Keywords
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.1.4. Multiscale modeling
 A6.1.5. Multiphysics modeling
 A6.2. Scientific computing, Numerical Analysis & Optimization
 A6.2.1. Numerical analysis of PDE and ODE
 A6.2.8. Computational geometry and meshes
 A6.3. Computationdata interaction
 A6.3.4. Model reduction
 A6.3.5. Uncertainty Quantification
 A6.5.2. Fluid mechanics
 B3.3.2. Water: sea & ocean, lake & river
 B3.3.3. Nearshore
 B3.4.1. Natural risks
 B4.3.2. Hydroenergy
 B5.2.1. Road vehicles
 B5.2.3. Aviation
 B5.2.4. Aerospace
 B5.5. Materials
1 Team members, visitors, external collaborators
Research Scientists
 Mario Ricchiuto [Team leader, INRIA, Senior Researcher, HDR]
 Remi Abgrall [Univ. Zurich, Chair]
 Elena Gaburro [INRIA, Researcher]
 Maria Kazolea [INRIA, Researcher]
 Martin Parisot [INRIA, Researcher]
Faculty Members
 Nicolas Barral [BORDEAUX INP, Associate Professor]
 Héloïse Beaugendre [BORDEAUX INP, Associate Professor, HDR]
 Mathieu Colin [BORDEAUX INP, Associate Professor, HDR]
PostDoctoral Fellows
 Sourabh Bhat [INRIA, from Aug 2022]
 Michele Giuliano Carlino [INRIA]
 Mariem Makni [INRIA, until Aug 2022]
 Sergey Tkachenko [INRIA, from Jun 2022]
PhD Students
 Tiffanie Carlier [UNIV BORDEAUX]
 Manon Carreau [INRIA]
 Aurore Cauquis [CEA]
 Mirco Ciallella [INRIA, until Sep 2022]
 Bastien Jouy [EDF, CIFRE]
 Sixtine Michel [INRIA]
 Florent Nauleau [CEA]
 Eli Solai [INRIA, until Mar 2022]
 Ishak Tifouti [INRIA, from Oct 2022]
Technical Staff
 Francesco Brarda [INRIA, Engineer, until Jul 2022]
 Luca Cirrottola [INRIA, Engineer]
 Pierre Clouzet [INRIA, Engineer, from Dec 2022]
 Christopher Poette [INRIA, Engineer, until Mar 2022]
Administrative Assistant
 AnneLaure Gautier [INRIA]
Visiting Scientists
 Alessia Assonitis [University of Sapienza, from Mar 2022 until Jun 2022]
 Lorenzo Micalizzi [UNIV ZURICH, until Feb 2022]
External Collaborators
 Cristian Brutto [Univ. Trent]
 Leo Nouveau [INSA Rennes]
 Ilya Peshkov [Univ. Trento]
 Davide Torlo [University of Zurich]
2 Overall objectives
CARDAMOM is a joint team of INRIA Bordeaux  SudOuest, University of Bordeaux and Bordeaux Inst. Nat. Polytechnique) and IMB (Institut de Mathématiques de Bordeaux – CNRS UMR 5251, University of Bordeaux). CARDAMOM$\phantom{\rule{0.277778em}{0ex}}$has been created on January 1st, 2015 (website).
The CARDAMOM project aims at providing a robust modelling strategy for engineering applications involving complex flows with moving fronts. The term front here denotes either an actual material boundary (e.g. multiple phases), a physical discontinuity (e.g. shock waves), or a transition layer between regions with completely different dominant flow behaviour (e.g. breaking waves). These fronts introduce a multiscale behaviour. The resolution of all the scales is however not feasible in certification and optimization cycles. Moreover, the full scale behaviour is not necessary in many engineering applications, while in others it is enough to model the average effect of small scales on large ones (closure models). We plan to develop applicationtailored models obtained by a tight combination of asymptotic PDE (Partial Differential Equations) modelling, adaptive high order PDE discretizations, and a quantitative certification step assessing the sensitivity of outputs to both model components (equations, numerical methods, etc) and random variations of the data. The goal is to improve operational models used in parametric analysis and design cycles, by increasing both accuracy and confidence in the results. This is achieved by combining improved physical and numerical modelling, and assessment of output uncertainties. This requires a research program mixing of PDE analysis, high order discretizations, Uncertainty Quantification (UQ), and to some extend optimization and inverse modelling. These skiss need to be also combined with some specific engineering know how to tackle specific applications. Part of this scientific themes and of these activities have been part of the work of the BACCHUS and MC teams. CARDAMOM harmonizes and gives new directions to this know how.
2.1 Scientific context and challenges
The objective of CARDAMOM is to provide improved analysis and design tools for engineering applications involving fluid flows with moving fronts. In our applications a front is either an actual material interface, a boundary of the domain, or a well identified transition region in which the flow undergoes a change in its dominant macroscopic character. One example is the certification of wing deanti icing systems, involving the predictions of ice formation and detachment, and of ice debris trajectories to evaluate the risk of downstream impact on aircraft components 114, 58. Another application, relevant for space reentry, is the study of transitional regimes in high altitude gas dynamics in which extremely thin layers appear in the flow which cannot be analysed with classical continuous models (NavierStokes equations) used by engineers 65, 87. A classical example relevant in coastal engineering is free surface flows. The free surface itself is a material interface, but we can identify also other fronts as e.g. the flooding line (wet/dry transition) or the transition between propagating and breaking waves, across which relevance of dissipation and vorticity changes dramatically 66. For wave energies, as well as for aquifers, the transition between free surface and congested flows (below a solid surface) is another example 78. Other similar examples exist in geophysics, astrophysics, aeronatic and aerospace engineering, civil engineering, energy engineering, material engineering, etc.
In all cases, computationally affordable, fast, and accurate numerical modelling is essential to allow reliable predictions in early stages of the design/analysis 117. Such computational models are also needed for simulations over very long times, especially if changes in many variable input parameters need to be investigated.
To achieve this goal one needs to have a physically relevant Partial Differential Equation (PDE) model, which can be treated numerically efficiently and accurately, which means possibly with some adaptive numerical technique allowing to mimimize the computational effort. To this end, the dynamics of some of the fronts can be modelled by appropriate asymptotic/homogeneised PDEs, while other interfaces are explicitly described. Even in the best of circumstances in all practical applications the reliability of the numerical predictions is limited by the intrinsic uncertainty on the operational conditions (e.g. boundary/initial conditions, geometry, etc.). To this aleatory uncertainty we must add the structural epistemic uncertainty related possibly to the use of approximate PDE models. Besides the limited validity of the derivation assumptions, these models are often calibrated/validated with experimental data which is itself subject to errors and postprocessing procedures (filtering, averaging, etc ..) 73, 106. This is even worse in complex flows for which measurements are difficult or impossible to plan or perform due to the inherent exceptional character of the phenomenon (e.g. tsunami events), or technical issues and danger (e.g. high temperature reentry flows, or combustion), or impracticality due to the time scales involved (e.g. study of some new materials' micro/meso structure 74). So the challenge is to construct computationally affordable models robust under variability of input paramters due to uncertainties, certification/optimization, as well as coming from modelling choices.
To face this challenge and provide new tools to accurately and robustly modelize and certify engineering devices based on fluid flows with moving fronts, we propose a program mixing scientific research in asymptotic PDE analysis, high order adaptive PDE discretizations and uncertainty quantification.
2.2 Our approach and objectives
We propose a research program mixing asymptotic PDE analysis, high order adaptive discretizations, and uncertainty quantification. In a standard approach a certification study can be described as a modelling exercise involving two black boxes. The first box is the computational model itself, composed of: PDE system, mesh generation/adaptation, and discretization of the PDE (numerical scheme). The second box is the main robust certification loop which contains separate boxes involving the evaluation of the physical model, the postprocessing of the output, and the exploration of the spaces of physical and stochastic parameters (uncertainties). Many interactions exist in this process. Exploiting these interactions could allow to tap as much as possible into the potential of high order methods 91 such as e.g. h, p, r adaptation in the physical model w.r.t. some parametric quantity/sensitivity non necessarily associated to the solution's smoothness.
Our objective is to provide some fundamental advances allowing to bring closer to the operational level modern high order numerical techniques and multifidelity certification and optimization algorithms, possibly using some clever paradigm different from the 2black box approaches above, and involving tight interactions between all the parts of the play: PDE modelling, numerical discretization techniques, uncertainty quantification methods, mesh generation/adaptation methods, physical model validation/calibration, etc. The initial composition of the team provided a unique combination of skills covering all the necessary topics allowing to explore such an avenue. The questions that need to be tackled can be organized in the following main axes/scientific questions:
 Continuous modelling: how to obtain the PDE description most suited for a given application, and make sure that on one hand its structure embeds sufficiently the physics sudied, and on the other the system is in a form suitable for efficient numerical discretization ?
 Higher order adaptive discretization: what are the relations between PDE model accuracy (e.g. asymptotic error), PDE constraints (e.g. entropy inequalities, particular steady states, etc) and the scheme consistency ? how to account for additional contraints in the scheme ?
 Parameter uncertainty and robust modelling: how to properly account when build models on one hand for the variability of physical states defining a processs in realistic environments, and on the other of data possibly available for the proces in consideration ? is it possible to couple the sampling in the space of parameters with the approximation in physical space ?
These themes are discussed in the following sections together with some challenges specific to the engineering applications considered:
 Aeronautics and aerospace engineering (deanti icing systems, space reentry, complex materials);
 Coastal engineering (coastal protection, hazard assessment etc.);
 Energy engineering with a focus on wave energy conversion
 Large scale models on manifolds with a focus on geophysics and recent models from applications in astrophysics and relativity.
3 Research program
3.1 Continuous and discrete asymptotic modelling
In many of the applications we consider intermediate fidelity models can be derived using an asymptotic expansion for the relevant scale resolving PDEs, possibly combined with some form of homogeneization or averaging. The resulting systems of PDEs are often very complex. One of the main challenges is to characterize the underlying structure of such systems: possible conservation laws embedded; additional constraints related to consistency with particular physical states (exact solutions), or to stability (entropy/energy dissipation); etc. A question of paramount importance in practical applications is also the formulation of the boundary conditions. The understanding of these properties is necessary for any new model. Moreover, different forms of the PDE may be better suited to enforce some of these properties at the numerical level.
Another issue when working with asymptotic approximations is that of closure. Indeed, important physical phenomena may be unaccounted for either due to some initial modelling assumptions, or because they involve scales much smaller than those modelled. A typical example is wave breaking in some depth averaged models. Another, relevant for our work, is the appropriate prediction of heat fluxes in turbulent flows.
So our main activities on this axis can be classified according to three main questions:
 what is the structure of the PDE model (exact solutions, stability and algebraic or differential constraints embedded, boundary conditions) ?
 what is the form of the model better suited to reproduce numerically certain constraints ?
 how to embed and design closure laws for relevant phenomena not modelled by the main PDE ?
3.2 High order discretizations on moving adaptive meshes
The efficient and robust discretization of complex PDEs is a classical and widespread research subject. The notion of efficiency is in general related to the combination of high order of accuracy and of some adaptation strategy based on an appropriate model of the error 108, 116.
This strategy is of course also part of our work. However, we are convinced that a more effective path to obtain effective discretizations consists in exploiting the knowledge of the PDE structure, embedding as much as possible the PDE structure in the discrete equations. This is related to the notion of enhanced consistency that goes in the direction of what is today often referred to as constraint or property preserving discretizations. For the type of PDE systems of our interest, the properties which are of paramount importance to be controlled are for example: the balance between flux divergence and forcing terms (so called well balanced of Cproperty 61, 105) and the preservation of some specific steady states; the correct reproduction of the dispersion relation of the system, especially but not only for dispersive wave propagation; the preservation of some algebraic constraints, typically the nonnegativity of some thermodynamic quantities; the respect of a discrete entropy/energy equality or inequality (for stability); the strong consistency with some asymptotic limit of the PDE (AP property); etc.
A fundamental issue is the efficient and accurate treatment of boundary and interface conditions. The idea is to have some approach which tolerates the use of nonconformal meshes, which is genuinely high order, and compatible with adaptation, and of course conformal meshing of the boundary/discontinuity. Techniques allowing the control of the geometrical error due to nonconformity is required. For discontinuities, this also requires an adhoc treatment of the jump condition. For wall boundaries, initial work using penalization has been done in CARDAMOM in the past 55, 98. On Cartesian meshes several techniques exist to control the consistency order based on extrapolation/interpolation, or adaptive methods (cf e.g. 109, 96, 56, 71, 80, 115 and references therein). For discontinuities, we can learn from fitting techniques 62, and from some past work by Prof. Glimm and coworkers 69.
For efficiency, mesh adaptation plays a major role. Mesh size adaptation based on both deformation, radaptation, or remeshing hadaptation, can be designed based on some error model representative. For unsteady flows, the capability to use moving meshes becomes necessary, and geometrical conservation (GCL) needs to be added to the list of constraints to be accounted for 110, 92. In particular, one technique that provides meshes with optimal quality moving together with the unsteady flows, reduction of errors due to convective terms, GCL respected up to machine precision, and high order of accuracy, is offered by the Direct ArbitraryLagrangianEulerian (ALE) methods on moving Voronoi meshes with topology changes 82, 81 that will be further investigated.
3.3 Applications in physics and engineering
As already mentioned, our focus is on four main classes of problems:
 Aeronautics and aerospace engineering (deanti icing systems, space reentry, complex materials)
 Coastal engineering (coastal protection, hazard assessment etc.)
 Energy engineering with a focus on wave energy conversion
 Large scale models on manifolds with a focus on geophysics and recent models from applications in astrophysics and relativity.
There are several common aspects. One is the use of asymptotic vertically averaged approximations to produce efficient applicationTaylored PDE models. Another common point is the construction of possibly high order constraint/property preserving numerical approximations. This entails the characterization of the underlying PDE models with a set of embedded properties, which go from classical conservation, to exact solutions (steady or moving), to the preservation of differential operators, to the thermodynamic adissibility (nonnegativity, preservation of physical bounds). For all applications, the investigation of the parameter dependence of the results will take several forms from sensitivity analyses, to classical parametric studies to understand physical processes, to approximation in parameter space in the framework of hybrid PDEmeta/reducedorder models.
4 Application domains
4.1 Deanti icing systems
Impact of large ice debris on downstream aerodynamic surfaces and ingestion by aft mounted engines must be considered during the aircraft certification process. It is typically the result of ice accumulation on unprotected surfaces, ice accretions downstream of ice protected areas, or ice growth on surfaces due to delayed activation of ice protection systems (IPS) or IPS failure. This raises the need for accurate ice trajectory simulation tools to support predesign, design and certification phases while improving cost efficiency. Present ice trajectory simulation tools have limited capabilities due to the lack of appropriate experimental aerodynamic force and moment data for ice fragments and the large number of variables that can affect the trajectories of ice particles in the aircraft flow field like the shape, size, mass, initial velocity, shedding location, etc... There are generally two types of model used to track shed ice pieces. The first type of model makes the assumption that ice pieces do not significantly affect the flow. The second type of model intends to take into account ice pieces interacting with the flow. We are concerned with the second type of models, involving fully coupled timeaccurate aerodynamic and flight mechanics simulations, and thus requiring the use of high efficiency adaptive tools, and possibly tools allowing to easily track moving objects in the flow. We will in particular pursue and enhance our initial work based on adaptive immerse boundary capturing of moving ice debris, whose movements are computed using basic mechanical laws.
In 59 it has been proposed to model ice shedding trajectories by an innovative paradigm that is based on CArtesian grids, PEnalization and LEvel Sets (LESCAPE code). Our objective is to use the potential of high order unstructured mesh adaptation and immersed boundary techniques to provide a geometrically flexible extension of this idea. These activities will be linked to the development of efficient mesh adaptation and time stepping techniques for time dependent flows, and their coupling with the immersed boundary methods we started developing in the FP7 EU project STORM 55, 98. In these methods we compensate for the error at solid walls introduced by the penalization by using anisotropic mesh adaptation 76, 93, 94. From the numerical point of view one of the major challenges is to guarantee efficiency and accuracy of the time stepping in presence of highly stretched adaptive and moving meshes. Semiimplicit, locally implicit, multilevel, and split discretizations will be explored to this end.
Besides the numerical aspects, we will deal with modelling challenges. One source of complexity is the initial conditions which are essential to compute ice shedding trajectories. It is thus extremely important to understand the mechanisms of ice release. With the development of next generations of engines and aircraft, there is a crucial need to better assess and predict icing aspects early in design phases and identify breakthrough technologies for ice protection systems compatible with future architectures. When a thermal ice protection system is activated, it melts a part of the ice in contact with the surface, creating a liquid water film and therefore lowering ability of the ice block to adhere to the surface. The aerodynamic forces are then able to detach the ice block from the surface 60. In order to assess the performance of such a system, it is essential to understand the mechanisms by which the aerodynamic forces manage to detach the ice. The current state of the art in icing codes is an empirical criterion. However such an empirical criterion is unsatisfactory. Following the early work of 64, 58 we will develop appropriate asymptotic PDE approximations to describe the water runoff on the wing surface, also accounting for phase change, thus allowing to describe the ice formation and possibly rupture and detachment. These models will constitute closures for aerodynamics/RANS and URANS simulations in the form of PDE wall models, or modified boundary conditions.
In addition to this, several sources of uncertainties are associated to the ice geometry, size, orientation and the shedding location. In very few papers 101, some sensitivity analysis based on Monte Carlo method have been conducted to take into account the uncertainties of the initial conditions and the chaotic nature of the ice particle motion. We aim to propose some systematic approach to handle every source of uncertainty in an efficient way relying on some stateofart techniques developed in the Team. In particular, we will perform an uncertainty propagation of some uncertainties on the initial conditions (position, orientation, velocity,...) through a lowfidelity model in order to get statistics of a multitude of particle tracks. This study will be done in collaboration with ETS (Ecole de Technologies Supérieure, Canada). The longterm objective is to produce footprint maps and to analyse the sensitivity of the models developed.
4.2 Modeling of wave energy converters
Wave energy conversion is an emerging sector in energy engineering. The design of new and efficient Wave Energy Converters (WECs) is thus a crucial activity. As pointed out by Weber 117, it is more economical to raise the technology performance level (TPL) of a wave energy converter concept at low technology readiness level (TRL). Such a development path puts a greater demand on the numerical methods used.
Our previous work 7863 has shown the potential of depthaveraged models for simulating wave energy devices. The approach followed so far relies on an explicit coupling of the different domains involving the flow under the structure and the free surface region. This approach has the advantage to need efficient solvers of wellknown system of equations (compressible and incompressible flow). However, the transmission condition between this two regimes is now always well understood, depending on the underlying PDE models. Moreover, several sources of numerical instabilities exist because of the different nature of the regions involved (compressible/incompressible). A different approach is proposed in 86, 85, and will be pursued in the comping years. The idea is to solve a unique model in the whole computational domain, with the effect of the structure being accounted for by means of an appropriate pressure variable playing the role of a Lagrange multiplier. Out numerical developments will be performed withing the parallel platform GeoFun, based on the Aerosol library. In order to simulate the dynamic of the floating structures, we will consider the coupling with the open source code tChrono1, an external code specialized in the resolution of the rigid body dynamics. The coupling is still under development. In parallel, we will add closure for other complex physical effects as e.g. the modeling of air pocket trapped under the structures. Several industrial processes (SeaTurns, Hace...) are based on chamber compressing air inside by the movement of the water surface. This strategy has the advantage of taking the turbines for energy production out of the water. The strategy is based on a polytropic modeling of the gas dynamics taking into account merging and splitting of the pockets, without a major impact on the efficiency of the simulation (robustness and numerical cost). This works benefits of the associated team LARME with RISE (C. Eskilson).
4.3 Materials engineering
Because of their high strength and low weight, ceramicmatrix composite materials (CMCs) are the focus of active research for aerospace and energy applications involving high temperatures, either military or civil. Selfhealing (SH) CMCs are composed of a complex threedimensional topology of woven fabrics containing fibre bundles immersed in a matrix coating of different phases. The oxide seal protects the fibres which are sensitive to oxidation, thus delaying failure. The obtained lifetimes reach hundreds of thousands of hours 104.
The behaviour of a fibre bundle is actually extremely variable, as the oxidation reactions generating the selfhealing mechanism have kinetics strongly dependent on temperature and composition. In particular, the lifetime of SHCMCs depends on: (i) temperature and composition of the surrounding atmosphere; (ii) composition and topology of the matrix layers; (iii) the competition of the multidimensional diffusion/oxidation/volatilization processes; (iv) the multidimensional flow of the oxide in the crack; (v) the inner topology of fibre bundles; (vi) the distribution of critical defects in the fibres. Unfortunately, experimental investigations on the full materials are too long (they can last years) and their output too qualitative (the coupled effects can only be observed aposteriori on a broken sample). Modelling is thus essential to study and to design SHCMCs.
In collaboration wit the LCTS laboratory (a joint CNRSCEASAFRANBordeaux University lab devoted to the study of thermostructural materials in Bordeaux), we are developing a multiscale model in which a structural mechanics solver is coupled with a closure model for the crack physico chemistry. This model is obtained as a multidimensional asymptotic crack averaged approximation fo the transport equations (Fick's laws) with chemical reactions sources, plus a potential model for the flow of oxide 74, 77, 102. We have demonstrated the potential of this model in showing the importance of taking into account the multidimensional topology of a fibre bundle (distribution of fibres) in the rupture mechanism. This means that the 0dimensional model used in most of the studies (see e.g. 72) will underestimate appreciably the lifetime of the material. Based on these recent advances, we will further pursue the development of multiscale multidimensional asymptotic closure models for the parametric design of self healing CMCs. Our objectives are to provide: (i) new, nonlinear multidimensional mathematical model of CMCs, in which the physicochemistry of the selfhealing process is more strongly coupled to the twophase (liquid gas) hydrodynamics of the healing oxide ; (ii) a model to represent and couple crack networks ; (iii) a robust and efficient coupling with the structural mechanics code ; (iv) validate this platform with experimental data obtained at the LCTS laboratory. The final objective is to set up a multiscale platform for the robust prediction of lifetime of SHCMCs, which will be a helpful tool for the tailoring of the next generation of these materials.
4.4 Coastal and civil engineering
Our objective is to bridge the gap between the development of high order adaptive methods, which has mainly been performed in the industrial context and environmental applications, with particular attention to coastal and hydraulic engineering. We want to provide tools for adaptive nonlinear modelling at large and intermediate scales (near shore, estuarine and river hydrodynamics). We will develop multiscale adaptive models for free surface hydrodynamics. Beside the models and codes themselves, based on the most advanced numerics we will develop during this project, we want to provide sufficient know how to control, adapt and optimize these tools.
We will focus our effort in the understanding of the interactions between asymptotic approximation and numerical approximation. This is extremely important in several ways. An example is the capability of a numerical model to handle highly dispersive wave propagation. This is usually done by high accuracy asymptotic PDE expansions of by means of multilayer models. In the first case, there is an issue with the constraints on the numerical approximation. Investigations of approriated error models for adaptivity in the horizontal may permit to alleviate some of these constraints, allowing a reasonable use of lower order discretizations. Concerning multilayer models, we plan can use results concerning the relations between vertical asymptotic expansions and truncation/approximation error to improve the models by some adaptive approach.
Another important aspect which is not understood well enough at the moment is the role of dissipation in the evolution of the free surface dynamics, and of course in wave breaking regions. There are several examples of breaking closure, going from algebraic and PDEbased eddy viscosity methods 90, 107, 100, 75, to hybrid methods coupling dispersive PDEs with hyperbolic ones, and trying to mimic wave breaking with travelling bores 112, 113, 111, 88, 79. In both cases, numerical dissipation plays an important role and the activation or not of the breaking closure, as well as on the establishement of stationary travelling profiles, or on the appearance of solitary waves. These aspects are related to the notion of numnerical dissipation, and to its impact on the resulting numerical solutions. These elements must be clarified to allow full control of adaptive techniques for the models used in this type of applications.
A fundamental issue that needs to be adressed is the proper discrete formulation of the boundary conditions for dispersive wave approximations. These conditions play of course a critical role in applications and remain an open problem for most Boussinesq models.
4.5 Geophysics and astrophysics
This is work is related to large scale simulations requiring the solution of PDEs on manifolds. Examples are tsunami simulations, as those performed in the past in the TANDEM project, as well as some applications considered in the ANR LAGOON for climate change. The MSCA project SuPerMan proposes applciations in astrophysics which also involve similar issues. The idea is to consider both coordinate changes related to mesh movement, and in ALE formulations, as well as genuinely spacetime manifolds as in hyperbolic reformulations of relativity 83, and combinations of both when for example considered mesh movement and adaptation in curvilinear coordinates 57. Challenges are related to the appropriate PDE formulation, and the respect of continuous constraints at the discrete level.
The objective here is to devise the most appropriate manifold representation, and formulate the PDE system in the appropriate way allowing to embed as many continuous constraints as possible (well balancing, energy conservation, positivity preservation, etc). Embedding the ALE mapping will be necessary to envisage adaptive strategies, improving on 57 and 84.
Geophysical applications are of interest for BRGM, while the more exploratory application to general relativity of the MSCA project SuPerMan will push the numerical discretizations to their limit, due to the great complexity of the model, and allow new collaborations in the domain of astrophysics, as e.g. with Max Planck institute.
5 Highlights of the year
Cardamom passed with success its second evaluation in September 2022.
Luca Cirrottola, who is a permanent research engineer in scientific computing and high performance computing in the SED department, joint CARDAMOM and CAGIRE teams. He is working on the AEROSOL software.
Mathieu Colin has been promoted to a professor’s position.
5.1 Awards
 Elena Gaburro was finalist for the ERCIM Cor Baayen Young Researcher Award, the European Award for promising young researcher in Applied Mathematics.
5.2 Grants
 Nicolas Barral was awarded an Inria Action Exploratoire grant, with Tommaso Taddei (Inria, MEMPHIS). The AM${}^{2}$OR project aims at exploring how modern mesh adaptation techniques can help Reduced Order Modelling workflows scale up in the context of complex advection dominated problems.
5.3 International events
 MultiMat 2022. Elena Gaburro has been cochair of the organizing committee and member of the scientific committee of MultiMat 2022, an important international conference on numerical methods for multimaterial fluid flow. The conference has been successfully organized in Zurich during August 2022 in a fully in presence modality, and the number of participants was the highest of all its 10 past editions. Participants were coming from all over the world with 16 countries represented.
 A Special Issue entitled Numerical Methods and Applications for Waves in Coastal Environments was published in Water Waves journal , (Volume 4, issue 3, November 2022). Maria Kazolea was a guest editor of the issue.
6 New software and platforms
6.1 New software
6.1.1 SHCOMP

