NORMA DELIVRABLES




Task 1: Hybrid modelling for aeroacoustics (Resp. Montpellier)


Task 2: Dedicated high-order schemes for aeroacoustics (Resp. INRIA)


Task 3: Geometrical strategies: IBM and mesh adaptation (Resp. KIAM)


Task 4: Time-advancing algorithmics and parallelism (Resp. INRIA)


Task 5: Validations and challenging applications (Resp. KIAM)


Task 6: Coordination/dissemination (Resp. Montpellier and KIAM)

  • A paper, entitled "Simulation of the flow past a circular cylinder from sub-critical to super-critical Reynolds numbers using an intermittency-based hybrid model", was published in november 2023 in Journal of Fluids and Structures. It deals with the impact of intermittency modeling in hybrid turbulence models.
  • Tatiana Kozubskaya (org.), Nishikawa Hiroaki, Yi Liu, Li Wang, Alain Dervieux and Frédéric Alauzet were resp. of the minisymposium MS286 "High-accuracy finite-volume methods on unstructured meshes for aviation applications", at the conference ECCOMAS 2020 which was finally held on January 2021.
  • Alain Dervieux and Bruno Koobus were resp. of the minisymposium MS7-06 "Scale-resolving simulation of massively separated flows and rotating machines", at the "22nd IACM Computational Fluids Conference, CFC 2023, Cannes".

          T6-D1: Six-months periodic progress reports (starting date: 01/03/2020):

    For periodic progress, see also the presentations of the "Work Progress Meetings" on the Home page.
          1.- First six-month report (scheduled for 01/09/2020 ; completed on 15/10/2020):
    One point to mention is that, at least for the computational / development aspects, KIAM started earlier while Montpellier+INRIA started with the arrival of the two doctoral students on 01/09/2020.
    - V. Bobkov (KIAM) presented the case of Caradonna-Tung rotating helix (Caradonna F. X., Tung C. Experimental and analytical studies of a model helicopter rotor in hover: tech. rep. ; NASA's Ames Research Center, Moffett Field, California, Sept. 1981. NASA-TM-81232) together with a first computation done with a mixed structured (near wing) / unstructured mesh.
    - P. Bakhvalov (KIAM) has started a study on the artificial viscosity in WENO-EBR schemes.
    - I. Abalakin, V. Bobkov, T. Kozubskaya, L. Kudryavtsev, V. Tsertkova, N. Zhdanova (KIAM) worked on a novel combination of the Immersed Boundary Method with adaptive meshes with, as first application, the flow around an helix geometry.
    - F. Mirales and B. Koobus (IMAG Montpellier) started to work on a bibliographic study of (1) Immersed Boundary Methods (2) hybrid RANS-LES modeling methods.
    - M. Gschwend and A. Dervieux (Ecuador INRIA) started a bibliographic study of higher-order approximations.
    - Discussion started on common test cases and meshes for turbulent flows around cylinders.
    - A mesh of the Caradonna-Tung rotating helix was generated by the Russian team and delivered to Montpellier.

          2.- Second six-month report (scheduled for 01/03/2021 ; completed on 20/04/2021):
    For the 12th month of Norma project, the partners have identified the important questions on which to exchange.
    The approximation methods used by partners are close, but with differences, and continuous progress are made (improvements, novel approaches like CENO4). Then, two test cases have been chosen for comparaison purposes: (1) pure advection schemes with the advection of a Gaussian pulse, (2) steady Euler schemes with the subsonic inviscid flow past a cylinder.
    The turbulence models used by the partners are also close but with differences.
    Geometries of industrial interest involve thin shapes like wings, helices, together with blunt shapes like helicopter fuselage. A study is started for addressing the difficult simulation around blunt bodies.
    Three challenging test cases related to the unique geometry of a circular cylinder were chosen: flows with Reynolds number 0.14, 1. and 2. millions. Meanwhile, the investigation of more efficient treatment of rotating geometries, in particular with IB, taking account of boundary layers has continued.
    - V. Tsvetkova (KIAM) has worked on the IB method with adaptative mesh, applying it to rotating propeller simulation, Another approach studied was moving mesh-adaptation in 3D, applications being done on flow around an helicopter fuselage.
    - A. Duben (KIAM) has continued on Turbulent flow computations, with application to the common test cases of the circular cylinder at medium and high Reynolds numbers.
    - V. Bobkov (KIAM) has been working on turbulent flow computations around rotor blades.
    - N. Zhdanova (KIAM) designed an IB method for unstructured meshes and for wall modeling.
    - V. Vershkov (KIAM) has been applying turbulent flow computations on helicopter fuselage.
    - P. Rodionov (KIAM) developed new versions of HO methods, namely EBR schemes, studying more precisely the extension to prismatic layers.
    - S. Wornom and B. Koobus (IMAG Montpellier) have been working on hybrid turbulence modeling, with applications to the common tests cases of the cylinder flow computations.
    - F. Miralles has designed and implemented an Immersed Boundary Method in an incompressible CFD kernel.
    - A. Dervieux and M. Gschwend (Ecuador INRIA) have written a review of high-order approximations for CFD models.
    - M. Gschwend (Ecuador INRIA) has designed and developed a novel CENO method, based on a partition of cells which provides much faster polynomial reconstructions.

