Keywords
 A6.1. Methods in mathematical modeling
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.2. Stochastic Modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.2. Numerical probability
 A6.2.3. Probabilistic methods
 A6.2.4. Statistical methods
 A6.2.7. High performance computing
 A6.3. Computationdata interaction
 A6.3.5. Uncertainty Quantification
 A6.4.1. Deterministic control
 A6.5. Mathematical modeling for physical sciences
 A6.5.2. Fluid mechanics
 B1.1.8. Mathematical biology
 B3.2. Climate and meteorology
 B3.3.2. Water: sea & ocean, lake & river
 B3.3.4. Atmosphere
 B4.3.2. Hydroenergy
 B4.3.3. Wind energy
 B9.5.2. Mathematics
 B9.5.3. Physics
1 Team members, visitors, external collaborators
Research Scientists
 Mireille Bossy [Team leader, INRIA, Senior Researcher, HDR]
 Jérémie Bec [CNRS, Senior Researcher, HDR]
 Laetitia Giraldi [INRIA, Researcher]
 Christophe Henry [INRIA, Researcher]
PhD Students
 Lorenzo Campana [Université Côte d'Azur (January 2022), Inria (February, March 2022) , until Mar 2022]
 Zakarya El Khiyati [Université Côte d'Azur]
 Paul Maurer [INRIA, from Oct 2022]
 Nicolas Valade [INRIA, from Oct 2022]
Interns and Apprentices
 Carlamaria Cosenza [Politecnico di Torino, from May 2022 until Aug 2022]
 Matéo Ghezal [INRIA, from Jun 2022 until Aug 2022, Université Paris Saclay]
 Hao Liu [INRIA, from Jun 2022 until Aug 2022, Technology University Darmstad]
 Paul Maurer [INRIA, from Apr 2022 until Sep 2022, Sorbonne Université]
 Belgacem Othman [INRIA, from Apr 2022 until Aug 2022, Sorbonne Université]
 Nicolas Valade [INRIA, from Mar 2022 until Sep 2022, Mines ParisTech]
Administrative Assistant
 Sandrine Boute [INRIA]
External Collaborators
 Christophe Brouzet [CNRS, from Nov 2022, InPhyNi]
 Areski Cousin [Université de Strasbourg , until Aug 2022, HDR]
 Eric Simmonet [CNRS, from Nov 2022, InPhyNi]
 Simon Thalabard [Université Côte d'Azur, InPhyNi]
2 Overall objectives
Turbulence modeling and particle dynamics are at play in numerous situations in which inertial particles are transported by turbulent flows. These particles can interact with each other, form aggregates which can fragment later on, and deposit on filters or solid walls. In turn, this deposition phenomenon includes many aspects, from the formation of monolayer deposits to heavy fouling that can clog flow passage sections. Taking into account the potentially complex morphology of these particles requires the development of new approaches to predict the resulting statistical quantities (turbulent dispersion, formation of aggregates, nature of the deposits formed, etc.).
The variety of situations (deposition, resuspension, turbulent mixing, droplet/matter agglomeration, thermal effect) involves specific models that need to be improved. Yet, one of the key difficulties lies in the fact that the relevant phenomena are highly multiscale in space and time (from chemical reactions acting at the microscopic level to fluid motion at macroscopic scales), and that consistent and coherent models need to be developed together. This raises many challenges related both to physical sciences (i.e. fluid dynamics, chemistry or material sciences) and to numerical modeling. These challenges represent critical technological locks. To address them, industrial design increasingly relies on macroscopic numerical models, broadly known as “Computational Fluid Dynamics” (CFD). However, such largescale approaches are only well deployed on crude particle descriptions (monodisperse sizes, spherical shapes, rigid bodies), with oversimplified smallscale physics. They often rely on statistical closures for singletime, singleparticle probability distributions. Yet, these meanfield simplifications do not accurately reproduce complex features of the involved physics, which require more advanced approaches to reproduce higherorder correlations.
Through the unique synergy between team members from various disciplines, Calisto is developing Stochastic Approaches for complex Flows and Environment to address the following challenges:
 produce original answers (methodological and numerical) for challenging environmental simulation models, with applications to renewable energy, filtration/deposition technology in industry (cooling of thermal or nuclear power plants), climate and meteorological prediction, and dispersion of materials or active agents (such as biological organisms, microrobots);
 design new mathematical tools to analyze the fundamental physics of turbulence;
 develop numerical methods to analyze, control and optimize the displacement of microswimmers in fluids of various natures, ranging from water to nonNewtonian mucus;
 optimize and control the displacement of artificial microswimmers;
 develop stochastic modeling approaches and approximation methods, in the rich context of particleparticle and fluidparticle interactions in complex flows;
 contribute to the field of numerical probability, with new simulation methods for complex stochastic differential equations (SDEs) arising from multiscale Lagrangian modeling for the dynamics of material/fluid particle dynamics with interactions.
3 Research program
Calisto is structuring its research according to five interacting axes.

Axis A
Complex flows: from fundamental science to applied models.

Axis B
Particles and flows near boundaries: specific Lagrangian approaches for largescale simulations.

Axis C
Active agents in a fluid flow.

Axis D
Mathematical and numerical analysis of stochastic systems.