Keywords:
Finite element modelling, Multiphysics simulation, Chemistry, Incompressible flows, 2D

Functional Description:
SHCOMP solves a diffusionreaction model for the healing process in ceramic matrix composites. The model is averaged across transversal cracks and accounts for the heterogenous properties of the matrix of the composite with reactive and nonreactive layers arranged around the carbon fibers. The model is solved with a finite element approximation, and a temporal splitting in time exploiting the large differences between reaction and diffusion time scales. the code is written in a mix of python and cython.

Contact:
Mario Ricchiuto

Participants:
Gérard Vignoles, Gregory Perrot, Guillaume Couegnat, Mario Ricchiuto, Giulia Bellezza

Partner:
LCTS (UMR 5801)
6.1.2 SLOWS

Name:
Shallowwater fLOWS

Keywords:
Simulation, Free surface flows, Unstructured meshes

Scientific Description:
Three different approaches are available, based on conditionally depthpositivity preserving implicit schemes, or on conditionally depthpositivity preserving genuinely explicit discretizations, or on an unconditionally depthpositivity preserving spacetime approach. Newton and frozen Newton loops are used to solve the implicit nonlinear equations. The linear algebraic systems arising in the discretization can be solved either with the MUMPS library or with the MKL Intel library. Implicit and explicit (extrapolated) multistep higher order time integration methods are available, and a mesh adaptation technique based on simple mesh deformation are also included. This year a new higher order reconstruction for the FV scheme has been added.

Functional Description:
SLOWS is a Cplatform allowing the simulation of free surface shallow water flows with friction. It can be used to simulate near shore hydrodynamics, wave transformations processes, etc.
 URL:

Contact:
Mario Ricchiuto

Participants:
Maria Kazolea, Mario Ricchiuto
6.1.3 GeoFun

Keywords:
Geophysical flows, Unified models, Finite volume methods

Scientific Description:
GeoFun focuses on applications where different models in different regions in space are needed, with interfaces between these regions that depend on the solution. To deal with this complex boundary problem, the code aims at exploiting unified models available everywhere in the computational domain, and at using asymptotic preserving numerical schemes to recover specific regime flows without an a priori detection of the interfaces.

Functional Description:
The GeoFun library is developed as a module on top of the kernel provided by AeroSol. Its objective is to simulate geophysical flows, free surface and underground, at large time and space scales. For this reason, unified vertically integrated (shallow water type) models are considered.

News of the Year:
In 2021, the development of GeoFun focused on:  Setup of Continuous Integration (both compilation and unitary tests).  Implementation and verification of shallow water model.  Implementation and verification of Congested Shallow water model (maximum water depth constraint).  Start Implementation of Congested crowd motion model (maximum density constraint).  Start coupling with the software Chrono (for floating structures).  Fix memory leak bug  Reports, documentation and wiki redaction.

