2025Activity reportProject-Team‌GAMMAO

5.1 Latest​​​‌ software developments

6.1 Practical​​ Use of Metric-Based Anisotropic​​​‌ Mesh Adaptation for Industrial‌ Applications

Participants: Cosimo Tarsia‌​‌ Morisco, Eloi Guilbert​​, Matthieu Maunoury,​​​‌ Frederic Alauzet [correspondant].‌

Feature-based and goal-oriented error‌​‌ estimates for the Reynolds-Averaged​​ Navier-Stokes equations are presented,​​​‌ together with mesh adaptation‌ algorithms for practical study‌​‌ where mesh convergence analysis​​ is mandatory. Several useful​​​‌ results, associated with the‌ errors estimates are demonstrated‌​‌ such as the equidistribution​​ principle, handling several sensors​​​‌ or treating multidomain problems.‌ Numerical results on three‌​‌ industrial application cases highlight​​ the powerfulness of anisotropic​​​‌ mesh adaptation to achieve‌ high-accuracy with moderate mesh‌​‌ size. They demonstrate that​​ mesh-independent certified numerical solutions​​​‌ can be obtained thanks‌ to anisotropic mesh adaptation‌​‌ and that it is​​ possible to run high-fidelity​​​‌ CFD on unstructured adapted‌ meshes composed only of‌​‌ tetrahedra which is fundamental​​ to design robust meshing​​​‌ process for complex geometries.‌

6.2 Assessment of Spalart-Allmaras‌​‌ One-equation BCM Transitional Model​​ using anisotropic metric-based mesh​​​‌ adaptation

Participants: Cosimo Tarsia‌ Morisco [correspondant], Frederic‌​‌ Alauzet.

The intent​​ of this work is​​​‌ to investigate whether the‌ Anisotropic Metric-Based mesh adaptation‌​‌ can provide mesh convergence​​ for transitional flows. The​​​‌ model considered is the‌ Spalart-Allmaras BCM Transitional Model.‌​‌ Three test cases of​​ the 1st AIAA CFD​​​‌ Transition Modeling and Prediction‌ Workshop are considered: two-dimensional‌​‌ Zero-Pressure-Gradient Flat Plate; two-dimensional​​​‌ subsonic flow past the​ NLF-0416 airfoil; three-dimensional subsonic​‌ flow past the 6:1​​ Prolate Spheroid. Attention is​​​‌ dedicated to the mesh-convergence​ of the transition point,​‌ which is automatically detected​​ and meshed with low​​​‌ level of anisotropy. Conversely,​ high level of anisotropy​‌ is observed before and​​ after transition. These requirements​​​‌ permit to significantly limit​ the number of Degrees​‌ of Freedom.

6.3 Applications​​ of Implicit Edge-Based Gradients​​​‌ to Third-Order Edge-Based Scheme​ for Adaptive Tetrahedral Grids.​‌

Participants: Cosimo Tarsia Morisco​​ [correspondant], Hiroaki Nishikawa​​​‌.

We investigated the​ use of the implicit​‌ edge-based gradient method to​​ a third-order edge-based Euler​​​‌ solver on adaptive tetrahedral​ grids. The third-order edgebased​‌ method is an economical​​ high-order discretization method, typically​​​‌ implemented with a quadratic​ least-squares gradient method, achieving​‌ third-order accuracy on arbitrary​​ tetrahedral grids. For robustness,​​​‌ however, the least-squares gradient​ stencil often needs to​‌ be extended beyond neighbors,​​ which not only increases​​​‌ the cost of gradient​ computations but also increases​‌ the error level. To​​ preserve high accuracy and​​​‌ maintain robustness, we employ​ the implicit edge-based gradient​‌ method instead of a​​ quadratic least-squares method, and​​​‌ investigate the performance of​ the resulting third-order solver​‌ with a special focus​​ on adaptive grids.

6.4​​​‌ 5th AIAA CFD High​ Lift Prediction Workshop Results​‌ Using Metric-Based Anisotropic Mesh​​ Adaptation.

Participants: Frederic Alauzet​​​‌ [correspondant], Thomas Gauchery​, Matthieu Maunoury,​‌ Cosimo Tarsia Morisco,​​ Sylvain Mouton.