Axis E
Variability and uncertainty in flows and environment.
3.1 Axis A Complex flows: from fundamental science to applied models
This axis aims at promoting significant advances in the understanding and modeling of realistic dispersed, multiphase turbulent flows. In situations where basic mechanisms are still not fully apprehended, the proposed research aims at bringing out the underlying physics by identifying novel effects and quantifying their impacts. These results will then be used to foster new macroscopic models that are expected to be computationally sufficiently undemanding. These models should also be adaptable to open the way to systematic studies of turbulent suspensions as a function of settings, parameters, system geometry. Such aspects are essential in exploratory researches aimed at optimizing combustion processes, heat transfers, phase changes, or the design of energyefficient hydraulic or aerodynamic processes.
Accurate modeling of the location, attributes, and effects of particles transported by turbulent flows is key to optimize the design and performance of several processes in industry, in particular in power production. Yet, current macroscopic approaches often oversimplify physical phenomena related to smallscale physics and fail to capture various effects, such as heterogeneous distributions of sizes and shapes, particle deformation, agglomeration, as well as their interactions with boundaries. Improving models remains a huge challenge that requires monitoring spatial and temporal correlations through particle relative dynamics.
Our overall objective here is to design, validate and apply new efficient modeling and simulation tools for fluidparticle systems that account for relative particle motions, twoparticle interactions and complex flow geometries. Our methodology consists in simultaneously (i) building up a comprehensive microscopic description, (ii) developing efficient macroscopic models, and (iii) applying these two approaches to study practical situations to compare and validate them.
Continuous exchanges between these two viewpoints make it possible to quickly identify pitfalls in models. Furthermore, finescale descriptions will progressively provide suggestions for improvements.
This research axis is currently investigating the following distinct topics
 Models for polydisperse, complexshaped, deformable particles;
 Particle interactions and size evolution;
 Transfers between the dispersed phase and its environment.
3.2 Axis B Particles and flows near boundaries: specific Lagrangian approaches for large scale simulations
This research axis aims at developing Lagrangian macroscopic models for single phase and particleladen turbulent flow simulations. This activity addresses important situations of environmental flows, such as atmospheric boundary layer (ABL), and pollutants, pollen, microplastic dispersion and resupension in the atmosphere or river/marine systems. These are situations where boundaries bring additional complexity, in terms of turbulent description, and in terms of the interaction between wall and particles.
In the hierarchy of turbulent models, the Lagrangian stochastic approach (or probability density function (PDF) approach) is distinguished by several important features, mainly: (i) it is a stochastic method that resolves the probability density function of some physical relevant variables, needed to provide sufficient statistical information. For example, in the case of singlephase turbulent flows, this method provides the velocity distribution, compatible with the imposed momentum turbulent closure of the considered model. In particular, it delivers the whole tensor of correlations between the flow velocity components in adequacy with the given closure; (ii) thanks to its Lagrangian formulation, this approach allows to develop a fully coherent model of a turbulent flow, of particles embedded in it, as well as their interactions.
For twophase turbulent flows, the combination of fluidparticle approaches with discrete particle approaches –called here LagrangeLagrange approaches– appears to be particularly interesting for near boundary flows where interactions with surface boundaries are coming into the problem. Until now, this LagrangianLagrangian modelling approach has never really been explored. The Calisto inhouse SDM software, as a mature fluidparticle Lagrangian simulation code, offers an exciting opportunity to investigate this direction.
This research axis is currently investigating the following distinct topics.
3.2.1 Standalone Lagrangian simulations in atmospheric boundary layer (ABL)
The turbulent nature of the atmospheric boundary layer (ABL) contributes to the uncertainty of the wind energy estimation. This has to be taken into account in the modeling approach when assessing the wind power production. The purpose of the Stochastic Downscaling Model (SDM) is to compute the wind at a refined scale in the ABL, from a coarse wind computation obtained with a mesoscale meteorological solver. The main features of SDM reside in the choice of a fully Lagrangian viewpoint for the turbulent flow modeling. This is allowed by stochastic Lagrangian modeling approaches that adopt the viewpoint of a fluidparticle dynamics in a flow. Such methods are computationally inexpensive when one needs to refine the spatial scale. This is a main advantage of the SDM approach, as particles methods are free of numerical constraints (such as the Courant Friedrichs Lewy condition that imposes a limit to the size of the time step for the convergence of many explicit timemarching numerical methods).
A particular attention is now focused on improving standalone Lagrangian numerical models in the ABL (such as additional buoyancy model, canopy models). Furthermore, the coupling of fluid particle modeling with phase particle models is of crucial interest for some of our applications.
3.2.2 Advanced stochastic models for discrete particle dispersion and resuspension
As a particle nears a surface, deposition can occur depending on the interactions between the two objects. Deposits formed on a surface can then be resuspended, i.e. detached from the surface and brought back in the bulk of the fluid. Resuspension results from a subtle coupling between forces acting to move a particle (including hydrodynamic forces) and forces preventing its motion (such as adhesive forces, gravity). In the last decades, significant progresses have been achieved in the understanding and modeling of these processes within the multiphase flow community. Despite these recent progresses, particle resuspension is still often studied in a specific context and crosssectoral or crossdisciplinary exchange are scarce. Indeed, resuspension depends on a number of processes making it very difficult to come up with a general formulation that takes all these processes into account.
Our goal here is to improve deposition law and resuspension law for more complex deposits in turbulent flows, especially towards multilayered deposits. For that purpose, we are improving existing Lagrangian stochastic models while resorting to metamodeling to develop tailored resuspension law from experimental measurements and finescale numerical simulations. We are targeting practical applications such as pollutants in the atmosphere and plastic in marine systems.
3.2.3 Coherent descriptions for fluid and particle phases
Various particles are present in the ABL, such as pollutant, fog or pollen. This surface layer is characterized by various complex terrains (as urban cities or forests), forming the socalled canopy. This canopy strongly affects the nearwall turbulent motion as well as the radiative and thermal transfers.
Simulations of twophase flows require the coupling of solvers for the fluid and particle phases. Numerical Weather Prediction (NWP) software usually rely on a Eulerian solver to solve NavierStokes equations. Solid particles are often treated using a Lagrangian point of view, i.e. their motion is explicitly tracked by solving Newton's equation of motion, the key difficulty being then to couple these intrinsically different approaches together. In line with the models and numerical methods developed in Sections 3.2.1 and 3.2.2, as an alternative to EulerianLagragian approaches, Calisto is developing a new LagrangeLagrange formulation that remains tractable to perform simulations for twophase turbulent flows. We are particularly interested in LagrangeLagrange models for interactions with surfaces, as turbulence and collisions with surfaces can significantly affect the concentration of particles in the nearwall region.
3.2.4 Active particles near boundary
Surface effects can lead to the trapping of microswimmers near boundaries, as the presence of a boundary breaks both the symmetry of the fluid (leading to strong anisotropy) and the symmetry of the fluidswimmer system. The better understanding of fluidparticle interactions near boundaries are expected here to help in the design of new control actuation for driving artificial swimmers in confined environments (developed in Axis C).
3.3 Axis C Active agents in a fluid flow
Active agents are entities immersed into a fluid, capable of converting stored or ambient free energy (for instance through deformation) into systematic movement. Active agents, also called swimmers, can interact with each other as well as with the surrounding medium. Such active agents can be microorganisms, such as bacteria or plankton, as well as artificial devices used for micromanufacturing, toxic waste disposal, targeted drug delivery or localized medical diagnostics.
This research axis is devoted to new mathematical modeling approaches to simulate the displacement of swimmers, to get results on control and optimal control associated with them, to study the presence of an additional stochastic effect for driving a swarm of such microswimmers.
Modeling approach
The equations of motion of the swimmer derive from its hydrodynamical interactions with the fluid through Newton laws. At a high level of description, this can be described by coupling the NavierStokes equations with the hyperelastic equations describing the swimmer's deformation (in the case of elastic body). In the case of artificial magnetic swimmers, additional contribution representing the action of an external magnetic field on the swimmer needs to be added in the equations of motion. Solving the resulting system of PDEs is a challenging task, since it combines a set of equations deemed to be numerically difficult to solve even when they are decoupled. To overcome these difficulties, Calisto considers various types of models, ranging from simpler but rough models to more realistic but complex models.
Control and optimal control for swimmers displacement
Calisto investigates the controllability issues and the optimal control problems related in particular to two situations: the displacement of (i) real selfpropelled swimmer by assuming that the control is the deformation of its body (ii) artificial bioinspired swimmers that are able to swim using an external magnetic field.
Another line of research concerns optimal path planning in turbulent flow. As a microswimmer swims towards a target in a dynamically evolving turbulent fluid, it is buffeted by the flow or it gets trapped in whirlpools. The general question we want to address is whether such a microswimmer can develop an optimal strategy that reduces the average time or energy it needs to reach a target at a fixed distance.
Stochastic effect on artificial swimmers
Calisto investigates also the effect of the presence of noise in the response of a microrobot (to the external magnetic field for instance) by developing new model and related numerical simulation of such systems.
3.4 Axis D Mathematics and numerical analysis of stochastic systems
Stochastic analysis, and related numerical analysis, together with improved statistical descriptions of highlynonlinear dynamics are central topics in Calisto. This research axis encompasses activities aiming, either (a) at strengthening our understanding on the origin and nature of fluctuations that are inherent to turbulent flows, or (b) at providing a coherent framework in response to the various mathematical challenges raised by the development of novel models in other research axes. Addressing these two fundamental aspects concomitantly to more practical and applied objectives is again a hallmark of the team.
Mathematics for fundamental aspects of turbulence and turbulence transport
This research line has the scope of providing a unified description of turbulent flows in the limit of large Reynolds numbers and thus will be applicable to a large range of physical applications. It is conjectured since Kolmogorov and Onsager that the flow develops a sufficiently singular structure to provide a finite dissipation of kinetic energy when the viscosity vanishes. This dissipative anomaly gives a consistent framework to select physically acceptable solutions of the limiting inviscid dynamics. However, recent mathematical constructions of weak dissipative solutions face the problem of nonuniqueness, raising new questions on the relevance to turbulence and on the notion of physical admissibility.
On the one hand, the conservation of kinetic energy is actually not the only symmetry that is broken by turbulence. Various experimental and numerical measurements show significant deviations from simple scaling, timeirreversible fluctuations along fluid elements trajectories, and possibly other broken inviscid symmetries, such as circulation. Still, these anomalies may have a universal nature and, as such, provide new constraints for the design of physically admissible solutions. On the other hand, nonuniqueness could be an intrinsic feature of turbulence. Singular solutions to nonlinear problems have an explosive sensitivity leading to spontaneously stochastic behaviors, thus questioning the pertinence of uniqueness and providing a framework to interpret solutions at a probabilistic level. To address such issues and provide unified appreciation, we simultaneously develop three strongly interrelated viewpoints: a) numerical approach, exploiting relevant and efficient fullyresolved simulations; b) new theoretical approaches based on the statistical physics of turbulent flow; c) mathematical construction of "very weak" flows, such as measurevalued solutions to the Euler equations.
Interacting Stochastic Systems and nonlinear SDEs
Calisto considers examples of particle systems in interaction, possibly under mean field interaction, with the overall goal of analyzing the effect of stochasticity in such system. In particular, we aim to detect and analyze conditions for the emergence of collective behaviors such as collective motions, synchronization and organization with or without the notion of leaders.
An important example of complex interacting system is given by collisioning particle system under Langevin dynamics. If the case of collisioning systems in the context of gas dynamics –where particles experiment free path between two collision events– and in the context of overdamped Brownian dynamics have been largely studied, until now, situation of a finite number of particles collisioning under a Langevin dynamics is poorly addressed. This last case, describing particles in turbulent flow, is of great interest for Calisto from both numerical and theoretical view points.
The modeling activities carried out in Calisto require to develop continuously our mathematical toolbox and expertise on nonlinear SDEs driven by complex noises, in particular nonMarkovian ones. We are particularly concerned with strong and weak solution behaviors, longtime behaviors, approximation techniques including numerical ones, and the study of singular situations arising for instance from boundary conditions.
3.5 Axis E Variability and uncertainty in flows and environment
Uncertainty has become a very important research topic for predictive systems involving an ever increasing number of parameters. This analysis effort is particularly present in CFD, all the more so when dealing with particleladen turbulent flows. It becomes critical for environmental applications, among which we can mention in the first place climate uncertainty. Our position on these subjects is based on the stochastic modeling of the variability of the phenomena under study. Crossing the analysis in uncertainty with solution formulations that already incorporate a statistical approach allows a great flexibility, both in modeling the uncertainty sources and in numerical implementation. This line of research allows us to enhance our expertise on essential tools for the evaluation of our models.
Variability in wind/hydro simulation at small scale: application to wind/hydro energy
The turbulent nature of the atmospheric boundary layer (ABL) contributes to the uncertainty of the wind energy estimation. This has to be taken into account in the modeling approach when assessing the wind power production. The stochastic nature of the SDM approach developed in Axis B offers some rich perspectives to asses variability and uncertainty quantification issues in the particular context of environmental flows and power extraction evaluation. In particular, as a PDF method, SDM delivers a probability distribution field of the computed entities. Merging such numerical strategy with Sensitivity Analysis (SA)/Uncertainty Quantification (UQ) are potentially fruitful in terms of computational efficiency.
Metamodeling and uncertainty
While building and using computational fluid dynamics (CFD) simulation models, sensitivity analysis and uncertainty quantification methods allow to study how the uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input. UQ approaches allow to model verification and factor prioritization. It is a precious aid in the validation of a computer code, guidance research efforts, and in terms of system design safety in dedicated application. As CFD code users, we aim at applying UQ tools in our dedicated modeling and workflow simulation. As Stochastic Lagrangian CFD developers, we aim at developing dedicated SA and UQ tools as Stochastic solvers have the ability to support cross Monte Carlo strategy at the basis of SA methodology.
Another goal is to address some control and optimization problems associated with the displacement of swimmers through metamodeling, such as Gaussian process regression model, proved to be efficient for solving optimization of PDEs systems in other contexts.
Anomalies modeling through machinelearned dataset of meteorological observations and forecasts
Stochastic modeling approaches are known to be able to describe the intrinsic variability of a phenomenon, preserving the spatial coherence of variability and interacting with the dynamics of the physical processes involved. The machine learning (or meta model) approach is recognized for these prediction capabilities. It is nowadays everywhere in the forecast data delivered, using past events to debias/select the future, when the physical dynamic model becomes too heavy to handle. We aim at intersecting the two approaches to develop methodologies for selecting/enriching future scenarios, starting from the observation that we can not calibrate the model of variability to be associated with a future forecast (distribution of extremes accounts for climatic changes), the same way one calibrates the variability model to be associated with observables.
4 Application domains
Environmental challenges: predictive tools for particle transport and dispersion
Particles are omnipresent in the environment:
 formation of clouds and rain results from the coalescence of tiny droplets in suspension in the atmosphere;
 fog corresponds to the presence of droplets in the vicinity of the Earth's surface, reducing the visibility to below 1 km 26;
 pollution corresponds to the presence of particulate matter in the air. Due to their impact on human health 35, the dispersion of fine particulate matter is of primary concern: PM2.5 and PM10 (particles smaller than 2.5 or 10 $\mu $ m) and Ultra Fine Particles (UFP) are particularly harmful for human respiratory systems while pollen can trigger severe allergies;
 the dispersion of radioactive particles following their release in nuclear incidents has drawn a great deal of attention to deepen our understanding and ability to model these phenomena 41;
 the dispersion/deposition of ash and soots and their consequences for the environment and health have been highlighted by recent events in France and abroad;
 plastic contamination in oceans impacts marine habitats and human health 29;
 suspension of real microswimmers 19 such as sperm cell, bacteria, and in environmental issues with animal flocks attracted intrinsic biological interest 31;
 accretion of dusts is responsible for the formation of planetesimals in astrophysics 30.
These selected examples show that the presence of particles affects a wide range of situations and has implications in public, industrial and academic sectors.
Each of these situations (deposition, resuspension, turbulent mixing, droplet/matter agglomeration, thermal effect) involves specific models that need to be improved. Yet, one of the key difficulties lies in the fact that the relevant phenomena are highly multiscale in space and time (from chemical reactions acting at the microscopic level to fluid motion at macroscopic scales), and that consistent and coherent models need to be developed together. This raises many issues related both to physical sciences (i.e. fluid dynamics, chemistry or material sciences) and to numerical modeling.
Next generation of predictive models for complex flows
Many processes in power production involve circulating fluids that contain inclusions, such as bubbles, droplets, debris, sediments, dust, powders, microswimmers or other kinds of materials. These particles can either be inherent components of the process, for instance liquid drops in sprays and soot formed by incomplete combustion, or external foul impurities, such as debris filtered at water intakes or sediments that can obstruct pipes. Active particles, seen as artificial microswimmers, have attracted particular attention for medical applications since they can be used as vehicles for the transport of therapeutics or as tools for limited invasive surgery. In these cases, optimization and control requires monitoring the evolution of their characteristics, their trajectories (with/without driving), and their effects on the fluid with a sufficiently high level of accuracy. These are very challenging tasks given a numerical complexity of the numerical models.
These challenges represent critical technological locks and power companies are devoting significant design efforts to deal with these issues, increasingly relying on the use of macroscopic numerical models. This framework is broadly referred to as “Computational Fluid Dynamics”. However, such largescale approaches tend to oversimplify smallscale physics, which limits their suitability and precision 20. Particles encountered in industrial situations are generally difficult to model: they are polydisperse, not exactly spherical but of any shape, and deform; they have complex interactions, collide and can agglomerate; they usually deposit or stick to the walls and can even modify the very nature of the flow (e.g. polymeric flows). Extending present models to these complex situations is thus key to improve their applicability, fidelity, and performance.
Models operating in industry generally incorporate rather minimalist descriptions of suspended inclusions. They rely on statistical closures for singletime, singleparticle probability distributions, as is the case for the particletracking module in the opensource CFD software Code_Saturne developed and exploited by EDF R&D. The underlying meanfield simplifications do not accurately reproduce complex features of the involved physics that require higherorder correlation descriptions and modeling. Indeed, predicting the orientation and deformation of particles requires suitable models of the fluid velocity gradient along their trajectories 42 while concentration fluctuations and clustering depend on relative particle dispersion 38, 27. Estimates of collision and aggregation rates should also be fed by twoparticle dynamics 36, while wall deposition is highly affected by local flow structures 39. Improving existing approaches is thus key to obtain better prediction tools for multiphase flows.
New simulation approach for renewable energy and meteorological/climate forecast
A major challenge of sustainable power systems is to integrate climate and meteorological variability into operational processes, as well as into medium/long term planning processes 25. Wind, solar, marine/rivers energies are of growing importance, and the demand for forecasts goes hand in hand with it 24, 18. Numerous methods exist for different forecast horizons 22. One of the main difficulties is to address refined spatial description. In the case of wind energy, wind production forecasts are submitted to the presence of turbulence in the near wall atmospheric boundary layer. Turbulence increases the variability of wind flows interacting with mill structures (turbine, mast, nacelle), as well as neighboring structures, terrain elevation and surface roughness. Although some computational fluid dynamics models and software are already established in this sector of activity 3734, the question of how to enrich and refine wind simulations (from meteorological forecast, or from larger scale information, eventually combined with local measurements) remains largely open.
Though hydro turbine farms are of a less assertive technological maturity than wind farms, simulating hydro turbines farms in rivers and sea channels submitted to tidal effect present similar features and challenges. Moreover in the marine energy context, measures are technically more difficult and more costly, and the demand in weather forecast concerns also the safety in maintenance operations.
At the time scale of climate change, the need for uncertainty evaluation of predictions used in longterm planning systems is increasing. For managers and decision makers in the field of hydrological forecasts, assessing hydropower predictions taking into account their associated uncertainties is a major research issue, as shown by the recent results of the European QUICS project 40. The term uncertainty here refers to the overall error of the output of a generic model 33. Translating time series of meteorological forecast into time series of runofriver hydropower generation necessitates to capture the complex relationship between the availability of water and the generation of electricity. The water flow is itself a nonlinear function of the physical characteristics of the river basins and of the weather variables whose impact on the river flow may occur with a delay.
5 New software and platforms
5.1 New software
5.1.1 CDMSci

