The project-team CAGIRE is an interdisciplinary project, which brings together researchers with different backgrounds (applied mathematics and fluid mechanics), who elaborated a common vision of what should be the numerical simulation tools in fluid dynamics of tomorrow.
The targeted fields of application are mainly those corresponding to the aeronautical/terrestrial transportation and energy production sectors, with particular attention paid to the issue of energy transition and the reduction of environmental impacts. This panel has been extended to medical applications recently, where numerical simulation plays an increasingly important role.
Through our numerous industrial collaborations, we have been able to refine our vision of the future of numerical simulation, which is subject to ambitious industrial objectives, constant evolution of computing resources and increasingly present environmental constraints.

The flows under consideration involve many physical phenomena: they can be turbulent, compressible, multiphase, anisothermal. Even if these phenomena are not necessarily present at the same time, our strategy for developing models and numerical schemes must take them into account. Turbulence plays a central role insofar as it is a dimensioning constraint for CFD in most industrial configurations. It is indeed the comparison of the requirements in terms of scale of description, numerical accuracy and computational cost that guides the choice of physical models and numerical methods.

Because such flows are exhibiting a multiplicity of length and time scales resulting from complex interactions, their simulation is extremely challenging. Even though various simulation approaches are available and have significantly improved over time, none of them does satisfy all the needs encountered in industrial and environmental configurations. We consider that different methods will be useful in the future in different situations, or regions of the flow if combined in the same simulation, in order to benefit from their respective advantages wherever relevant, while mutually compensating for their limitations. For instance, for turbulent flows, it will thus lead to a description of turbulence at widely varying scales in the computational domain. The RANS1 method may cover regions where turbulence is sufficiently close to equilibrium, leaving to LES2 the regions where the RANS description is insufficient, leadind to a hybrid RANS-LES approach. Similarly, for two-phase flows, one of the greatest challenges is to be able to tackle simultaneous and dynamical modelling of the multi-scale features and their transition, e.g., from cavitation pockets to tiny bubbles. The models and numerical methods must also be flexible enough to accurately represent all the above-mentioned phenomena in complex geometries, with efficient and robust resolution algorithms to preserve an optimal computational cost. It is this flexibility and adaptability of models and numerical methods that we call “computational agility", which is in the title of the CAGIRE team: Computational AGility for internal flow sImulations and compaRisons with Experiments.

Therefore, the long-term objective of this project is to develop, validate, promote and transfer original and effective approaches for modeling and simulating generic flows representative of configurations encountered in the field of transportation, energy production and medicine. In order to progress in this direction, many building blocks have to be assembled, which motivates a variety of research topics described in the following sections and divided into four main research axes. The topics addressed, ranging from advanced physical modelling to high-order numerical discretization, require the multi-disciplinary skills that constitute the CAGIRE project-team:

In the “agile" simulation methods introduced above, a flexible representation of turbulence is essential: in the same simulation, depending on the regions of the flow, it is necessary to be able to switch from a fine-grained to a coarse-grained representation of turbulence. Numerous methods, called hybrid RANS/LES, go in this direction, by associating LES and RANS. In order to ensure such a flexibility, it is preferable not to rely on a preliminary partition of the domain (the so-called zonal approach), but rather on a continuous transition from one model to the other (the so-called continuous approach).

Various questions then arise: how can we improve the RANS models so as to accurately represent most of the physical phenomena in order to avoid having to switch to LES in large regions; how to play on the terms of the models, and on which criteria, to switch from RANS to LES; how to improve the robustness of the method with respect to the choices made by the user (in particular the near-wall mesh). Our research work, described below, aims at answering these questions.

Today, even though the industrial demand for more accurate and robust RANS models is very significant, very few academic teams are active in this field (for instance, 113, 84, 52, 117), most of them being participants to the European ERCOFTAC SIG-15 group of which we are an active member. In France, we collaborate with most of the teams, mainly in the industry (EDF, Dassault, PSA) or applied research organizations (ONERA, CEA). The CAGIRE team is particularly renowned for its work on the interaction between turbulence and the wall by elliptic blending (EB-RSM, 93, 97), and is solicited by these partners to improve the representation of complex effects on turbulence (buoyancy, conjugate heat transfer, adverse pressure gradients, impingement, etc.).