We​​​‌ performed Computational Fluid Dynamics​ (CFD) analyses with the​‌ Inria metric-based mesh adaptation​​ platform for the 5th​​​‌ AIAA CFD High-Lift Prediction​ Workshop (HLPW-5) on the​‌ Common Research Model High-Lift​​ (CRM-HL) geometry. The HLPW-5​​​‌ is organized to assess​ the numerical prediction and​‌ physical modeling capabilities of​​ CFD technology on a​​​‌ realistic aircraft shape in​ landing and takeoff high​‌ lift configurations. Multiple CRM-HL​​ variants with increasing geometry​​​‌ complexity are the target​ of this investigation. This​‌ work shows the obtained​​ results for Case 1​​​‌ and all the Cases​ 2 geometries proposed by​‌ the workshop for RANS​​ modeling with the baseline​​​‌ Spalart-Allmaras (SA) turbulence model.​ Validation and verification results​‌ are presented with mesh​​ convergence study for some​​​‌ of the test cases​ and comparison with experimental​‌ data.

6.5 Reviewing the​​ Vertex-Centered V4 Scheme for​​​‌ More Accurate Mesh Adaptation.​

Participants: Yoan Gorschka,​‌ Guillaume Puigt [correspondant],​​ Alberto Remigi, Cedric​​​‌ Content, Bruno Maugars​, Cosimo Tarsia Morisco​‌.

In this study,​​ we focus on the​​​‌ V4 vertex-centered finite volume​ scheme developed initialy by​‌ A. Dervieux. This scheme​​ has shown very high​​​‌ robustness on highly anisotropic​ meshes, with an anisotropy​‌ factor of the order​​ of a million. This​​​‌ is why it is​ today one of the​‌ preferred schemes for anisotropic​​ mesh adaptation. In our​​​‌ work, we propose two​ approaches for improving the​‌ vertex-centered V4 scheme for​​ more accurate mesh adaptation.​​​‌ On the one hand,​ we tackle the problems​‌ associated with deconvolution. On​​ the other, we look​​​‌ at the geometric error​ made when calculating convective​‌ flux. We propose a​​ new correction based on​​ the derivative of the​​​‌ numerical flux and the‌ mesh metrics. Several deconvolution‌​‌ approaches are studied on​​ stationary cases.

6.6 From​​​‌ simplex to mixed element:‌ extension of a vertex-centered‌​‌ discretization, focus on accuracy​​ analysis and 3D RANS​​​‌ applications.

Participants: Cosimo Tarsia‌ Morisco [correspondant], Frederic‌​‌ Alauzet, Guillaume Puigt​​.

Standard unstructured-grid CFD​​​‌ simulations generally rely on‌ a cell-centered Finite Volume‌​‌ discretization applied to mixed-element​​ grids. The interest in​​​‌ such approach is using‌ elements that are aligned‌​‌ along a privileged direction​​ in the region close​​​‌ to the boundary, and‌ at the same time‌​‌ unstructured elements near complex​​ geometrical details or in​​​‌ farfield regions. This paper‌ proposes a novel version‌​‌ of the mixed Finite​​ Element / Finite Volume​​​‌ approximation, which is a‌ vertex-centered method known to‌​‌ produce second-order accurate solutions​​ even on highly anisotropic​​​‌ adapted meshes composed of‌ simplex elements (i.e., triangles‌​‌ and tetrahedra). The extension​​ of this approach for​​​‌ two-dimensional mixed-element meshes involves‌ the APproximated Finite Element‌​‌ -APFE- method to discretize​​ diffusion. In this work​​​‌ we make the definitive‌ step forward to handle‌​‌ three-dimensional mixedelement meshes: designing​​ a second-order accurate scheme​​​‌ for smooth meshes involving‌ tetrahedra, prisms and pyramids.‌​‌ The present work focuses​​ on two key aspects.​​​‌ One concerns the 3D‌ extension of the APFE‌​‌ method. A detailed error​​ analysis of this vertex-centered​​​‌ approach is provided for‌ prisms and pyramids. The‌​‌ second ingredient deals with​​ an innovative algorithm to​​​‌ compute the truncation error‌ for linear problems. In‌​‌ contrast to usual methods,​​ the one proposed here​​​‌ permits to compute exactly‌ the coefficients related to‌​‌ each terms of error​​ for any mesh, and​​​‌ can be implemented in‌ any solver with a‌​‌ low development effort.

