2023Activity reportProject-TeamMEMPHIS

2.1 Multi-physics numerical modeling

3.1 Numerical models

We aim to further develop automated model-order reduction (MOR) procedures for large-scale systems in computational mechanics — here, automated refers to the ability to complete the analysis with minimal user intervention. First, we wish to combine nonlinear MOR with mesh adaptation to simultaneously learn rapid and reliable ROMs and effective high-fidelity discretizations over a range of parameters. Second, we wish to develop component-based MOR procedures to build inter-operable components for steady and unsteady nonlinear PDEs: towards this end, we should develop efficient localized training procedures to build local ROMs for each archetype component, and also domain decomposition techniques to glue together the local models for prediction. We also wish to develop and analyze hybrid approaches that combine and merge first-principle models with data-fit models, and also full-order and reduced-order models for prediction of global engineering quantities of interest.

We envision that several methods that are currently developed in the team can be complemented by available tools from machine learning: representative examples include — but are not limited to — solution clustering, optimal sampling, classification. In this respect, a leap forward in industrial applications that we will pursue is without doubts the possibility of capitalizing on previous experience drawn from already acquired simulations to build non-intrusive models that combine non-linear interpolations and non-linear regression. New perspectives in this direction are offered by the Chair Onera-Nouvelle Aquitaine (cf. Regional initiatives).

As regards the work on numerical discretization of PDEs, compared to the previous evaluation, we focus on the representation of the solution in each computational cell by adopting a DG/ADER approach to improve the resolution of solution's discontinuities. This approach is complemented with a Chimera grid at the boundaries in order to improve accuracy by a body fitted mesh avoiding grid generation complexity for a general, possibly varying, geometrical topology. The thesis of Alexis Tardieu, which started in October 2021 and is funded by the University of Bordeaux, studies this approach.

In parallel, we continue our exploration of schemes in asymptotic regimes such as low- and high Mach numbers for multi-material flows. We aim for schemes that circumvent the problem of accuracy and time stepping in such regimes: the ultimate goal is to devise asymptotic-preserving schemes that are able to capture phenomena at the time scale of the fast waves and of the material waves with the same accuracy. For such a purpose, a new path based on numerical schemes with multi-dimensional knowledge is also being explored.

3.2 Applications

For energy applications, we will continue our investigations on wave energy converters and windturbines. Relative to wave energy converters, we are developing multifidelty models that couple the incompressible Navier-Stoke equations (NSE) around the floater with a Proper Orthogonal (POD) ROM or a simplified-physics model elsewhere.

• In October 2021, Nishant Kumar started a two-year postdoctoral fellowship in the team, which was funded by the Inria-IfpEN program; the aim is to couple an high-fidelity model and a POD model based on the LES Navier-Stokes equations; the coupling is implemented in the SOWFA framework of OpenFOAM.
• In December 2021, Caroline Le Guern started her PhD in the team, in the framework of the Inria-IfpEN program; Caroline works on the modeling and simulation of the fluid-structure interaction of next-generation windturbines with up to 250 meter rotor; the numerical implementation is based on the software Deeplines that is co-developed by IfpEN.
• In April 2022, Umberto Bosi started a two-year postdoctoral fellowship in the team, in collaboration with CARDAMOM: the project of Umberto, which was funded by Inria and the Region Nouvelle Aquitaine, focuses on the coupling between an high-fidelity (e.g., Navier-Stokes) model and an asymptotic (e.g., shallow water or Boussinesq) model.

We are also collaborating with EDF to devise effective ROMs for parametric studies. In this collaboration, we emphasize the implementation of projection-based ROMs for real-world applications exploiting industrial codes.

• In April 2021, Eki Agouzal started an industrial thesis to develop projection-based ROMs for nonlinear structural mechanics problems in Code Aster, with emphasis on thermo-hydro-mechanical (THM) applications.
• In December 2023, Abdessamad Moussaddak started his PhD thesis on model reduction for river and coastal hydraulics.

Within the ARIA project, in collaboration with Nurea and the bio-mechanics lab of the Politecnico di Torino, we investigate the idea of data augmentation starting from a given aneurysm database. We construct statistically relevant synthetic aneurysms that can provide both heterogeneity and closeness to reality to test new bio-markers for aneurysm rupture. The thesis of Ludovica Saccaro funded by Inria is dedicated to this subject.

In the framework of the ANR DRAGON, we also increase our interactions with researchers in biology and physical science. in the center of biological studies in Chizé (centre d'études biologiques de Chizé). The ANR funds the PhD thesis of Karl Maroun at University of Poitiers.