          3.- Third six-month report (scheduled for 01/09/2021 ; completed on 12/10/2021):
    - P. Bakhvalov (KIAM) has started the common test case of Gaussian advection, with the EBR scheme. He has developed his Collection of Exact Solutions of Euler, Navier-Stokes equations and their linearized versions ColESo to be used for testing the numerical methods.
    - A. Duben (KIAM) has performed DDES calculations for the cylinder at Reynolds 140K, 1M and 2M.
    - V. Bobkov (KIAM) has computed the Caradonna case using he hybrid IDDES method and compared the aerodynamic results with respect to the numerical data produced by the RANS model. The IDDES method predicts the localization of tip vortices more accurately.
    - V. Tsvetkova (KIAM) has simulated the 2D flow over the 2D projection of propeller using the IBC method and anisotropic moving-mesh adaptation technique developed within the project. The numerical results quite well correspond to those obtained using the body-fitted approach in non-inertial reference frame.
    - L. Kudryavtseva (KIAM) has developed the method of the anisotropic moving-mesh adaptation by introducing the information about the surface curvature to the controlling function.
    - N. Zhdanova (KIAM) has developed the original wall-function technique applicable both to body-fitted and IBC approaches to describe a moving obstacle. She has started testing cases.
    - V. Vershkov (KIAM) has computed the RANS flow over the ROBIN fuselage using the body-fitted approach. His results are in a good agreement with the available experimental data.
    - F. Miralles (IMAG Montpellier) has computed the flow past a circular cylinder at Reynolds 1M using hybrid turbulence models. The results will be presented at CMFF22 Budapest (october 2022). He has also developed, in the AIRONUM software, a hybrid turbulence approach using the k-R RANS model for the simulation of massively separated flows in the case of an integration of the equations up to the wall or in conjunction with a wall law.
    - S. Wornom (IMAG Montpellier) has performed hybrid turbulence computations of the cylinder at Reynolds 2M. The results will also be presented at CMFF22 Budapest (october 2022).
    - M. Gschwend (Ecuador INRIA) has designed and implemented a novel CENO4 of order four method. This method has been applied to the common test case of 3D Gaussian advection. The novel CENO4 has been introduced in the CFD code NiceFlow. A particular interest of NiceFlow is its different functionalities addressing rotating geometries, together with mesh adaptive capacities. With the enriched version of NiceFlow, M. Gschwend applied CENO4 to the common test case of inviscid flow past a cylinder. M. Gschwend stopped his PhD preparation to start a job. Ecuador has recruted Bastien Sauvage for a 3-year PhD prepararation.
    - B. Sauvage (Ecuador INRIA) has been studying the CENO4 method of M. Gschwend and started designing a method for the mesh adaptation of the CENO4 technology. He has started studying a Chimera approach for rotor/stator flow and worked on the combination of Chimera and mesh adaptation. The first demonstrative application is the flow in a mixing vessel containing a rotation cross-shaped device.