6.7​​ Metric-based mesh adaptation for​​​‌ hypersonic flows

Participants: Guillaume‌ Puigt [correspondant], Valentin‌​‌ Golliet, Frederic Alauzet​​.

Reentry is the​​​‌ capability of an object‌ launched from Earth to‌​‌ leave Earth’s atmosphere and​​ then come again. During​​​‌ reentry at the hypersonic‌ regime, the object encounters‌​‌ essentially two energetic phenomena:​​ a strong bow shock​​​‌ and the transformation of‌ kinetic velocity into heat‌​‌ in the boundary layer.​​ The most important quantity​​​‌ to compute is the‌ wall heat flux since‌​‌ dimensioning the object requires​​ good confidence in its​​​‌ computation. Heat flux in‌ the boundary layer varies‌​‌ mainly in the direction​​ normal to the wall.​​​‌ So, a standard prerequisite‌ is the definition of‌​‌ a mesh with mesh​​ lines perpendicular to the​​​‌ wall. The technique cannot‌ be applied successfully to‌​‌ complex geometry because the​​ required human resources are​​​‌ larger. On the other‌ hand, unstructured grids are‌​‌ generated automatically, even on​​ complex geometry. In this​​​‌ work, we introduce a‌ metric-based mesh adaptation procedure.‌​‌ Contrary to standard computation,​​ the mesh adaptation procedure​​​‌ converges the couple mesh‌ and solution. The automaticity‌​‌ of the process relies​​ on specific ingredients: a​​​‌ CFD solver robust on‌ anisotropic meshes composed of‌​‌ simplexes (triangles in 2D​​ and tetrahedrons in 3D)​​​‌ an error estimate procedure‌ to define the metrics‌​‌ for generating the new​​​‌ mesh a mesh generator​ method to build the​‌ mesh from metrics an​​ interpolation algorithm to interpolate​​​‌ the previous solution on​ the new mesh. The​‌ full procedure is applied​​ using a node-centered solver,​​​‌ and the remesher is​ the library feflo.a from​‌ Inria. The efficiency of​​ the mesh adaptation procedure​​​‌ will be demonstrated on​ test cases of increasing​‌ complexity. Laminar hypersonic flow​​ over a cylinder at​​​‌ Mach=5.73 and Re=2050. Comparison​ between error estimate efficiency.​‌ Edney Type IV shock/shock​​ interaction. Effect of geometry.​​​‌ Holden compression ramps. 2D/3D​ effects BOLT and HyTRV​‌ configurations. Pure 3D configurations.​​ The metric-based mesh adaptation​​​‌ is an automatic computational​ chain. It enables efficient​‌ capturing of wall heat​​ flux and highlights model​​​‌ limits, with a limited​ human being influence. We​‌ are currently extending the​​ procedure to deal with​​​‌ reactive flows.

6.8 Pixel-exact​ rendering for high-order meshes​‌ and solutions

Participants: Adrien​​ Loseille, Matthieu Maunoury​​​‌ [correspondant].

We are​ developing ViZiR 4,​‌ a visualization software with​​ pixel exact rendering to​​​‌ address the high-order visualization​ challenges 23, 5​‌. ViZiR 4 is​​ bundled as a light,​​​‌ simple and interactive high-order​ meshes and solutions visualization​‌ software. It is based​​ on OpenGL 4 core​​​‌ graphic pipeline. The use​ of OpenGL Shading Language​‌ (GLSL) allows to perform​​ pixel exact rendering of​​​‌ high order solutions on​ straight elements (without extra​‌ subdivision or ray casting)​​ and almost pixel exact​​​‌ rendering on curved elements​ (high-order meshes). ViZiR 4​‌ enables the representation of​​ high order meshes (up​​​‌ to degree 4) and​ high order solutions (up​‌ to degree 10) with​​ pixel exact rendering. Unlike​​​‌ other visualization software (ParaView​ 17, TecPlot 18​‌, Medit 7,​​ Vizir (OpenGL legacy based​​​‌ version) 25, Gmsh​ 15), there is​‌ no subdivision process that​​ is expensive nor visualization​​​‌ error that has to​ be controlled. Moreover, the​‌ subdivision of the curved​​ entities is done on​​​‌ the fly on GPU​ which leaves the RAM​‌ memory footprint at the​​ size of the loaded​​​‌ mesh. Furthermore, in comparison​ with standard visualization techniques​‌ based on legacy OpenGL,​​ the use of OpenGL​​​‌ 4 core version improves​ the speed of rendering,​‌ reduces the memory footprint​​ and increases the flexibility.​​​‌ Many post-processing tools, such​ as picking, hidding surfaces,​‌ isolines, clipping, capping, are​​ integrated to enable on​​​‌ the fly the analysis​ of the numerical results.​‌