Name:
Common Data Model for Scientific Workflows

Keywords:
Databases, Multiphysics modelling

Scientific Description:
CDMSci provides a unique framework to facilitate coupling/chaining of physical models, which operate at different scales or at different levels of description ranging from molecular dynamics to fluid mechanics, to build multiphysics and multiscale computational workflows that can be automatically executed. Hence, CDMSci is composed of two key ingredients:
1) A common data model for scientific computing: CDMSci offers a solution that collects information in a standardized method in the form a query tree designed to identify the physical and numerical models needed in a given situation. This means that each situation to be simulated is first decomposed into a set of physical components, which are defined as either discrete or continuum systems (quantum systems are not addressed in the present version). Then, a physical description is detailed for each component to fully characterize its nature as well as the physical processes at play. This can lead to introducing a number of subcomponents which play a specific physical role. Once the physics at stake (variables, laws, evolution equations) is clarified, a numerical description is chosen either in terms of a set of interacting particles or continuous fields for every component or subcomponent. By resorting to this combined physical and numerical points of view, the proposed solution offers naturally a way to specify the various numerical softwares needed to simulate the systems of interest. In addition, regardless of whether the workflow requires a single software or to couple several ones, the information exchanged between components, or subcomponents, is clearly identified thanks to specific queries. Finally, when the workflow combines several softwares, similar queries allow to identify the information exchanged between them (inputs/outputs identification), as well as the transformations required (mappers) and the format of the data to be exchanged (wrappers).
2) Computational sciences tools for automatic code generation and execution In order to facilitate coding of new models and execution of calculation workflows coupling different models (like discrete and continuum models), new tools for automatic code generation are developed and validated. For that purpose, CDMSci relies on a Model Driven Architecture (MDA) development approach, which is based on the assumption that codes can be produced from abstract, humanelaborated modelling diagrams. It allows to generate standardized data to describe models, such as XSD (XML Schema Definition).
Targeted audience: CDMSci is of great interest for physicsoriented users as well as computer scientists.
 From the perspective of physicsoriented users, CDMSci allows engineers and scientists to go beyond the simulation setups they are familiar with by offering them the possibility to explore new multiscale physics by linking/coupling with models developed in nearby areas.
 From a computer science perspective, CDMSci can help experts to understand the needs of engineers/scientists, so that they can adapt existing computational techniques or orient new developments to make them accessible and relevant to engineers/scientists. In short, CDMSci bridges the gap between physicsoriented users and computer scientists.