Contact:
Martin Parisot

Participants:
Martin Parisot, Marco Lorini
6.1.4 UHAINA

Keywords:
Simulation, Ocean waves, Unstructured meshes, Finite element modelling

Scientific Description:
Operational platform for near shore coastal application based on the following main elements:
 Fullynonlinear wave propagation.
 Wave breaking handled by some mechanism allowing to mimic the energy dissipation in breakers.
 A high order finite element discretization combined with mesh and polynomial order adaptation for optimal efficiency.
 An efficient parallel object oriented implementation based on a hierarchical view of all the data management aspects cared for by middleware libraries developed at Inria within the finite element platform Aerosol.
 A modular wrapping allowing for application tailored processing of all input/output data (including mesh generation, and high order visualization).
 Spherical coordinates based on a local projection on a real 3D spherical map (as of 2021)
 Compilation with GUIX available (as of 2022)
 Homogenization and standardization of code outputs and hazard quatification (as of 2022)
 Correction of the management of dry/wet fronts in the presence of structures represented by a single high point (as of 2022)
 Use of FES for the calculation of the tide directly in UHAINA through an API. New compilation option for activation (as of 2022)
 Boundary conditions accounting tides from FES and corrected with the effect of the inverse barometer, for the simulation of the tidal propagation and the surge on domains at the regional scale (as of 2022)
 Hydraulic connections (e.g. sewers) in the simulation of urban flooding (as of 2022)
 Mass source term, for the injection of the volume of water overtopping structures not accounted in the elevation model during flooding episodes by sea surges (as of 2022)

Functional Description:
Waves simulation

Contact:
Mario Ricchiuto

Participants:
Mario Ricchiuto, Philippe Bonneton, David Lannes, Fabien Marche

Partners:
EPOC, IMAG, IMB
6.1.5 AleVoronoi

Name:
Direct Arbitrary Lagrangian Eulerian Finite Volume and Discontinous Galerkin schemes on VORONOI moving meshes with topology changes

Keywords:
Finite volume methods, Discontinuous Galerkin, High order methods, Centroidal Voronoi tessellation, ALE, Fortran, OpenMP

Functional Description:
Explicit, arbitrary high order accurate, one step (ADER), Finite Volume and Discontinuous Galerkin schemes on 2D moving Voronoi meshes for the solution of general firstorder hyperbolic PDEs. Main peculiarity: the Voronoi mesh is moved according to the fluid flow using a direct ArbitraryLagrangianEulerian (ALE) method achieving high quality of the moving mesh for long simulation times. The high quality of the mesh is maintained thanks to a) mesh optimization techniques and b) the additional freedom of allowing topology changes. The high quality of the results is obtained thanks to the high order ADER schemes. The main novelty is the capability of using highorder schemes on moving Voronoi meshes with topology changes.
The code is written in Fortran + OpenMP.
 Publications:

Author:
Elena Gaburro

Contact:
Elena Gaburro
6.1.6 HOTHYPE

Name:
High Order shock Tracking for HYPerbolic Equations

Keywords:
Finite volume methods, Discontinuous Galerkin, Partial differential equation, Delaunay triangulation

Functional Description:
High order ADERtype Finite Volume and Discontinuous Galerkin schemes on 2D triangular meshes for the solution of hyperbolic partial differential equations.
 Publications:

Author:
Elena Gaburro

Contact:
Elena Gaburro
6.1.7 AeroSol

Keyword:
Finite element modelling

Functional Description:
The AeroSol software is a high order finite element library written in C++. The code has been designed so as to allow for efficient computations, with continuous and discontinuous finite elements methods on hybrid and possibly curvilinear meshes. The work of the team CARDAMOM (previously Bacchus) is focused on continuous finite elements methods, while the team Cagire is focused on discontinuous Galerkin methods. However, everything is done for sharing the largest part of code we can. More precisely, classes concerning IO, finite elements, quadrature, geometry, time iteration, linear solver, models and interface with PaMPA are used by both of the teams. This modularity is achieved by mean of template abstraction for keeping good performances. The distribution of the unknowns is made with the software PaMPA , developed within the team TADAAM (and previously in Bacchus) and the team Castor.

News of the Year:
The main highlight of 2022 concerning the AeroSol library was the hiring of Luca Cirrottola as an INRIA permanent engineer.
In 2022, the development of the library was focused on the following points
* Development environment  Work on the packaging with Guix.  Work on continuous integration by using Plafrim as gitlab runner, with dependencies handled by Guix (and Modules for legacy).  Fix of an old memory leak on PaMPA and integration in the packaging.  Beginning of work for merging the branch master, the branch used for Uhaina/Lagoon project, and the branch including turbulence models and axi models.  the development of a new library DM2 has started. It aims at replacing PaMPA.
* General numerical feature of the library  Postprocessing on wall and lines, including computation of Cp and Cf  New finite elements for quads and hexa, based on GaussLobatto or GaussLagrange elements were added.
* Work on SBM methods  Shifted boundary method for Neumann and Dirichlet boundary conditions,  development of high order derivative in some of the finite element classes
* Low Mach number flows:  Low Mach number filtering was extended on quads. Implementation of dicrete seminorms div and grad, extension of some fixes to full Euler with arbitrary EOS.
* RANS turbulent flow computations:  Inlet/Outlet boundary conditions for Euler/NavierStokes systems allowing to get a stationary solution  HLLC numerical flux, exact jacobian with frozen wave speeds and extension to the RANS equations coupled to transport equations (turbulence models)  test case: laminar and turbulent flat plate, development and documentation of axisymmetric test case,  Fix of SpalartAlmaras model, negative fix handle  Beginning of implementation of coupled elliptic problem with Neumann and Dirichlet boundary conditions on one variable.
* Fluxreconstruction  Implementation of FluxReconstruction methods on Cartesian meshes
 URL:

Contact:
Vincent Perrier

Participants:
Mario Ricchiuto, Vincent Perrier, Héloïse Beaugendre, Christopher Poette, Marco Lorini, Jonathan Jung, Anthony Bosco, Luca Cirrottola, Romaric Simo Tamou, Ibtissem Lannabi

Partner:
BRGM
6.1.8 DM2

Name:
Distributed Mesh and Data Manager

Keywords:
HPC, Data parallelism, High order finite elements, Unstructured meshes, Hybrid meshes

Functional Description:
DM2 is a C++ library for managing mesh and data on mesh in a MPI parallel environment. It is conceived to provide parallel mesh and data management in high order finite element solvers for continuum mechanics.
The user should provide a mesh file which is read by the library. Then DM2 is able to:
 Read the mesh, and read the data provided in the mesh file, possibly in parallel
 Redistribute the mesh in order to distribute the data on a given set of processors. This redistribution is made through a graph partitioner such as PARMETIS or PTSCOTCH.
 Allocate the memory in parallel if a number of unknown by entity type is provided by the user.
 Centralize the data.
 Compute the halo required for a numerical method. The halo is adapted for each of the possible discretization.
 Renumber mesh elements for making a difference between mesh elements that need or need not communication.
 Aggregate a mesh based on a metric for developing a multigrid method.

News of the Year:
This year, the development of the DM2 library began. We focused on  the mesh reading: the parallel mesh reader of AeroSol was reused and improved. It can
* read a GMSH file with lines, triangles, quads, prisms, tetrahedra or pyramids, each cell or face being straight or curved.
* the mesh reading can be performed in parallel
* the mesh distribution when reading in parallel can rely on a geometrical prepartitioner
 from the mesh reading, a C++ structure graph is built. When read in parallel, it is parallel consistent. Some work was done on the graph structure (c++ containers, adjacency list) for ensuring interoperability with C structures.
" from the c++ structure, a graph cstructure compatible with scotch or metis can be built. A parallel mesh redistribution of this graph can be performed based on these software