The software development will be continued. We will pursue the development of the NEOS library: NEOS will be distributed in open source LGPL-3.0. The HIWIND software will be rewritten based on NEOS library.

4.1 Energy conversion

We apply the methods developed in our team to the domain of wind engineering and sea-wave converters. In Figure 1, we show results of a numerical model for a sea-wave energy converter. We here rely on a monolithic model to describe the interaction between the rigid floater, air and water; material properties such as densities, viscosities and rigidity vary across the domain. The appropriate boundary conditions are imposed at interfaces that arbitrarily cross the grid using adapted schemes built thanks to geometrical information computed via level set functions 44. The background method for fluid-structure interface is the volume penalization method 32 where the level set functions is used to improve the degree of accuracy of the method 4 and also to follow the object. The underlined mathematical model is unsteady, and three dimensional; numerical simulations based on a grid with $𝒪\left({10}^8\right)$ degrees of freedom are executed in parallel using 512 CPUs.

See-wave converter

  

Wind turbine

In the context of the Aerogust (Aeroelastic gust modelling) European project, together with Valorem, we investigated the behavior of wind turbine blades under gust loading. The aim of the project was to optimize the design of wind turbine blades to maximize the power extracted. A meteorological mast (Figure 2(a)) has been installed in March 2017 in Brittany to measure wind on-site: data provided by the mast have been exploited to initialize the mathematical model. Due to the large cost of the full-order mathematical model, we relied on a simplified model 42 to optimize the global twist. Then, we validated the optimal configuration using the full-order Cartesian model based on the NaSCar solver. Figure 2(b) shows the flow around the optimized optimized wind turbine rotor.

4.2 Schemes for turbulent flow simulations using Octrees

We have initially developed and tested a 3D first-order Octree code for unsteady incompressible Navier-Stokes equations for full windmill simulations with an LES model and wall laws. We have validated this code on Occigen for complex flows at increasing Reynolds numbers. This step implied identifying stable and feasible schemes compatible with the parallel linear Octree structure. The validation has been conducted with respect to the results of a fully Cartesian code (NaSCAR) that we run on Turing (with significantly more degrees of freedom) and with respect to experimental results.

Subsequently, we have developed a second-order Octree scheme that has been validated on Occigen for a sphere at a moderate Reynolds number ($\mathrm{Re}=500$), see Table 1. Then, for a cylinder at ($\mathrm{Re}=140000$) (Figures 3(a) and 3(b)), close to real applications, we have preliminary validation results for the second-order scheme with respect to experimental drag coefficient (Table 2). Additional resources will be asked on Occigen to complete the study.

  

Turbulent simulations

4.3 Vascular flows

A new research direction pursued by the team is the mathematical modelling of vascular blood flows in arteries. Together with the start-up Nurea and the surgeon Eric Ducasse, we aim at developing reliable and automatic procedures for aneurysm segmentation and for the prediction of aneurysm rupture risk. Our approach exploits two sources of information: (i) numerical simulations of blood flows in complex geometries, based on an octree discretization, and (ii) computed tomography angiography (CTA) data. Figure 4 shows the force distribution on the walls of the abdominal aorta in presence of an aneurysm; results are obtained using a parallelized hierarchical Cartesian scheme based on octrees.

Further information is given in the sections dedicated to the new results.

Aneurysm simulation

4.4 Fluid-structure interactions using Eulerian non-linear elasticity models

Mathematical and numerical modeling of continuum systems undergoing extreme regimes is challenging due to the presence of large deformations and displacements of the solid part, and due to the strongly non-linear behavior of the fluid part. At the same time, proper experiments of impact phenomena are particularly dangerous and require expensive facilities, which make them largely impractical. For this reason, there is a growing interest in the development of predictive models for impact phenomena.

In MEMPHIS, we rely on a fully Eulerian approach based on conservation laws, where the different materials are characterized by their specific constitutive laws, to address these tasks. This approach was introduced in 39 and subsequently pursued and extended in 43, 38, 33, 34 and 9. In Figure 5, we show the results of the numerical simulation of the impact of a copper projectile immersed in air over a copper shield. Results are obtained using a fully parallel monolithic Cartesian method, based on a ${4000}^2$ fixed Cartesian grid. Simulations are performed on a cluster of 512 processors, and benefits from the isomorphism between grid partitioning and processor topology.

 

 

  

Impact simulation

In figure 6, we show the results of a three dimensional simulation of a cardiac pump (LVAD, left ventricule assisted device).