Functional Description:
CDMSci stands for "Common Data Model for Scientific Simulation Workflows". As a data model, CDMSci is a tool that organizes elements of data and standardizes how they relate to one another and to the properties of realworld entities. As applied to scientific simulations, CDMSci is specifically designed to organize elements of data corresponding to the physical and numerical information required to setup scientific simulations. CDMSci has been developed to address multiphysics and multiscale problems (e.g. multiphase flows involving fluid mechanics, surface sciences, material sciences and/or chemistry). CDMSci allows naturally such multiscale models to be mapped into computational workflows, which link/chain scientific softwares operating at different scales. These computational workflows can then be executed on a set of computational resources following an automatic procedure. In short, CDMSci provides a common standardized structure (Common Data Model) for the setup and execution of scientific simulation workflows.

Release Contributions:
CDMSci has been developed first conceptually (through a documentation in the form of a list, which gives the structure of the query tree). Second, an operational version of this query tree has been implemented in an Eficas catalog. It currently contains all the information to setup simulations of multiphase flows and, to a lesser extent, some Molecular Dynamics simulation. Since the structure is generic and open, extra information can be added to account for other physical phenomena (e.g. material science, chemistry, electromagnetism, quantum effects).

News of the Year:
CDMSci has been developed first conceptually (through a documentation in the form of a list, which gives the structure of the query tree). Second, an operational version of this query tree has been implemented in an Eficas catalog. It currently contains all the information to setup simulations of multiphase flows and, to a lesser extent, some Molecular Dynamics simulation.
Since the structure is generic and open, extra information can be added to account for other physical phenomena (e.g. material science, chemistry, electromagnetism, quantum effects).
 URL:

