6.1.1 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:
  Etienne Memin
• Participant:
  Etienne Memin

6.1.2 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:
  Etienne Memin

6.1.3 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:
  Etienne Memin
• Participant:
  Etienne Memin

6.1.4 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:
  Etienne Memin
• Participants:
  Anne Cuzol, Etienne Memin

6.1.5 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/
• Contact:
  Etienne Memin
• Participants:
  Christopher Mauzey, Etienne Memin, Pierre Dérian
• Partner:
  CSU Chico

6.1.6 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:
  Geraldine Pichot, Grégoire Lecourt, Jean-Raynald De Dreuzy, Jocelyne Erhel
• Partners:
  Université de Rennes 1, CNRS, Université de Lyon, Université de Poitiers

6.1.7 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, Geraldine Pichot, Lionel Lenôtre, Lionel Lenôtre
• Contact:
  Geraldine Pichot

6.1.8 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.

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

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

Participants: Dominique Heitz, Etienne Mémin.

7.1.2 3D flows reconstruction from image data

Participants: Dominique Heitz, Etienne Mémin.

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

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

In collaboration with the CSTB Nantes centre and within the PhD of Yacine Ben Ali we explored 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 a Sobolev space is highly beneficial as it brings natural smoothing to the sought solutions and avoids the use of regularization penalty. The techniques proposed consists in correcting the equations related to turbulent kinetic energy and dissipation. This work is thoroughly detailed in the PhD manuscript of Yacine Ben Ali 33. Two journal papers are currently under submission.

In another line of work, we addressed the study of variational data assimilation from a learning point of view. Data assimilation aims to reconstruct the time evolution of some state given a series of observations, possibly noisy and irregularly-sampled. Using automatic differentiation tools embedded in deep learning frameworks, we introduce end-to-end neural network architectures for data assimilation. It comprises two key components: a variational model and a gradient-based solver both implemented as neural networks. A key feature of the proposed end-to-end learning architecture is that we may train the NN models using both supervised and unsupervised strategies. This work has been published in 21

7.2.2 Ensemble data assimilation of large-scale dynamics with uncertainty

Participants: Benjamin Dufée, Etienne Mémin.

7.2.3 Reduced-order models for flows representation from image data

Participants: Dominique Heitz, Etienne Mémin.

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

Participants: Berenger Hug, Etienne Mémin, Gilles Tissot.

A methodological framework for ensemble-base estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system is embedded in a manifold of reproducible kernel Hilbert spaces with kernel functions driven by the dynamics. This manifold is nicknamed Wonderland for its appealing properties. In Wonderland the Koopman and Perron-Frobenius operator (also referred to in the literature as the composition and transfer operators, respectively) are unitary and uniformly continuous. They can be safely expressed in exponential series of diagonalizable bounded infinitesimal generators. Access to Lyapunov exponents and to exact ensemble based expressions of the tangent linear dynamics are directly available as well. Wonderland enables us the devise of strikingly simple ensemble data assimilation methods for trajectory reconstructions in terms of constant-in-time linear combinations of trajectory samples. Such an embarrassingly simple strategy is made possible through a fully justified superposition principle ensuing from several fundamental theorems. Numerical proofs of concept for data assimilation and trajectory recovery have been performed with a quasi-geostrophic flow model.

7.2.5 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 its non-linear behaviour, the associated structures and dynamical evolution are relatively easy to predict. Canonical configurations of this type of flows 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. As a consequence there is a high sensitivity to perturbations together with a broad band response that forbid any low rank representation. Jets and mixing layers show this behaviour and a wide range of industrial applications and geophysical flows 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 make the estimation of observation-driven flow reconstruction by data assimilation in realistic configurations.

The stochastic framework of the modelling under location uncertainty (LU) considers a separation between a resolved velocity field and unresolved incoherent turbulent fluctuations. Amplifier flows are particularly sensitive to these perturbations and we believe that LU would improve significantly the predictions of turbulent amplifier flows.

In a deterministic context, there exists a type of models, termed as "parabolised", that enable 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. The extension of parabolised models to a stochastic version is a promising approach which is perfectly adapted to represent the evolution and the variability of an instability propagating within a turbulent flow.

7.3.1 Quantification of high-frequency surface dynamics using models and observations

Participants: Noé Lahaye.