Concerning the development of original hybrid RANS/LES approaches, the main contributions in France are due to ONERA (ZDES 67 and PITM 64); IMF Toulouse in collaboration with the ECUADOR team of the Inria center of Sophia-Antipolis (OES 60, 103) and CAGIRE (HTLES 96, 4912, 58). The originality of our work lies in the concern to provide, through temporal filtering, a formally consistent link between the equations of motion and the hybridization method in order to reduce the level of empiricism, which is, for non-homogeneous turbulence, along with the additive filter method 78, 48, one of only two methods capable of providing such a consistent framework.

When dealing with RANS models, a second order finite volume method is usually used. In our project, we aim at addressing hybrid RANS/LES models, which include some regions in which essentially unstationary processes are approximated in LES regions. This usually requires to use low dissipative high order numerical methods. If a consensus has emerged for years on second order finite volume methods for the approximation of RANS models, investigations are still ongoing on finding the high order method that would be the best suited with the compressible Navier-Stokes system.

As far as high order numerical methods are concerned, they are addressed at Inria essentially by the Atlantis, Makutu, Poems and Rapsodi teams for wave-matter interaction problems, the Serena and Coffee project-team on porous media, the Tonus team on plasma physics problems, and the Acumes, Gamma, Cardamom and Memphis teams for systems that are closer of ours (shallow-water or compressible Euler). As far as we know, only the Cardamom and Gamma teams are using high order methods with turbulence models, and we are the only one to aim at hybrid RANS/LES models with such methods.

Our objective is to develop a fast, stable and high order code for the discretization of compressible Navier-Stokes equations with turbulence models (Reynolds-stress RANS models and hybrid RANS/LES methods) on unstructured meshes. From a numerical point of view, this raises several questions: how to derive a stable numerical scheme for shocks without destroying the order of accuracy, how to derive stable boundary conditions, how to implement the method efficiently, how to invert the system if implicit methods are used?

Concerning aeronautical applications, several groups are working on discontinuous Galerkin methods: in Europe, some of the groups participated to the TILDA project 3 (DLR, ONERA, CERFACS, Imperial College, UCL, Cenaero, Dassault, U. of Bergamo). As far as we know, none of them considered Reynolds-stress RANS models or hybrid RANS/LES models. Worldwide, we believe the most active groups are the MIT group 4, or Ihme's group5 which is rather oriented on combustion. Concerning HPC for high order methods, we carefully follow the advances of the parallel numerical algorithm group at Virginia Tech, and also the work around PyFR at Imperial College. Both of these groups are considering imperative parallelism, whereas we have chosen to consider task based programming. Task based parallelism was considered in the SpECTRE code 90 based on the Charm++ framework, and within a European project6, based on IntelTBB, but only for hyperbolic systems whereas we wish to address the compressible Navier-Stokes system.

In this section, we are interested in two specific regimes of compressible flows: low Mach number flows and compressible multiphase flows.

Low Mach number flows (or low Froude for Shallow-Water systems) are a singular limit, and therefore raise approximation problems. Two type of numerical problems are known: if convective time scales are considered, semi-implicit time integration is often preferred to explicit ones, because the acoustic CFL is very restrictive compared with the convective one in the low Mach number limit 68. The second numerical problem at low Mach number is an accuracy problem. The proposed fixes consist in changing the numerical flux either by centering the pressure 108 or are variant of the Roe-Turkel fix 80. Over the last years, we have been more focused on the accuracy problem, but our major originality with respect to other groups is to be interested in the acoustic wave propagation in low Mach number flows, which may also raise problems as first remarked in 102.