Cardiac pump simulation

5.1 Impact of research results

We are studying two types of green energy extractors: wave energy converters (WECs) and wind energy.

As regards WECs, we are working with the PoliTO (Torino, Italy) to model the behavior of inertial sea wave energy converters (ISWEC), and we are also working with a Bordeaux-based start-up for another device to extract energy from waves via an Inria-Tech project and a Nouvelle-Aquitaine Regional Project submitted by Memphis in collaboration with the CARDAMOM team.

As regards wind energy, we focus on the analysis of wind turbines. In the past, we have supervised two PhD CIFRE theses with VALOREM-Valeol, and are currently working with them in a European RISE ARIA project led by Memphis. We also work with IFPEN on the aeroelastic modeling of large wind turbines and the study and optimization of turbines farms in the framework of the joint laboratory Inria-IFPEN with a thesis funded by IFPEN and a post-doc funded by Inria (which started in October 2021).

In conjunction with these activities, in collaboration with ANDRA (the national agency for storage of nuclear waste), we investigated the development of reduced-order models to allow efficient and accurate simulations for deep geological storage planning. This activity was the subject of the PhD thesis of Giulia Sambataro who successfully defended her PhD thesis in December 2022.

7.1 New software

8.1 Component-based model order reduction for radioactive waste management

Participants: Angelo Iollo, Giulia Sambataro, Tommaso Taddei.

At the end of their cycle, radioactive materials are placed in arrays of cylindrical boreholes (dubbed alveoli) deep underground; due to the large temperatures of the radioactive waste, the thermal flux generated by the alveoli drives a complex time-dependent phenomenon which involves the thermal, hydraulic and mechanical (THM) response of the medium. The role of simulations is to predict the long-term system response and ultimately assess the impact of the repository site to the surrounding areas: Figure 8(a) shows a typical system configuration considered for numerical investigations.

Due to the complex nature of the equations (a system of five coupled nonlinear time-dependent three-dimensional equations) and due to the uncertainty in several parameters of the model and on boundary conditions, MOR techniques are important to reduce the computational burden associated with thorough parametric studies. In particular, it is important to study the system behavior for different numbers of alveoli: it is possible to show that changing the number of alveoli induces a change in the topology of the problem and thus prevents the application of standard monolithic MOR techniques developed for fixed domains or diffeomorphic families of parametric domains. We should thus devise component-based MOR procedures that are compatible with topology changes.

The PhD project of Giulia Sambataro aimed to devise a rapid and reliable component-based MOR technique for THM systems, for radioactive waste management applications. During the first year of her PhD, Giulia developed a monolithic MOR technique for THM systems which relies on a POD-Greedy algorithm to sample the parameter domain and to hyper-reduction based on empirical quadrature to reduce online prediction costs. During the second and third year, Giulia developed a component-based MOR formulation — which is dubbed one-shot overlapping Schwartz (OS2) method — for nonlinear steady PDEs and finally she extended the approach to THM systems with varying numbers of alveoli.

Giulia successfully defended her PhD thesis in December 2022; her work led to the publication of two articles on peer-reviewed journals, 40 and 15. Figure 8(b) shows the temporal behavior of the HF and predicted pressure and temperature in a select point in the proximity of one alveolus for an out-of-sample configuration. We observe that the ROM is able to adequately predict the solution behavior; in our numerical experiments, we experienced an average 20x speed-up over the range of configurations.

HM model problem

8.2 Registration methods for advection-dominated PDEs

Participants: Angelo Iollo, Tommaso Taddei.

A major issue of state-of-the-art MOR techniques based on linear approximation spaces is the inability to deal with parameter-dependent sharp gradients, which characterize the solutions to advection-dominated problems. To address this issue, we propose a registration technique to align local features in a fixed reference domain. In computer vision and pattern recognition, registration refers to the process of finding a transformation that aligns two datasets; here, registration refers to the process of finding a parametric spatio-temporal transformation that improves the linear compressibility of the solution manifold.

A registration procedure has been proposed in 45 and then further developed in 47, 46, 36. In particular, in 47, we considered the application to one-dimensional applications in hydraulics; in an ongoing collaboration with EDF, we aim to extend the approach to two-dimensional steady and unsteady problems. Figure 9 shows results for a Saint-Venant problem (flow past a bump): Figures 9(a) and 9(b) show the free surface $z$ for two different parameters and two time instants, while Figure 9(c) shows the behavior of the out-of-sample projection error associated with a snapshot-based POD space with and without registration. We observe that registration is key to improve performance of linear compression strategies such as POD.

