chandramouli, Noe Lahaye, Long Li, Etienne Mémin, Gilles Tissot, Francesco Tucciarone.

In a series of papers 19, 18, 34, 35, 29 we have shown how LU modeling can be applied to provide stochastic representations of a variety of classical geophysical flows dynamics. Numerical simulations and uncertainty quantification have been performed on Quasi Geostophic approximation (QG) of oceanic models. It has been shown that LU leads to remarkable estimation of the unresolved errors opposite to classical eddy viscosity based models. The noise brings also an additional degree of freedom in the modeling step and pertinent diagnostic relations and variations of the model can be obtained with different scaling assumptions of the turbulent kinetic energy (i.e. of the noise amplitude). For a wind forced QG model in a square box, which is an idealized model of north-Atlantic circulation, we have shown that for different versions of the noise the QG LU model leads to improve long-terms statistics when compared to classical large-eddies simulation strategies. For a QG model we have demonstrated that the LU model allows conserving the global energy. We have also shown numerically that Rosby waves were conserved and that inhomogeneity of the random component triggers secondary circulations. This feature enabled us to draw a formal bridge between a classical system describing the interactions between the mean current and the surface waves and the LU model in which the turbophoresis advection term plays the role of the classical Stokes drift.

Supported by funding from Inria-Mitacs Globalink, we hosted Ruediger Brecht, PhD student at Memorial University of Newfoundland, Canada, for a period of 3 months (May to August) in the Fluminance group. During his stay, Ruediger Brecht worked on the incorporation of a stochastic representation of the small-scale velocity component of a fluid flow in a variational integrator for the rotating shallow-water equations on the sphere, already developed within the first part of its PhD work. This work published as a preprint 44 has been recently submitted to a journal paper.

6.3.4 Large eddies simulation models under location uncertainty

Participants: Pranav Chandramouli, Dominique Heitz, Etienne Mémin, Gilles Tissot.

The models under location uncertainty recently introduced by Mémin (2014) 9 provide a new outlook on LES modeling for turbulence studies. These models are derived from a stochastic transport principle. The associated stochastic conservation equations are similar to the filtered Navier- Stokes equation wherein we observe a sub-grid scale dissipation term. However, in the stochastic version, an extra term appears, termed as "velocity bias", which can be treated as a biasing/modification of the large-scale advection by the small scales. This velocity bias, introduced artificially in the literature, appears here automatically through a decorrelation assumption of the small scales at the resolved scale. All sub-grid contributions for the stochastic models are defined by the small-scale velocity auto-correlation tensor. This large scale modeling has been assed and compared to several classical large-scale models on a flow over a circular cylinder at Re 3900 and wall-bounded flows. For all these flows the modeling under uncertainty has provided better results than classicallarge eddies simulation models.

6.3.5 Variational principles for structure-preserving discretizations in stochastic fluid dynamics

Participants: Werner Bauer, Long Li, Etienne Mémin.

6.3.6 Stochastic compressible fluid dynamics

Participants: Etienne Mémin, Gilles Tissot.

We are currently working on the extension of the stochastic formulation under location uncertainty to compressible flows. The interest is to extend the formulation on the one hand to compressible fluids (for instability mechanisms involved in areoacoustics for instance, or for thermal effects in mixing layers) and on the other hand to geophysical flows where the Boussinesq equation is not valid anymore (density variations due to temperature or salinity gradients). A theoretical study has been performed that opens the door to numerical validations. In particular a baroclinic torque term has been identified that could have major effects in some situations.

6.3.7 Stochastic hydrodynamic stability under location uncertainty

Participants: Etienne Mémin, Gilles Tissot.

6.3.8 Singular and regular solutions to the Navier-Stokes equations (NSE) and relative turbulent models

Participants: Roger Lewandowski, Etienne Mémin, Ding Duong Nguyen, Benoit Pinier.