    P.A. Bakhvalov. ColESo, Collection of Exact Solutions of Euler, Navier-Stokes equations and their linearized versions, https://caa.imamod.ru/index.php/research/coleso
    I.V. Abalakin, P.A. Bakhvalov, V.G. Bobkov, A.V. Gorobets. Parallel Algorithm for Flow Simulation in Rotor-Stator Systems Based on Edge-Based Schemes, Math. Mod. and Comp. Simul., 13(1), 2021, 172-180. ISSN 2070-0482.
    A.P. Duben, T.K. Kozubskaya, P.V. Rodionov, V.O. Tsvetkova. EBR Schemes with Curvilinear Reconstructions of Variables in the Near-Wall Region, Computational Mathematics and Mathematical Physics, 61(1) (2021) 3-19.
    P. A. Bakhvalov, T. K. Kozubskaya. On Using Artificial Viscosity in Edge-Based Schemes on Unstructured Grids. Mathematical Models and Computer Simulations, 13 (4), 2021, pp. 705-715.
    Bobkov, V.G., Bondarev, A.E., Bondarenko, A.V. et al. Numerical Simulation of the Aerodynamics of Vertical-Axis Wind Turbines. Math Models Comput Simul 13, 604-612 (2021). DOI:10.1134/S2070048221040074.
    Bobkov, V. G., Vershkov, V. A., Kozubskaya, T. K., & Tsvetkova, V. O. (2021). Deformation Technique of Unstructured Mesh Deformation to Find the Aerodynamic Characteristics of Bodies at Small Displacements. In Mathematical Models and Computer Simulations, Vol. 13, Issue 6, pp. 986\2261001, DOI:10.1134/s2070048221060028.

          4.- Fourth six-month report (scheduled for 01/03/2022 ; completed on 22/04/2022):
    - B. Sauvage (Ecuador INRIA) is continuing his studies towards mesh adaption and unsteady flows. He developed a study of the NACA0021 test case at high angle of attack, an unsteady flow adressed with a DDES model and mesh adaptation. He also continued his study of mesh adaptive calculation of rotation flows. He developped a Multiple Reference Frame method satisfying the Discrete Geometric Consevation Law. The new scheme together with the Chimera scheme are compared with the calculation of the Caradonna helix, both with mesh adaptation. The results will be presented in two communications of the team at ECCOMAS Oslo and CMFF22 Budapest. He started a more theoretical study of unsteady mesh adaptation, the purpose of which is to identify the best way to converge to continuous solution and the effective order of convergence for complex flows.
    - F. Miralles and S. Wornom (IMAG Montpellier) have computed the flow around a NACA0021 airfoil in a deep stall, a massively separated flow simulated with hybrid and non hybrid turbulence models using a low dissipation scheme. The results will be presented at ECCOMAS Oslo (june 2022).
    - F. Miralles (IMAG Montpellier) has developed a new blending function in our hybrid turbulence strategies which allows an automatic and progressive switch from RANS (or DDES) to DVMS where the grid resolution is fine enough and with the objective to prevent the activation of the DVMS model in the boundary layer (it will also be presented at ECCOMAS Oslo, june 2022).
    -F. Miralles (IMAG Montpellier) has also implemented in the AIRONUM software a two-equation RANS transitional turbulence model (which could possibly be used in our hybrid approaches). This model is currently evaluated on the flow past a cylinder at Reynolds number 1M. At the same time, he started an implementation of an IBM approach in the AIRONUM software with the aim of combining it with hybrid turbulence models, the first targeted application being the simulation of a periodic moving cylinder test case.

    D. Chargy, B. Sauvage. A mesh adaptative method for rotating machines, INRIA-RR-9464, 2022.
    F. Miralles, B. Sauvage, S. Wornom, B. Koobus, A. Dervieux. Hybrid RANS/DVMS modeling for static and rotating obstacles, INRIA-RR-9471, 2022.
    F. Miralles, B. Sauvage, S. Wornom, B. Koobus, A. Dervieux. Application of hybridRANS/VMS modeling to rotatingmachines CMFF'22, August 30 - September 2, 2022, Budapest, Hungary.
    F. Miralles, B. Sauvage, A. Duben, V. Bobkov, T. Kozubskaya, S. Wornom, B. Koobus, A. Dervieux. Simulation of massively separated flows and rotating machine flows using hybrid models ECCOMAS Congress, 5-9 June 2022, Oslo, Norway.