The dynamics of upper-ocean high-frequency motions — internal waves and, more specifically, internal tides, has been addressed using different strategies. As part of F. Le Guillou PhD work (IGE, Grenoble) and in collaboration with J. Le Sommer, E. Cosme, S. Metref (MEOM team, IGE, Grenoble), C. Ubelmann (Ocean Next, Grenoble), E. Blayo, A. Vidard (Inria, Grenoble) and A. Ponte (LOPS, Brest), a joint algorithm for estimating the vortices as well as first mode internal tide from future wide-swath altimeter data has been proposed and tested in an idealized framework 23. This work is being pursued in the Fluminance team. In the context of Z. Caspar-Cohen PhD work, the signature of internal tides collected by surface drifters has been investigated using idealized numerical simulations. It has been shown that an apparent loss of coherence (time regularity of the oscillations at the tidal frequencies) arises in the Lagrangian perspective, resulting from the drifters being advected by the slow flow 36, 29. A statistical model based on the statistical properties of the slow flow has been proposed and validated against the data in this framework. It allows to predict this « apparent » loss of coherence.

7.3.2 Reduced dynamical models for geophysical flows

Participants: Noé Lahaye.

7.3.3 Low order modelling of the interactions between internal tides and currents

Participants: Igor Maingonnat, Noé Lahaye, Gilles Tissot, Etienne Mémin.

7.3.4 Physical understanding of internal tides dynamics using high fidelity numerical simulations

Participants: Adrien Bella, Noé Lahaye, Gilles Tissot, Etienne Mémin.

7.3.5 Effects of smooth divergence-free flows on tracer gradients and spectra: Eulerian prognosis description

Participants: Etienne Mémin.

7.3.6 Geophysical flows modeling under location uncertainty

Participants: Noe Lahaye, Long Li, Etienne Mémin, Gilles Tissot, Francesco Tucciarone.

Within the PhDs of Long Li and Valentin Resseguier 34, 20, 26 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.

In collaboration with Ruediger Brecht, PhD student at Memorial University of Newfoundland, we 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 has been published in JAMES 20.

A study of a stochastic version of the primitive equations model is currently investigated within the PhD of Francesco Tucciarone. An investigation of such model in a realistic ocean numerical code with various noise assumptions is undergoing.

7.3.7 Hamiltonian formulation of the stochastic wave problem

Participants: Evgueni Dinvay, Etienne Mémin.

7.3.8 Parameterization for coarse-resolution ocean modeling

Participants: Louis Thiry, Long Li, Etienne Mémin.

We work on simple parameterization for coarse-resolution oceanic models to replace computationally expensive high-resolution ocean models. We focus on the eddy-permitting scale (grid step   Rossby radius) and computationally cheap parameterization. We are currently investigating the modification of the diffusion (friction) operator to reproduce the mean velocity observed via measurements or a high-resolution reference solution. To test this new parameterization on a double-gyre quasi-geostrophic model, we are implementing a fast and portable python implementation of the multilayer quasi-geostrophic model. Preliminary results are encouraging as they show that we can fairly reproduce the reference mean velocity and significantly improve energy statistics. This method shall serve as a deterministic basis for future coarse-resolution stochastic parameterizations.

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

Participants: Long Li, Etienne Mémin.

7.3.10 Higher order temporal numerical schemes in time for dynamics under location uncertainty

Participants: Pierre-Marie Boulvard, Camilla Fiorini, Long Li, Etienne Mémin.

7.3.11 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.

7.3.12 Stochastic hydrodynamic stability under location uncertainty

Participants: Etienne Mémin, Gilles Tissot.

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

Participants: Francois Legeais, Roger Lewandowski, Etienne Mémin.

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, and 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 of 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. We have studied in 17 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-$\alpha$ 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. We have derived in 18 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.

In 35 we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a) identifying a proper functional setting in weighted spaces and b) checking some easily verifiable assumptions, at fixed time. We also will discuss the critical role of the exponents present in the model (power of the distance function and power of the curl) for what concerns the application of the theory of pseudo-monotone operators.

Another study in collaboration with B. Pinier, P. Chandramouli and E. M/'emin 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 $\ell$. 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 in 24

7.3.14 Dissipation mechanisms in perforated liners with grazing flow

Participants: Gilles Tissot.

7.4.1 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.

7.4.2 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.

7.4.3 Mathematical models of kinetic reactions in geochemistry

Participants: Jocelyne Erhel.