6.9 Easy multithreaded parallelisation​​ of solvers dealing with​​​‌ unstructured and anisotropic meshes​

Participants: Loïc Maréchal.​‌

The previous year experimentations​​ with colored grains partitioning​​​‌ have proved successful so​ this new concurrent computing​‌ scheme has been integrated​​ into the production version​​​‌ of the LPlib.​ A new high-level API​‌ has been developed to​​ take care of all​​​‌ partitioning and renumbering aspects​ of a single procedure​‌ call. Likewise, the whole​​ colored-based parallelism is handled​​​‌ by a single procedure​ call that processes each​‌ color sequentially and all​​ of the color's subdomains​​​‌ (grains) concurrently. Thanks to​ its integration in the​‌ LPlib, the colored-grain method​​ now benefits from the​​ library's dynamic scheduling capacity​​​‌ to avoid costly synchronizations‌ and allows for concurrency‌​‌ levels that are closer​​ to the theoretical limit.​​​‌ This new approach and‌ the associated code have‌​‌ been validated on several​​ examples and the results​​​‌ have been presented and‌ published at the AIAA‌​‌ conference. Furthermore, this new​​ high-level API was also​​​‌ used to renumber the‌ meshes using the original‌​‌ Hilbert scheme, making the​​ integration of the LPlib​​​‌ even more straightforward.

6.10‌ INRIA HPC developers day‌​‌

Participants: Loïc Maréchal,​​ Luca Cirrotola, Alexandre​​​‌ Bilger, Florent Pruvost‌, Nathalie Furmento.‌​‌

In October 2025 we​​ organized a two-day event​​​‌ in Bordeaux to gather‌ many INRIA's engineers developing‌​‌ numerical simulation software. This​​ event was aimed at​​​‌ building a closer community‌ as all engineers are‌​‌ scattered between different teams​​ and INRIA facilities across​​​‌ the country. Talks were‌ given on topics covering‌​‌ many aspects of HPC​​ software development like, CI/CD,​​​‌ portability of numerical accuracy,‌ data structures and best‌​‌ practices. Round tables were​​ organized to discuss and​​​‌ address common issues like‌ mutualizing linear algebra toolkits‌​‌ or exchanging experiences with​​ new programing languages.

6.11​​​‌ Addition of Mixing Plane‌ in Wolf

Participants: Frédéric‌​‌ Alauzet, Eloi Guilbert​​ [correspondant].

The mixing​​​‌ plane method is used‌ typically on turbomachinery in‌​‌ order to model the​​ interaction between a rotor​​​‌ (rotating part) and a‌ stator (static part). Each‌​‌ row (stator, rotor) has​​ its own computation which​​​‌ is coupled with his‌ surroundings rows with the‌​‌ mixing plane. The idea​​ is to average quantities​​​‌ along the pitch direction‌ at the outlet of‌​‌ a row, those averaged​​ values are transferred to​​​‌ the next row. The‌ same process is done‌​‌ at the inlet of​​ a row and transferred​​​‌ at the previous row.‌ Associating mesh adaptation with‌​‌ mixing planes requires that​​ the position and the​​​‌ distribution radial discretization must‌ be automatic and consistent‌​‌ with the current adapted​​ mesh. Therefore, after each​​​‌ mesh adaptation, a specific‌ radial discretization for the‌​‌ mixing plane is built​​ based on the current​​​‌ adapted mesh size. These‌ radial discretizations are different‌​‌ on either side of​​ the mixing plane as​​​‌ the adapted meshes do‌ not match on either‌​‌ side. It allows removing​​ the dependency of the​​​‌ results on the relative‌ position between the rotor‌​‌ and the stator. Thus,​​ RANS simulation can be​​​‌ used, even if the‌ problem is naturally unsteady.‌​‌