          5.- Fifth six-month report (scheduled for 01/09/2022 ; completed on 20/09/2022):
    -B. Sauvage made advances in the theory of space-and-time mesh adaptation with the transient fixed pont algorithm, in cooperation with F. Alauzet, senior scientist at Saclay center of INRIA.
    Adapting the time step is an important issue for aerodynamic LES and hybrid RANS-LES calculations since implicit time advancing with large time steps is used for efficiency reasons while time truncation errors have to be mastered by identifying the best time step.
    He made progresses in the computation of the Caradonna-Tung rotor, with a new adapted calculation on 3 million vertices. He studied approximation issues, by comparing on test cases finite volume superconvergent quadratures of third order and fifth order truncature. The fifth order truncature has been improved.
    He also made studies on approximation, with comparison of several Riemann solvers, viz. Roe flux difference splitting (FDS), HLLC flux vector splitting (FVS), and a new variant of the Toro-Vazquez FVS. For pure advection, the Toro-Vazquez FVS proved to be less diffusive than HLLC, of comparable diffusion to Roe, while being much more robust than Roe FDS. These properties are important when mesh adaptation algorithms are applied, since these algorithms are more challenging for the approximation.
    B. Sauvage also focused on the new test case chosen by Norma, the flow past a NACA0018 at various angles of attack, for which several measurements are available in the litterature.
    A part of the work of B. Sauvage has been presented in CMMF'22 at Budapest and will be presented in DLES13 at Udine.
    -S. Wornom and F. Miralles have started the aerodynamic and aeroacoustic computation of the flow over a NACA0018 airfoil at incidence 0 and 6 degrees. Hybrid and non hybrid turbulence models are used, in combination with a low dissipation scheme.
    F. Miralles continued the calculations of the cylinder at Reynolds numbers 1 million and 2 million using wall laws and hybrid models of the DDES, RANS/DVMS and DDES/DVMS type, and progress has been made. Parallel to this benchmark, F. Miralles has also improved the simulation of the flow around a NACA0021 airfoil in a deep stall using hybrid models.
    F. Miralles has developped and implemented a new transition turbulence model based on the k-ε-γ model of Akhter. This transition model has been incorporated in our hybrid strategies (DDES, RANS/DVMS and DDES/DVMS) and evaluated with success on the simulation of the flow around a cylinder in the subcritical and supercritical regimes with integration of the equations up to the wall (an abstract is currently submitted to the CFC 2023 Cannes conference). F. Miralles has also started to perform the simulation of the transitional flow over a NACA0018 airfoil at incidence 6 degrees using hybrid models equipped with this transition model, with the aim of improving the aerodynamic and aeroacoustic characteristics of the flow, such as the airfoil self-noise generation and propagation.
    Part of this work carried out by F. Miralles and S. Wornom has been presented in CMMF'22 at Budapest and will be presented in DLES13 at Udine.

          6.- Sixth six-month report (scheduled for 01/03/2023 ; completed on 16/03/2023):
    -B. Sauvage has been working during more than two months at INRIA-Saclay in order to develop, with the help of F. Alauzet, a plateform for demonstrating a new method for space-and-time mesh adaptation. The platform is now running preliminary test cases.
    He will present this work at the "22nd IACM Computational Fluids Conference, CFC 2023" as part of the Minisymposium MS6-03 "Mesh and order (h/p) adaptation methods for scale-resolving simulations of turbulent flows" in Cannes, 25-28 avril 2023.
    B. Sauvage also improved his method for rotating machines and made new computations of the Norma test cases (NACA0018 and helicopter).
    B. Sauvage, F. Alauzet and A. Dervieux have started a study of methods tending to increase the accuracy of LES computation by using mesh adaptation.
    A. Dervieux has written a synthesis of the work done by the Russian and French Norma teams in the context of Norma. This synthesis will be presented in the Minisymposium MS7-06 "Scale-resolving simulation of massively separated flows and rotating machines" at the "22nd IACM Computational Fluids Conference, CFC 2023" in Cannes, 25-28 avril 2023.
    -F. Miralles has presented his results on the hybrid simulation of circular cylinder flows and the flow around a NACA0021 airfoil in a deep stall in the ERCOFTAC Workshop "Direct and Large-Eddy Simulation 13", October 26th-29th, 2022, Udine, Italy.
    F. Miralles has developped a new transition RANS model based on an intermittency equation derived from the works of Akhter and Menter. This model has been incorporated into a RANS/LES approach and successfully applied to the hybrid simulation of the flow past a circular cylinder from sub-critical to super-critical regime. In particular, the drag crisis phenomenon has been successfully predicted by the proposed intermittency-based hybrid model, even with the use of coarse grids.
    This work will be presented at the "22nd IACM Computational Fluids Conference, CFC 2023", 25-28 April 2023, in Cannes.
    F. Miralles and B. Koobus are currently writting a paper dealing with the impact of intermittency modeling in hybrid calculations for a future submission in an international journal.
    S. Wornom has implemented the SST "k-omega" turbulence model in AIRONUM (the CFD software shared by INRIA and Univ. Montpellier), with a view to integration into the DDES, RANS/LES and RANS/DDES hybrid approaches, the targeted applications being massively separated flows such as those encountered in rotating machines. Evaluation of the SST "k-omega" model is in progress.
    -A. Dervieux and B. Koobus have organised the Minisymposium MS7-06 "Scale-resolving simulation of massively separated flows and rotating machines", that they will chair in Cannes in April 2023, as part of the "22nd IACM Computational Fluids Conference, CFC 2023".