The common thread of this work is the problem set by J. Leray in 1934 : does a regular solution of the Navier- Stokes equations (NSE) with a smooth initial data develop a singularity in finite time, what is the precise structure of a global weak solution to the Navier-Stokes equations, and are we able to prove any uniqueness result of such a solution. This is a very hard problem for which there is for the moment no answer. Nevertheless, this question leads us to reconsider the theory of Leray for the study of the Navier-Stokes equations in the whole space with an additional eddy viscosity term that models the Reynolds stress in the context of large- scale flow modelling. It appears that Leray's theory cannot be generalized turnkey for this problem, so that things must be reconsidered from the beginning. This problem is approached by a regularization process using mollifiers, and particular attention must be paid to the eddy viscosity term. For this regularized problem and when the eddy viscosity has enough regularity, we have been able to prove the existence of a global unique solution that is of class C1 in time and space and that satisfies the energy balance. Moreover, when the eddy viscosity is of compact support in space, uniformly in time, we recently shown that this solution converges to a turbulent solution to the corresponding Navier-Stokes equations carried when the regularizing parameter goes to 0. These results are described in a paper published in JMAA

In the framework of the collaboration with the University of Pisa (Italy), namely with Luigi Berselli collaboration, we considered the three dimensional incompressible Navier-Stokes equations with non stationary source terms chosen in a suitable space. We proved the existence of Leray-Hopf weak solutions and that it is possible to characterize (up to sub-sequences) their long-time averages, which satisfy the Reynolds averaged equations, involving a Reynolds stress. Moreover, we showed that the turbulent dissipation is bounded by the sum of the Reynolds stress work and of the external turbulent fluxes, without any additional assumption, than that of dealing with Leray-Hopf weak solutions. This is a very nice generalisation to non stationnary source terms of a famous results by Foais. In the same work, we also considered ensemble averages of solutions, associated with a set of different forces and we proved that the fluctuations continue to have a dissipative effect on the mean flow. These results have been published in Nonlinearity. These results have been extended in the framework of POD for reduced models 21. We have studied in 20 the rate of convergence of the weak solutions u$\alpha$ of $\alpha$-regularization models to the weak solution u of the Navier-Stokes equations in the two-dimensional periodic case, as the regularization parameter $\alpha$ goes to zero. More specifically, we have considered the Leray-$\alpha$, the simplified Bardina, and the modified Leray-α models. We have improved known results in terms of convergence rates and also to show estimates valid over long-time intervals. The results also hold in the case of bounded domain with homogeneous Dirichlet boundary conditions

In another paper 27 we have shown the existence of a solution to a 1D Reynolds Averaged Navier-Stokes vertical model suitable in the atmospheric boundary layer, under suyitable assumption on the data.

We also have introduced a turbulence model including a backscatter term, which has the same structure as the Voigt model. The additional term is derived in certain specific regimes of the flow, such as the convergence to stable statistical states. We get estimates for the velocity $v$ in $L_t^{\infty }{H}_x^1\cap W_t^{1,2}{H}_x^{1/2}$, that allow us to prove the existence and uniqueness of a regular-weak solutions $(v,p)$ to the resulting system, for a given fixed eddy viscosity. We then prove a structural compactness result that highlights the robustness of the model. This allows us to pass to the limit in the quadratic source term in the equation for the turbulent kinetic energy $k$, which yields the existence of a weak solution to the corresponding Reynolds Averaged Navier-Stokes system satisfied by $(v,p,k)$. These results are published in 17. We have derived in 22 from the laws of the turbulence and Leray’s energy inequality for weak solutions of the Navier-Stokes equations, a back-scatter rotational Large Eddy Simulation model, which is the extension of the Baldwin and Lomax model to non-equilibrium problems. The model is particularly designed to mathematically describe a fluid filling a domain with solid walls and consequently the differential operators appearing in the smoothing terms are degenerate at the boundary. After the derivation of the model, we have prove some of the mathematical properties coming from the weighted energy estimates and which allow to prove existence and uniqueness of a class of regular weak solutions.

Another study in collaboration with B. Pinier, P. Chandramouli and E. Memin has been undertaken. This work takes place within the context of the PhD work of B. Pinier. We have tested the performances of an incompressible turbulence Reynolds-Averaged Navier-Stokes one-closure equation model in a boundary layer, which requires the determination of the mixing length l. A series of direct numerical simulation have been performed, with flat and non trivial topographies, to obtain by interpolation a generic formula $l=l(Re\delta ,z)$, $Re\delta$ being the frictional Reynolds number, and z the distance to the wall. Numerical simulations have been carried out at high Reynolds numbers with this turbulence model, in order to discuss its ability to properly reproduce the standard profiles observed in neutral boundary layers, and to assess its advantages, its disadvantages and its limits. We also proceeded to a mathematical analysis of the model. The study has been published 28

6.3.9 Stochastic flow model to predict the mean velocity in wall bounded flows

Participants: Roger Lewandowski, Etienne Mémin, Benoit Pinier.