Contact:
Christophe Henry

Participants:
Christophe Henry, Mireille Bossy

Partner:
Edf
6 New results
6.1 Axis A – Complex flows: from fundamental science to applied models
6.1.1 Lagrangian stochastic model for the orientation of nonspherical particles in turbulent flow: an efficient numerical method for CFD approach
Participants: Jérémie Bec, Mireille Bossy, Lorenzo Campana, Christophe Henry.
Suspension of anisotropic particles can be found in various industrial applications. Microscopic ellipsoidal bodies suspended in a turbulent fluid flow rotate in response to the velocity gradient of the flow. Understanding their orientation is important since it can affect the optical or rheological properties of the suspension. The equations of motion for the orientation of microscopic ellipsoidal particles were obtained by Jeffery 28. But so far, this description has always been investigated in the framework of direct numerical simulations (DNS) and experimental measurements. In particular, inertiafree particles, with sizes smaller than the Kolmogorov length, follow the fluid motion with an orientation generally defined by the local turbulent velocity gradient.
In this work, our focus is to characterize the dynamics of these objects in turbulence by means of a stochastic Lagrangian approach. The development of a model that can be used as a predictive computational tool in industrial computational fluid dynamics (CFD) codes is highly valuable for practical applications. Models that reach an acceptable compromise between simplicity and accuracy are needed for progressing in the field of medical, environmental and industrial processes. A large part of our activity dealt with the dynamics of ellipsoidal particles in turbulent flows, with the main motivation of improving models used in applications. Actually, the translational and rotational dynamics of such nonspherical particles is directly related to their orientation, which has to be properly calculated. Micro and macroscopic viewpoints were addressed simultaneously.
More precisely, we have introduced a stochastic Lagrangian model for the angular dynamics of inertialess spheroids. The model consists of superimposing a shortcorrelated random component to the largescale average fluidvelocity gradient 8. In 2D flow with a mean shear, comparison with DNS allowed a precise calibration of this approach and emphasized the role played by the coherent structures of the flow in the particles angular dynamics 4. These promising Lagrangian stochastic approaches were then extended to 3D cases and implemented in a practical macroscopic model for turbulent transport 12 (currently available in the opensource CFD software Code_Saturne).
6.1.2 Clusters of heavy particles in twodimensional Keplerian turbulence
Participants: Jérémie Bec.
In collaboration with Fabiola Antonietta Gerosa and Héloïse Meheut, (Observatoire de la Côte d'Azur – Lagrange), we have studied particles in flows with a homogeneous shear, motivated by the formation of planets and the smallscale dynamics of the gasdust mixture in Keplerian rotation around the star.
Protoplanetary disks are gaseous systems in Keplerian rotation around young stars, known to be turbulent. They include a small fraction of dust from which planets form. In the incremental scenario for planet growth, the formation of kilometersize objects (planetesimals) from pebbles is a major open question. Clustering of particles is necessary for solids to undergo a local gravitational collapse. To address this question, we studied the dynamic of inertial particles in turbulent flows with Keplerian rotation and shear. Twodimensional direct numerical simulations are performed to explore systematically two physical parameters: the rotation rate, which depends on the distance to the star, and the particle response time, which relates to their size. We found that in such situations shear drastically affects the characteristics of the turbulent flow destroying cyclones and favoring the survival of anticyclones 13. Faster rotation enhances clustering of particles in anticyclones, especially for intermediate particle sizes. These clusters form in a hierarchical manner and merge together with time. For parameter values falling outside this regime, solids still concentrate on fractal sets. The mass distribution of particles is then found to be multifractal with small dimensions at large orders, intriguing for triggering their gravitational collapse. Such results are promising for a precise description and better understanding of planetesimal formation.
6.1.3 Modeling of the formation and maturation of soot particle aggregates
Participant: Christophe Henry.
Studying the agglomeration of small nanoparticles (a few nanometers in size) or atomic clusters has remarkable importance for the synthesis of nanoparticles at industrial scale. However, this is a challenge since different physical phenomena have to be considered for instance atomic clusters can experience coalescence upon collisions while larger nanoparticles may experience a rebound after collisions. This means that a sticking probability has to be taken into account. This sticking probability is currently poorly understood especially for nanoparticles formed in flames where changes in agglomeration and flow regimes occur simultaneously.
This study focuses on the aggregation of nascent soot particles, which are very important to predict well soot particle size distribution and morphology in flames. Such nascent soot particles may grow in the reactionlimited aggregation regime (sticking probability $\ll $ 1). However, it is currently unknown how fast would be the transition towards diffusion/ballisticlimited aggregation regimes as observed for mature soot (sticking probability close to 1). In this collaborative work, we intend to fill this gap by focusing on numerically simulated soot particles formed in a laminar premixed flame. To this end, a recent fast and accurate Monte Carlo discrete element code called MCAC (developed at CORIA) is used. In these simulations the individual trajectories of particles are integrated in time. The MCAC has been adapted to nonunitary collision and sticking probability considering three different outcomes for interacting aggregates: no collision, sticking or rebound. Using such finescale simulations, we have shown that assuming a unitary sticking and collision probability produces no big changes in the aggregation kinetics, particle size distribution, and aggregate morphology. Meanwhile, the soot particles' bulk density was found to affect the aggregation kinetics and particle size distribution. This is an important result for macroscopic models: such effects should be considered in future simulations relying on Population Balance Equations (PBE).
This work is a collaboration with José Moran and Jérôme Yon from Coria which started in 2021 and has been pursued in 2022. It was presented at the French Congress on Aerosol in 2022 17.
6.2 Axis B – Particles and flows near boundaries: specific Lagrangian approaches for largescale simulations
6.2.1 New spatial decomposition method for accurate, meshindependent agglomeration predictions in particleladen flows
Participants: Mireille Bossy, Christophe Henry.
Computational fluid dynamics simulations in practical industrial/environmental cases often involve nonhomogeneous concentrations of particles. In EulerLagrange simulations, this can induce the propagation of numerical error when the number of collision/agglomeration events is computed using meanfield approaches. In fact, meanfield statistical collision models allow to sample the number of collision events using a priori information on the frequency of collisions (the collision kernel). Yet, since such methods often rely on the mesh used for the Eulerian simulation of the fluid phase, the particle number concentration within a given cell might not be homogeneous, leading to numerical errors. In this article, we apply the datadriven spatial decomposition (D2SD) algorithm, recently proposed in a previous work reported in 32, to control such error in simulations of particle agglomeration. This D2SD algorithm provides a spatial splitting according to the spatial distribution of particles. More precisely, the D2SD algorithm uses as input data only the information on the location of the center of gravity of each particle. One of the many advantages of the D2SD algorithm is that the parameters leading to the optimal domain decomposition are automatically tuned through the statistical information coming from the data (position of particles). Thus, there is no bias coming from the choice of arbitrary parameters.
Significant improvements are made to design a fast D2SD version, minimizing the additional computational cost by developing remeshing criteria. Several options are assessed, introducing a criterion to avoid applying the full version of the D2SD algorithm every time step, or simplifying uniformity tests. The main difficulty is to ensure that the adapted algorithm keeps an appropriate balance between its accuracy and its computational costs.
Through the application to some practical simulation cases, we show the importance of splitting the domain when computing agglomeration events in Euler/Lagrange simulations, so that there is a spatially uniform distribution of particles within each elementary cell. The algorithm is coupled to 3D simulations of particle agglomeration in practical cases with a twofold objective: first, we assess the accuracy and efficiency of the method in a validation case; second, we illustrate how the D2SD can be applied in a practical case that is representative of situations of interest in the multiphase flow community.
This study is detailed in 7 in collaboration with Kerlyns Martinez (University of Valparaiso), published in the International Journal of Multiphase Flow.
6.2.2 Evidence of collisioninduced resuspension of microscopic particles from a monolayer deposit and new models
Participants: Mireille Bossy, Christophe Henry.
This study aims at bridging the gap between the understanding and modeling of particle resuspension in monolayer deposits and multilayer deposits. More precisely, modeling resuspension is indeed a challenging task owing to its complexity and multiscality. In practice, numerical concepts describing the resuspension at the particle scale, that is in the micron to millimeter size, exist. However, such models have been designed to treat two limit cases: monolayer or multilayer deposits. In the monolayer case, the interparticle distance $L$ is implicitly assumed to be much greater than the particle diameter ${D}_{p}$ ($L\gg {D}_{p}$), so that each resuspension event can be treated independently. In the multilayer case where particles sit on top of one another ($L\ll {D}_{p}$), resuspension events involve either single particles or clusters of particles depending on the local deposit structure and interparticle cohesion forces. Yet, a unified description of particle resuspension from monolayer to multilayer deposits is still missing.
The collaboration with researchers from Technische Universität Dresden in Germany (especially Grégory Lécrivain) has been pursued this year. The results obtained last year revealed the role of interparticle collisions on particle resuspension even for monolayer deposits at intermediate surface coverage (where $L\sim {D}_{p}$) 21. These results have been presented at the French Congress on Aerosol in 2022 16. Drawing on these results, more systematic analysis of the images obtained by experimental observations performed at TUD have been carried out. The idea is to extract detailed information on the outcome of each collision that happens between particles at the surface, especially to monitor the kinetic energy and momentum of both particles involved in the collision. By comparing these values, the objective is to determine if collisions at the surface conserve the kinetic energy and momentum (as is the case for elastic collisions in the bulk of a fluid) and, if not, to evaluate the loss of kinetic energy and/or momentum. These works are still in progress due to the difficulties encountered in the precision of the image analysis techniques (used to extract the particle positions at subsequent times).
6.2.3 Challenges in the modeling of particle resuspension
Participants: Christophe Henry.
The purpose of this work is to review the current challenges in the field of particle resuspension. In particular, we analyze the physics at play in particle resuspension in order to bring insights into the rich complexity of this common but challenging concern. This is performed by starting from a range of practical observations and experimental data. We then work our way through the investigation of the key mechanisms which play a role in the overall process. At the core of this analysis are descriptions of these physical phenomena and the different ways through which they are intertwined to build up various models used to provide quantitative assessment of particle resuspension. The physics of particle resuspension implies to hold together processes occurring at extremely different space and time scales. This raises questions on what makes up a model and one objective of the present work is to clarify the essence of a modeling approach.
This collaborative work with researchers from Los Alamos National Laboratory (Sara Brambilla) and from EDF R&D (JeanPierre Minier) is published in Physics Reports 6.
6.3 Axis C – Active agents in a fluid flow
This research axis deals with the study of selfpropelled particles, which have the ability to convert internal or ambient free energy into dynamical motion. Such active agents can be microorganisms, such as bacteria or plankton, as well as artificial devices used for micromanufacturing, toxic waste disposal, targeted drug delivery or localized medical diagnostics. Many questions remain open on how to control the displacement of these microswimmers, in particular for complex flows comprising inhomogeneities, fluctuations, obstacles, walls, or having a nonNewtonian rheology. Studying and optimizing the displacement of these swimmers is generally done in two successive steps. The first is to find a locomotion strategy by choosing the composition, shape, and deformation for an efficient swimming. The second is to define a navigation strategy aimed at minimizing the energy needed to reach a target in a given environment. Calisto works rely on crossdisciplinary skills, comprising the optimal control of viscous flows, smallscale fluidstructure interactions, statistical modeling, and largescale turbulent transport to tackle both aspects, locomotion and navigation, at once.