Understanding and controlling complex and physically rich flows, such as unsteady multiphase compressible flows, are of great importance in various fields such as aeronautics, automotive, aerospace, nuclear energy, naval and also medicine. If we note the efforts established so far to partially respond to the problems linked to these flows, we also note major remaining challenges, particularly when different spatial and temporal scales or multiple physical phenomena, such as phase change, viscoelasticity or more generally interactions with solids, are to be considered. Good examples are cavitating flows such as the ones encountered around naval propellers where cavitation pockets form at the vicinity of the blades and lead to a turbulent bubbly flow in the wake 109. Or in biomedical applications such as in lithotripsy (treatment for kidney stones) 106 or, recently, histotripsy (non-invasive treatment for cancers) 89 where cavitation bubbles, induced by shock waves, laser energy deposit or high-intensity focused ultrasound waves, violently collapse and interact with biomaterials. In this context, we aim to tackle the particularly challenging and ambitious modelling of these extremely complex multiphase compressible flows where numerous scientific and technical obstacles remain to be overcome. Among them, we could cite:

The numerous discussions with our industrial partners make it possible to define configurations to carry out comparison between computations and experiments aimed at validating the fundamental developments described in the previous sections. Reciprocally, the targeted application fields play an important role in the definition of our research axes, by identifying the major phenomena to be taken into account. This section gathers applications which essentially deal with turbulent internal flows, most often with heat transfer.

Detailed data are required for a fine validation of the methods. In addition to the active participation and co-organizing of the SIG-15 group of the ERCOFTAC network, which gives us access to various experimental or DNS data and enables us to carry out model and code benchmarking exercises with other European teams 92, 99, 56, 95, we generate experimental data ourselves when possible and develop collaborations with other research groups when necessary (ONERA, institute Pprime, CEA).

Historically, the scientific convergence between the team members that led to the development of our project and the creation of the CAGIRE project-team in 2016 was based on scientific themes related to aeronautical combustion chambers (hence the term internal flows in the name of the team), with our industrial partners SAFRAN and Turbomeca (now SAFRAN-Helicopter Engines). If the scientific and application themes of the team are now much more diverse, these applications to aeronautical combustors are at the origin of the existence of the MAVERIC experimental facility (which is in itself an originality within Inria), allowing the study of turbulent flows at low Mach number over multi-perforated walls subjected to a coupling with acoustic waves, representative of the flows in combustors. This wind tunnel is thus complementary to those developed at ONERA, with which we collaborated 107 when it was necessary to add thermal measurements, within the framework of the European project SOPRANO.

Cagire is active in the field of aeronautics through the following activities:

Many medical applications exist where interactions between bubbles and biomaterials appear. CAGIRE is interested in a better understanding of the fundamental physics involved in such interactions, leading to improvements and innovation in current and future medical treatments with regard to their success rate, cost and safety:

The availability of improved RANS models and hybrid RANS/LES methods offering a better physical representativeness than models currently used in the industry, at a reasonable computational cost, will make it possible to improve the reliability of industrial numerical simulations, and thus to better optimize the systems, in order to reduce the environmental impact of transportation and industrial processes, and to improve the safety of installations and reduce the risks of accidental pollution.

Moreover, previous applications of hybrid RANS/LES methods have shown that it is possible to obtain an accuracy equivalent to LES with an energy consumption of the simulation reduced by a factor of about 200. This gain can be considerably increased in a complete industrial simulation with a much higher Reynolds number, leading to a drastic reduction of the environmental impact of the simulations themselves.

Kevin Schmidmayer was hired on an ISFP position (permanent researcher position). He joined the CAGIRE team in April 2022. His arrival in the team strengthen and extend the research themes in the direction of the advanced modelling and simulation of multiphase compressible flows, with medical and industrial applications.

A permanent Inria engineer position shared between the CAGIRE and CARDAMOM teams has been opened to manage the software development of the Aerosol finite element library. Luca Cirrottola, a former non permanent engineer on the MMG meshing library joined the AeroSol development team in February 2022.

The EB-RSM RANS model, developed by CAGIRE, is now avalaible in the standard version of OpenFOAM7. After the open-source code Code Saturne, the commercial code StarCCM+, the codes Cedre of ONERA and Aether of Dassault Aviation, our favorite RANS model is now available in this widespread open-source software.