Contact:
Vincent Perrier

Participants:
Vincent Perrier, Luca Cirrottola
7 New results
7.1 Structure preserving numerical methods for evolutionary PDEs
Participants: Rémi Abgrall, Elena Gaburro, Mario Ricchiuto, Michele Giuliano Carlino, Mirco Ciallella, Sixtine Michel.
 Corresponding member: Mario Ricchiuto
7.1.1 Stabilized continuous finite elements for hyperbolic PDEs
Fundamental work on schemes. To reduce the costs associated with the DG finite element method in the previous approach we study the use of (both continuous and discontinuous) cubature elements allowing a considerable reduction of the number of operations, including a full diagonalization of the mass matrix. In 97 we have provided a first investigation of the fully discrete linear stability of continuous finite elements with different stabilization operators. The theoretical results are confirmed by numerical computations on linear and nonlinear problems, confirming the potential of the cubature approach in temps of CPU time for a given error. This year we have propose a multidimensional extension of this fully discrete analysis. The challenges in twodimensions are related to the Fourier analysis. Here, we perform it on two types of periodic triangular meshes varying the angle of the advection, and we combine all the results for a general stability analysis. Due to the large number of modes involved, in the fully fiscrete case we have combined the basic Fourier stability criterion with the one obtained from Dahlquist’s equation for the spatial discretization alone. Furthermore, we introduce additional a high order viscosity to stabilize the discontinuities, in order to show how to use these methods for tests of practical interest. A simple model for this nonlinear term has been included in the spectral analysis as well. All the theoretical results are thoroughly validated numerically both on linear and nonlinear problems, and errorCPU time curves are provided. Our final conclusions suggest that Cubature elements combined with SSPRK and OSS stabilization is the most promising combination. Work discussed in 21 (accepted on J.Sci.Comp.).
7.1.2 High order well balanced discretizations
Global flux based schemes. We have developed schemes based on a fully discrete well balanced criterion which exploits the idea of a global flux formulation. In this framework, classically some primitive function of the source terms is defined and included in the hyperbolic flux. In our work however this idea is mostly used to infer an adhoc quadrature strategy of the soource which we refer to as "global flux quadrature". This quadrature approach allows to establish a one to one correspondence, for a given local set of data on a given stencil, between the discretization of a nonlocal integral operator, and the discretization of the local steady differential problem. This equivalence is a discrete well balanced notion which allows to construct balanced schemes without explicit knowledge of the steady state, and in particular without the need of solving a local Cauchy problem. We have used this idea in the setting of finite elements, both discontinuous in 50 and continuous n the framerowk of the PhD of Lorenzo Micalizzi at U. Zurich, coadvised by R. Abgrall and M. Ricchiuto. We have shown that the used of specific finite element spaces allows to provide a very precice characterization of the discrete solution. For example, the use of GaussLobatto elements provides a natural connection to continuous collocation methods for integral equations. This allows to prove superconvergence estimates for the steady discrete solution. In the continuous finite element case, this new well balanced criterion requires the design of compatible stabilization operators. This aspect was presented at the HONOM2022 conference. A paper on the latest developments is in preparation. Similar ideas have been used to build fully well balanced WENO finite volume schemes in 47. Genuinely multidimensional extensions, as well as extensions to time dependent solutions are also in the works.
Shallow water equations on manifolds. The work on well balanced schemes for shallow water type models had major enhancements. We proposed a novel hyperbolic reformulation of the shallow water model written in covariant coordinates, i.e. metric independent, and for this system we derived a cheap well balanced method able to maintain at machine precision water at rest equilibria for general metrics and complexshaped domains. The obtained numerical results, both in 1D and 2D are reported in the following publications: 10, 40. This work has been presented at Shark 2022 (Portugal), HYP 2022 (Spain) and in the conference Essentially hyperbolic problems: unconventional numerics, and applications 2022 (Switzerland).
Astrophysics. Following the work in 83, we have continued our research on the implementation of robust and accurate numerical schemes for the simulation of hyperbolic models of general relativity. We investigated in particular the general relativistic magnetohydrodynamics (GRMHD) equations and the Einstein field equations with different first order reformulations as the Z4 and CCZ4 models. We also considered the Buchman 67 and the novel TEGR 103 tedrad formualations. The implementation work is done in a 3D Cartesian code. In particular, the need for well balanced techniques appears to be more and more crucial as the applications increase their complexity and a series of numerical tests of increasing difficulty shows how the well balancing significantly improves the longtime stability of the finite volume scheme compared to a standard one, in particular for the study of neutron stars. Various manuscripts are in preparation. The obtained results have been presented during the HYP conference in Malaga (Spain) and at the "Seminarire du Laboratoire LJLL" in November in Paris.
7.1.3 Schemes embedding additional discrete conservation constraints
Entropy conservative ADERDG. We have developed a fully discrete entropy preserving ADERDiscontinuous Galerkin (ADERDG) method. To obtain this result, we have equipped the space part of the method with entropy correction terms that balance the entropy production in space, inspired by the work of Abgrall. Whereas for the timediscretization we have applied the relaxation approach introduced by Ketcheson that allows to modify the timestep to preserve the entropy to machine precision. Up to our knowledge, this is the first time that a provable fully discrete entropy preserving ADERDG scheme has been constructed. We have also verified our theoretical results with various numerical simulations, reporting our results in 16.
A posteriori subcell conservative correction of nonconservative schemes. We proposed a novel quasiconservative high order discontinuous Galerkin (DG) method able to capture contact discontinuities avoiding any spurious numerical artifacts, thanks to the PDE evolution in primitive variables, while at the same time being strongly conservative on shocks, thanks to a conservative a posteriori subcell finite volume (FV) limiter. In particular, we have verified the improved reliability of our scheme on the multifluid Euler system on examples like the interaction of a shock with a helium bubble. The obtained results have been presented in a seminar at the CEA center of Bruyeres le Chatel and a paper is in preparation.
7.2 Modelling of free surface flows
Participants: Mathieu Colin, Maria Kazolea, Martin Parisot, Mario Ricchiuto.
 Corresponding member: Maria Kazolea
Coupling dispersive and nondispersive models. We continue our work on the coupling of dispersive shallow water models, by deriving asymptotic interface operators. We derived transmission operators for coupling linear GreenNaghdi equations (LGNE) with linear shallow water equations (LSWE) –the heterogeneous case – or for coupling LGNE with LGNE –the homogeneous case. We derived them from a domain decomposition method (NeumannDirichlet) of the linear Euler equations by applying the same verticalaveraging process and truncation of the asymptotic expansion of the velocity field used in the derivation of the equations. We find that the new asymptotic transmission conditions also correspond to Neumann and Dirichlet operators. In the homogeneous case the method has the same convergence condition as the parent domain decomposition method but leads to a solution that is different from the monodomain solution due to an $O\left(\Delta x\right)$ term. In the heterogeneous case the NeumannDirichlet operators translate into a simple interpolation across the interface, with an extra $O\left(\Delta {x}^{2}\right)$ term. We show numerically that in this case the method introduces oscillations whose amplitude grows as the mesh is refined, thus leading to an unstable scheme. The work was presented in the 27th International Domain Decomposition Conference, DD27, in Prague. It is also submitted for publication in the proceedings of the conference 48.
Dispersive waves with porous media. This year we started working in a conservative form of the extended Boussinesq equations for waves in porous media. This model can be used in both porous and nonporous media since it does not requires any boundary condition at the interface between the porous and nonporous media. A hybrid Finite Volume/Finite Difference (FV/FD) scheme has been coded in order to solve the conservative form of the extended Boussinesq equations for waves in porous media. For the hyperbolic part of the governing equations, the FV formulation is applied with Riemann solver of Roe approximation. Whereas, the dispersive and porosity terms are discretized by using the FD. The model is validated with experimental data for solitary waves interacting with porous structures and a porous dam break in a onedimensional flow. The work was published in the Ocean engineering journal 27
Wave breaking. 2022 we continued our work on wave breaking for Boussinesq type modeling and more precisely for the GN equations. Using the numerical model already discribed in 79 we attempted at providing some more understanding of the sensitivity of some closure approaches to the numerical setup. More precisely and based on 89 we focus on two closure strategies for modelling wave breaking. The first one is the hybrid method consisting of suppressing the dispersive terms on a breaking region and the second one is an eddy viscosity approach based on the solution of a turbulent kinetic energy model. The two closures use the same conditions for the triggering of the breaking mechanisms. Both the triggering conditions and the breaking models themselves use case dependent, ad hoc, parameters which are affecting the numerical solution while changing. The scope of this work is to make use of sensitivity indexes computed by means of Analysis of Variance (ANOVA) to provide the sensitivity of wave breaking simulation to the variation of parameters such as the breaking parameters involved in each breaking model. The paper was published in Water Waves journal 18.
Hyperbolicelliptic spliting. We performed additional work on the use of the splitting between hyperbolic and elliptic steps proposed in 79 to solve Boussinesq type equations. For the GreenNaghdi (GN) model the latest results and developments are discussed in 19. In this paper we use a high order FV method to solve the hyperbolic step, and a standard P1 finite element method for the elliptic system associated to the dispersive correction. We study the impact of the reconstruction used in the hyperbolic phase; the representation of the FV data in the FE method used in the elliptic phase and their impact on the theoretical accuracy of the method; the wellposedness of the overall method. For the first element we proposed a systematic implementation of an iterative reconstruction providing on arbitrary meshes up to third order solutions, full second order first derivatives, as well as a consistent approximation of the second derivatives. These properties are exploited to improve the assembly of the elliptic solver, showing dramatic improvement of the finale accuracy, if the FV representation is correctly accounted for. Concerning the elliptic step, the original problem is usually better suited for an approximation in H(div) spaces. However, it has been shown that perturbed problems involving similar operators with a small Laplace perturbation are well behaved in H1 provided that some numerical dissipation is embedded in the overall discretization. In our case, the use of upwind numerical fluxes in the hyperbolic step suffices to this end, allowing to not only obtain convergent results, but also provide the expected convergence rates.
One of the drawbacks of this splitting approach is that a linear system needs to be assembled and solved at each substep. For multistage temporal integration, as in classical high order RK methods, this leads to schemes with a considerable overhead when passing from shallow water to Boussinesq. In 11 we have proposed a strategy to design one step discretizations based on the splitting strategy allowing a single evaluation of the elliptic step. The schemes are based on a simplified LaxWendroff procedure in which polynomial extrapolation in time is used to evaluate part of the dispersive terms required to obtain the necessary truncation order in the Taylor development in time underlying the LaxWendroff process. Second and third order schemes are constructed based on this idea, their spectral properties are analyzed, and several nonlinear 1D benchmarks are used to show the benefits of the proposed method. The multidimensional extension has already been implemented and its study is ongoing.
Model order reduction for weakly dispersive waves. To alleviate the overheads related to the approximation of dispersive effects we have explored a hybrid strategy using the hyperbolicelliptic splitting in which a reduced model is used to approdimate the dispersive elliptic operator. The numerical evidence suggests that not only this is possible, but the resulting discrete model provides accurate predictions with computational savings of at least one order of magnitude, with increased robustness compared to fully reduced approximations 26. This work opens the way to many developments the first of which will be related to the extension of the initial results to breaking waves, and to the multidimensional case.
Projection structure of the timediscrete GreenNaghdi equations. The direct use of this structure has allowed to answer to several open questions. One of the most pressing is the correct imposition of the boundary conditions. In particular, using techniques inspired by the discretization of incompressible flow equations, we proposed in 22 a numerical treatment allowing to account for very general boundary conditions, while guaranteeing that the whole scheme is entropystable. We are currently working on exploiting this structure to design a wellbalanced numerical scheme, i.e. a scheme able to preserved all the steady states even not at rest.
7.3 Modelling of icing and deicing of aircrafts
Participants: Héloïse Beaugendre, Mathieu Colin.
 Corresponding member: Héloïse Beaugendre
Inflight icing is a major source of incidents and accidents. The effects of atmospheric icing can be anticipated by Computational Fluid Dynamics (CFD). Past studies show that the convective heat transfer influences the ice accretion and is itself a function of surface roughness. Uncertainty quantification (UQ) could help quantify the impact of surface roughness parameters on the reliability of ice accretion prediction. The prediction of heat transfers in ReynoldsAveraged Navier–Stokes (RANS) simulations requires corrections for rough surfaces. The turbulence models are adapted to cope with surface roughness impacting the nearwall behaviour compared to a smooth surface. These adjustments in the models correctly predict the skin friction but create a tendency to overpredict the heat transfers compared to experiments. These overpredictions require the use of an additional thermal correction model to lower the heat transfers. Finding the correct numerical parameters to best fit the experimental results is nontrivial, since roughness patterns are often irregular. The objective of this paper 17 is to develop a methodology to calibrate the roughness parameters for a thermal correction model for a rough curved channel test case. First, the design of the experiments allows the generation of metamodels for the prediction of the heat transfer coefficients. The polynomial chaos expansion approach is used to create the metamodels. The metamodels are then successively used with a Bayesian inversion and a genetic algorithm method to estimate the best set of roughness parameters to fit the available experimental results. Starting with unknown roughness parameters, this methodology allows calibrating them and obtaining between 4.7% and 10% of average discrepancy between the calibrated RANS heat transfer prediction and the experimental results. The methodology is promising, showing the ability to finely select the roughness parameters to input in the numerical model to fit the experimental heat transfer, without an a priori knowledge of the actual roughness pattern.
This year, numerical investigations have been performed on the Eulerian droplet model to solve the droplet impingement. The model equations are close to the Euler equations but without a pressure term. Consequently, the resulting system is weakly hyperbolic and standard Riemann solvers cannot be used. To circumvent this problem, the system is modified to include the divergence of a particle pressure. The main purpose of this work 31 is to implement a multidimensional HLLC Riemann solver for the modified formulation of the Eulerian droplet model. The method should preserve physical properties such as the density positivity and must produce accurate results compared to existing codes.
7.4 High order embedded and immersed boundary methods
Participants: Héloïse Beaugendre, Tiffanie Carlier, Mirco Ciallella, Benjamin Constant, Elena Gaburro, Marco Lorini, Florent Nauleau, Mario Ricchiuto.
 Corresponding member: Héloïse Beaugendre
We have continued exploring new ideas allowing to improve the accuracy of immersed and embedded boundary methods, both on a fundamental level and in applications.
Shifted boundary method, extensions and developments. We have proposed several applications and extensions of the original ideas behind the shifted boundary method of 95. This method is based on the simple idea that when applying the boundary conditions on a modified boundary we can modify the imposed conditions to account for this offset by means of a Taylor series expantion truncated to the desired accuracy. First of all, we extended the enriched formulation proposed in 99 to the approxiamtion of parabolic problems with moving interfaces, modeling phase change. This is being done in the PhD of T. Carlier 34, 45.
We have worked on extending the use of the same idea to higher orders. In this case the evaluation of the entire Taylor expansion in each boundary quadrature point is quite expensive. On the other hand, when using local data to evaluate the Taylor series this procedure can be readily shown to be simply a local change in polynomial basis. This has allowed to rewrite the method via a simple but effective high order polynomial correction based on the polynomial representation already available in the cell. This approach has been thoroughly tested for hyperbolic problems in 2D and 3D in 12. Its in depth study for elliptic problems is ongoing in collaboration with DTU compute and Duke University.