6.12 Localized flux limiting​​ for Mixed Element Volume​​​‌ scheme on anisotropic adapted‌ meshes

Participants: Frédéric Alauzet‌​‌, Julien Vanharen,​​ Andrea Gobbi [correspondant].​​​‌

We are working on‌ decreasing the amount of‌​‌ numerical dissipation introduced by​​ flux limiters in a​​​‌ Mixed Element Volume (MEV)‌ scheme, that uses MUSCL‌​‌ extrapolations and the HLLC​​ approximated Riemann solver to​​​‌ solve the convective part‌ of the compressible Navier-Stokes‌​‌ equations. The computations are​​ performed in the context​​​‌ of metric-based anisotropic mesh‌ adaptation, thus it is‌​‌ essential to be both​​ accurate and robust. The​​​‌ numerical approach consists in‌ using the Larsson sensor‌​‌ in order to detect​​​‌ shocks and possibly other​ unstable regions of the​‌ solution, and use the​​ flux limiters locally in​​​‌ those regions. The strategy​ is being tested for​‌ different flow configurations, both​​ transonic, where shocks are​​​‌ expected and need to​ be treated accordingly, and​‌ subsonic, where flux limiters​​ should not be needed.​​​‌ A case with a​ contact discontinuity is also​‌ considered.

6.13 Comparison of​​ several shared-memory parallel linear​​​‌ solvers for the Navier-Stokes​ primal and adjoint equations​‌ on anisotropic adapted meshes​​

Participants: Frédéric Alauzet,​​​‌ Loïc Maréchal, Julien​ Vanharen, Thomas Gauchery​‌ [correspondant].

We presented​​ and studied a new​​​‌ methodology to improve linear​ solvers on parallel shared-memory​‌ architecture in the context​​ of Reynolds-Averaged Navier-Stokes primal​​​‌ and adjoint equations. The​ computations are realized in​‌ the context of metric-based​​ anisotropic mesh adaptation, thus​​​‌ efficiency and robustness of​ the new approach are​‌ crucial. For this purpose,​​ a domain decomposition approach​​​‌ coupled with coloring algorithm​ for unstructured meshes is​‌ considered. It improves the​​ convergence of the iterative​​​‌ solvers considered to solve​ the linear systems. The​‌ new strategy is validated​​ on multiple realistic test​​​‌ cases to highlight the​ improved convergence for primal​‌ and adjoint problems. The​​ results obtained have been​​​‌ presented during the AIAA​ SciTech 2025 conference in​‌ Orlando 8.

7.1 Bilateral​ contracts with industry

Participants:​‌ Frédéric Alauzet.

8.1 European initiatives: NumPEx​​​‌

Participants: Loic Marechal,​ Julien Vanharen.

Since​‌ COVID crisis the air​​ traffic is getting back​​​‌ to normal with a​ growing trend. Aeronautical engines'​‌ manufacturer did realize this​​ as a critical time​​​‌ for aviation and huge​ effort should be made​‌ to reduce our environmental​​ impact. For instance, The​​​‌ Advisory Council for Aeronautics​ Research in Europe aka​‌ ACARE 2050 objectives set​​ a reduction of 75%​​​‌ in production of CO2​ and of 90% of​‌ NOx. This objective brings​​ to the design of​​​‌ new and groundbreaking parts​ and requires more efficient​‌ and complex numerical tools.​​ To cope with new​​​‌ challenges an increase in​ simulation complexity and representativity​‌ is needed. It leads​​ industrials like Safran to​​​‌ wonder if current numerical​ toolchains can still address​‌ those issues or should​​ we optimize it. Parts,​​​‌ like propellers and turbines​ are very complex with​‌ a large number of​​ technological effect, taking into​​​‌ account all physical aspect​ is often not possible​‌ since it leads to​​ an exponential growth of​​​‌ the number of degrees​ of freedom with no​‌ convergence or accuracy guarantee.​​ Thus designers simplify the​​​‌ geometry to use their​ traditional old simulation methods.​‌ For this reason, SAFRAN​​ is pushing to develop​​​‌ new numerical toolchains that​ allows to reach better​‌ accuracy and scalability on​​ the key design parameters.​​​‌ The recent studies in​ this sense (3​‌ is an example of​​ application of remeshing technique​​ with a turbine) highlights​​​‌ how the combination of‌ an anisotropic meshing technique,‌​‌ a robust and accurate​​ solver and the use​​​‌ of a remeshing technology‌ would bring an improvement‌​‌ on physical quantities accuracy​​ and reliability. The need​​​‌ of testing integrated parts,‌ like propellers installed on‌​‌ wide body aircraft or​​ multi-stage turbomachine, shows the​​​‌ interest for industrials of‌ scaling the numerical toolchain‌​‌ to exascale machines in​​ order to have accurate​​​‌ results to real world‌ design problems.