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 Gauss-Lobatto or Gauss-Lagrange 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 semi-norms div and grad, extension of some fixes to full Euler with arbitrary EOS.

* RANS turbulent flow computations: - Inlet/Outlet boundary conditions for Euler/Navier-Stokes 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 Spalart-Almaras model, negative fix handle - Beginning of implementation of coupled elliptic problem with Neumann and Dirichlet boundary conditions on one variable.

* Flux-reconstruction - Implementation of Flux-Reconstruction methods on Cartesian meshes

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 PT-SCOTCH.

- 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.

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 c-structure compatible with scotch or metis can be built. A parallel mesh redistribution of this graph can be performed based on these software

Operational platform for near shore coastal application based on the following main elements:

- Fully-nonlinear 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 middle-ware 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)

In order to accurately represent the complexity of the phenomena that govern the evolution of turbulent flows, an important part of our research focuses on the development of Reynolds-stress RANS models that take into account the wall/turbulence interaction by an original approach, elliptic blending 93, 97. Although this approach, has been successfully applied to various configurations (for instance 55), in order to take into account more subtle effects, during the theses of A. Colombié and G. Sporschill, in collaboration with ONERA and Dassault Aviation, respectively, we identified the importance of introducing a specific pressure diffusion model to correctly reproduce the dynamics of turbulence in impingement regions and in boundary layers subject to adverse pressure gradients, paving the way towards a wider application of the EB-RSM in aeronautics 116, 65, 114, 115, 15.

In the mixed and natural convection regimes, as presented in two invited lectures 94, 95, the interaction mechanisms between dynamic and thermal fluctuations are complex and very anisotropic due to buoyancy effects, so that the natural turbulence modelling level to take them into account is second-moment closure, i.e., Reynolds-stress models. When associating the EB-RSM and the EB-DFM, several modifications had to be introduced in natural convection for the scrambling term, the length scale of the elliptic blending, and especially by substituting a mixed time scale for the dynamic time scale in the buoyancy production term of the dissipation equation, which has a drastic positive impact on the predictions in the natural convection regime. This work, carried out in collaboration with EDF, leads to the first linear Reynolds-stress model able to accurately represent the wall/turbulence interaction in forced, mixed and natural convection regimes 69. However, some industrial partners, in particular PSA Group (now Stellantis), who encounter natural convection flows in the underhood compartment of vehicles, do not wish to use such sophisticated models, so we have developed an algebraic version of the Reynolds stress equation which thus constitutes an extension of the eddy-viscosity models (buoyancy-extended Boussinesq relation), within the framework of S. Jameel thesis 87, 86, 85, which can be easily implemented into any industrial and/or commercial CFD code. The application of such models to various configurations of differentially-heated cavities showed that, depending on the situation, such buoyancy extensions can have an influence ranging from very significant to negligible 21.

Regarding hybrid RANS/LES, we have developed the HTLES (hybrid temporal LES) approach. The wall/turbulence interaction being fundamental for the applications of interest to EDF, V. Duffal's thesis 72 focused on the precise control of the transition from RANS to LES when moving away from the wall, through the improvement of the theoretical link between the turbulent scales and the form of the model equations, as well as the introduction of two different shielding functions to avoid the classical grid-induced separation and log-layer mismatch 1273, i.e., the strong erroneous sensitivity of the results to the near-wall mesh. A significant result is that the study of wall pressure fluctuations and their spectra on periodic hills showed that the HTLES approach could reproduce these spectra as well as LES, down to a lower cut-off frequency than in LES due to the coarser mesh and the presence of the RANS zone 72, which suggests encouraging prospects for the prediction of mechanical and thermal fatigue. In the framework of the ANR project Monaco_2025, the thesis of P. Bikkanahally is devoted to the extension of the HTLES approach to natural convection. In differentially heated cavities, due to the coexistence of turbulent boundary layers and a laminar region in the centre, the shielding function introduced by V. Duffal causes a deterioration of the results. Good results are obtained by using instead a new shielding function based on the resolution of an elliptic relaxation equation 91, 58. Moreover, the thesis of H. Afailal, in collaboration with IFPEN, was dedicated to the development of the HTLES for the non-reactive internal aerodynamics of spark ignition engines. The aim was to adapt this approach to non-stationary, cyclic flows with moving walls, for which the main challenge was to provide a reliable evaluation of the mean turbulent energy, which is a crucial parameter for the control of the transition from RANS to LES, and is obtained by explicitly applying a differential temporal filter during the simulation to separate the time-dependent mean and turbulent components of the flow 50.