6.3.1 Finite Element Methods for simulate displacement of flagellated microswimmers
Participants: Laetitia Giraldi.
In collaboration with Lucas Berti (IRMA, Strasbourg), Vincent Chabannes (IRMA, Strasbourg) and Christophe Prud'Homme (IRMA, Strasbourg), in 10, we consider the problem of moving rigid bodies in a Newtonian fluid. The fluidsolid problem is solved using the finite element method, and the solution is based on the ArbitraryLagrangianEulerian description of the fluid with conforming treatment of moving interfaces. Numerical experiments are discussed, and the results are validated with the literature. The results are obtained with the Feel++ open source library.
6.3.2 Reinforcement learning with function approximation for 3spheres swimmer
Participants: Luca Berti, Zakarya Elkhyiati, Laetitia Giraldi.
In collaboration with Christophe Prud'Homme (IRMA, Strasbourg) and Youssef Essoussy (IRMA, Strasbourg), the paper 11 investigates the swimming strategies that maximize the speed of the threesphere swimmer using reinforcement learning methods. First of all, we ensure that for a simple model with few actions, the Qlearning method converges. However, this latter method does not fit a more complex framework (for instance the presence of boundary) where states or actions have to be continuous to obtain all directions in the swimmer's reachable set. To overcome this issue, we investigate another method from reinforcement learning which uses function approximation, and benchmarks its results in absence of walls.
6.3.3 Necessary conditions for local controllability of a particular class of systems with two scalar controls
Participant: Laetitia Giraldi.
In this paper 14 in collaboration with Pierre Lissy (Ceremade, Paris), JeanBaptiste Pomet (Inria, McTAO) and Clement Moreau (RIMS, Kyoto, Japan), we consider controlaffine systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in ${\mathrm{L}}^{\infty}$ or small in ${\mathrm{W}}^{1,\infty}$. These results were deduced from the behavior of the magnetic flagellated swimmers and they are illustrated with several examples.
The paper is submitted. It was also a chapter of the PhD thesis of Clement Moreau.
6.3.4 Reinforcement learning for the locomotion and navigation of undulatory microswimmers in chaotic flow
Participants: Zakarya El Khyiati, Jérémie Bec, Laetitia Giraldi.
We developed a framework to study the motion of vermiform microswimmers, selfpropelling by undulating their body. Such deformable swimmers have a high potential because of their aptness to carry out a broad set of swimming strategies and to select the most efficient one according to the biological media where they evolve. Many questions are still open on how these microswimmers optimize their displacement, in particular when they are embedded in a complex environment. In practice the swimmers navigate in a fluctuating medium comprising walls and obstacles, a fluid flow possibly with nonNewtonian properties or containing other swimmers. In this framework, optimizing their navigation requires dealing with a strongly nonlinear and chaotic highdimensional dynamics.
Using machine learning tools, we have developed new methods to address this optimisation problem where swimming and navigation are closely related. Techniques borrowed from partiallyobservable Markov decision processes were found to be particularly promising. Combining an efficient locomotion strategy with optimal navigation and pathplanning is particularly novel in the field. An article demonstrating the efficiency of genetic reinforcement learning for the displacement of undulatory swimmers in twodimensional flow is currently in preparation and will be submitted in the coming months to Physical Review Letters.
6.4 Axis D – Mathematics and numerical analysis of stochastic systems
Stochastic analysis, and related numerical analysis, together with improved statistical descriptions of highlynonlinear dynamics are central topics in Calisto. This research axis encompasses activities aiming, either (a) at strengthening our understanding on the origin and nature of fluctuations that are inherent to turbulent flows, or (b) at providing a coherent framework in response to the various mathematical challenges raised by the development of novel models in other research axes. Addressing these two fundamental aspects concomitantly to more practical and applied objectives is again a hallmark of the team.
6.4.1 Anomalous fluctuations for the Lyapunov exponents of tracers in developed turbulent flow
Participants: Jérémie Bec, Simon Thalabard.
The infinitesimal separation between tracers transported by a turbulent flow is generally characterized in terms of stretching rates and Lyapunov exponents obtained from the integration of the tangent system to the dynamics. We have shown that turbulent intermittency is responsible for longrange correlations in the Lagrangian fluid velocity gradient. This behavior, which does not question the existence of a law of large numbers and of Lyapunov exponents, seriously questions largedeviation approaches that are usually used to characterize the fluctuations of finitetime stretching rates and thus to quantify smallscale turbulent mixing. We propose alternative manners to qualify fluctuations based on generalizations of the centrallimit theorem to sums of correlated variables. These results were obtained in the framework of the ANR TILT project and are the subject of a manuscript that will be soon submitted to Physical Review Letters.
These results suggest introducing new Lagrangian stochastic models for smallscale turbulent mixing that extend traditional diffusive approach to noises with longrange time correlations. Fractional Brownian motion seems a promising candidate.
6.4.2 Anomalous dissipation and spontaneous stochasticity in deterministic surface quasigeostrophic flow
Participants: Jérémie Bec, Simon Thalabard, Nicolas Valade.
Surface quasi geostrophy (SQG) describes the twodimensional active transport of a temperature field in a strongly stratified and rotating environment. Besides its relevance to geophysics, SQG bears formal resemblance with various flows of interest for turbulence studies, from passive scalar and Burgers to incompressible fluids in two and three dimensions. This analogy is here substantiated by considering the turbulent SQG regime emerging from deterministic and smooth initial data prescribed by the superposition of a few Fourier modes. While still unsettled in the inviscid case, the initial value problem is known to be mathematically wellposed when regularised by a small viscosity. In practice, numerics reveal that in the presence of viscosity, a turbulent regime appears in finite time, which features three of the distinctive anomalies usually observed in threedimensional developed turbulence: (i) dissipative anomaly, (ii) multifractal scaling, and (iii) superdiffusive separation of fluid particles, both backward and forward in time. These three anomalies point towards three spontaneously broken symmetries in the vanishing viscosity limit: scale invariance, time reversal and uniqueness of the Lagrangian flow, a fascinating phenomenon that Krzysztof Gawedzki dubbed spontaneous stochasticity. In the light of Gawedzki's work on the passive scalar problem, in 15, we argue that spontaneous stochasticity and irreversibility are intertwined in SQG, and provide numerical evidence for this connection. Our numerics, though, reveal that the deterministic SQG setting only features a tempered version of spontaneous stochasticity, characterised in particular by nonuniversal statistics.
6.4.3 Strong rate of convergence of approximation scheme for SDEs with superlinear coefficients
Participants: Mireille Bossy.
In collaboration with Kerlyns Martinez (University of Valparaiso), we consider the problem of the approximation of the solution of a onedimensional SDE with nonglobally Lipschitz drift and diffusion coefficients behaving as ${x}^{\alpha}$ , with $\alpha >1$. On the basis of the previously proposed (semiexplicit) exponentialEuler scheme 23, we analyse its convergence through its strong approximation error. The main proof arguments developed in this study, based on a stochastic time change technique is rather generic and particularly useful for the strong error control of a Euler type scheme when the polynomial behavior of the coefficients only increases the number of moments to be bound in the dynamics of the error itself. With such a technique we explicit the rather accurate conditions on the parameters of the stochastic equation to get the classical order for the strong convergence rate. A journal paper will be submitted soon.
6.5 Axis E – Variability and uncertainty in flows and environment
6.5.1 Instantaneous turbulent kinetic energy modeling based on Lagrangian stochastic approach in CFD and application to wind energy
Participants: Mireille Bossy.
The need of statistical information on the wind, at a given location and on large time period, is of major importance in many applications such as the structural safety of large construction projects or the economy of a wind farm, whether it concerns an investment project, a wind farm operation or its repowering. The evaluation of the local wind is expressed on different time scales: monthly, annually or over several decades for resource assessment, daily, hourly or even less for dynamical forecasting (these scales being addressed with an increasing panel of methodologies). In the literature, wind forecasting models are generally classified into physical models (numerical weather prediction models), statistical approaches (timeseries models, machine learning models, and more recently deep learning methods), and hybrid physical and statistical models. At a given site and height in the atmospheric boundary layer, measuring instruments record time series of characteristics of the wind, such as wind speed characterizing load conditions, wind direction, kinetic energy and possibly power production. Such observations should feed into forecasting, but also uncertainty modeling. In this context, probabilistic or statistical approaches are widely used, helping to characterize uncertainty through quantile indicators.
In 3 in collaboration with Kerlyns Martinez (University of Valparaiso), we construct an original stochastic model for the instantaneous turbulent kinetic energy at a given point of a flow, and we validate estimator methods on this model with observational data examples. Motivated by the need for wind energy industry of acquiring relevant statistical information of air motion at a local place, we adopt the Lagrangian stochastic description of fluid flows to derive, from the 3D+time equations of the physics, a 0D+timestochastic model for the time series of the instantaneous turbulent kinetic energy at a given position. First, we derive a family of meanfield dynamics featuring the square norm of the turbulent velocity. By approximating at equilibrium the characteristic nonlinear terms of the dynamics, we recover the socalled CoxIngersollRoss process, which was previously suggested in the literature for modeling wind speed. We then propose a calibration procedure for the parameters employing both direct methods and Bayesian inference. In particular, we show the consistency of the estimators and validate the model through the quantification of uncertainty, with respect to the range of values given in the literature for some physical constants of turbulence modeling.
We pursue our work by now focusing on a reduced model for the short term prediction of wind gust risk.
6.5.2 Methodology to quantify uncertainties in dispersed twophase flows
Participants: Christophe Henry, Mireille Bossy.
Within the framework of the VIMMP EU project (Virtual Materials Market Place), one objective is to set up a methodology to analyze the sensitivity (SA) and then quantify uncertainty (UQ) in numerical simulations of multiphase flows to a number of input variables. For that purpose, a Common Data Model (CDM) has been developed to provide a comprehensive, adequate and standardized structure to collect all the physical and numerical information required to setup scientific simulation workflows (possibly including various software) while allowing for a systematic analysis of the results obtained using UQ&SA tools.
This collaborative work with partners involved in the VIMMP project (Pascale Noyret, Eric Fayolle and JeanPierre Minier from EDF R&D) resulted in the development of the new software CDMSci (see Section 5). An article is in preparation to describe the CDM and illustrate it on a few selected examples.
7 Bilateral contracts and grants with industry
7.1 Bilateral grants with industry
aVENTage – Towards a very high resolution wind forecast chain on the sailing basin of Marseilles.
Participants: Mireille Bossy.
aVENTage is an industrial partnership project with the two French startups SportRizer and RiskWeatherTech. Starting at the end of 2020, the genesis of this project was motivated by the next Paris 2024 Olympic Games, where the sailing events will take place in the Marseilles sailing basin. The reading of the wind is one of the major stakes in the search for performance for the sailing Olympics. However, the exhaustive knowledge of the wind on a body of water is not yet resolved.
aVENTage aims to complete the knowledge database of the different local effects in the Marseilles sailing basin, thus facilitating the exploitation of the water body.
A high resolution wind forecast allows to reduce the margin of error in the decision making. This is a determining factor for progress, accelerating learning and supporting the material and technical development underlying performance. To reach a very high resolution of 50 m horizontally, aVENTage relies on two distinct and successive downscaling processes to produce its results.