Nowadays, industrials‌​‌ such as Airbus, Safran​​ or ArianeGroup, are facing​​​‌ major technological challenges, which‌ include the design of‌​‌ the Airbus A350 high-lift​​ configuration, the cooling system​​​‌ of turbomachinery involving microperforated‌ panels, the Ariane 6‌​‌ launch vehicle or the​​ consideration of ice accretion​​​‌ on aircraft wings. All‌ of these challenges imply‌​‌ an intensive use of​​ Computational Fluid Mechanics (CFD)​​​‌ in order to alleviate‌ design and manufacturing costs‌​‌ and environmental impacts. However,​​ three technological roadblocks need​​​‌ to be overwhelmed in‌ the coming decades to‌​‌ treat the previous quoted​​ industrial applications: the ability​​​‌ to handle very complex‌ geometries, to predict‌​‌ unsteady turbulent flows with​​ a high-fidelity and very​​​‌ quickly, which necessitates‌ the High-Performance Computing (HPC).‌​‌ The application proposed in​​ this project is out​​​‌ of reach with the‌ present technology. Hence, disruptive‌​‌ methods need to be​​ proposed to maximize the​​​‌ socio-economic impact. The first‌ challenge requires to use‌​‌ the automatic generation of​​ tetrahedra meshes, which​​​‌ is developed in our‌ team for more than‌​‌ thirty years 9,​​ 30, 16,​​​‌ 6, 10,‌ 11, 12,‌​‌ 13, 14,​​ 21, 20,​​​‌ 19, 32,‌ 31, 22,‌​‌ 24. Indeed, it​​ is for instance impossible​​​‌ to generate a structured‌ mesh around a real‌​‌ landing gear and even​​ if it would be​​​‌ possible, it would require‌ an enormous amount of‌​‌ time and resources compared​​ with our automatic unstructured​​​‌ mesh generator. The last‌ two challenges deal with‌​‌ the importance of having​​ accurate and fast numerical​​​‌ methods on unstructured tetrahedra‌ meshes to capture unsteady‌​‌ turbulent three-dimensional flows. Last​​ but not least, these​​​‌ challenges have to be‌ simultaneously addressed and impose‌​‌ strong constraints on the​​ whole computational workflow. Moreover,​​​‌ anisotropic mesh adaptation,‌ developed in our team‌​‌ 28, 26,​​ 27, 29 works​​​‌ like a catalyst since‌ it allows to:

1. efficiently‌​‌ discretize complex industrial geometries,​​
2. increase accuracy of numerical​​​‌ schemes,
3. reduce the computational‌ time to achieve the‌​‌ same accuracy thanks to​​ the generation of an​​​‌ optimal mesh in terms‌ of degrees of freedom‌​‌ for a given configuration.​​

Our simulation suite is​​​‌ made of two main‌ softwares: Feflo.a and Wolf.‌​‌ Feflo.a is our robust​​ anisotropic local remeshing software​​​‌ for three-dimensional volume and‌ parametric surface mesh generation‌​‌ conforming in sizes and​​ orientations to a prescribed​​​‌ input metric field. It‌ is based on a‌​‌ unique cavity-based operator 29​​, 34. It​​​‌ also includes many components‌ required to generate an‌​‌ initial mesh or generate​​​‌ highly-adapted meshes. It also​ handles non-manifold geometries and​‌ boundary layer mesh generation.​​ Wolf is a mixed​​​‌ Finite Volume Finite Element​ flow solver for the​‌ compressible Euler and Navier​​ Stokes equations with or​​​‌ without moving geometries. It​ also solves the steady​‌ and unsteady adjoint problems.​​ It achieves second-order accuracy​​​‌ in space and up​ to fourth-order accuracy in​‌ time with explicit or​​ implicit schemes. These suite​​​‌ has demonstrated its incredible​ potential and provided substantial​‌ breakthroughs in industrial applications​​ 35, 34,​​​‌ 4.