In the framework of hybrid RANS/LES, a particularly attractive approach is Embedded LES, which consists in reserving the LES to a small area included in a global RANS domain, which is a particular strategy for using the zonal hybrid RANS/LES. However, the zonal approach is characterized by a pre-division between RANS and LES zones and a discontinuous interface, which prohibits any evolution of the scale of description of turbulence during the calculation, which would allow an adaptability of the model according to physical criteria determined during the calculation. Our objective is therefore to develop embedded LES in the context of continuous approaches (CELES, Continuous Embedded LES), in which the interface between RANS and LES is now a diffuse interface. In these approaches, the domain is not split into sub-domains, but the model evolves in a continuous manner so that it tends towards a RANS model or towards a LES model. The diffuse interface (grey area) is the transition area in which the model transitions from a RANS model to a LES model. It is then necessary, as in the zonal approach, to enrich the RANS solution by adding synthetic turbulence to avoid the drastic decrease of the total turbulent stress at the beginning of the LES zone which would strongly degrade the results. In the framework of the hybrid RANS/LES approach developed by Cagire, HTLES, this aspect consists in developing a volume enrichment approach based on a fluctuating force 26. The development of such a CELES approach is the main purpose of the just started CELTIC project (post-doc of P. Bikkanahally), in collaboration with the SME GD-Tech. An adaptive determination of the RANS and LES regions based on physical criteria is the subject of the post-doc of M. David, in the framework of the Asturies project.

Task based programming has emerged over about a decade as an alternative to classical imperative parallel programming based on MPI or on coarse grain OpenMP, since it provides more flexibility for addressing heterogeneous architectures. Task based programming has began entering the OpenMP standard since the 4.0 version, but still remains in specific libraries such as OMPss 74, Parsec 59 or StarPU 51 for their most advanced features. In 75, we have developed a two dimensional mock-up code for the first order finite volume approximation of the Euler system on structured meshes based on StarPU, yielding interesting results; for example, for a mesh partitioned into

Unfortunately, the only fix we found in our previous work 63 that is accurate for high order acoustics computation is not Galilean invariant. This led us to try to tackle the problem in a different way than the numerical flux modification. We raised more fundamental questions on the connection between the low Mach number spurious mode responsible for a low accuracy and the long time behaviour of the wave system. In 88, we proved that on some finite domain configurations, the long time limit of the wave system exists, and that a numerical flux is low Mach number accurate if and only if its low Mach number acoustic development has a consistent long time behaviour. The spurious mode on the velocity at low Mach number can therefore be identified as the non-divergence-free part of the long time limit of the asymptotic acoustic system. Once this spurious mode is sharply identified, it can be filtered. This result is published in 14. Still based on this filtering method, a spurious mode was identified in the velocity obtained by the low Mach number fix which consists in centering the pressure. This spurious mode may jeopardize the convergence of the velocity. These results were communicated in 37, 38. We also had the opportunity to disseminate our previous work on low Mach number flows at different conferences 23, included invited ones 24, 22.

Part of the Asturies project aims at deriving high order numerical schemes for turbulent compressible flows in axisymmetric geometry. This year, the work was focused on the three following points:

As a first step towards the simulation of low Mach reacting flows, an efficient methodology to simulate variable density flows in the Mach zero limit, either inert or reacting was developed. The approach combined a finite volume framework on fully staggered grids with the artificial compressibility method and a dual-time stepping. The resulting code proved to be versatile enough to cope with excellent accuracy with flow configurations ranging from unsteady cylinder wakes to unsteady laminar diffusion flames 70.