          7.- Seventh six-month report (scheduled for 01/09/2023 ; completed on 18/10/2023):
    -A research purpose of the INRIA Sophia team is the assembly of methods for computing with an efficient mesh adaptation the unsteady flows involving turbulent wake, with an emphasis on the flows considered by Norma. Two research directions are currently explored, first the investigation of a space-time mesh and timestep adaptation for the computation of transient flows with an implicit time-advancing scheme, second the design of a spatial mesh adaptation method for the computation of LES and DDES modeled flows.
    As concerned the first investigation, Bastien Sauvage, Frederic Alauzet and Alain Dervieux have completed the theoretical part of the paper defining the new space-time fixed point algorithm, covering the two cases of feature-based adaptation criterion and goal-oriented adaptation criterion. Bastien Sauvage has worked on the implementation of this method. In particular, he has developed a non-oscillatory approximation of the temporal error term. These novelties are demonstrated in the software WOLF for a series of 2D computations of the flow around a cylinder. A pre-print is available in the Norma communication list.
    For the second research theme, Bastien Sauvage, Frederic Alauzet and Alain Dervieux have written a first theoretical paper combining a review of adaptation models for LES and the proposition of a Flow+LES criterion for adapting spatial meshes to a complex flow with boundary layers and turbulent wake. The resulting report is proposed as T3-D4 deliverable for the Norma project.
    -Florian Miralles has developped a transitional hybrid turbulence approach which combines an intermittency-based RANS model and a dynamic variational multiscale method. This hybrid approach has been successfully applied to the simulation of circular cylinder flows from sub-critical to super-critical Reynolds numbers using relatively coarse meshes. It has been shown that the drag crisis phenomenon, the sharp increase in vortex shedding frequency and the Kelvin-Helmholtz instabilities are in particular well predicted. This joint work with Bruno Koobus has led to the writting of a paper which has been accepted for publication in Journal of Fluids and Structures (see the Communications section of the Norma website).
    -Florian Miralles has also performed aerodynamic and aeroacoustic simulations of transitional flows over NACA0018 and NACA0021 airfoils at incidence (this work has been included in his PhD manuscript).
    -Stephen Wornom has implemented the K-Omega model in the Aironum software and written two reports detailing its implementation. Validation is in progress.
    -Stephen Wornom and Bastien Sauvage have been validating the Vms-Wale turbulence model for adaptive meshes for Reynolds number 3900. The results obtained have been compared to the Re=3900 published results using the coarse and fine benchmark meshes created by Hilde Ouvrard in collaboration with the university of Pisa. This validation continues.
    -Stephen Wornom has been computing the flow over a cylinder at Reynolds number 10000 using the transitional hybrid model of Florian Mirales.