It is​ absolutely crucial to keep​‌ in mind that the​​ challenge to handle highly​​​‌ anisotropic unstructured meshes arise​ from the connectivity table​‌ needed to represent an​​ unstructured mesh which induces​​​‌ loop indirections and load​ imbalances during computations and​‌ from the anisotropy which​​ invalidates most of the​​​‌ standards geometric algorithms. Very​ simple standard algorithm such​‌ as a cut plane​​ in an anisotropic tetrahedra​​​‌ mesh should be revised​ to efficiently run on​‌ a distributed memory architecture.​​ Furthermore, the GPU algorithm​​​‌ has very little to​ do with the CPU​‌ one which notably increases​​ the development cost to​​​‌ obtain a portable solution.​

To continue and improve​‌ the capabilities of our​​ suite, we propose a​​​‌ new library GMlib to​ specifically address the issue​‌ of handling anisotropic unstructured​​ meshes on GPU and​​​‌ an industrial test case​ in agreement with the​‌ Safran Tech's roadmap.

8.2​​ European initiatives: Nextair

Participants:​​​‌ Frederic Alauzet, Eloi​ Guilbert, Cosimo Tarsia​‌ Morisco.

Radical changes​​ in aircraft configurations and​​​‌ operations are required to​ meet the target of​‌ climate-neutral aviation. To foster​​ this transformation, innovative digital​​​‌ methodologies are of utmost​ importance to enable the​‌ optimisation of aircraft performances.​​ NEXTAIR will develop and​​​‌ demonstrate innovative design methodologies,​ data-fusion techniques and smart​‌ health-assessment tools enabling the​​ digital transformation of aircraft​​​‌ design, manufacturing and maintenance.​ NEXTAIR proposes digital enablers​‌ covering the whole aircraft​​ life-cycle devoted to ease​​​‌ breakthrough technology maturation, their​ flawless entry into service​‌ and smart health assessment.​​ They will be demonstrated​​​‌ in 8 industrial test​ cases, representative of multi-physics​‌ industrial design, maintenance problems​​ and environmental challenges and​​​‌ interest for aircraft and​ engines manufacturers. NEXTAIR will​‌ increase high-fidelity modelling and​​ simulation capabilities to accelerate​​​‌ and derisk new disruptive​ configurations and breakthrough technologies​‌ design. NEXTAIR will also​​ improve the efficiency of​​​‌ uncertainty quantification and robust​ optimisation techniques to effectively​‌ account for manufacturing uncertainty​​ and operational variability in​​​‌ the industrial multi-disciplinary design​ of aircraft and engine​‌ components. Finally, NEXTAIR will​​ extend the usability of​​​‌ machine learning-driven methodologies to​ contribute to aircraft and​‌ engine components’ digital twinning​​ for smart prototyping and​​​‌ maintenance. NEXTAIR brings together​ 16 partners from 6​‌ countries specialised in various​​ disciplines: digital tools, advanced​​​‌ modelling and simulation, artificial​ intelligence, machine learning, aerospace​‌ design, and innovative manufacturing.​​ The consortium includes 9​​​‌ research organisations, 4 leading​ aeronautical industries providing digital-physical​‌ scaled demonstrator aircraft and​​ engines and 2 high-Tech​​​‌ SME providing expertise in​ industrial scientific computing and​‌ data intelligence.