As far as multiphase models are concerned, based on the ideas of 71, we have revisited the derivation of Baer-and-Nunziato models 53. Usually, models are derived by averaging the Euler system; then the system of PDE on the mean values contains fluctuations which are modeled, often leading to relaxation terms and interfacial velocity and pressure which should also be modeled. This can be achieved by using physical arguments 111 or by ensuring mathematical properties 66. In 105, we have followed a slightly different path: we have supposed that the topology of the different phases follows an explicit model: the sign of a Gaussian process. Some parameters of the Gaussian process (mean, gradient of the mean) are linked with the averaged values of the flow (volume fraction), whereas others (auto-correlation function) are linked with the subscale structure of the flow. The obtained system is closed provided the parameters of the Gaussian process are known. Also, the system dissipates the phase entropies. Under some hypotheses that can be interpreted physically, asymptotic models can be derived in the interface flow limit or in the limit where the two fluids are strongly mixed. In these limits, different previously proposed models are recovered 111, 77, which does not necessarily ensure the same phase entropy dissipation properties. This work was disseminated in the conferences 27, 28. V. Perrier was also invited in 29 for talking about this topic.

In 11, we investigated the shock-induced cavitation within a droplet which is highly challenged by the multiphase nature of the mechanisms involved. Within the context of heterogeneous nucleation, we introduced a thermodynamically well-posed multiphase numerical model accounting for phase compression and expansion, which relies on a finite pressure-relaxation rate formulation. We simulated (i) the spherical collapse of a bubble in a free field, (ii) the interaction of a cylindrical water droplet with a planar shock wave, and (iii) the high-speed impact of a gelatin droplet onto a solid surface. The determination of the finite pressure-relaxation rate was done by comparing the numerical results with the Keller–Miksis model, and the corresponding experiments of Sembian et al. and Field et al., respectively. For the latter two, the pressure-relaxation rate was found to be

As a work in progress, an extension of the model of diffuse solid–fluid interfaces 104, 76 is proposed to deal with arbitrary complex materials such as porous materials in presence of plasticity and damage. These are taken into account through Maxwell-type models and are cast in the standard generalized materials. The specific energy of each solid is given in separable form: it is the sum of a hydrodynamic part of the energy depending only on the density and the entropy, an elastic part of the energy which is unaffected by the volume change, and a compaction part taking into account the compaction effects. It allows us to naturally pass to the fluid description in the limit of vanishing shear modulus. In spite of a large number of governing equations, the model has a simple mathematical structure. The model is well posed both mathematically and thermodynamically, i.e. it is hyperbolic and compatible with both laws of thermodynamics. The resulting model can be applied in situations involving an arbitrary number of fluids and solids. In particular, we are showing the ability of the model to describe complex plasticity (Gurson 81) and damage (Mazars 101) models.

As regards wall cooling by effusion (multiple jets in crossflow), our MAVERIC experimental facility does not allow us to carry out thermal measurements, so we approached ONERA Toulouse to collaborate on the effects of gyration (angle of the jets with respect to the incident flow) on the heat transfer between the fluid and the wall, within the framework of the European project SOPRANO. We then took up the challenge of carrying out RANS simulations with the EB-RSM model on a configuration of unprecedented complexity for us, consisting of 10 rows of 9 holes, in 90-degree gyration, representative of effusion cooling problems in aeronautical combustion chambers. Comparisons between calculations and experiments have shown the relevance of using the EB-RSM model and the importance of taking into account conjugate heat transfer 107, 25.

In the framework of the cooperation with our international partners in Kazakhstan and Argentina, simulations of turbulent flows in different configurations were performed. The flow configurations ranged from the injection of a sonic jet in a supersonic crossflow 54, the interaction of an atmospheric boundary layer with aerial reservoir(s) 110 or of a channel flow with cylinders in tandem 79 to the simulation of a blast wave of Sedov-like type 82. The objectives of these simulations were twofold: 1) Assessing the predictive capabilities of conventional RANS approaches by comparisons with experimental data in order to establish the margin of progression that could be subsequently brought about by the recourse to the more elaborated turbulence models developed by our team and 2) Providing a knowledge of the sensitivity of the different flow topologies and characteristics to the variation of the relevant parameters describing the different configurations at hand. In parallel, our test facility MAVERIC was upgraded in order to accompany the forthcoming validation activities in the framework of the ASTURIES project and the partnership with our Argentinian colleagues.

