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. In the near future, this panel will also be extended to medical applications, 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.

Even though it is far from being the only complex phenomenon to be taken into account and the only subject of our research, turbulence plays a central role in this project 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. However, these choices must also take into account the fact that the applications may involve many other important phenomena: for example, shocks; but also couplings of low-Mach-number aerodynamics with acoustic waves; multiphase flows; variable density; conjugate heat transfer; etc.

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 (DNS, LES, RANS, Hybrid RANS-LES) 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 all these 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. It will thus lead to a description of turbulence at widely varying scales in the computational domain. For example, the RANS method may cover regions where turbulence is sufficiently close to equilibrium, leaving to LES the regions where the RANS description is insufficient. 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 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, , , , ), 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, , ), 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 and PITM ); IMF Toulouse in collaboration with the ECUADOR team of the Inria center of Sophia-Antipolis (OES , ) and CAGIRE (HTLES , , ). 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 , , 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 (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 , or Ihme's group 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 based on the Charm++ framework, and within a European project, 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 multi-phase 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 . 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 or are variant of the Roe-Turkel fix . 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 .

Derivation of averaged compressible multi-phase models is currently less active than in the 2000s, and only few teams are interested in such problems. Recent advances were made at RWTH , and also mostly in France at EDF R&D by J.M. Hérard or also by . This low interest in this type of challenging modeling and mathematical analysis was noticed in the review paper as an obstacle for the improvement of numerical methods.

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 , , , , our strategy is to generate experimental data ourselves when possible and to 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, with our industrial partners SAFRAN and Turbomeca (now SAFRAN-Helicopter Engines). If the scientific and application themes of the team are 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 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:

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 will join the CAGIRE team in April 2022. His arrival in the team will 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 in 2021 to manage the software development of the Aerosol finite element library. Luca Cirrottola, a former non permanent engineer on the MMG meshing library will join the AeroSol development team in February 2022.

The ANR project Lagoon has been accepted. Coordinated by V. Perrier, it includes CAGIRE, CARDAMOM and the BRGM. It aims at improving implicit multi-grid methods and large scale IO for near shore applications.

Beyond the open-source code Code_Saturne, developed by EDF , and the commercial code StarCCM+, the EB-RSM RANS model developed by the team is now available in the codes Cedre of ONERA and Aether of Dassault Aviation.

The hybrid RANS/LES model HTLES, developed by the team, has been implemented in the commercial code Star CCM+, under the name SRH (Scale-Resolving Hybrid), and has shown its robustness and advantages over the most widely used method (DDES).

In order 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 , . Although this approach, has been successfully applied to various configurations (for instance ), 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 , , .

In the mixed and natural convection regimes, as presented in two invited lectures , , 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 . 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 , , , which can be easily implemented into any industrial and/or commercial CFD code.

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 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 , , 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 , 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 , . Finally, 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 .

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 , Parsec or StarPU for their most advanced features. In , 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 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 , 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, which we did in an article currently in review. From an inaccurate solution, an accurate solution can be obtained by solving a Laplace equation, see . Last, we proved that a known result on finite volume schemes, namely the accuracy of the Roe scheme on triangular meshes holds also for discontinuous Galerkin methods .

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 .

As far as multi-phase models are concerned, based on the ideas of , we have revisited the derivation of Baer-and-Nunziato models . 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 or by ensuring mathematical properties . In , 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 phasic entropies. Under some hypothesis 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 , , which does not necessarily ensure the same phasic entropy dissipation properties.

In collaboration with the LaTEP laboratory of Pau, we have extended the validation of the EB-RSM model to flows encountered in the solar receivers of concentrated solar power plants with very large temperature differences between two walls, such that variations of the molecular viscosity can lead to relaminarization . This work, which demonstrated the ability of the EB-RSM model to reproduce these effects , allowed a broad parametric study to determine physical criteria to guide the design of future solar receivers .

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 .

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 , the interaction of an atmospheric boundary layer with aerial reservoir(s) or of a channel flow with cylinders in tandem to the simulation of a blast wave of Sedov-like type . 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.

Finally, 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.

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.

SEIGLE means "Simulation et Expérimentation pour l'Interaction de Gouttes Liquides avec un Ecoulement fortement compressible". It is a 3-year program which started in October 2017 and is funded by Région Nouvelle-Aquitaine, ISAE-ENSMA, CESTA and Inria. The interest of understanding aerodynamic mechanisms and liquid drop atomization is explained by the field of applications where they play a key role, specially in the new propulsion technologies through detonation in the aerospace as well as in the securities field. The SEIGLE project was articulated around a triptych experimentation, modeling and simulation. An experimental database will be constituted. It will rely on a newly installed facility (Pprime), similar to a supersonic gust wind tunnel/ hypersonic from a gaseous detonation tube at high pressure. This will allow to test modeling approaches (Pprime / CEA) and numerical simulation (Inria / CEA) with high order schemes for multiphasic compressible flows, suitable for processing shock waves in two-phase media.

HPC scalable ecosystem is 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 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.

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.

(Legend: L1-L2-L3 corresponds to the 3 years of undergraduate studies, leading to the BSc degree; M1-M2 to the 2 years of graduate studies, leading to the MSc degree; E1-E2-E3 to the 3 years of engineering school, equivalent to L3-M1-M2, leading to the engineer/MSc degree)

Vincent Perrier animated a debate around the release of the movie "Adventures Of A Mathematician".