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, has been published in 37 .

7.5.1 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.

8.1.1 Contract ITGA

Participants: Dominique Heitz, Etienne Mémin.

8.1.2 Contract CSTB

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

9.1.1 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.

9.3.1 ERC Synergy Grant STUOD: Stochastic Transport in Upper Ocean Dynamics

PI: Etienne Mémin

Duration: 01/03/2020 - 01/03/2026

Participants: Evgueni Dinvay, Benjamin Dufée, Camilla Fiorini, Beranger Hug, Long Li, Etienne Mémin, Louis Thiry, Francesco Tucciarone.

Partners: IFREMER, IMPERIAL COLLEGE London ((UK))

Summary: 71 percent of Earth is covered by ocean. The ocean has absorbed 93 percent of the heat trapped by human’s greenhouse gas emissions. The ocean’s future responses to continued warming are uncertain. Our project will deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. Our approach accounts for transport on scales that are currently unresolvable in computer simulations, yet are observable by satellites, drifters and floats. Four scientific capabilities will be engaged: (i) observations at high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; (ii) large scale numerical simulations; (iii) data-based stochastic equations for upper ocean dynamics that quantify simulation error; and (iv) stochastic data assimilation to reduce uncertainty. These four scientific capabilities will tackle a network of joint tasks achieved through cooperation of three world-calibre institutions: IFREMER (ocean observations, reanalysis); INRIA (computational science); and Imperial College (mathematics, data assimilation). Our complementary skill sets comprise a single systemic effort: (1) Coordinate and interpret high-resolution satellite and in situ upper ocean observations (2) Extract correlations from data needed for the mathematical model (3) Perform an ensemble of computer simulations using our new stochastic partial differential equations (SPDE) which are derived by matching the observed statistical properties (4) Apply advanced data assimilation and computer simulations to reduce model uncertainty The key to achieving these goals will be synergy in our combined expertise.

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

Participants: Etienne Mémin.

duration 48 months. The SEACS project whose acronym stands for: “Stochastic modEl-dAta-Coupled representationS for the analysis, simulation and reconstruction of upper ocean dynamics” is a Joint Research Initiative between the three Britanny clusters of excellence of the "Laboratoires d'Excellence" program: Cominlabs, Lebesgue and LabexMer centered on numerical sciences, mathematics and oceanography respectively. Within this project we aim at studying the potential of large-scale oceanic dynamics modeling under uncertainty for ensemble forecasting and satellite image data assimilation.

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

Participants: Dominique Heitz.

9.4.3 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.

9.4.4 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.

9.4.5 LEFE MANU: ADOTSAD

Participants: Gilles Tissot, Etienne Mémin.

9.5.1 ARED COMIOE

Participants: Adrien Bela, Noé Lahaye, Gilles Tissot, Etienne Mémin.

10.1.1 Journal

10.1.2 Research administration

Dominique Heitz

• Member of INRAE OPAALE research unit scientific council
• Member of INRAE OPAALE research unit council
• Head of INRAE ACTA Team

Roger Lewandowski

• President du Comité de liaison du groupe GAMNI-SMAI
• President of the Blaise Pascal award jury
• President of GAMNI-SMAI PhD thesis award
• Corresponding person of the SMAI in Rennes
• Responsible of the group "Mathematical modeling" of IRMAR
• Member of the scientific council of IRMAR,
• Member of Mathematical teaching council of U. Rennes I
• Member of the scientific council of the Henri Lebesgue Centre

Etienne Mémin

• Member of the scientific council of LEFE-MANU action of CNRS INSU
• Member of the comity GAMNI-SMAI

10.2.1 Teaching

• Licence: Jocelyne Erhel, Optimisation, 12h, niveau L3, ENSAI Rennes
• Licence : Dominique Heitz, Mécanique des fluides, 30h, niveau L2 INSA Rennes
• Licence: Noé Lahaye, thermo-energetics, 50h, 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, Motion analysis , 9h, Master 2 SISEA Université de Rennes 1.
• Master : Gilles Tissot, mathematics for acoustics, 20h, niveau M1, Université du Mans.