9.1 Publications of​​ the year

9.2 Cited publications

• 3​​ inproceedingsF.F. Alauzet​​​‌, L.L. Billon‌, E.E. Parente‌​‌, M.M. Philit​​, A.A. Remigi​​​‌ and D.D. Papadogiannis‌. Evaluation of heat‌​‌ transfer performance of a​​ film-cooled turbine vane using​​​‌ metric-based anisotropic mesh adaptation‌.AIAA SCITECH 2023‌​‌ ForumNational Harbor, MD,​​ USA2023DOIback​​​‌ to text
• 4 inproceedings‌F.Frédéric Alauzet,‌​‌ F.Francesco Clerici,​​ A.Adrien Loseille,​​​‌ M.Matthieu Maunoury,‌ L.Lucien Rochery,‌​‌ C.Cosimo Tarsia-Morisco,​​ L.-M.Lucille-Marie Tenkes and​​​‌ J.Julien Vanharen.‌ 4th AIAA CFD‌​‌ High Lift Prediction Workshop​​ results using metric-based anisotropic​​​‌ mesh adaptation.AIAA‌ Fluid Dynamics ConferenceChicago,‌​‌ IL, USA6 2022​​back to text
• 5​​​‌ articleR.Rémi Feuillet‌, M.Matthieu Maunoury‌​‌ and A.Adrien Loseille​​. On pixel-exact rendering​​​‌ for high-order mesh and‌ solution.Journal of‌​‌ Computational Physics4242021​​, 109860back to​​​‌ text
• 6 bookP.‌P.J. Frey and P.‌​‌P.L. George. Mesh​​ generation. Application to finite​​​‌ elements.ISTE Ltd‌ and John Wiley &‌​‌ Sons2008back to​​ text
• 7 miscP.​​​‌ J.P. J. Frey‌. Medit: An interactive‌​‌ mesh visualization software, INRIA​​ Technical Report RT0253.​​​‌2001back to text‌
• 8 inbookT.Thomas‌​‌ Gauchery, J.Julien​​ Vanharen, L.Loïc​​​‌ Maréchal and F.Frederic‌ Alauzet. Comparison of‌​‌ Several Linear Solvers on​​ Shared-Memory Architecture for Navier-Stokes​​​‌ Equations and Adjoint System‌ on Anisotropic Adapted Meshes‌​‌.AIAA SCITECH 2025​​ Forum2021, 20​​​‌back to text
• 9‌ bookP.P.L. George‌​‌ and H.H. Borouchaki​​. Delaunay triangulation and​​​‌ meshing : application to‌ finite elements.Paris,‌​‌ OxfordHermès Science1998​​back to text
• 10​​​‌ bookP.P.L. George‌ and H.H. Borouchaki‌​‌. Delaunay triangulation and​​ meshing. Application to finite​​​‌ elements.ParisHermès‌1998back to text‌​‌
• 11 articleP.P.L.​​ George and H.H.​​​‌ Borouchaki. ``Ultimate'' robustness‌ in meshing an arbitrary‌​‌ polyhedron.International Journal​​ for Numerical Methods in​​​‌ Engineering5872003‌, 1061-1089back to‌​‌ text
• 12 articleP.​​P.L. George, F.​​​‌F. Hecht and E.‌E. Saltel. Automatic‌​‌ mesh generator with specified​​ boundary.Computer Methods​​​‌ in Applied Mechanics and‌ Engineering921991,‌​‌ 269-288back to text​​
• 13 articleP.P.L.​​​‌ George, F.F.‌ Hecht and E.E.‌​‌ Saltel. Fully automatic​​​‌ mesh generator for 3D​ domains of any shape​‌.Impact of Computing​​ in Science and Engineering​​​‌231990,​ 187-218back to text​‌
• 14 articleP.P.L.​​ George and F.F.​​​‌ Hermeline. Delaunay's mesh​ of a convex polygon​‌ in dimension d. Application​​ to arbitrary polyedra.​​​‌International Journal for Numerical​ Methods in Engineering33​‌1992, 975-995back​​ to text
• 15 article​​​‌C.C. Geuzaine and​ J.-F.J.-F. Remacle.​‌ Gmsh: A 3-D finite​​ element mesh generator with​​​‌ built-in pre- and post-processing​ facilities.International Journal​‌ for Numerical Methods in​​ Engineering79112009​​​‌, 1309-1331back to​ text
• 16 articleF.​‌F. Hermeline. Triangulation​​ automatique d'un polyèdre en​​​‌ dimension $N$.RAIRO.​ Analyse numérique163​‌1982, 211--242DOI​​back to text
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