1.
An operational processing chain from largescale weather forecasts (GFS 50 km) up to 1 km resolution. Each day, the SportRIZER & RiskWeatherTech operational chain downloads the 0h00 GFS forecast data for the 0h00+1h to 0h00+48h time frames and performs a downscaling simulation with the WRF model down to 1 km resolution over the Marseilles area.

2.
A specific downscaling from the previous operation. To refine the wind simulation up to a resolution of 50 m, this second step relies on the SDMWindPoS model.
Preliminary results and case studies, as well as detailed methodologies are available on the SDMWindPos software webpage.
8 Partnerships and cooperations
8.1 International initiatives
IFCAM
Participants: Jéremie Bec, Nicolas Valade.
IFCAM:IndoFrench Center for Applied Mathematics is a CNRS IRL that provides support for a collaboration on “Turbulence in classical and quantum fluids” with teams at the Indian Institute of Science and the International Center for Theoretical Science in Bangalore. With the pandemic, the 2022 planed visit was postponed in January 2023.SDE:TNA (RSE Saltire Facilitation Network)
Participants: Mireille Bossy.
Started in 2022, Calisto takes part to the Royal Society of Edinburgh (RSE) Saltire Facilitation Network on SDEs: Theory, Numerics and Applications. This 2 years network project involves mathematicians of 9 European countries on the theme of (numerical) analysis for highly nonlinear SDEs. On the same themes, a submission of an European COST action is under preparation.
8.2 European initiatives
8.2.1 H2020 projects
Participant: Mireille Bossy, Christophe Henry.
VIMMP (Virtual Materials Market Place) is a EU H2020 project (started in January 2018 and ended in June 2022) in the program Industrial Leadership project in Advanced materials. VIMMP is a development project for a software platform and simulation market place on the topic of complex multiscale CFD simulations. As a VIMMP partner, Calisto is coworking with EDF R&D at designing complex workflows through the EDF’s crossplatform SALOME, involving Lagrangian aggregations, fragmentation with Code_Saturne. Calisto also addresses some typical workflow design for uncertainty quantification, and experiments with them in twophase flow simulation situation.
Design of a standardized method for multiphysics simulations.
Within the framework of the European VIMMP project, Calisto members have been coworking with EDF R&D at designing a standardized method (in the form of a query tree) that allows to collect all the physical and numerical information required to setup scientific workflows for multiphysics simulations. During this final phase of the project, the CDMSci software (see section 5) has been illustrated on a scientific workflow used to compute particle aggregation in a turbulent pipe flow (using the opensource CFD code Code_Saturne). A publication is in preparation.
8.2.2 ANR PRC TILT
Participant: Jérémie Bec.
The ANR PRC project TILT (Time Irreversibility in Lagrangian Turbulence) started on Jan. 1, 2021. It is devoted to the study and modeling of the fine structure of fluid turbulence, as it is observed in experiments and numerical simulations. In particular, recall that the finite amount of dissipation of kinetic energy in turbulent fluid, where viscosity seemingly plays a vanishing role, is one of the main properties of turbulence, known as the dissipative anomaly. This property rests on the singular nature and deep irreversibility of turbulent flows, and is the source of difficulties in applying concepts developed in equilibrium statistical mechanics. The TILT project aims at exploring the influence of irreversibility on the motion of tracers transported by the flow. The consortium consists of 3 groups with complementary numerical and theoretical expertise, in statistical mechanics and fluid turbulence. They are located in Saclay, at CEA (Bérengère Dubrulle), in Lyon, at ENSL (Laurent Chevillard, Alain Pumir), and in Sophia Antipolis (Jérémie Bec). Within TILT, a new postdoc joined Calisto in January 2023.
8.2.3 ANR JCJC NEMO
Participant: Laetitia Giraldi.
The JCJC project NEMO (controlliNg a magnEtic Microswimmer in cOnfined and complex environments) was selected by ANR in 2021, and started on Jan. 1, 2022 for four years. NEMO team is composed of Laetitia Giraldi, Mickael Binois (Inria, Acumes) and Laurent Monasse (Inria, Coffee).
NEMO aims at developing numerical methods to control a microrobot swimmer in the arteries of the human body. These robots could deliver drugs specifically to cancer cells before they form new tumors, thus avoiding metastasis and the traditional chemotherapy side effects.
NEMO will focus on microrobots, called Magnetozoons, composed of a magnetic head and an elastic tail immersed into a laminar fluid possibly nonNewtonian. These robots imitate the propulsion of spermatozoa by propagating a wave along their tail. Their movement is controlled by an external magnetic field that produces a torque on the head of the robot, producing a deformation of the tail. The tail then pushes the surrounding fluid and the robot moves forward. The advantage of such a deformable swimmer is its aptness to carry out a large set of swimming strategies, which could be selected according to the geometry or the rheology of the biological media where the swimmer evolves (blood, eye retina, or other body tissues).
Although the control of such microrobots has mostly focused on simple unconfined environments, the main challenge is today to design external magnetic fields that allow them to navigate efficiently in complex realistic environments.
NEMO aims at elaborating efficient controls, which will be designed by tuning the external magnetic field, through a combination of Bayesian optimization and accurate simulations of the swimmer's dynamics with Newtonian or nonNewtonian fluids. Then, the resulting magnetic fields will be validated experimentally in a range of confined environments. In such an intricate situation, where the surrounding fluid is bounded laminar and possibly nonNewtonian, optimization of a strongly nonlinear, and possibly chaotic, highdimensional dynamical system will lead to new paradigms.
8.2.4 ANR PRC NETFLEX
Participant: Jérémie Bec, Mireille Bossy, Laetitia Giraldi, Christophe Henry, Paul Maurer.
The ANR PRC project NEFFLEX (Tangles, knots, and breakups of flexible fibers in turbulent fluids) started on January 1, 2022. NETFLEX is a four years project that aims at advancing our knowledge on the dynamics of long, flexible, macroscopic fibres in turbulent flow, and to understand and model the processes of fibre fragmentation and aggregation. NETFLEX brings together Université Côte d'Azur (INPHYNI, LJAD), Inria (Calisto) and AixMarseille University (IRPHE). NETFLEX approach combines three levels of description (micro, meso, and macroscopic) and relies on a synergy between mathematical modeling, numerical simulations, and laboratory experiments. It relies on the development of newly designed experiments and a substantial improvement of the mathematical and numerical tools currently used in the study of fibre dynamics. An overall aim is to develop a new framework able to cope with such intricate effects of turbulence and to reproduce the significant observable features in a macroscopic approach.
Improved modelling of turbulent fluctuations and effective transport models for aggregates are among the key issues to be addressed in order to extend the macroscopic models.
Starting in October 2022, Paul Maurer's thesis work on analysis and simulation for temporal intermittency and longrange correlation models is part of this project, and will be applied to the dynamics of flexible particles.
9 Dissemination
Participants: Jérémie Bec, Mireille Bossy, Laetitia Giraldi, Christophe Henry.
9.1 Promoting scientific activities
9.1.1 Scientific events
Chairing / Organizing events
 Mireille Bossy chaired and coorganized the EMRSIM 2022 Conference on simulation and optimization for marine renewable energy, which was held in Roscoff (May 2022).
Scientific seminars of the Team

Since November 2020, Calisto is organizing a Periodic Team Seminar every 4 weeks.
In 2022, the following researchers were invited to give a presentation: Raphael Chetrite (LJAD, Nice), Michel Bergmann (Team Memphis, Inria, Bordeaux), Roxane Letournel (Safran, Chateaufort), Guillaume Cordonnier (Team GraphDeco, Inria, Sophia Antipolis), Valentina Sessa (CMA, Mines ParisTech, Sophia Antipolis), Eric Simonnet (InPhyNi, Nice), Sebastian Jara (University of Valparaiso, Chile), Nicolas Valade (Team Calisto, Inria, Sophia Antipolis), Sugan Murugan (ICTS, Bengalore, India).
9.1.2 Journal
Member of the editorial boards
 Jérémie Bec acted as a guest editor for a special issue of the Philosophical Transactions of the Royal Society A entitled “Scaling the turbulence edifice”, which gathered 25 contributions.
Reviewer  reviewing activities
 Mireille Bossy acted in 2022 as a reviewer for the following international journals: Stochastics, Journal of Mathematical Analysis and Applications; ESAIM: M2AN, IMA Journal of Numerical Analysis.
 Christophe Henry acted as a reviewer for Acta Mechanica, Journal of Aerosol Science and Physical Review Fluids.
9.1.3 Invited talks
 Jérémie Bec was invited speaker to the following events: Atmospheres, Oceans, Earths – Unifying perspectives on geophysical and environmental multiphase flows (Santa Barbara, October 2022); Challenges and benchmarks for AI in complex fluids and flows (Rome, July 2022); Complex Lagrangian problems of particles in flows (Bangalore, March 2022), Modelling and analysis of turbulent transport, mixing and scaling (Cambridge, March 2022); Stochastic approaches to turbulence in hydrodynamical equations (Banff, March 2022).
 Mireille Bossy was invited speaker to the following events: International Seminar on SDEs and Related Topics (February 2022), RSE Saltire Facilitation Network on SDEs Seminar (February 2022), RSE Saltire Facilitation Network on SDEs Workshop (August 2022).
9.1.4 Leadership within the scientific community
 Jérémie Bec is in charge of the Academy of excellence "Complex Systems" of the IDEX Université Côte d’Azur (Decisionmaking role for funding; Coordination and animation of federative actions; Participation in the IDEX evaluation).
 Mireille Bossy is Chairing of the Scientific Council of the Academy of excellence "Complex Systems" of the IDEX Université Côte d’Azur.
Calisto team members are involved in the scientific/steering committees of several national research networks. This includes the following GdR (CNRS Research network): GdR MascotNUM on stochastic methods for the analysis of numerical codes, GdR Défis théoriques pour les sciences du climat on theoretical aspects for climate science, and GDR Calcul that promotes communication and exchange within the computing community in France. Calisto team members are also involved as partners in other networks including: GdR NavierStokes 2.0 on turbulence, and ASFERA, the French Association on Studies and Research on Aerosols.
9.1.5 Scientific expertise
 Mireille Bossy reviewed project propositions from the generic ANR AAP 2022 and from H2020MSCACOFUND.
9.2 Teaching  Supervision  Juries
9.2.1 Teaching
Calisto scientific staff have been involved in the following teaching activities:
 Stochastic modeling and numerical tools around the physics of complex flows (M. Bossy) a 10h course as guest lecturer to the 31st International Jyväskylä Summer School (advance graduate and PhD students).
 Fluid dynamics and turbulence (J. Bec): Doctoral Mines Paris (6h), ICTS (12h).
 The physics of turbulent flow (J. Bec): 2ndyear Mines Paris (4h).
 Microswimming (L. Giraldi): Master 2 cell physics Université de Strasbourg (6h).
 Assignments (Khôlles) in preparatory schools MPSI, MP* (Laetitia Giraldi, 2h weekly, Centre International de Valbonne).
 Advanced models for hydrology (C. Henry): master students in their final (5th) year within the program “Génie de l'eau” (58h) at the engineering school Polytech'Nice.
9.2.2 Supervision
 PhD in progress: Paul Maurer, “ Stochastic models for deformable particle dynamics in turbulence: mathematical analysis and simulation for temporal intermittency and longrange correlation models” started in October 2022; supervised by Mireille Bossy.
 PhD in progress: Nicolas Valade, “Spontaneous stochasticity of quasigeostrophic surface turbulence” started in October 2022; supervised by Jérémie Bec.
 PhD in progress: Zakarya El Khiyati, “Reinforcement learning for the optimal locomotion of microswimmers in a complex chaotic environment” started in October 2021; supervised by Jérémie Bec and Laetitia Giraldi.
 PhD in progress: Fabiola Gerosa, “Turbulent fluidparticles coupling and applications to planet formation” started in October 2021; supervised by Jérémie Bec and Héloïse Méheut (Lagrange, Observatoire de la Côte d'Azur).
 PhD defended in March 29, 2022: Lorenzo Campana, “Stochastic modeling of nonspherical particles in turbulence”; supervised by Mireille Bossy.
 M2 Internship: Belgacem Othman (Sorbonne University, Paris), “Particle resuspension: modeling the effect of interparticle collisions”, supervised by Christophe Henry.
 M2 Internship: Paul Maurer (Sorbonne University), "Stochastic dynamics of particles in turbulence", supervised by Mireille Bossy.
 M2 Internship: Nicolas Valade (Mines ParisTech), "Spontaneous stochasticity of quasigeostrophic surface turbulence", supervised by Jérémie Bec.
 M2 Internship: Carlamaria Cosenza (Politecnico di Torino), "Simulation of the dynamics of inertial particles in model flows", supervised by Jérémie Bec.
 M2 Internship: Hao Liu (Technology University Darmstad), "Numerical methods for optimizing the locomotion of flagellated microswimmers", supervised by Laetitia Giraldi and Jérémie Bec.
 M1 Internship: Mateo Ghezal (Université ParisSaclay), "Tangent velocity of a reflected Langevin process and related bridge of the Brownian integral", supervised by Mireille Bossy.
9.2.3 Juries
 Mireille Bossy served as an examiner for the Ph.D. theses of Roxane LETOURNEL (CentralSupÉlec, February 2022), Rémi GERARD (Mines ParisTech, July 2022), Jean Michel MASEO (Université Côte d’Azur, November 2022).
9.3 Popularization
9.3.1 Interventions