To date no satisfying model exists to explain the mean velocity profile within the whole turbulent layer of canonical wall bounded flows. We propose a modification of the velocity profile expression that ensues from the stochastic representation of fluid flows dynamics proposed recently in the group and referred to as "modeling under location uncertainty" 9. This framework introduces in a rigorous way a subgrid term generalizing the eddy-viscosity assumption and an eddy-induced advection term resulting from turbulence inhomogeneity. This latter term gives rise to a theoretically well-grounded model for the transitional zone between the viscous sublayer and the turbulent sublayer. An expression of the small-scale velocity component is also provided in the viscous zone. Numerical assessment of the results have been performed for turbulent boundary layer flows, pipe flows and channel flows at various Reynolds numbers.

6.3.10 Numerical and experimental image and flow database

Participants: Pranav Chandramouli, Dominique Heitz.

6.3.11 Fast 3D flow reconstruction from 2D cross-plane observations

Participants: Pranav Chandramouli, Dominique Heitz, Etienne Mémin.

6.3.12 Dissipation mechanisms in perforated liners with grazing flow

Participants: Gilles Tissot.

6.4.1 A state space representation for the closed-loop control of shear flows

Participants: Johan Carlier, Christophe Collewet.

6.4.2 Closed-loop control of a spatially developing shear layer

Participants: Christophe Collewet, Johan Carlier.

6.4.3 Design of a DBD plasma actuator for closed-loop control

Participants: Johan Carlier, Christophe Collewet.

The goal of this study is to design a DBD plasma actuator for closed-loop control. This kind of actuator is widely used in the flow control community however, it is more appropriate to force a flow than to control it. Indeed, to control a flow under a closed-loop fashion, the action must be proportional to the control signal provided by the control law. It is unfortunately not the case with these actuators. We have modified the classical DBD plasma actuator so that the action is almost a linear fonction of the control signal. Our approach has been first experiments.

6.5.1 Reactive transport in multiphase flow

Participants: Jocelyne Erhel.

Groundwater resources are essential for life and society, and should be preserved from contamination. Pollutants are transported through the porous medium and a plume can propagate. Reactive transport models aims at simulating this dynamic contamination by coupling advection dispersion equations with chemistry equations. If chemistry is at thermodynamic equilibrium, then the system is a set of partial differential and algebraic equations (PDAE). Space discretization leads to a semi-discrete DAE system which should be discretized in time. An explicit time scheme allows an easy decoupling of transport and chemistry, but very small timesteps should be taken, leading to a very large CPU time. Therefore, an implicit time scheme is preferred, coupling transport and chemistry in a nonlinear system. The special structure of linearized systems can be used in preconditioned Newton-Krylov methods in order to improve efficiency. Some experiments illustrate the methodology and show also the need for an adaptive timestep and a control of convergence in Newton's iterations.

This work was presented at a workshop.

6.5.2 Characterizations of Solutions in Geochemistry at equilibrium

Participants: Jocelyne Erhel.

Geochemistry at thermodynamic equilibrium involves aqueous reactions and mineral precipitation or dissolution. Quantities of solute species are assumed to be strictly positive, whereas those of minerals can vanish. The mathematical model is expressed as the minimization of Gibbs energy subject to positivity of mineral quantities and conservation of mass. Optimality conditions lead to a complementarity problem. We show that, in the case of a dilute solution, this problem can also be considered as optimality conditions of another minimization problem, subject to inequality constraints. This new problem is easier to handle, both from a theoretical and a practical point of view. Then we define a partition of the total quantities in the mass conservation equation. This partition builds a precipitation diagram such that a mineral is either precipitated or dissolved in each subset. We propose a symbolic algorithm to compute this diagram. Simple numerical examples illustrate our methodology.