10.2.2 Supervision

• PhD in progress: Adrien Bella, Understanding interactions between internal tides and currents in the ocean using high-fidelity numerical simulations, started October 2021, supervised by Noé Lahaye, Gilles Tissot, Etienne Mémin
• PhD in progress: Francois Legeais, Mathematical and numerical modeling of the sea atmosphere interface, started october 2021, supervised by Roger Lewandowski
• PhD in progress: Igor Maingonnat, Understanding and modelling nonlinear mechanisms in the ocean: internal waves / background flow interactions. Started November 2021, supervised by Noé Lahaye, Gilles Tissot, Etienne Mémin
• PhD in progress: Manolis Perrot, student at U. Grenoble Alpes, Consistent modelling of subgrid scale for ocean climate models. Started October 2021, supervised by Eric Blayo, Florian Lemarié, Etienne Mémin
• 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 models, started November 2020 Long Li, Etienne Mémin.
• 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: Robin Billard, Modelling of non-conventional perforated acoustic liners, Université du Mans, supervised by Gilles Tissot, defended 14/04/2021.
• PhD successfully defended: Bastien Hamlat, University of Rennes 1, co-advisors Jocelyne Erhel and A. Michel. 21 march 2021
• PhD successfully defended: Yacine Ben Ali, Variational assimilation of RANS models for wind engineering, supervised by Dominique Heitz, Etienne Mémin, Gilles Tissot, defended 24/03/2021.
• PhD successfully defended: Long Li, Data assimilation and stochastic transport for the upper ocean dynamics, supervisor: Etienne Mémin, defended 25/03/2021.

10.2.3 Juries

Dominique Heitz

• Walid MRAD, PhD, IMT Atlantique (Examinateur)
• Mathias LEMKE, HDR, TU Berlin (Rapporteur)

Etienne Mémin

• Said Ouala, IMT Atlantic (President), 17/03/2021
• Nishant Kupar, Institut P', U. Poitiers (Examinateur), 08/09/2021
• Vincent Le Guen Cnam Paris (Examinateur), 30/11/2021

International journals

• 17 articleL. C.Luigi C. Berselli, A. A.Argus Adrian Dunca, R.Roger Lewandowski and D.Dinh Duong Nguyen. Modeling Error of $$-Models of Turbulence on a Two-Dimensional Torus.Discrete and Continuous Dynamical Systems - Series B2692021, 4613-4643
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• 18 articleL. C.Luigi C. Berselli, R.Roger Lewandowski and D. D.Dinh Duong Nguyen. Rotational forms of Large Eddy Simulation turbulence models: modeling and mathematical theory.Chinese Annals of Mathematics - Series B4212021, 1-24
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• 19 articleR.Robin Billard, G.Gilles Tissot, G.Gwénaël Gabard and M.Marc Versaevel. Numerical simulations of perforated plate liners: Analysis of the visco-thermal dissipation mechanisms.Journal of the Acoustical Society of America1491January 2021, 16-27
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• 20 articleR.Rüdiger Brecht, L.Long Li, W.Werner Bauer and E.Etienne Mémin. Rotating shallow water flow under location uncertainty with a structure-preserving discretization.Journal of Advances in Modeling Earth SystemsOctober 2021
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• 21 articleR.Ronan Fablet, B.Bertrand Chapron, L.Lucas Drumetz, E.Etienne Mémin, O.Olivier Pannekoucke and F.François Rousseau. Learning Variational Data Assimilation Models and Solvers.Journal of Advances in Modeling Earth Systems132021, article n° e2021MS002572
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• 22 articleN.Noé Lahaye, A.Alexandre Paci and S.Stefan Llewellyn Smith. Instability of Lenticular Vortices: Results from Laboratory Experiments, Linear Stability Analysis and Numerical Simulations.Fluids611November 2021, 1-25
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• 23 articleF.Florian Le Guillou, N.Noé Lahaye, C.Clément Ubelmann, S.Sammy Metref, E.Emmanuel Cosme, A.Aurélien Ponte, J.Julien Le Sommer, E.Eric Blayo and A.Arthur Vidard. Joint Estimation of Balanced Motions and Internal Tides From Future Wide‐Swath Altimetry.Journal of Advances in Modeling Earth Systems1312December 2021, 1-17
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• 24 articleB.Benoît Pinier, R.Roger Lewandowski, E.Etienne Mémin and P.Pranav Chandramouli. Testing a one-closure equation turbulence model in neutral boundary layers.Computer Methods in Applied Mechanics and Engineering3762021, article n° 113662
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• 25 articleV.Valentin Resseguier, B.Bertrand Chapron and E.Etienne Mémin. Effects of smooth divergence-free flows on tracer gradients and spectra: Eulerian prognosis description.Journal of Physical Oceanography2021
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• 26 articleV.Valentin Resseguier, L.Long Li, G.Gabriel Jouan, P.Pierre Dérian, E.Etienne Mémin and B.Bertrand Chapron. New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics.Archives of Computational Methods in Engineering281January 2021, 215-261
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• 27 articleV.Valentin Resseguier, A. M.Agustin M Picard, E.Etienne Mémin and B.Bertrand Chapron. Quantifying truncation-related uncertainties in unsteady fluid dynamics reduced order models.SIAM/ASA Journal on Uncertainty Quantification932021, 1152–1183
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• 28 articleG.Gilles Tissot, A. .André V. G. Cavalieri and E.Etienne Mémin. Stochastic linear modes in a turbulent channel flow.Journal of Fluid Mechanics9122021, 1-33
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• 29 articleX.Xiaolong Yu, A.Aurélien Ponte, N.Noé Lahaye, Z.Zoé Caspar‐Cohen and D.Dimitris Menemenlis. Geostrophy Assessment and Momentum Balance of the Global Oceans in a Tide‐ and Eddy‐Resolving Model.Journal of Geophysical Research. Oceans12610October 2021, 1-19
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International peer-reviewed conferences