At the same time, we have tried to reformulate the problem based on a continuous view of the scheme. Using the anisotropy of the thin region between the underresolved and physical boundaries we have been able to derive a subgrid asymptotic approaximation whose trace on the surrogate boundary is precisely the condition used in the shifted boundary method. This allows to design several boundary conditions within any desired order of accuracy. This work is perfomed in collaboration with L. Nouveau (INSA Rennes), and C. Poignard (Inria, MONC).
Embedding shock waves and discontinuities. Using similar ideas we have proposed a discontinuity tracking approach which uses polynomial extrapolation to pass from the computational mesh to a mesh approximating the discontinuity. This method, originally introduced in 70 avoids introducing small cut cells, as the original front tracking method does, and allows to recover the formal accuracy of the scheme, without the need of any limiter and with none of the spurious effects related to the capturing of strong shocks. This year we have extended this work to the approximation of interactions of several discontinuities using both unstructured 14 and structured flow solvers 4. Preliminary results in 3D are discussed in 30.
Immersed boundaries for turbulent flows. Realistic applications to external aerodynamics are being pursued in collaboration with ONERA and CEACesta. Within the PhD of Benjamin Constant (ONERA) we have proposed an improved Immersed Boundary Method based on volume penalization for turbulent flow simulations on Cartesian grids. The proposed approach enables to remove spurious oscillations on the wall on skin pressure and friction coefficients. Results are compared to a bodyfitted simulations using the same wall function, showing that the stairstep immersed boundary provides a smooth solution compared to the bodyfitted one. The IBM has been modified to adapt the location of forced and forcing points involved in the immersed boundary reconstruction to the Reynolds number. This method has been validated either for subsonic and transonic flow regimes, through the simulation of the subsonic turbulent flow around a NACA0012 profile and the transonic flow around a RAE2822 profile and the threedimensional ONERA M6 wing. This work has been extended to more complex 3D geometries and presented in 35. This work continues with the thesis of Michele Romanelli. In 23, Michele presents a databased methodology to build ReynoldsAveraged Navier–Stokes (RANS) wall models for aerodynamic simulations at low Mach numbers. Like classical approaches, the model is based on nondimensional local quantities derived from the wall friction velocity, the wall viscosity, and the wall density. A fullyconnected neural network approximates the relation. We consider reference data (obtained with RANS simulations based on fine meshes up to the wall) of attached turbulent flows at various Reynolds numbers over different geometries of bumps, covering a range of wall pressure gradients. After training the neural networks on a subset of the reference data, the paper assesses their ability to accurately recover data for unseen conditions on meshes that have been trimmed from the wall up to an interface height where the learned wall law is applied. The network’s interpolation and extrapolation capabilities are quantified and carefully examined. Overall, when tested within its interpolation and extrapolation capabilities, the neural network model shows good robustness and accuracy. The global error on the skin friction coefficient is a few percent and behaves consistently over all the considered test cases.
Florent Nauleau doctoral work aims at adapting the immersed boundary conditions (IBC) technique to threedimensional (3D) large eddy simulations (LES) of viscous hypersonic flows around complex vehicles. The work relies on a preexisting inhouse IBC code, HYPERION (HYPERsonic vehicle design using Immersed bOuNdaries). As a first step towards the optimization of the 3D HYPERION, we discuss in this paper 32 a novel MPI/OpenMP hybrid rasterization algorithm allowing for the detection of immersed cells in record time even for very large problems. We then consider the leastsquarebased reconstruction algorithm from HYPERION. In 3D configurations it is found that the number of neighbors has to be very high to ensure the proper conditioning of the leastsquare matrix. If the computation is distributed on several MPI processes (as is always the case in 3D for realistic return times), gathering the information from that many neighbors can cause obvious communication issues  it amounts to covering large stencils with unrealistically large MPI halos. We therefore introduce an algorithm designed for a hybrid MPI/OpenMP environment based on migratable tasks and the consensus algorithm to remedy the former shortcoming. Finally, we discuss the premise of the implementation of LES capabilities in HYPERION.
Another aspect of the work of Florent Nauleau concerns scientific visualisation. This application paper 33 presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence diagram of the maxima of flow enstrophy (an established vorticity indicator), for the topological representation of 180 ensemble members, generated by a coarse sampling of the parameter space of five numerical solvers. We document five main hypotheses reported by domain experts, describing their expectations regarding the variability of the flows generated by the distinct solver configurations. We contribute three evaluation protocols to assess the validation of the above hypotheses by two comparison measures: (i) a standard distance used in scientific imaging (the L2 norm) and (ii) an established topological distance between persistence diagrams (the L2 Wasserstein metric). Extensive experiments on the input ensemble demonstrate the superiority of the topological distance (ii) to report as close to each other flows which are expected to be similar by domain experts, due to the configuration of their vortices. Overall, the insights reported by our study bring an experimental evidence of the suitability of TDA for representing and comparing turbulent flows, thereby providing to the fluid dynamics community confidence for its usage in future work. Also, our flow data and evaluation protocols provide to the TDA community an applicationapproved benchmark for the evaluation and design of further topological distances.
7.5 Modeling selfhealing materials for aeronautics
Participants: Giulia Bellezza, Mario Ricchiuto.
 Corresponding member: Mario Ricchiuto
We have completed in collaboration with the LCTS laboratory a first fully coupled study of a self healing minicomposite. To this end we have proposed a slow crack growth model explicitly dependent on the environmental parameters which we calibrated using a particular exact solution of the corresponding ODE, and integrated numerically in the general case. The tow failure results from the statistical distribution of the fibres’ initial strength, the slow crack growth kinetics, and the load transfer following fibres breakage. The lifetime prediction capabilities of the model, as well as the effect of temperature, spatial variation of the statistical distribution of fibres strength, and applied load, are investigated highlighting the influence of the diffusion/reaction processes (healing) on the fibre breakage scenarios. This work is reported in 6.
Based on this model we have proposed an extensive characterization of the uncertainty propagation as well as a sensitivity analysis study which has permitted to envision a first approach to upscale the closure for the healing to a single (or to a finite number of) ODE(s) in each crack. Results are discussed in the dissertation 41. A paper is in preparation.
7.6 Adaptation techniques
Participants: Nicolas Barral, Héloïse Beaugendre, Sourabh Bhat, Mirco Ciallella, Luca Cirrottola, Pierre Clouzet, Mario Ricchiuto, Ishak Tifouti.
 Corresponding member: Nicolas Barral
Parallel mesh adaptation. Taskbased parallelism using Mmg tools was investigated within the European project Microcard. Several approaches were considered to implement MMG algorithms in the StarPU framework, although none yet was really successful. Broader investigations on adaptation of the code base for sharedmemory parallelism were also carried on. The source code, documentation and contributions to these projects are hosted at github.
Goal oriented mesh adaptation. The work on goaloriented mesh adaptation techniques for geophysical flows has continued, in the context of the collaboration with Imperial College London.
The MPIparallel metricbased mesh adaptation toolkit ParMmg was integrated into the solver library PETSc. This coupling brings robust, scalable anisotropic mesh adaptation to a wide community of PETSc users, as well as users of downstream packages. We demonstrate the new functionality via the solution of Poisson problems in three dimensions, with both uniform and spatiallyvarying righthand sides.
Metricbased mesh adaptation methods was applied to advectiondominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered were built upon goaloriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant’s outfall. Four approaches were considered, one of which yields isotropic meshes. The focus on advectiondominated problems means that flows are often anisotropic; thus, three anisotropic approaches were also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology was validated using an existing 2D tracer transport test case with a known analytical solution. Goaloriented meshes for an idealised timedependent desalination outfall scenario were also presented.
Further work was carried out to examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goaloriented mesh adaptation. We seeked to improve the accuracy of the discontinuous Galerkin method applied to a depthaveraged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goaloriented adaptation strategies were considered, which give rise to meshes with isotropic and anisotropic elements. We reproduced results from the literature which demonstrate how a staggered array configuration extracts more energy than an aligned array. We also made detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs. The proposed goaloriented mesh adaptation strategies were validated for the purposes of tidal energy resource assessment. Using 10% as many degrees of freedom as a high resolution fixed mesh benchmark, they are shown to enable energy output differences smaller than 10%. Applied to a tidal array with aligned rows of turbines, the anisotropic adaptation scheme is shown to yield differences smaller than 1
Coupling mesh adaptation with model reduction. We started a new line of research investigating the introduction of anisotropic mesh adaptation techniques in Model Order Reduction. In the framwework of the Eflows4HPC project, Sourabh Bhat and Pierre Clouzet have started to design a coupling approach for the linear heat equation. Ishak Tifouti was hired on the AM${}^{2}$OR Action Exploratoire and has started looking into how mesh adaptation could help Model Order Reduction for nonlinear hyperbolic problems.
7.7 Direct ArbitraryLagrangian Eulerian methods on Voronoi meshes
Participants: Elena Gaburro, Mario Ricchiuto, Michele Giuliano Carlino.
 Corresponding member: Elena Gaburro
We have continued with the development of the code called AleVoronoi: Direct Arbitrary Lagrangian Eulerian high order finite volume and discontinous Galerkin schemes on VORONOI moving meshes with topology changes. The code is written in Fortran with the OpenMP parallel paradigm. It implements an arbitrary high order accurate numerical scheme which exploits the ADER paradigm both for the Finite Volume and Discontinous Galerkin case and can be used for studying the Burgers equation, Euler equations, multimaterial Euler equations, Shallow Water models written in various system of coordinates and in covariant form, MHD equations, and the GPR model. It belongs to the family of ArbitraryLagrangianEulerian methods, so it can be used in fixed Eulerian framework or with a moving Voronoi mesh regenerated at each time step. Its peculiarity is the capability of dealing with topology changes maintaining the high order of accuracy.
The work of 2022 has been devoted to the following major improvements. First, we have inserted in AleVoronoi a robust a posteriori subcell Finite Volume limiter and we have started the implementation of novel mesh adaptation strategies. A manuscript completely devoted to these major implementation works is in preparation and a book chapter collecting some preliminary results can be found in 39. In particular, the manuscript aims at showing, by simple and very salient examples, the capabilities of highorder ALE schemes, and of our novel technique, based on the highorder spacetime treatment of topology changes.
Then, we have compared the capabilities of different sets of basis functions on Voronoi meshes: the obtained results are described in 9. There indeed we have proposed a new high order accurate nodal discontinuous Galerkin (DG) where, rather than using classical polynomials of degree $N$ inside each element, we represent the discrete solution by piecewise continuous polynomials of degree $N$within each Voronoi element, using a continuous finite element basis defined on a subgrid inside each polygon. We call the resulting subgrid basis an agglomerated finite element (AFE) basis for the DG method on general polygons, since it is obtained by the agglomeration of the finite element basis functions associated with the subgrid triangles. The basis functions on each subtriangle are defined, as usual, on a universal reference element, hence allowing to compute universal mass, flux and stiffness matrices for the subgrid triangles once and for all in a preprocessing stage for the reference element only. Consequently, the construction of an efficient quadraturefree algorithm is possible, despite the unstructured nature of the computational grid.
Finally, we have implemented a novel quasiconservative strategy to deal with multimaterial flow simulations that we have already described above and for which here we want just to underline that the method has been implemented in twodimension on unstructured Voronoi meshes.
The main developer of AleVoronoi is Elena Gaburro. The described work has been realized in collaboration with MArio Ricchiuto, Michele Giuliano Carlino, Walter Boscheri (University of Ferrara, Italy) and Simone Chiocchetti (University of Trento, Italy).
7.8 Modeling of flows in aquifers
Participants: Manon Carreau, Marco Lorini, Martin Parisot.
 Corresponding member: Martin Parisot
The objective of this project is to propose a numerical tool (software GeoFun) for the simulation of flows in aquifers based on unified models. Different types of flows can appear in an aquifer: free surface flows (hyperbolic equations) for lakes and rivers, and porous flows (elliptic equations) for ground water. The variation in time of the domain where each type of flow must be solved makes the simulation of flows in aquifers a scientific challenge. Our strategy consists of writing a model that can be solved in the whole domain, i.e. without domain decomposition.
For the beginning of the project we start by considering only the saturated areas. In 46, we propose and study a unified model between shallow water and DupuitForchheimer models, which are both classical models in each areas. A numerical scheme has been proposed and analysed. It satisfies a discrete entropy dissipation which ensure a strong stability.
In 51, we also propose a model and a numerical strategy to take into account the air pockets that can be trapped under a impermeable structure. This work can also be used for the simulation of some marine energy conververters such are the solution of Seaturns of Hace. In parallel, we work on the structure of the code in order to integrate more easily the furthers ideas. In particular, specific numerical integrators and time schemes have been implemented.
8 Bilateral contracts and grants with industry
8.1 Bilateral Contracts
CEADAM/DIF
Participants: Aurore Cauquis, Mario Ricchiuto.
 Title: Development of a numerical model for tsunamis: from propagation to breking in realistic coastal environnements.
 Type: contrat d'accompagnement for Aurore Cauquis' PhD.
 Duration: 36 months
 Starting date : 1st Nov 2019
 Coordinator: Mario Ricchiuto and Philippe Heinrich (CEA)
 Summary: The objective of this contract is to develop efficient temporal and spatial discretizations for dispersive waves on Cartesian grids based on ad hoc LaxWendroff finite difference methods, possibly combined with WENO approximations. The schemes are to be implemented in the code of CEA and applied to tsunami simulations in realistic coastal environnements.
CEACESTA
Participants: Héloïse Beaugendre.
 Title: Immersed boundary method applied to large eddy simulations of hypersonic reentry vehicles
 Duration: 36 months
 Starting date : 19 October 2020
 Coordinator: Heloise Beaugendre Fabien Vivodtzev and Thibault BridelBertomeu (CEA)
 Summary: The aim of this work is to provide improved tools for the aerothermal dimensioning of a reentry vehicle. Operational codes are based on NavierStokes averaged (RANS) equations and bodyfitted structured meshes. The project aims at developing an LES code based on an existing DNS one (finite volumes, Cartesian mesh, hybrid parallelism, high order WENO type) to be enhanced with an SGSM closure adapted to hypersonic flows. The work will include immersed boundaries on Cartesian grids and to adapt the technique to reentry flows. Finally, in order to exploit the results of simulations carried out for the development and validation of models, the PhD student will bring a critical look at them using a recent technique, topological data analysis (TDA) using the TTK opensource platform.
EDF
Participants: Bastien Jouy, Mario Ricchiuto.
 Title: Numerical modelling of Favre waves and undular bores in channels with banks
 Duration: 36 months
 Starting date : 08 November 2021
 Coordinator: Mario Ricchiuto
 Summary: The collaboration with EDF (Eleectricité de France) focuses on the improvement of their in house code TELEMACMascaret, initially for the advection of passive scalars (pollutant transport), and more recently for the simulation of hydrostatic and dispersive (undular) bore dynamics in networks of channels (application to abrupt closing/opening of valves). The past work on advection schemes has been done with J.M. Hervouet (retired) and R. Ata (riadh.ata@edf.fr  currently at FLOW3D) was an informal collaboration. The ongoing collaboration on bore dynamics is with D. Violeau (damien.violeau@edf.fr) is object of a CIFRE contract. This work aims at increasing the capabilities of EDF’s code to simulate the undulating bores studied in 68. The PhD started last November.
UHAINA intercarnot
Participants: Christopher Poette, Mario Ricchiuto.
 Title: développement d'une plateforme opérationnelle pour la simulation des risques côtiers (UHAINA)
 Duration: 30 months
 Starting date : 1st Steptember 2019
 Coordinator: Mario Ricchiuto and Rodrigo Pedreros (BRGM).
 Summary: The objective of this contract is to develop and implement the necessary functionalities to allow the use of the UHAINA platform in an operational context. This involves both pre and post processing tools based on standard data formats, as well as extension of the models themselves (nonuniform friction, wind forcing, curvilineear coordinates, etc). Applications to storm surge and real tsunami events are sought.
9 Partnerships and cooperations
9.1 International initiatives
9.1.1 Inria associate team not involved in an IIL or an international program
ANEMONE
Participants: Mirco Ciallella, Elena Gaburro, Marco Lorini, Mario Ricchiuto.