This work was published in the journal Computational Geosciences and presented at an international conference.

6.5.3 Mathematical models of kinetic reactions in geochemistry

Participants: Jocelyne Erhel, Bastien Hamlat.

In geochemistry, kinetic reactions can lead to the appearance or disappearance of minerals or gas. We defined two mathematical models based first on a differential inclusion system and second on a projected dynamical system. We proposed a regularization process for the first model and a projection algorithm for the second one.

This work, supported by IFPEN, was presented at a conference and a workshop.

6.6.1 Parallel GMRES

Participants: Jocelyne Erhel.

Sparse linear systems $Ax=b$ arise very often in computational science and engineering. Krylov methods are very efficient iterative methods, and restarted GMRES is a reference algorithm for non-symmetric systems. A first issue is to ensure a fast convergence, by preconditioning the system with a matrix $M$. Preconditioning must reduce the number of iterations, and be easy to solve. A second issue is to achieve high performance computing. The most time-consuming part in GMRES is to build an orthonormal basis $V$. With the Arnoldi process, many scalar products involve global communications. In order to avoid them, s-step methods have been designed to find a tradeoff between parallel performance and stability. Also, solving a system with the matrix $M$ and for multiplying a vector by the matrix $A$ should be efficient. A domain decomposition approach involves mainly local communications and is frequently used. A coarse grid correction, based on deflation for example, improves convergence. These techniques can be combined to provide fast convergence and fast parallel algorithms. Numerical results illustrate various issues and achievements.

This work was presented at an international conference (invited talk).

Contract ITGA

Participants: Dominique Heitz, Etienne Mémin.

Contract CSTB

Participants: Mohamed Yacine Ben Ali, Dominique Heitz, Etienne Mémin.

8.1.1 Participation in other international programs

Noé Lahaye and Etienne Mémin are part of the SWOT Science Team. They participate to the DIEGO project (CNES-NASA) headed by Aurélien Ponté (Ifremer). Noé Lahaye is leader of WP4: Internal tide mapping and predictability.

8.2.1 Visits to international teams

8.3.1 FP7 & H2020 Projects

Comins'lab: SEACS : Stochastic modEl-dAta-Coupled representationS for the analysis, simulation and reconstruction of upper ocean dynamics

Participants: Etienne Mémin.

ANR BECOSE : Beyond Compressive Sensing: Sparse approximation algorithms for ill-conditioned inverse problems.

Participants: Dominique Heitz.

8.4.1 IFPEN project

Participants: Jocelyne Erhel, Bastien Hamlat.

Contract with IFPEN (Institut Français du Pétrole et Energies Nouvelles) Duration: three years from October 2016. Title: Fully implicit Formulations for the Simulation of Multiphase Flow and Reactive Transport Coordination: Jocelyne Erhel. Contract with IFPEN (Institut Français du Pétrole et Energies Nouvelles). Duration: three years October 2016-September 2019. Title: Fully implicit Formulations for the Simulation of Multiphase Flow and Reactive Transport. Coordination: Jocelyne Erhel. Abstract: Modeling multiphase flow in porous media coupled with fluid-rock chemical reactions is essential in order to understand the origin of sub-surface natural resources and optimize their use. This project focused on chemistry models, with kinetic reactions. We developed a mathematical tool, which can be embedded into a reactive transport code.

8.4.2 LEFE MANU: MSOM

Participants: Long Li, Etienne Mémin.

Title: Multiple Scale Ocean Model

Duration: From 2018 to 2021

Coordination: Bruno Deremble (CNRS LMD/ENS Paris)

Abstract: The objective of this project is to propose a numerical framework of a multiscale ocean model and to demonstrate its utility in the understanding of the interaction between the mean current and eddies.

8.4.3 LEFE MANU: ADOTSAD

Participants: Gilles Tissot, Etienne Mémin.

9.2.1 Member of the editorial boards

Jocelyne Erhel

• member of the editorial board of ETNA.
• member of the editorial board of ESAIM:Proceedings and Surveys.