A collaboration started at the end of 2020 with the CEA LITEN in Grenoble and the LaTEP of UPPA on thermocline energy storage. An experimental facility is being developed at the CEA and RANS simulations are underway to understand the dynamics of this type of flows, to determine the influence of the turbulence generated by the filling of the tank on the quality of the thermocline, in order to optimize the system and provide data to support the development of 1D models used in the optimization of heat networks. A particular attention has been paid to the approximation used for variations of density with temperature. Due to the wide range of temperatures, it was shown that the standard Boussinesq approximation is not valid but a quadratic Boussinesq approximation was proposed, which gives results very close to the more complex low-Mach number approximation, with a computational cost reduced by a factor of two and an improved numerical stability 20.

ECOS-Sud A17A07 project with UNC (Córdoba, Argentine). 2022 was the last year of this project devoted to the experimental and numerical study of the wind around aerial fuel tanks. 1316.

The ambition of the MONACO_2025 project, coordinated by Rémi Manceau, is to join the efforts made in two different industrial sectors in order to
tackle the industrial simulation of transient, turbulent flows affected by buoyancy effects. It brings together two academic partners, the project-team Cagire hosted by the university of Pau, and the institute Pprime of the CNRS/ENSMA/university of Poitiers (PPRIME), and R&D departments of two industrial partners, the PSA group and the EDF group, who
are major players of the automobile and energy production sectors, respectively.

The ANR project Lagoon was funded by ANR in 2021 within the section CE46 - Modèles numériques, simulation, applications.

Coastal areas host around 10% of the world's population and a huge amount of economic activities. Climate change is expected to increase coastal flooding hazard in years to come. In this project, we propose to develop a numerical tool for the stormsurges predictions.

For four years, a joint effort between the partners of this project among others has been done for the development of a numerical tool able to tackle planetary computations with high resolution at the coast: the Uhaina code, based on top of the AeroSol library. The scope of this project is to increase the computational performance of our modelling platform, in order to upgrade it as an efficient and accurate tool for storm-surge predictions in different future climate scenarios. To achieve this goal and producing results which go beyond the state-of-the-art, our efforts will be focused on the following numerical and informatics developments, devoted to decrease the run time of the model in operational conditions:

The code developed within this project will be freely distributed, with a strong effort put on reproducibility of results. Data generated for both the sea level reanalysis and the database of sea level projection for future climate projections will be distributed towards the community.

Call: ISite E2S UPPA "Exploring new topics and facing new scientific challenges for Energy and Environment Solutions"

Dates: 2020-2024

Partners: CEA CESTA ; IFPEN

In the context of internal turbulent flows, relevant to aeronautic and the automotive propulsion and energy production sectors, ASTURIES aims at developing an innovative CFD methodology. The next generation of industrial CFD tools will be based on the only approach compatible with admissible CPU costs in a foreseeable future, hybrid RANS/LES. However, state-of-the-art hybrid RANS/LES methods suffer from a severe limitation: their results are strongly user-dependant, since the local level of description of the turbulent flow is determined by the mesh designed by the user.

In order to lift this technological barrier, an agile methodology will be
developed: the scale of description of turbulence will be locally and automatically adapted during the computation based on local physical criteria independent of the
grid step, and the mesh will be automatically refined in accordance.
Such an innovative approach requires the use of advanced near-wall turbulence
closures, as well as high-order numerical methods for complex geometries, since
low-dissipative discretization is necessary in LES regions. Morevover, the
identification of relevant physical RANS-to-LES switchover criteria and the refined
validation of the method will strongly benefit from dedicated experiments.