Title:
AdvaNced Embedded MethOds for flows with NonlinEar moving fronts

Duration:
2020 >

Coordinator:
Guglielmo Scovazzi (guglielmo.scovazzi@duke.edu)

Partners:
 Duke University Durham (ÉtatsUnis)

Inria contact:
Mario Ricchiuto

Summary:
ANEMONE focuses on the numerical treatment of flows with moving fronts with complex and possibly nonlinear dynamics. There exist many examples of such fronts, related to different physics. Some of these represent in some sense boundaries of the fluid domain, as for example the waterline in floods and tsunami inundations, or the rigid walls of bodies freely moving in the flow. Other fronts involve abrupt changes in the physics. This is the case for example of shock waves occurring in compressible flows (and in some flows with similar nonlinear behaviour), or fronts coupling flows with different behaviours, as it occurs in some models for wavebody interactions. To handle in an accurate and flexible manner these features, ANEMONE will focus on the improvement and application of high order embedding techniques based on ideas similar to the shifted boundary method, initially developed by the groupe at Duke University. This approach, initially developed to set boundary conditions on complex boundaries, will be extended to deal with several different types of nonlinear moving interfaces, while studying simplified formulations allowing an easier implementation, as well as the interaction of the accuracy of the embedding procedure with mesh adaptation. The results of ANEMONE are expected to have an impact on the activities of the participants in domains such as from wave energy extraction, coastal risk assessment, as well as applications in aeronautics related to wing icing.
LARME
Participants: Manon Carreau, Martin Parisot, Mario Ricchiuto.

Title:
Largescale simulations of renewable marine energy

Duration:
2021 >

Coordinator:
Martin Parisot and Claes Eskilsson (claes.eskilsson@ri.se)

Partners:
 Rise/Aalborg University (Danemark)

Inria contact:
Martin Parisot

Summary:
During this collaboration, we propose to focus on the modeling and simulation of marine renewable energy converters based on wave or current energy. Among marine renewable energies, only offshore wind energy is truly exploited today. However, this sector only uses large marine surfaces, without exploiting the true potential of the sea. Indeed, water being 1000 times heavier than air, its energy potential is also much higher.
9.2 International research visitors
9.2.1 Visits of international scientists
Inria International Chair
Participants: Remi Abgrall.
Other international visits to the team
Ilya Peshkov

Status
Researcher

Institution of origin:
University of Trento

Country:
Italy

Dates:
1721/01 2022

Context of the visit:
Scientific collaboration with Elena Gaburro on General Relativity

Mobility program/type of mobility:
Short research stay funded by SuPerMan
Davide Torlo

Status
Postdoctoral researcher

Institution of origin:
Sissa, Scuola Internazionale Superiore di Studi Avanzati

Country:
Italy

Dates:
28/02  04/03 2022

Context of the visit:
Collaboration with Sissa

Mobility program/type of mobility:
Research stay
François Morency

Status
Professor

Institution of origin:
ETS

Country:
Canada

Dates:
30/03 01/04 2022

Context of the visit:
Collaboration between Onera and Inria on inflight icing

Mobility program/type of mobility:
Research stay
Alessia Assonitis

Status
PhD student

Institution of origin:
Università la Sapienza, Roma

Country:
Italy

Dates:
07/03  07/06/2022

Context of the visit:
Collaboration with Università la Sapienza

Mobility program/type of mobility:
Research stay
Cristian Brutto

Status
PhD student

Institution of origin:
University of Trento

Country:
Italy

Dates:
24/05  28/05 2022

Context of the visit:
Collaboration with University of Trento

Mobility program/type of mobility:
Research stay
Lorenzo Micalizzi

Status
PhD student

Institution of origin:
University of Zurich

Country:
Switzerland

Dates:
18/07  29/07 2022

Context of the visit:
Collaboration with University of Zurich

Mobility program/type of mobility:
Research stay
9.2.2 Visits to international teams
Research stays abroad
Elena Gaburro

Visited institution:
University of Trento

Country:
Italy

Dates:
2023/02 and 1118/06 and 24/0905/10 and 1023/12 2022

Context of the visit:
Scientific collaboration with Prof. Michael Dumbser, Dr. Ilya Peshkov and Dr.Ing. Simone Chiocchetti

Mobility program/type of mobility:
Research stay funded by SuPerMan

Visited institution:
University of Zurich

Country:
Switzerland

Dates:
2430/ 04 2022 and 1627/08 2022

Context of the visit:
Scientific collaboration with Prof. Remi Abgrall and organization of the International Conference MultiMat 2022

Mobility program/type of mobility:
Research stay funded by the University of Zurich

Visited institution:
Technical University of Crete

Country:
Greece

Dates:
2023/09 2022

Context of the visit:
Scientific collaboration with Prof. Anargiros Delis and organization of the International Conference HONOM2024

Mobility program/type of mobility:
Research stay funded by SuPerMan
9.3 European initiatives
9.3.1 H2020 projects
SuPerMan
Participants: Elena Gaburro, Michele Giuliano Carlino, Mario Ricchiuto.
SuPerMan project on cordis.europa.eu

Title:
Structure Preserving schemes for Conservation Laws on Space Time Manifolds

Duration:
From June 1, 2021 to May 31, 2023

Partners:
 INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE (INRIA), France