Etienne Mémin

• Associate editor for the Image and Vision Computing Journal (IVC)

9.2.2 Reviewer - reviewing activities

Jocelyne Erhel: Reviewer for the journals Computational Geosciences, SISC, M2AN, JCAM, PARCO

Dominique Heitz: Reviewer for Exp. in Fluids, AMI Région Auvergne Rhone Alpes

Noé Lahaye : Reviewer for Journal of Physical Oceanog­raphy, Journal of Geophysical Research:Ocean, Geophysical Research Letters, Journal of Fluid Mechanics, Physics of Fluids, Fluid Dynamics Research Etienne Mémin: Reviewer for Tellus-A, Quat. J. of the Roy. Met. Soc., Journ. of Fluid Mech., Im. Vis. Comp., Exp. in Fluids, Journ. of Comp. Phys., Journ. of Math. Imaging and Vis.

Gilles Tissot: Reviewer for Journal of Sound and Vibration, Fluid Dynamics Research, Journ. of Fluid Mech.

9.6.1 Teaching

• Licence: Jocelyne Erhel, Optimisation, 12h, niveau L3, ENSAI Rennes
• Licence : Dominique Heitz, Mécanique des fluides, 30h, niveau L2 INSA Rennes
• Master: Jocelyne Erhel, arithmétique flottante, 4h, niveau M1, INSA Rennes
• Master : Dominique Heitz, Mécanique des fluides, 25h, niveau M1, Dep GMA INSA Rennes
• Master: Roger Lewandowski, Euler and the Navier-Stokes equations, M2, master « fondamental mathematics».
• Master : Etienne Mémin, Analyse du mouvement, Master Informatique, 15h, niveau M2, Université de Rennes 1.
• Master : Etienne Mémin, Vision par ordinateur , 15h, niveau M2, ESIR Université de Rennes 1.
• Master : Etienne Mémin, Motion analysis , 9h, Master 2 SISEA Université de Rennes 1.
• Master : Gilles Tissot, mathematics for acoustics, 20h, niveau M1, Université du Mans.

9.6.2 Supervision

• PhD in progress: Clara Le Cap, Numerical simulations and field measurements of frosty events in viticultural area protected by wind machine farm: Application to the Quincy vineyard, started April 2020, supervised by Dominique Heitz, Johan Carlier, Hervé Quénol, Emmanuel Buisson.
• PhD in progress : Corentin Cazès, Experimental study of the resuspension of microparticles in air induced by transient events, started October 2020, supervised by Dominique Heitz, Lionel Fiabane, Félicie Théron, Laurence Le Coq.
• PhD in progress : Berenger Hug, analysis of stochastic models under location uncertainty started November 2020, supervisors: Etienne Mémin, Arnaud Debussche.
• PhD in progress: Benjamin Dufée, Particle filters in high dimentional spaces, started November 2020, supervisors: Dan Crisan, Etienne Mémin
• PhD in progress: Francesco Tuccarone, Stochastic models for high resolution oceanic odels, started November 2020, Etienne Mémin
• PhD in progress: Bastien Hamlat, University of Rennes 1, October 2016, co-advisors Jocelyne Erhel and A. Michel.
• PhD in progress : Long Li, Data assimilation and stochastic transport for the upper ocean dynamics, started November 2017, supervisor: Etienne Mémin.
• PhD in progress : Yacine Ben Ali, Variational assimilation of RANS models for wind engineering, started November 2017, supervised by Dominique Heitz, Etienne Mémin, Gilles Tissot.
• PhD in progress : Robin Billard, Modelling of non-conventional perforated acoustic liners, Université du Mans, started December 2017, supervised by Gilles Tissot.
• PhD in progress : Z. Caspar-Cohen, PhD student at Ifremer, LOPS, Signatures des ondes de marée internes et des mouvements en équilibre quasi-géostrophique sur les courants de surface : perspectives eulérienne vs lagrangienne. Started 15/10/2019. Supervised by Noé Lahaye with X. Carton (UBO) and A. Ponte (Ifremer).
• PhD successfully defended : Dienh Duong Nguyen, October 1st, 2020.