The objectives of the project thus consist in:

The development of such a methodology, based on hybrid RANS/LES modelling, with low-dissipative and robust numerical methods, independant of the initial design of a grid by the user, compatible with unstructured meshes for complex industrial geometries, in the context of HPC, is thus the ambitious, but reachable, objective of the project.

HPC scalable ecosystem was a 3-year program funded by Région Nouvelle-Aquitaine (call 2018), Airbus, CEA-CESTA, University of Bordeaux, INRA, ISAE-ENSMA and Inria. Sangeeth Simon was hired as a post-doc with the objective of extending the prototype code developed in 75 to high order (discontinuous Galerkin) and non-reactive diffusive flows in 3D. The same basis will be developed in collaboration with Pprime for WENO based methods for reactive flows.

CELTIC (Continuous Embedded LES for Turbulent flows in Industrial Configurations) is a projet accepted in the call ESR 2022 of the New-Aquitaine Region, in partnership with the local SME GDTech.

The project aims at proposing a new model of the forcing term allowing enrichment at the diffuse interfaces between RANS and LES in continuous hybrid RANS/LES models for the simulation of turbulent flows. This will make possible the development of an innovative simulation methodology, continuous embedded LES (CELES), which consists in restricting the fine-grained model (LES) to regions where it is necessary, surrounded by the rest of the domain using a statistical approach (RANS). The combination of the fact that CELES will be based on hybrid RANS/Continuous LES approaches, easy to use in industrial applications, and on a seeding by volume forcing applicable in all situations will make it a particularly attractive method for the industry, which will bring to our industrial partner GDTech and its regional customers (for example SAFRAN HE) a real value compared to the numerical simulation methods available today.

29 V. Perrier. “Stochastic derivation of models and numerical methods for multiphase compressible flows”. In: 34e Séminaire sur la mécanique des fluides numérique. Paris, France, 24th Jan. 2022.

25 F. Mastrippolito, R. Manceau and P. Bruel. “Modélisation des effets de giration pour les jets en écoulement transverse”. In: Journée thématique SFT : Aérothermique des systèmes propulsifs pour l'aéronautique. Paris, France, 20th Oct. 2022.

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24 Jonathan Jung, Vincent Perrier "Relations between the low Mach number problem and the long time limit of the wave system". In Rencontres de la thermohydraulique numérique du CEA/STMFSaint-Rémy-lès-Chevreuse, France, 27th June, 2022

33 K. Schmidmayer. “Modeling and simulation of bubble dynamics in the diffuse-interface framework”. In: Workshop on Cavitation, bubble dynamics and mass transfer. Strasbourg, France, 31st May 2022.

34 K. Schmidmayer. “Modeling and simulation of bubble dynamics in the diffuse-interface framework”. In: ETH Zürich seminar. Zürich, Switzerland, 22th August 2022.

31 K. Schmidmayer. “Droplet shock-induced cavitation using a multiphase modelling approach”. In: Sorbonne University Seminar, Pierre and Marie Curie Campus, Institut Jean le Rond

39 J. Jung. Les mathématiques appliquées au service de la sureté nucléaire: Nuit européenne des chercheurs, château de Pau, 30th Sept. 2022.

Intervention about "scientists facing war" following the movie "Adventures of a Mathematician", adapted from the autobiography of Stan Ulam at Cinéma de Mourenx (Vincent Perrier).

40 J. Jung. Quelques applications de la recherche en mathématiques appliquées. 4th May 2022.

41 J. Jung. Quelques applications de la recherche en mathématiques appliquées. 6th May 2022.

42 I. Lannabi and J. Cresson. Village des sciences. 15th Oct. 2022.

43 I. Lannabi and I. Greff. Journée Maths et filles. 8th Dec. 2022.

44 R. Manceau. Prévoir l'imprévisible. Nuit Européenne des chercheur.e.s, Château de Pau. Pau, France, 30th Sept. 2022.

45 K. Schmidmayer. 'Les bulles de cavitation et leurs interventions inattendues en médecine'. In: Nuit Européenne des chercheur.e.s, Château de Pau. Pau, France, 30th Sept. 2022.