Inria contact:
Elena Gaburro

Coordinator:
Elena Gaburro

Summary:
SuPerMan proposes the development and efficient implementation of new structure preserving schemes for conservation laws formulated in an elegant and universal form through covariant derivatives on spacetime manifolds.
Indeed, nonlinear systems of hyperbolic PDEs are characterized by invariants, whose preservation at the discrete level is not trivial, but plays a fundamental role in improving the long term predictivity and reducing the computational effort of modern algorithms. Besides mass and linear momentum conservation, typical of any Finite Volume scheme, the preservation of stationary and moving equilibria, asymptotic limits and interfaces still represents an open challenge, especially in astrophysical applications, such as turbulent flows in gas clouds rotating around black holes.
In this project, our focus will thus be on General Relativistic Hydrodynamics (GRHD) for which such Well Balanced (WB) Structure Preserving (SP) schemes have never been studied before. In particular, we plan to devise smart methods, independent of the coordinate system. This will be achieved by directly including the metric, implicitly contained in the covariant derivative, as a conserved variable inside the GRHD model.
This approach will first be tested on the Euler equations of gasdynamics with Newtonian gravity, extending already existing WBSP techniques to general coordinate systems. All novel features will be carefully proven theoretically. Next, the new schemes will be incorporated inside a massively parallel high order accurate ArbitraryLagrangianEulerian Finite Volume (FV) and Discontinuous Galerkin (DG) code, to be released as open source. The feasibility of the project is guaranteed by the strong network surrounding the ER, including experts on WBSP techniques and mesh adaptation (INRIA France), FVDG schemes and GRHD (UniTN Italy) and computational astrophysics (MPG Germany). This MSCA project will allow the applicant transition to become an independent researcher.
eFlows4HPC
Participants: Nicolas Barral, Héloïse Beaugendre, Sourabh Bhat, Pierre Clouzet, Mario Ricchiuto.
eFlows4HPC project on cordis.europa.eu

Title:
Enabling dynamic and Intelligent workflows in the future EuroHPCecosystem

Duration:
From January 1, 2021 to February 29, 2024

Partners:
 INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE (INRIA), France
 DTOK LAB SRL, Italy
 FORSCHUNGSZENTRUM JULICH GMBH (FZJ), Germany
 SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE (SISSA), Italy
 INSTYTUT CHEMII BIOORGANICZNEJ POLSKIEJ AKADEMII NAUK, Poland
 ALFREDWEGENERINSTITUT HELMHOLTZZENTRUM FUR POLAR UND MEERESFORSCHUNG (AWI), Germany
 EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH (ETH Zürich), Switzerland
 INSTITUT POLYTECHNIQUE DE BORDEAUX (Bordeaux INP), France
 STIFTELSEN NORGES GEOTEKNISKE INSTITUTT (NGI), Norway
 BULL SAS (BULL), France
 CENTRE INTERNACIONAL DE METODES NUMERICS EN ENGINYERIA (CIMNECERCA), Spain
 UNIVERSIDAD DE MALAGA (UMA), Spain
 UNIVERSITAT POLITECNICA DE VALENCIA (UPV), Spain
 ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA, Italy
 FONDAZIONE CENTRO EUROMEDITERRANEOSUI CAMBIAMENTI CLIMATICI (FONDAZIONE CMCC), Italy
 SIEMENS AKTIENGESELLSCHAFT, Germany
 BARCELONA SUPERCOMPUTING CENTER CENTRO NACIONAL DE SUPERCOMPUTACION (BSC CNS), Spain

Inria contact:
Mario Ricchiuto

Coordinator:
Rosa Badia (BSC)

Summary:
Today, developers lack tools that enable the development of complex workflows involving HPC simulation and modelling with data analytics (DA) and machine learning (ML). TheFlows4HPC aims to deliver a workflow software stack and an additional set of services to enable the integration of HPC simulation and modelling with big data analytics and machine learning in scientific and industrial applications. The software stack will allow to develop innovative adaptive workflows that efficiently use the computing resources and also considering innovative storage solutions.
To widen the access to HPC to newcomers, the project will provide HPC Workflows as a Service (HPCWaaS), an environment for sharing, reusing, deploying and executing existing workflows on HPC systems. The workflow technologies, associated machine learning and big data libraries used in the project leverages previous open source European initiatives. Specific optimization tasks for the use of accelerators (FPGAs, GPUs) and the EPI will be performed in the project use cases.
To demonstrate the workflow software stack, use cases from three thematic pillars have been selected. Pillar I focuses on the construction of DigitalTwins for the prototyping of complex manufactured objects integrating stateoftheart adaptive solvers with machine learning and datamining, contributing to the Industry 4.0 vision. Pillar II develops innovative adaptive workflows for climate and for the study of Tropical Cyclones (TC) in the context of the CMIP6 experiment, including insitu analytics. Pillar III explores the modelling of natural catastrophes  in particular, earthquakes and their associated tsunamis shortly after such an event is recorded. Leveraging two existing workflows, the Pillar will work of integrating them with the eFlows4HPC software stack and on producing policies for urgent access to supercomputers. The pillar results will be demonstrated in the target community CoEs to foster adoption and get feedback.
Microcard
Participants: Nicolas Barral, Mariem Makni, Francesco Brarda.
Microcard project on cordis.europa.eu

Title:
Numerical modeling of cardiac electrophysiology at the cellular scale

Duration:
From April 1, 2021 to September 30, 2024

Partners:
 INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE (Inria), France
 INSTITUT POLYTECHNIQUE DE BORDEAUX (Bordeaux INP), France
 UNIVERSITE DE STRASBOURG, France
 SIMULA RESEARCH LABORATORY AS, Norway
 UNIVERSITA DEGLI STUDI DI PAVIA, Italy
 UNIVERSITA DELLA SVIZZERA ITALIANA, Switzerland
 KARLSRUHER INSTITUT FUER TECHNOLOGIE (KIT), Germany
 ZUSEINSTITUT BERLIN, Germany
 MEGWARE COMPUTER VERTRIEB UND SERVICE GMBH, Germany
 NUMERICOR GMBH, Austria
 OROBIX SRL, Italy

Contact:
Nicolas BARRAL

Summary:
Cardiovascular diseases are the most frequent cause of death worldwide and half of these deaths are due to cardiac arrhythmia, a disorder of the heart's electrical synchronization system. Numerical models of this complex system are highly sophisticated and widely used, but to match observations in aging and diseased hearts they need to move from a continuum approach to a representation of individual cells and their interconnections. This implies a different, harder numerical problem and a 10,000fold increase in problem size. Exascale computers will be needed to run such models.
We propose to develop an exascale application platform for cardiac electrophysiology simulations that is usable for cellbycell simulations. The platform will be codesigned by HPC experts, numerical scientists, biomedical engineers, and biomedical scientists, from academia and industry. We will develop, in concert, numerical schemes suitable for exascale parallelism, problemtailored linearsystem solvers and preconditioners, and a compiler to translate highlevel model descriptions into optimized, energyefficient system code for heterogeneous computing systems. The code will be parallelized with a recently developed runtime system that is resilient to hardware failures and will use an energyaware task placement strategy.
The platform will be applied in reallife use cases with high impact in the biomedical domain and will showcase HPC in this area where it is painfully underused. It will be made accessible for a wide range of users both as code and through a web interface.
We will further employ our HPC and biomedical expertise to accelerate the development of parallel segmentation and (re)meshing software, necessary to create the extremely large and complex meshes needed from available large volumes of microscopy data.
The platform will be adaptable to similar biological systems such as nerves, and components of the platform will be reusable in a wide range of applications.
ExaQUte
Participants: Luca Cirrottola, Heloise Beaugendre, Mario Ricchiuto.
ExaQUte project on cordis.europa.eu

Title:
EXAscale Quantification of Uncertainties for Technology and Science Simulation

Duration:
From November 30, 2021 to December 1, 2022
 Partners:

Inria contact:
Luca Cirrottola

Coordinator:
CENTRE INTERNACIONAL DE METODES NUMERICS EN ENGINYERIA

Summary:
The ExaQUte project aims at constructing a framework to enable Uncertainty Quantification (UQ) and Optimization Under Uncertainties (OUU) in complex engineering problems using computational simulations on Exascale systems. The stochastic problem of quantifying uncertainties will be tackled by using a Multi Level MonteCarlo (MLMC) approach that allows a high number of stochastic variables. New theoretical developments will be carried out to enable its combination with adaptive mesh refinement, considering both, octreebased and anisotropic mesh adaptation. Gradientbased optimization techniques will be extended to consider uncertainties by developing methods to compute stochastic sensitivities, This requires new theoretical and computational developments. With a proper definition of risk measures and constraints, these methods allow highperformance robust designs, also maximizing the solution reliability. The description of complex geometries will be possible by employing embedded methods, which guarantee a high robustness in the mesh generation and adaptation steps, while allowing preserving the exact geometry representation. The efficient exploitation of Exascale system will be addressed by combining StateoftheArt dynamic taskscheduling technologies with spacetime accelerated solution methods, where parallelism is harvested both in space and time. The methods and tools developed in ExaQUte will be applicable to many fields of science and technology. The chosen application focuses on wind engineering, a field of notable industrial interest for which currently no reliable solution exists. This will include the quantification of uncertainties in the response of civil engineering structures to the wind action, and the shape optimization taking into account uncertainties related to wind loading, structural shape and material behavior. All developments in ExaQUte will be opensource and will follow a modular approach, thus maximizing future impact.
9.4 National initiatives
ANR VISCAP
Participants: Giulia Bellezza, Mathieu Colin, Mario Ricchiuto.

Title:
VIrtual Selfhealing Composites for Aeronautic Propulsion

Type:
ANR

Duration:
48 months

Starting date :
1st Jan 2018

Coordinator:
Vignoles Gerard (Université de Bordeaux and LCTS  UMR 5801)

Abstract:
Selfhealing CeramicMatrix Composites (SHCMCs) have extremely long lifetimes even under severe thermal, mechanical and chemical solicitations. These materials have the particularity of protecting themselves against corrosion by the formation of a sealing oxide that fills the matrix cracks, delaying considerably the fibres degradation. Applications encompass civil aeronautic propulsion engine hot parts and they represent a considerable market; however this is only possible if the lifetime duration of the materials is fully certified. The ambition of this innovative project is to provide reliable, experimentally validated numerical models able to reproduce the behaviour of SHCMCs. The starting point is an existing imagebased coupled model of progressive oxidative degradation under tensile stress of a minicomposite (i.e. a unidirectional bundle of fibres embedded in multilayered matrix). Important improvements will be brought to this model in order to better describe several physicchemical phenomena leading to a nonlinear behaviour: this will require an important effort in mathematical analysis and numerical model building. A systematic benchmarking will allow creating a large database suited for the statistical analysis of the impact of material and environmental parameter variations on lifetime. It is planned to perform experimental verifications of this model with respect to tests, carried out on model materials using insitu Xray tomography, in a specially adapted hightemperature environmental & mechanical testing cell. Other characterizations are also proposed. The extension of the modelling procedure to Discrete Crack Networks for the largescale description of the material life will be the next action; it will require important developments on mesh manipulations and on mathematical model analysis. Finally, experimental validation will be carried out by comparing the results of the newly created software to tests run on 3D composite material samples provided by the industrial partner of the project.
ANR GEOFUN
Participants: Manon Carreau, Marco Lorini, Martin Parisot.

Title:
GEOphysical Flows with UNified models

Type:
ANR

Duration:
48 months

Starting date :
1st Jan 2020

Coordinator:
Martin Parizot

Abstract:
The objective of the GeoFun project is to improve the modeling and simulation of geophysical flows involving at least two different processes. The main application we have in mind is water catchment areas, where a shallow free surface flow stands above a underground flow on porous medium. Our vision of water transport is often naive, because we first think of rivers, lakes, and flooding, but actually, $80\%$ of water in continental areas is underground. Sometimes, the porous substrate is covered with an impermeable rock stratum, which confines the flow as in pipelines, except at certain points where springs and resurgences appear. Our long term goal is to propose a global and unified model of an aquifer. By global, we mean a complete description, including free surface flow (rivers), exchanges with the groundwater in unsaturated area, flows in caves, that might be congested or not, and might contain air pockets. By unified, we mean that we do not aim to decompose the domain and use different models for each part of the aquifer. On the contrary, we plan to propose and study models able to pick the relevant physic by themselves in a multiphysics context. The numerical approximation will be a main concern all along the way. The final contribution of the GeoFun project is the development of a scientific computing library, simulating complex flows in water catchment areas thanks to the numerical strategies analyzed in this project. Since unified models are design to be applied in the whole computational domain with no domain decomposition, the robustness of the numerical strategy at all regime are essential. Our unified numerical schemes will degenerate towards existing schemes in those regions, in order to guarantee a similar feasibility and robustness. Moreover, since the final goal is to test the library on realistic aquifers, the efficiency of the methods is of crucial importance.
ANR LAGOON
Participants: Maria Kazolea, Martin Parisot, Mario Ricchiuto.

Title:
Large scale global storm surge simulations

Type:
ANR

Duration:
48 months

Starting date :
1st Oct 2021

Coordinator:
Vincent Perrier (U.Pau et des Pays de l'Adour)

Abstract:
The aim of the project is to develop an allscale shallow water stormsurge model simulating different features of oceanic flows: from large scale linear waves in open ocean to small scale nonlinear flows in coastal areas, and using high resolution by combining novel numerical approaches on unstructured grids and high performance computing.
Inria Challenges: SURF
Participants: Maria Kazolea, Mario Ricchiuto.

Title:
SURF: a groundbreaking project in oceanographic simulation

Type:
Inria Challenges

Duration:
48 months

Starting date :
1st Jan 2019

Coordinator:
Arthur Vidard (AirSea)

Abstract:
Understanding the dynamics of the oceans is a key scientific issue. It has many applications in coastal zone management, the regulation of maritime traffic and the prevention of ecological, meteorological and industrial risks. While scientific computing is now one of the most widelyused tools to explain or predict changes in the ocean, simulation tools are still reserved for specific purposes. The SURF project brings together several Inria teams that are pooling their expertise to develop a common platform for computing oceanic flows in littoral and coastal zones.
Inria Action Exploratoire: AM${}^{2}$OR
Participants: Nicolas Barral.

Title:
AM${}^{2}$OR: Adaptive meshes for Model Order Reduction

Type:
Inria Action Exploratoire

Duration:
48 months

Starting date :
1st October 2022

Coordinator:
Nicolas Barral

Partner:
Tommaso Taddei (Inria MEMPHIS)

Abstract:
Mesh adaptation and Model Order Reduction both aim at reducing significantly the computational cost of numerical simulations by taking advantage of the solution's features. Reduced Order Modelling is a method that builds lighter surrogate models of a system's response over a range of parameters, which is particularly useful in the solution of design and optimization inverse problems. Reducedorder models rely on a highfidelity (e.g., finite element) approximation that should be sufficiently accurate over the whole range of parameters considered: in presence of structures such as shocks and boundary layers, standard mesh refinement techniques would lead to highfidelity models of intractable size. In this project, we propose a novel adaptive procedure to simultaneously construct a highfidelity mesh (and associated discretisation) and a reducedorder model for a range of parameters, with particular emphasis on inverse problems in computational fluid dynamics.
RENOVABLE
Participants: Martin Parisot, Mario Ricchiuto.