9.6.3 Juries

Jocelyne Erhel

• Etienne Ahusborde, HdR, Univ. Strasbourg (rapporteur)
• Benoit Pinier, PhD, Univ. Rennes (examinatrice)
• Quentin Tournois, PhD, Univ. Rennes (examinatrice)

Etienne Mémin

• Anthony Fillion, Ecoles des Ponts, U. Paris-Est (Rapporteur)
• Alban Farchi, Ecoles des Ponts, U. Paris-Est (Examinateur)
• Arthur Pajot, Sorbonne Université, (Rapporteur)

Dominique Heitz

• Georges HALIM ATALLAH, PhD, U Gustave Eiffel (Rapporteur), 17 décembre 2020.

International journals

• 17 article ChérifC. Amrouche, Luigi C.L. Berselli, RogerR. Lewandowski and DinhD. Duong Nguyen. Turbulent flows as generalized Kelvin-Voigt materials: modeling and analysis Nonlinear Analysis: Theory, Methods and Applications 196 July 2020
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• 18 articleWernerW. Bauer, PranavP. Chandramouli, BertrandB. Chapron, LongL. Li and EtienneE. Mémin. Deciphering the role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approachJournal of Physical Oceanography5042020, 983-1003
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• 19 articleWernerW. Bauer, PranavP. Chandramouli, LongL. Li and EtienneE. Mémin. Stochastic representation of mesoscale eddy effects in coarse-resolution barotropic modelsOcean Modelling1512020, 1-50
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• 20 article Luigi C.L. Berselli, Argus AdrianA. Dunca, RogerR. Lewandowski and DinhD. Duong Nguyen. Modeling Error of $$-Models of Turbulence on a Two-Dimensional Torus' Discrete and Continuous Dynamical Systems - Series B 2021
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• 21 articleLuigi C.L. Berselli, TraianT. Iliescu, BirgulB. Koc and RogerR. Lewandowski. Long-Time Reynolds Averaging of Reduced Order Models for Fluid Flows: Preliminary ResultsMathematics in Engineering212020, 1-25
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• 22 articleLuigi C.L. Berselli, RogerR. Lewandowski and Dinh DuongD. Nguyen. Rotational forms of Large Eddy Simulation turbulence models: modeling and mathematical theoryChinese Annals of Mathematics - Series B4212021, 1-24
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• 23 articleRobinR. Billard, GillesG. Tissot, GwenaelG. Gabard and MarcM. Versaevel. Numerical Simulations of Perforated Plate Liners: Analysis of the Visco-Thermal Dissipation MechanismsJournal of the Acoustical Society of America1491January 2021, 16-27
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• 24 article PranavP. Chandramouli, EtienneE. Mémin and DominiqueD. Heitz. 4D large scale variational data assimilation of a turbulent flow with a dynamics error model Journal of Computational Physics 412 July 2020
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• 25 article NoéN. Lahaye, JonathanJ. Gula and GuillaumeG. Roullet. Internal tide cycle and topographic scattering over the North Mid-Atlantic Ridge Journal of Geophysical Research. Oceans November 2020
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• 26 articleNoéN. Lahaye, VladimirV. Zeitlin and ThomasT. Dubos. Coherent dipoles in a mixed layer with variable buoyancy: Theory compared to observationsOcean Modelling153September 2020, 101673
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• 27 articleRogerR. Lewandowski. On a one dimensional turbulent boundary layer modelPure and Applied Functional Analysis552020, 1115–1129
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• 28 articleBenoîtB. Pinier, RogerR. Lewandowski, EtienneE. Mémin and PranavP. Chandramouli. Testing a one-closure equation turbulence model in neutral boundary layersComputer Methods in Applied Mechanics and Engineering3762021, 113662
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• 29 articleValentinV. Resseguier, LongL. Li, GabrielG. Jouan, PierreP. Dérian, EtienneE. Mémin and BertrandB. Chapron. New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamicsArchives of Computational Methods in Engineering281January 2021, 215-261
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• 30 articleRomainR. Schuster, DominiqueD. Heitz, PhilippeP. Georgeault and EtienneE. Mémin. On-site airflow measurement of a laboratory fume hood using customized large-scale image-based velocimetryIndoor and Built Environment296July 2020, 810-819
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• 31 articleGillesG. Tissot, RobinR. Billard and GwenaelG. Gabard. Optimal cavity shape design for acoustic liners using Helmholtz equation with visco-thermal lossesJournal of Computational Physics4022020, 109048
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• 32 articleGillesG. Tissot, André V. G.A. Cavalieri and EtienneE. Mémin. Stochastic linear modes in a turbulent channel flowJournal of Fluid Mechanics912February 2021, A51
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• 33 articleGoloG. Wimmer, Colin JC. Cotter and WernerW. Bauer. Energy conserving upwinded compatible finite element schemes for the rotating shallow water equationsJournal of Computational Physics401January 2020, 109016
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International peer-reviewed conferences