• 30 inproceedingsL.Long Li, D.Deremble Bruno, N.Noé Lahaye and E.Etienne Mémin. Stochastic modeling of the oceanic mesoscale eddies.6th Sandbox STUOD Sandbox WorkshopLondon, United KingdomFebruary 2021, 1-24
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Conferences without proceedings

• 31 inproceedingsL.Long Li, B.Bertrand Chapron, B.Bruno Deremble, N.Noé Lahaye and E.Etienne Mémin. Statistically data-driven modelling Location Uncertainty in mesoscale dynamics.STUOD 2021 - 2nd Stochastic Transport in Upper Ocean Dynamics Annual WorkshopLondon, United KingdomSeptember 2021
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• 32 inproceedingsA. M.A M Picard, M.M Ladvig, V.Valentin Resseguier, D.D Heitz, E.E Mémin and B.B Chapron. Real-time flow estimation from reduced order models and sparse measurements.AERO2020+1 - International Conference on Applied AerodynamicsVirtual, FranceApril 2021, 1-20
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Doctoral dissertations and habilitation theses

• 33 thesisM. Y.Mohamed Yacine Ben Ali. Investigating Data-Model coupling using adjoint techniques for wind engineering.Université de Rennes 1March 2021
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• 34 thesisL.Long Li. Stochastic modeling and numerical simulation of ocean dynamics.Université de Rennes 1March 2021
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Reports & preprints

• 35 miscL. C.Luigi C Berselli, A.Alex Kaltenbach, R.Roger Lewandowski and M.Michael Růžička. On the existence of weak solutions for a family of unsteady rotational smagorinsky models.September 2021
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• 36 miscZ.Zoé Caspar-Cohen, A.Aurélien Ponte, N.Noé Lahaye, X.Xavier Carton, X.Xiaolong Yu and S.Sylvie Le Gentil. Characterization of internal tide incoherence : Eulerian versus Lagrangian perspectives.January 2022
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• 37 miscB.Bastien Hamlat, J.Jocelyne Erhel, A.Anthony Michel and T.Thibault Faney. Analysis and numerical computation of geochemical systems with kinetic precipitation and dissolution reactions involving several minerals.March 2021
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Other scientific publications

• 38 miscC.Camilla Fiorini, L.Long Li and É.Étienne Mémin. Higher order schemes in time for the surface quasigeostrophic system under location uncertainty.Vienna / Virtual, AustriaApril 2021, 1
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• 39 miscL.Long Li, B.Bruno Deremble, N.Noé Lahaye and E.Etienne Mémin. Stochastic modeling of mesoscale eddies.Vienne, AustriaApril 2021
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• 40 miscV.Valentin Resseguier, M.Matheus Ladvig, A. M.Agustin Martin Picard, E.Etienne Mémin, D.Dominique Heitz, D.Dimitry Voisin and C.Caroline BRAUD. Real-time unsteady air flow prediction to reduces mechanic load variations and wind turbine maintenance costs.Nantes, Saint-Nazaire, FranceSeptember 2021, 1
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