          8.- Eigth six-month report (scheduled for 01/03/2024 ; completed on 11/03/2024):
    -Florian Miralles successfully defended his thesis "Simulation aérodynamique et aéroacoustique d’écoulements massivement décollés par des modèles de turbulence hybrides et de transition" in November 2023 at the University of Montpellier.
    -The Montpellier and Sophia teams continued to work on the transitional turbulence model which was at the center of Florian Miralles' thesis. Calculations were carried out on new meshes and new Reynolds numbers. A summary of the progress made by the two teams in adaptive mesh, in approximation and modeling, and experienced on circular cylinder flows, is currently being written.
    -As regards rotating machine aspects, an unsteady mesh adaptation calculation of the Caradonna-Tung test case is in progress, and is beginning to yield encouraging results. A simple multi-rotor test case is in preparation.
    -The works on space and time adaptation has been continued to reach sucessful outputs. This resulted in the writing of an article submitted to an international journal: ``B. Sauvage, F. Alauzet, A. Dervieux, A space and time fixed point mesh adaptation method".
    -With statistical turbulence models, only a part of turbulent industrial flows can be predicted with an affordable cost. The rest of flows may involve large detached regions which cannot be accurately described by statistical modeling, or may involve vortices producing noise that the engineer wants to predict accurately. The Large Eddy Simulation (LES) is a model which predicts a part of the vortices of industrial interest. LES relies on a filtering of the too small vortices and a modeling of their effect on larger ones. But this approach is one or two orders of magnitude more computer intensive than statistical modeling, and therefore cannot be routinely used by engineers. Germano proposed an analysis using two different filters in order to measure the efficicency of a family of LES models. Recently, Toosi and Larsson demonstrated that Germano's analysis actually deals with the source term of the LES modeling error. We introduce this error term in our mesh adaptation process for RANS flows in order to obtain an approach for adapting the mesh to hybrid RANS/LES flow calculations. Applications to vortex shedding flows are being performed, cf. ``B. Sauvage, B. Koobus, F. Alauzet, A. Dervieux, A metric-based mesh adaptation for hybrid RANS/LES flow calculations, in preparation.''
    -Thanks to anisotropic mesh adaptation, high-fidelity industrial calculations can be made to converge at actual second-order (steady case), even for rather singular cases, and convergence error can be evaluated. We are investigating the way to extend this to higher order. Our research relies on a fourth-order accurate three-dimensional vertex-centered Central Essentially Non Oscillating (CENO) scheme. During the last period, computations were performed in order to more accurately evaluate the gain in prediction of LES and hybrid simulations when the fourth-order CENO scheme is used instead of the MUSCL scheme. The test cases concern the flow around a cylinder at different Reynolds number.
    -In parallel with these works, Stephen Wornom carried out the following tasks :
    validation of the adapted mesh generated by Bastien Sauvage using the Niceflow and Aironum softwares for the simulation of circular cylinder flows with different turbulence models, including the transition model of Florian Miralles; continuation of the Aironum installation work on the Adastra supercomputer at CINES; study of low Mach preconditionners.

          9.- Nineth six-month report (scheduled for 01/09/2024 ; completed on 30/09/2024):
    An important output of the Norma study by INRIA-Sophia is the research of an efficient combination of MRF rotating formulation with dynamic mesh adaptation. A first version of this combination has been defined and validated by Bastien Sauvage. With this new method, Bastien Sauvage has finalized two unsteady mesh-adaptive computations, one of a single Caradonna-Tung helicopter rotor and one of the combination of the Caradonna-Tung rotor with the Robin fuselage. The computation of the single Caradonna-Tung rotor showed a well-formed vortex shedding at the end of the two rotor wings, corresponding to high-frequency sound emission.
    In association with the university of Montpellier, a wide series of test cases was recomputed in order to measure the progress in turbulence computation obtained thanks to the three novelties introduced by the university of Montpellier-INRIA Sophia cooperation:
    - a novel hybrid LES-RANS model with intermittency,
    - a fourth-order CENO4 advective approximation for RANS and hybrid calculations,
    - the new unsteady mesh adaptation for RANS and hybrid calculations.
    A paper "Computing the flow past a cylinder : influence of models and numerics", B. Sauvage, F. Miralles, S. Wornom, B.Koobus, A. Dervieux, is in preparation from these calculations and comparisons.
    Although the new approach combining RANS/hybrid modeling, MRF, and adaptation has produced good results, two new investigations have been undertaken to improve our mesh adaptation methods:
    - A novel adaptation method in space and time was developed for implicit time advancing as used in turbulence computations.
    B. Sauvage, F. Alauzet, A. Dervieux, "A space and time fixed point adaptation method", Journal of Computational Physics, Volume 519, 2024, 113389.
    - A novel adaptation method based on the Germano dynamic-LES analysis which takes into account the LES model error has been proposed and validated on a set of test cases.
    "A metric-based mesh adaptation for hybrid RANS/LES flow calculations", B. Sauvage, B. Koobus, F. Alauzet, A. Dervieux. An article is being finalized (collaboration with the university of Montpellier).
    All these methodological and software advances are capitalized by the two teams (and by the Saclay INRIA team, F. Alauzet, who cooperated to the NORMA study) for further research.
    They are also communicated and capitalized by the engineering company Lemma who landed the software NiceFlow for the two investigations concerning Hybrid-LES mesh adaptation and high-order Ceno4 approximation.






Updated september 30, 2024.