• 34 inproceedings LongL. Li, DerembleD. Bruno, NoéN. Lahaye and EtienneE. Mémin. Stochastic modeling of the oceanic mesoscale eddies 6th Sandbox STUOD Sandbox Workshop London, United Kingdom February 2021
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• 35 inproceedingsLongL. Li, EtienneE. Mémin and BertrandB. Chapron. Quasi-geostrophic flow under location uncertaintySeminar of Stochastic Transport in Upper Ocean Dynamics (STUOD) projectRennes, FranceMay 2020, 1-52
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• 36 inproceedings LionelL. Pénard, Khalid S.K. Mohammad and EtienneE. Mémin. Monocular 3D reconstruction for image-based velocity estimation Proceedings of the 10th Conference on Fluvial Hydraulics Delft, Netherlands July 2020
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Conferences without proceedings

• 37 inproceedings RobinR. Billard, GwenaelG. Gabard, MarcM. Versaevel and GillesG. Tissot. A non-minear impedance model for micro-perforated liners e-Forum Acusticum 2020 online, France December 2020
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• 38 inproceedings RüdigerR. Brecht, LongL. Li, WernerW. Bauer and EtienneE. Mémin. Rotating shallow water flow under location uncertainty: Part II: some numerical results Seminar STUDO Rennes, France September 2020
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• 39 inproceedings RonanR. Fablet, LucasL. Drumetz, FrançoisF. Rousseau, OlivierO. Pannekoucke, BertrandB. Chapron and EtienneE. Mémin. Joint learning of variational data assimilation models and solvers ECMWF-ESA 2020 - Workshop on Machine Learning for Earth System Observation and Prediction Reading, United Kingdom October 2020
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• 40 inproceedings MatheusM. Ladvig, Agustin MartinA. Picard, ValentinV. Resseguier, DominiqueD. Heitz, EtienneE. Mémin and BertrandB. Chapron. Real-time observer from stochastic reduced order model GDR Flow Separation Control Poitiers, France November 2020
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• 41 inproceedings LongL. Li, EtienneE. Mémin and DerembleD. Bruno. Stochastic modeling of the oceanic mesoscale eddies Stochastic Transport in Upper Ocean Dynamics Workshop London, United Kingdom September 2020
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Scientific book chapters

• 42 inbookSouleymaneS. Kadri and EtienneE. Mémin. A stochastic sub-grid viscosity model and wavelet based method for images assimilationIdentification and Control : some challenges2020, 1-23
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Reports & preprints

• 43 misc Mohamed YacineM. Ben Ali, GillesG. Tissot, DominiqueD. Heitz, SylvainS. Aguinaga and EtienneE. Mémin. An adjoint approach for the analysis of RANS closure using pressure measurements on a high-rise building December 2020
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• 44 misc RüdigerR. Brecht, LongL. Li, WernerW. Bauer and EtienneE. Mémin. Rotating shallow water flow under location uncertainty with a structure-preserving discretization February 2021
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• 45 misc RonanR. Fablet, BertrandB. Chapron, LucasL. Drumetz, EtienneE. Mémin, OlivierO. Pannekoucke and FrançoisF. Rousseau. Learning Variational Data Assimilation Models and Solvers July 2020
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• 46 misc Agustin MartinA. Picard, MatheusM. Ladvig, ValentinV. Resseguier, DominiqueD. Heitz, EtienneE. Mémin and BertrandB. Chapron. Real-time flow estimation from reduced order models and sparse measurements October 2020
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Other scientific publications

• 47 misc ValentinV. Resseguier, MatheusM. Ladvig, Agustin MA. Picard, EtienneE. Mémin and BertrandB. Chapron. Toward real-time embedded observer of unsteady fluid flow environment Toulouse, France January 2020
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