Title:
RENOVABLES

Type:
EuroRegion

Duration:
24 months

Starting date :
17 Dec 2020

Coordinator:
Martin Parisot

Abstract:
RENOVABLES is a natworking program involving several universities and reserach centers from France and the French and Spanish basque region. Its objective is to share progress on ongoing activities related to renewable energies.
10 Dissemination
10.1 Promoting scientific activities
10.1.1 Scientific events: organisation
General chair, scientific chair
 Mario Ricchiuto : Essentially hyperbolic problems: unconventional numerics, and applications: A conference in honor of Rémi Abgrall's 61st birthday, October 9  14, 2022  Monte Verità, Ascona.
 Elena Gaburro : cochair of the organizing committe and memeber of the scientific committee of MultiMat 2022, the 10th International Conference on Numerical Methods for MultiMaterial Fluid Flow, 2226 of August 2022, Zurich, Switzerland.
 Mathieu Colin is a member of the scientific comittee of the "Journée Jeunes EDPistes".
Member of the organizing committees
 Martin Parisot : EmrSim'22, HYWEC'22.
 Maria Kazolea : AGU Fall meeting, NH23B: Interdisciplinary Tsunami Science Session, Chicago, Il and online everywhere, 1216 December 2022.
Member of scientific committees
 Martin Parisot : HYWEC'22.
 Mario Ricchiuto : EmrSim'22, HYWEC'22, GdR MathGeoPhy, Essentially Hyperbolic Problems
10.1.2 Scientific events: selection
 Elena Gaburro , Maria Kazolea and Mario Ricchiuto will be in charge of the organization of the next HONOM 2024, HighOrder NOnlinear numerical Methods for evolutionary PDEs: Theory and applications, that will be held in Crete, Greece. The organization already started with the reservation of the conference center and some preparatory work.
10.1.3 Journal
Member of the editorial boards
 Mathieu Colin is a member of the Editorial board of Application and Applied Mathematics : An International Journal.
 Elena Gaburro is Associate Editor of the Elsevier Journal Applied Mathematics and Computation
 Maria Kazolea was a guest editor of the Special Issue Numerical Methods and Applications for Waves in Coastal Environments, Water Waves, Volume 4, issue 3, November 2022
 Mario Ricchiuto is member of the editorial boards of Computers $\&$ Fluids (advisory editorial board), Journal of Computational Physics (associate editor), Numerical methods for partial differential equations (editor), Water Waves (editor)
Reviewer  reviewing activities
 Martin Parisot : Applied Mathematics and Computation, Computers and Mathematics with Applications (2 articles), The European Physical Journal Plus, Journal of Computational Physics (2 articles), Water Waves, Zeitschrift für angewandte Mathematik und Physik.
 Maria Kazolea : Ocean Engineering, Wave motion, Journal of Computational Physics, Water Waves, Journal of Fluid Mechanics, ESAIM: Mathematical Modelling and Numerical Analysis.
 Elena Gaburro : Applied Mathematics and Computations, Computer and Fluids, Journal of Computational Physics, Journal of Scientific Computing, International Journal for Numerical Methods in Fluids, Journal of Computational and Applied Mathematics, SIAM Journal on Scientific Computing
10.1.4 Invited talks
 Mathieu Colin : Workshop "Numerical and analytical approaches for nonlinear dispersive PDEs", Dijon, june, 2022.
 Martin Parisot : Workshop Nabuco (Toulouse), Journée inriaIFPEN, Lab. seminar : Institut Camille Jordan (Claude Bernard University Lyon 1), LAboratoire de MAthématiques (Université Savoie Mont Blanc Chambery).
 Second Congress of Greek mathematicians, 48/07, Athens Greece, 2022 (Maria Kazolea).
 Scientific workshop for 10th anniversary of CENALT, 2930/09, Paris, 2022 (Maria Kazolea).
 Elena Gaburro : Seminaire du laboratoire de Mathematiques de Rennes (February 2022), CIRM WorkShop, Marseille (March 2022), Oberwolfach workshop, Germany (April 2022), Seminaire du laboratoire Jacques Louis Lions, Paris (November 2022), Seminaire du laboratoire CEADAM Bruyeres le Chatel (November 2022)
 Héloïse Beaugendre : Key note speaker, workshop on immersed boundary methods, Poiters, France (Ocotber 2022)
 Mario Ricchiuto Keynote speaker at the 2022 HONOM workshop Honom 2022, EDANYA Seminar in December 2022
10.1.5 Scientific expertise
 Martin Parisot : Reviewer for the ANR.
 Elena Gaburro : Reviewer for the ANR.
10.1.6 Research administration
 Mathieu Colin is Director of the Mathematics department of the ENSEIRBMATMECA/Bordeaux INP school
 Mario Ricchiuto is deputy scientific head of the Inria Bordeaux SudOuest center.
10.2 Teaching  Supervision  Juries
10.2.1 Teaching
 License: Nicolas Barral, TD d'Analyse Numérique, 24h, L3, ENSEIRBMATMÉCA, France
 License: Nicolas Barral, Calcul Scientifique en Fortran 90, 22h, L3, ENSEIRBMATMÉCA, France
 License : Nicolas Barral, TP Fortran 90, 44h, M1, ENSEIRBMATMÉCA, France
 Master : Nicolas Barral, TD C++, 48h, M1, ENSEIRBMATMÉCA, France
 Master : Nicolas Barral, Calcul Haute Performance (OpenMPMPI), 45h, M1, ENSEIRBMATMÉCA et Université de Bordeaux, France
 Master : Nicolas Barral, Techniques de maillage, 36h, M2, ENSEIRBMATMÉCA et Université de Bordeaux, France
 Master : Nicolas Barral, Encadrement de projet de Calcul Haute Performance, 14h, M2, ENSEIRBMATMÉCA, France
 Master : Nicolas Barral : projet professionnel et suivi de stages, 14 h, ENSEIRBMATMÉCA, France
 Master : Nicolas Barral : responsable des stages 2A, 20 h, ENSEIRBMATMÉCA, France
 License: Héloïse Beaugendre, Encadrement de projets sur la modélisation de la portance, 20h, L3, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, TD C++, 48h, M1, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, Calcul Haute Performance (OpenMPMPI), 40h, M1, ENSEIRBMATMÉCA et Université de Bordeaux, France
 Master : Héloïse Beaugendre, Responsable de filière de 3ème année, 15h, M2, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, Calcul parallèle (MPI), 39h, M2, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, Encadrement de projets de la filière Calcul Haute Performance, 11h, M2, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, Encadrement de projets sur la modélisation de la pyrolyse, 20h, M1, ENSEIRBMATMÉCA, France
 Master : Héloïse Beaugendre, Projet fin d'études, 4h, M2, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : Integration, M1, 54h, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : Fortran 90, M1, 44h, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : PDE, M1, 30h, University of Bordeaux, France
 Master : Mathieu Colin : Analysis, L1, 47h, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : projet professionnel and internship responsibility : 15 h, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : Encadrement de projets TER, 20h, ENSEIRBMATMÉCA, France
 Master : Mathieu Colin : Head of Matmeca’s Department of the EnseirbMatmeca (96h)
 Master : Mathieu Colin : suivi d'apprenti en entreprise (35h)
 License: Martin Parisot, TP Fortran, 21h, M1, ENSEIRBMATMÉCA, France
 Master : Mario Ricchiuto, Multiphysics Course, 26h cours magistrale, M2, ENSEIRBMATMÉCA, France
 Doctorat: Elena Gaburro, Advanced Numerical Methods for the solution of Hyperbolic Equations, 12h (EDMIUniversitè de Bordeaux)
10.2.2 Supervision
 PhD in progress: J. Galaz Mora, Coupling of free surface coastal models, started in February 2021, cosupervised by M. Kazolea and A. Rousseau.
 PhD in progress: M. Carreau, Modeling, analysis and scientific computing for the simulation of geophysical flows with unified models, started in November 2020, cosupervised by M. Parisot and R. Masson.
 PhD in progress : B. Constant, Amélioration d’une méthode de frontières immergées pour la simulation d’écoulements turbulents autour de géométries complexes, started in October 2019, defense expected in March 2023, supervised by H. Beaugendre and S. Péron (ONERA).
 PhD in progess : T. Carlier, Modeling of an icing system using shifted boundary method, started in October 2020, cosupervised by H. Beaugendre and M. Colin.
 PhD in progress : F. Nauleau, Immersed boundary method applied to large eddy simulations of hypersonic reentry vehicles, started in October 2020, cosupervised by H. Beaugendre and T. BridelBertomeu and F. Vivodtzev (CEA).
 PhD in progress: M. Romanelli, Deep Wall Models for Aerodynamic Simulations, started in october 2021, cosupervised by H. Beaugendre and M. Bergmann (MEMPHIS).
 PhD (defended in November 2022) : A. Cauquis, High order shock capturing methods for tsunami simulations, supervised by M. Ricchiuto and P. Heinrich (CEA).
 PhD (defended in September 2022) G. Bellezza, Multi scale modelling for selfhealing composite materials, supervised by M. Ricchiuto and G. Vignoles (LCTS).
 PhD (defended in September 2022) M. Ciallella, Bridging shock fitting and embedded methods to handle shock waves in hyperbolic systems, supervised by M. Ricchiuto and R. Paciorri (U. Roma La Sapienza).
 PhD (defended in March 20222) S. Michel, Shallow water simulations with immersed higher order residual methods on adaptive meshes, supervised by M. Ricchiuto.
 PhD (defended in April 2022) E. Solai, Numerical Simulation and Uncertainty Quantiﬁcation for Immersion Cooling of Lithiumion Batteries 44, supervised by H. Beaugendre and P. Congedo.
 Postdoc (until August 2022): Mariem Makni (Université de Bordeaux, EU project MICROCARD).
 Supervision of the postdoc Michele Giuliano Carlino by Elena Gaburro funded by the the MSCAIF SuperMan, 0112/2022
10.2.3 Juries
 Aurore Cauquis, Development of a numerical model of dispersive propagation of tsunamis, PhD Inria centre of the University of Bordeaux, 29 November 2022 (Maria Kazolea Examiner).
 Nelly Boulos Al Makary, Modélisation et simulation numérique de la dynamique d'un aquifère érodable, PhD Paris 13, 13 December 2022 (Martin Parisot coencadrant).
 Martin Parisot was member of the selection comity for the Maitre de conférence position at Institut de Mathématiques of the University of Toulouse.
 Elena Gaburro was member of the PhD committee of Ali HAIDAR, Montpellier, France (in quality of Examinateur)
 Héloïse Beaugendre , PhD jury of Francesca Basile, Sorbonne University, Reporter, September 2022.
 Héloïse Beaugendre , PhD jury of Agnès Chan, Bordeaux University, Examiner, November 2022.
 Héloïse Beaugendre , PhD jury of Rémi Harry, ISAE Toulouse, Reporter, December 2022.
 Héloïse Beaugendre , member of the MCF selection comity for Valencienne, May 2022.
 Héloïse Beaugendre , member of the MCF selection comity for LIFSE/ENSAM, May 2022.
 Mario Ricchiuto , president of the PhD committee of Irene GomezBueno, University of Malaga, December 2022
10.3 Popularization
10.3.1 Education
 Elena Gaburro organized and taught in a PhD school on Advanced Numerical Methods for the solution of hyperbolic equations and elements of parallel implementation
 Mario Ricchiuto participated to the event “Projet COP27 : voix lycéenne”. On the occasion of the COP27, the Region's Scientific Culture Centers wanted to propose a project on climate issues to high school students. The objective is to raise questions, to take stock and to accompany the students in their reflection with the help of researchers and professionals and to bring them to debates and exchanges during a dedicated day in November. M. Ricchiuto has given a presentation on the use of numerics to simulate
11 Scientific production
11.1 Major publications
 1 inbookHighorder ArbitraryLagrangianEulerian schemes on crazy moving Voronoi meshes.Numerical aspects of hyperbolic balance laws and related problems2022
 2 articleLow dispersion finite volume/element discretization of the enhanced GreenNaghdi equations for wave propagation, breaking and runup on unstructured meshes.Ocean Modelling182April 2023, 102157
 3 articleA class of boundary conditions for timediscrete GreenNaghdi equations with bathymetry.SIAM Journal on Numerical Analysis2022
11.2 Publications of the year
International journals
 4 articleExtrapolated Shock Fitting for TwoDimensional Flows on Structured Grids.AIAA Journal6011November 2022, 63016312
 5 articleTetrahedral Remeshing in the Context of LargeScale Numerical Simulation and High Performance Computing.MathematicS In Action1112022, 129164
 6 articleA 2D imagebased multiphysics model for lifetime evaluation and failure scenario analysis of selfhealing ceramicmatrix minicomposites under a tensile load.Journal of the European Ceramic SocietyJuly 2022
 7 articleSecond Order ADER Scheme for Unsteady AdvectionDiffusion on Moving Overset Grids with a Compact Transmission Condition.SIAM Journal on Scientific Computing441February 2022, A524A553
 8 articleADER scheme for incompressible NavierStokes equations on overset grids with a compact transmission condition.Journal of Computational Physics467October 2022, 111414
 9 articleContinuous Finite Element Subgrid Basis Functions for Discontinuous Galerkin Schemes on Unstructured Polygonal Voronoi Meshes.Communications in Computational Physics321August 2022, 259298
 10 articleWell balanced finite volume schemes for shallow water equations on manifolds.Applied Mathematics and Computation441March 2023, 127676
 11 articleLax–Wendroff Schemes with Polynomial Extrapolation and Simplified Lax–Wendroff Schemes for Dispersive Waves: A Comparative Study.Water Waves2022
 12 articleShifted boundary polynomial corrections for compressible flows: high order on curved domains using linear meshes.Applied Mathematics and Computation441March 2023, 127698
 13 articleAn arbitrary high order and positivity preserving method for the shallow water equations.Computers and Fluids247October 2022, 105630
 14 articleExtrapolated DIscontinuity Tracking for complex 2D shock interactions.Computer Methods in Applied Mechanics and Engineering391March 2022, 114543
 15 articleOn the Numerical Solution of Sparse Linear Systems Emerging in Finite Volume Discretizations of 2D BoussinesqType Models on Unstructured Grids.Water1421November 2022, 3584
 16 articleHigh order entropy preserving ADERDG schemes.Applied Mathematics and Computation440March 2023, 127644
 17 articleDataDriven Calibration of Rough Heat Transfer Prediction Using Bayesian Inversion and Genetic Algorithm.Energies1510May 2022, 3793
 18 articleParameter Sensitivity for WaveBreaking Closures in BoussinesqType Models.Water Waves2022
 19 articleIntroduction to the special issue on numerical methods and applications for waves in coastal environments.Water WavesNovember 2022
 20 articleLow dispersion finite volume/element discretization of the enhanced GreenNaghdi equations for wave propagation, breaking and runup on unstructured meshes.Ocean Modelling182April 2023, 102157
 21 articleSpectral analysis of high order continuous FEM for hyperbolic PDEs on triangular meshes: influence of approximation, stabilization, and timestepping.Journal of Scientific Computing943January 2023, 49
 22 articleA class of boundary conditions for timediscrete GreenNaghdi equations with bathymetry.SIAM Journal on Numerical Analysis2022
 23 articleDatadriven wall models for Reynolds Averaged NavierStokes simulations.International Journal of Heat and Fluid Flow99January 2023, 109097
 24 articleAccuracy assessment of an internal resistance model of Liion batteries in immersion cooling configuration.Applied Thermal Engineering220119656February 2023
 25 articleValidation of a datadriven fast numerical model to simulate the Immersion Cooling of a Lithiumion Battery Pack.Energy249May 2022, 123633
 26 articleModel order reduction strategies for weakly dispersive waves.Mathematics and Computers in Simulation2052023, 9971028
 27 articleA hybrid FV/FD scheme for a novel conservative form of extended Boussinesq equations for waves in porous media.Ocean Engineering269February 2023, 113491
 28 articleGoalOriented Error Estimation and Mesh Adaptation for Tracer Transport Modelling.ComputerAided Design145April 2022, 103187
International peerreviewed conferences
 29 inproceedingsA new shockfitting technique for 2D structured grids.AIAA SCITECH 2022 ForumSan Diego, United StatesAmerican Institute of Aeronautics and Astronautics2022
 30 inproceedingsA shockfitting technique for 2D/3D flows with interactions using structured grids.AIAA AVIATION 2022 ForumChicago, United StatesAmerican Institute of Aeronautics and Astronautics2022
 31 inproceedingsMultidimensional aware Riemann solver for the Eulerian droplet equation system.Eleventh International Conference on Computational Fluid Dynamics (ICCFD11)Maui, United StatesJuly 2022
 32 inproceedingsImmersed boundaries in hypersonic flows with considerations about highfidelity and massive parallelism.8th European Congress on Computational Methods in Applied Sciences and EngineeringOslo, NorwayCIMNEJune 2022
 33 inproceedingsTopological Analysis of Ensembles of Hydrodynamic Turbulent Flows An Experimental Study.2022 IEEE 12th Symposium on Large Data Analysis and Visualization (LDAV)Oklahoma City, United StatesIEEEOctober 2022, 111
Conferences without proceedings
 34 inproceedingsHigh Order Scheme for Mixed Formulation of Problems with Moving Internal Boundaries.European Congress on Computational Methods in Applied Sciences and EngineeringOslo, NorwayJune 2022
 35 inproceedingsTOWARDS A BETTER PREDICTION OF AERODYNAMIC COEFFICIENTS IN AN IMMERSED BOUNDARY CONTEXT.The 8th European Congress on Computational Methods in Applied Sciences and EngineeringOslo Norway, NorwayJune 2022
 36 inproceedingsDeep learningbased wall models for aerodynamic simulations: A new approach inspired by classical wall laws.ODAS 2022  OneraDLR Aerospace SymposiumHambourg, GermanyJune 2022
Scientific book chapters
 37 inbookHyperbolic Balance Laws: Residual Distribution, Local and Global Fluxes.Numerical Fluid DynamicsForum for Interdisciplinary MathematicsSpringer Nature SingaporeMay 2022, 177222
 38 inbookh and rAdaptation on Simplicial Meshes Using MMG Tools.30Mesh Generation and AdaptationSEMA SIMAI Springer SeriesSpringer International PublishingFebruary 2022, 183208
 39 inbookHighorder ArbitraryLagrangianEulerian schemes on crazy moving Voronoi meshes.Numerical aspects of hyperbolic balance laws and related problems2022
Edition (books, proceedings, special issue of a journal)
 40 proceedingsM. G.Michele Giuliano CarlinoE.Elena GaburroSecond Order Finite Volume Scheme for Shallow Water Equations on Manifolds.2022
Doctoral dissertations and habilitation theses
 41 thesisImagebased multiphysics modelling, lifetime evaluation, and failure scenario analysis of selfhealing CeramicMatrix miniComposites under a tensile load.Université de BordeauxSeptember 2022
 42 thesisHigh order methods for hyperbolic balance laws : from embedded fronts to structurepreserving schemes.Université de BordeauxSeptember 2022
 43 thesisFinite Element Methods for Shallow Water Equations : Analysis, Modeling and Applications to Coastal Hydrodynamic.Université de BordeauxMarch 2022
 44 thesisNumerical Simulation and Uncertainty Quantiﬁcation for Immersion Cooling of Lithiumion Batteries.Université de BordeauxMarch 2022
Reports & preprints
 45 miscAn Enriched Shifted Boundary Method to Account For Moving Fronts.May 2022
 46 miscA unified modeling of undergroundsurface hydraulic processes with verticalintegrated approach.November 2022
 47 miscArbitrary High Order WENO Finite Volume Scheme with Flux Globalization for Moving Equilibria Preservation.December 2022
 48 miscCoupling Dispersive Shallow Water Models by Deriving Asymptotic Interface Operators.November 2022
 49 miscParameter sensitivity for wave breaking closures in Boussinesqtype models.February 2022
 50 miscFully well balanced entropy controlled DGSEM for shallow water flows: global flux quadrature and cell entropy correction.January 2023
 51 miscCongested shallow water model: trapped air pockets modeling.August 2022
 52 miscAnalytical travelling vortex solutions of hyperbolic equations for validating very high order schemes.January 2022
 53 miscTidal Turbine Array Modelling using GoalOriented Mesh Adaptation.January 2023
 54 miscParallel MetricBased Mesh Adaptation in PETSc using ParMmg.January 2023
11.3 Cited publications
 55 articleAn immersed boundary method using unstructured anisotropic mesh adaptation combined with levelsets and penalization techniques.Journal of Computational Physics2572014, 83101
 56 articleAn Immersed Boundary Method with Formal SecondOrder Accuracy and Reduced Numerical Viscosity.Journal of Computational Physics16022000, 705719URL: https://www.sciencedirect.com/science/article/pii/S0021999100964830
 57 articleWell balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes.Journal of Computational Physics4052020, 109173
 58 articleDevelopment of a Second Generation Inflight Icing Simulation Code.Journal of Fluids Engineering1282006
 59 articleComputation of Ice Shedding Trajectories Using Cartesian Grids, Penalization, and Level Sets.Modelling and Simulation in Engineering20112011, 115
 60 articleNumerical simulation and modeling of ice shedding: Process initiation.Computers & Structures1422014, 1527
 61 articleUpwind Methods for Hyperbolic Conservation Laws with Source Terms.Comput. Fluids23581994, 10491071
 62 articleAn unstructured, threedimensional, shockfitting solver for hypersonic flows.Computers & Fluids732013, 162  174
 63 articleA spectral/hp element depthintegrated model for nonlinear wavebody interaction.Computer Methods in Applied Mechanics and Engineering3482019, 222249
 64 articleDevelopment of a ShallowWater icing model in FENSAPICE.Journal of Aircraft372000
 65 articlePredicting the Failure of the Continuum Fluid Equations in Transitional Hypersonic Flow.Physics of Fluids71995, 210219
 66 articleA reasoned overview on Boussinesqtype models: the interplay between physics, mathematics and numerics.Proc. Royal Soc. A4692014
 67 articleHyperbolic tetrad formulation of the Einstein equations for numerical relativity.Physical Review D6782003, 084017
 68 articleDispersive and dispersivelike bores in channels with sloping banks.Journal of Fluid Mechanics8702019, 595616
 69 articleFront tracking for gas dynamics.Journal of Computational Physics6211986, 83110URL: https://www.sciencedirect.com/science/article/pii/0021999186901014
 70 articleExtrapolated Shock Tracking: bridging shockfitting and embedded boundary methods.Journal of Computational PhysicsApril 2020, 109440
 71 articleVery highorder Cartesiangrid finite difference method on arbitrary geometries.Journal of Computational Physics4342021, 110217URL: https://www.sciencedirect.com/science/article/pii/S0021999121001121
 72 articleMechanical behaviour and lifetime modelling of selfhealing ceramicmatrix composites subjected to thermomechanical loading in air.Composites Part A: Applied Science and Manufacturing4082009, 976984
 73 bookGuide for the Verification and Validation of Computational Fluid Dynamics Simulations.American Institute for Aeronautics and Astronautics1998
 74 inproceedingsVirtual material approach to selfhealing CMCs.4th European Conference for Aerospace Sciences (EUCASS)Saint Petersurg, RussiaJuly 2011
 75 inproceedingsBoussinesq Modeling of Wave Propagation and Runup over Fringing Coral Reefs, Model Evaluation Report.Coastal and Hydraulics Laboratory Technical Note CHLTR0712Vicksburg, MS: U.S. Army Engineer Research and Development Center2007
 76 articleFast and accurate simulations of aircooled structures.Computer Methods in Applied Mechanics and Engineering1952006, 31683180
 77 inproceedingsImageBased 2D Numerical Modeling of Oxide Formation in SelfHealing CMCs.Developments in Strategic Materials and Computational Design IIIJohn Wiley & Sons, Inc.2013, 117125URL: http://dx.doi.org/10.1002/9781118217542.ch11
 78 inproceedingsWave Induced Motions of PointAbsorbers: a Hierarchical Investigation of Hydrodynamic Models.11th European Wave and Tidal Energy Conference (EWTEC)Nantes, FranceSeptember 2015
 79 articleA flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and runup.Journal of Computational Physics3102016
 80 articleA HigherOrder Boundary Treatment for CartesianGrid Methods.Journal of Computational Physics14021998, 259277URL: https://www.sciencedirect.com/science/article/pii/S0021999198958910
 81 articleA unified framework for the solution of hyperbolic PDE systems using high order direct ArbitraryLagrangianEulerian schemes on moving unstructured meshes with topology change.Archives of Computational Methods in Engineering2832021, 12491321
 82 articleHigh order direct ArbitraryLagrangianEulerian schemes on moving Voronoi meshes with topology changes.Journal of Computational Physics4072020, 109167
 83 articleA well balanced finite volume scheme for general relativity.SIAM Journal on Scientific Computing4362021, B1226B1251
 84 articleWellbalanced ArbitraryLagrangianEulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity.Monthly Notices of the Royal Astronomical Society47722018, 22512275
 85 articleCongested shallow water model: on floating body.The SMAI journal of computational mathematics62020, 227251URL: https://smaijcm.centremersenne.org/item/SMAIJCM_2020__6__227_0/
 86 articleCongested shallow water model: roof modeling in free surface flow.ESAIM: Mathematical Modelling and Numerical Analysis525Sep 2018, 16791707URL: http://dx.doi.org/10.1051/m2an/2018032
 87 inproceedingsReview of Rarefied gas effects in hypersonic applications.RTO AVT/VKI Lecture Series  Models and Computational Methods for Rarefied Flows2011
 88 articleNumerical treatment of wavebreaking on unstructured finite volume approximations for extended Boussinesqtype equations.Journal of Computational Physics2712014
 89 articleOn wave breaking for Boussinesqtype models.Ocean Modelling1232018, 1639
 90 articleBoussinesq modeling of wave transformation, breaking and runup. Part I: 1D.J. Waterw. PortCoast. Ocean Eng.1262000, 3947
 91 inproceedingsResults and Conclusions of the European Project IDIHOM on HighOrder Methods for Industrial Aerodynamic Applications.53rd AIAA Aerospace Sciences Meeting2015
 92 articleGeometric Conservation Laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations.Comput. Method Appl. M.134121996, 7190
 93 articleContinuous mesh framework, Part II: validations and applications.SIAM in Numerical Analysis4912011
 94 inproceedingsAchievement of global secondorder mesh convergence for discontinuous flows with adapted unstructured meshes.18th AIAA Computational Fluid Dynamics Conference, Miami (FL)AIAA paper 200741862007
 95 articleThe shifted boundary method for embedded domain computations. Part I: Poisson and Stokes problems.Journal of Computational Physics2017, URL: http://www.sciencedirect.com/science/article/pii/S0021999117307799
 96 articleA highorder accurate embedded boundary method for first order hyperbolic equations.Journal of Computational Physics3342017, 255279URL: https://www.sciencedirect.com/science/article/pii/S0021999116306969
 97 articleSpectral Analysis of Continuous FEM for Hyperbolic PDEs: Influence of Approximation, Stabilization, and TimeStepping.Journal of Scientific Computing892November 2021
 98 articleAn explicit, adaptive, residual based splitting approach for the steardy and time dependent penalized Navier Stokes equations.Comput. Meth. Appl. Mech. Engrg.3032016, 208230
 99 articleHighOrder Gradients with the Shifted Boundary Method: An Embedded Enriched Mixed Formulation for Elliptic PDEs.Journal of Computational Physics2019, 108898
 100 inproceedingsNumerical prediction of breaking waves and currents with a Boussinesq model.Proceedings 25th International Conference on Coastal Engineering1996
 101 inproceedingsSimulation of Ice Shedding from a Business Jet Aircraft.AIAA, Aerospace Sciences Meeting and Exhibit, 45 th, Reno, NVAIAA Paper 20075062007
 102 inproceedings2D numerical modelling of the twoscale lifetime of selfhealing CMCs.International Workshop on Testing and Modeling Ceramic and Carbon Matrix CompositesAbstract reviewENS Cachan, FranceJune 2014
 103 articleFirstorder hyperbolic formulation of the pure tetrad teleparallel gravity theory.arXiv preprint arXiv:2211.136592022
 104 inproceedingsAdvances in selfhealing ceramic matrix composites.Advances in Ceramic Matrix CompositesWoodhead2014, 369409
 105 articleOn the Cproperty and Generalized Cproperty of Residual Distribution for the Shallow Water Equations.Journal of Scientific Computing4812011, 304318
 106 bookVerification and validation in computational science and engineering.Albuquerque, NMHermosa1998, URL: https://cds.cern.ch/record/580994
 107 articleShockcapturing Boussinesqtype model for nearshore wave processes.Coastal Engineering572010, 407423
 108 inproceedingsCFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences.NASA/CR20142181782014
 109 articleInverse LaxWendroff procedure for numerical boundary conditions of conservation laws.Journal of Computational Physics229212010, 81448166URL: https://www.sciencedirect.com/science/article/pii/S0021999110003979
 110 articleGeometric Conservation Law and Its Application to Flow Computations on Moving Grids.AIAA Journal17101979, 10301037
 111 articleA new approach to handle wave breaking in fully nonlinear Boussinesq models.Coastal Engineering672012, 5466URL: http://www.sciencedirect.com/science/article/pii/S0378383912000749
 112 articleHybrid finite volumefinite difference scheme for 2DH improved Boussinesq equations.Coastal Engineering 562009, 609620
 113 articleSimulation of wave breaking over complex bathymetries by a Boussinesq model.Journal of Hydraulic Research4942011, 473486
 114 inproceedingsDesign of Ice Protection Systems and Icing Certification Through Cost  Effective Use of CFD.AIAA Aerospace Sciences Meeting and ExhibitAIAACP 200203822002
 115 articleAn immersed boundary method for compressible flows using local grid refinement.Journal of Computational Physics22522007, 20982117URL: https://www.sciencedirect.com/science/article/pii/S0021999107001222
 116 articleHighorder CFD methods: current status and perspective.International Journal for Numerical Methods in Fluids7282013, 811845
 117 inproceedingsWEC Technology Readiness and Performance Matrix, finding the best research technology development trajectory.4th International Conference on Ocean Engineering  ICOE2012