General audience talks (within Inria):
The communication team within Inria Centre at Université Côte d’Azur is organizing general audience talks where researchers present some of their activities to staffs&researchers from the Inria centre.
 Christophe Henry gave a presentation in February 2022 at Café In about the “Physics of sand castles”.
 Laetitia Giraldi gave a presentation in March 2022 at Café In about the “Scallop theorem”.

Fête de la Science:
Every year, a science festival is held across France in autumn where researchers present their activities to the public (especially for kids and young students).
 Christophe Henry took part in the festival held in Valbonne (Terra Numerica) and in Mouans Sartoux in October 2022, presenting a workshop on the “Physics of sand castles”.
10 Scientific production
10.1 Publications of the year
International journals
 1 articleEditorial: Scaling the Turbulence Edifice.Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences3802218March 2022
 2 articleEditorial: Scaling the Turbulence Edifice (part 2).Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences3802219March 2022
 3 articleInstantaneous turbulent kinetic energy modelling based on Lagrangian stochastic approach in CFD and application to wind energy.Journal of Computational PhysicsSeptember 2022
 4 articleStochastic model for the alignment and tumbling of rigid fibres in twodimensional turbulent shear flow.Physical Review Fluids7122022, 124605
 5 articleTurbulent route to twodimensional soft crystals.Physical Review E 2022
 6 articleParticle resuspension: challenges and perspectives for future models.Physics Reports2022
 7 articleParticle agglomeration in flows: fast datadriven spatial decomposition algorithm for CFD simulations.International Journal of Multiphase Flow149April 2022, 103962
Doctoral dissertations and habilitation theses
 8 thesisStochastic modelling of nonspherical particles in turbulence.Université Côte d'AzurMarch 2022
Reports & preprints
 9 reportReport SEME for SCALIAN.IRMAR  Université Rennes 1; Université Bretagne Sud; Université Cote d'AzurMay 2022, 14
 10 miscFLUIDRIGID BODY INTERACTION USING THE FINITE ELEMENT METHOD AND ALE FORMULATION: FRAMEWORK, IMPLEMENTATION AND BENCHMARKING.October 2022
 11 miscReinforcement learning with function approximation for 3spheres swimmer.January 2022
 12 miscLagrangian stochastic model for the orientation of inertialess non spherical particles in turbulent flows: an efficient numerical method for CFD approach.November 2022
 13 miscClusters of heavy particles in twodimensional Keplerian turbulence.November 2022
 14 miscNecessary conditions for local controllability of a particular class of systems with two scalar controls.September 2022
 15 miscAnomalous dissipation and spontaneous stochasticity in deterministic surface quasigeostrophic flow.November 2022
Other scientific publications
 16 miscEVIDENCE OF COLLISIONINDUCED EFFECTS IN PARTICLE RESUSPENSION.Paris, FranceMay 2022
 17 inproceedingsVan der Waals interaction forces between raspberrylike Agglomerates of Nanoparticles.CFA 2022  Congres Français sur les AérosolsParis, FranceMay 2022
10.2 Cited publications
 18 miscAdaptation challenges and opportunities for the European energy system Building a climate‑resilient low‑carbon energy system.2019
 19 articleSelfpropulsion of slender microswimmers by curvature control: Nlink swimmers.International Journal of NonLinear Mechanics562013, 132141
 20 articleTurbulent Dispersed Multiphase Flow.Annual Review of Fluid Mechanics4212010, 111133
 21 articleEvidence of collisioninduced resuspension of microscopic particles from a monolayer deposit.Physical Review Fluids682021, L082301
 22 articleThe quiet revolution of numerical weather prediction.Nature52575672015, 4755
 23 articleOn the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth.Bernoulli271https://arxiv.org/abs/1904.094412021, 312347
 24 misc10 Trends Reshaping Climate and Energy.2018
 25 inbookWhat Does the Energy Industry Require from Meteorology?Weather & Climate Services for the Energy IndustryA.A. TroccoliChamSpringer International Publishing2018, 4163
 26 techreportFog, Glossary of Meteorology.American Meteorological Society2017
 27 articleStatistical models for spatial patterns of heavy particles in turbulence.Advances in Physics6512016, 157
 28 articleThe motion of ellipsoidal particles immersed in a viscous fluid.Proc. Royal Soc. Lond. A1027151922, 161179
 29 articleSources, fate and effects of microplastics in the marine environment: part 2 of a global assessment.Reports and studiesIMO/FAO/UnescoIOC/WMO/IAEA/UN/UNEP Joint Group of Experts on the Scientific Aspects of Marine Environmental Protection (GESAMP) eng no. 932015
 30 articlePlanet formation.Annual review of astronomy and astrophysics3111993, 129172
 31 articleHydrodynamics of soft active matter.Reviews of Modern Physics8532013, 1143
 32 articleNew spatial decomposition method for accurate, meshindependent agglomeration predictions in particleladen flows.Applied Mathematical Modelling902021, 582614
 33 articleWhat do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology.Hydrological Processes: An International Journal2162007, 841845
 34 articleAnalytical Modeling of Wind Farms: A New Approach for Power Prediction.Energies99, 7412016
 35 articleAmbient air pollution: A global assessment of exposure and burden of disease.2016
 36 articleCollisional Aggregation Due to Turbulence.Annual Review of Condensed Matter Physics712016, 141170
 37 articleAerodynamic Aspects of Wind Energy Conversion.Annual Review of Fluid Mechanics4312011, 427448
 38 articleTURBULENT RELATIVE DISPERSION.Annual Review of Fluid Mechanics3312001, 289317
 39 articlePhysics and modelling of turbulent particle deposition and entrainment: Review of a systematic study.International Journal of Multiphase Flow359Special Issue: PointParticle Model for Disperse Turbulent Flows2009, 827  839
 40 techreportQUICS  D.1.1 Report on uncertainty frameworks; QUICS  D.4.2 Report on application of uncertainty frameworks, potential improvements.USFD and TUD2017
 41 articleModel of particle resuspension in turbulent flows.Nuclear Engineering and Design238112008, 29432959
 42 articleAnisotropic Particles in Turbulence.Annual Review of Fluid Mechanics4912017, 249276