$t=1.5$

$t=3$

$t=3$

Space time registration

In 41, Iollo and Taddei proposed a general (i.e., independent of the underlying PDE) nonlinear interpolation technique based on optimal transportation of Gaussian models of coherent structures of the flow.

In 31, Cucchiara et al. extended such a technique to deal with multi-dimensional parameter domains and with datasets of several snapshots. The method of 41 relies on optimal transportation to perform accurate nonlinear interpolations between two solution snapshots. The method of 31 combines a boundary-aware registration procedure with a regression technique to properly exploit datasets with more than two snapshots for interpolation and to cope with multi-dimensional parameter domains. See the Highlights section 6 for more information.

8.3 Aortic aneurysms: automatic segmentation and registration

Participants: Angelo Iollo, Gwlady Ravon, Sebastien Riffaud, Ludovica Saccaro.

In 37, we developed a new artificial neural network to automatically segment aortic aneurysm. The main idea with this approach was to consider each pixel of the image individually and to see if a model could learn how to categorize it as lumen only from its own intensity and the intensity of its 26 neighbors. We tested different inputs (values, means, variances...) and architectures: a sequential model was retained. For the input, each sample is a vector of 27 intensity values. Only pixels whose intensity is between 100 and 700 are kept for training and prediction.

The second axis of development concerned registration. In her PhD, Ludovica Saccaro presents several complete and automated working pipelines for clinical applications, for the pathology of abdominal aortic aneurysm. Her work is based on a mathematical modeling of aneurysm geometry, used for registration, risk assessment using a reduced modeling approach, and a generative algorithm. First, she introduced the geometric modeling technique, using B-spline functions and Fourier series for modeling. The geometric modeling presented in this work ensures the isolation of the aortic vessel, even in the presence of secondary vessels, while smoothing and regularizing its shape. The entire modeling process is automated, making it a crucial step for clinical support in aneurysm pathology. It aims to ensure that different geometrical shapes are comparable in a mathematical sense. To highlight the practical application, she integrated the modeling into a registration pipeline for clinical diagnosis and follow-up, providing automated tools for quantitative measurement and qualitative indication of disease progression by mathematically standardizing the aneurysm shape. Looking ahead, the registration pipeline could track the entire pathology, enabling close monitoring of patient-specific aneurysm evolution for valuable data in population studies, prevention and surgical planning. Then, she extended the use of the modeling as a basis for hemodynamic simulations, aiming to create a pipeline for constructing a projection space to assess abdominal aneurysm risk. The space created is meant to be used in a predictive sense, namely to derive hemodynamical quantities solely from geometry, to maintain the patient-specific approach, and on a dataset of previous simulations. The same procedure could be applied to other indicators, such as the pressure field or the WSS, as the choice of the indicator does not impact any steps in the proposed procedure, which remains a key achievement of our work. The limited accuracy of the approximated fields is partly due to the lack of a large amount of data, and the absence of personalized boundary conditions for each patient. In this context, she also proposed an automated pipeline that starts from the geometrical modeling and outputs synthetic aneurysm shape, by creating a mathematical space for modeling aortic aneurysms, using reduced-order model techniques. This part of the work is of interest since in clinical settings datasets are often scarce, and synthetic data emerged as a promising solution.

The PhD thesis of Ludovica Saccaro is expected to be defended in February 2023. A paper is in preparation.

Aneurysm geometries

Aneurysm geometries

8.4 Model reduction for aerodynamic applications

8.4.1 Deep learning wall laws for aerodynamic simulations

Participants: Michel Bergmann, Thomas Philibert, Angelo Iollo, Michele Romanelli.

The availability of reliable and accurate wall laws is one of the main challenges of modern Computational Fluid Dynamics (CFD). Wall models are mandatory for the application of large-scale turbulence (LES) simulations for flows representative of aeronautical applications, and they are also indispensable for Reynolds-Averaged-Navier-Stokes (RANS) simulations, either when using immersed boundary methods (IBM) methods, or for the implementation of light calculations useful for parametric studies, flow control or shape optimization, where multiples simulations are often required and the cumulative computational cost can become prohibitive. Wall laws help to lighten the computational load by replacing the resolution of the parietal flow (typically the most densely meshed zone) with a model. Given the complexity of phenomena that can be modeled thanks to the flexibility of neural networks neural networks, these methods show undeniable potential in their application to the modelling of flows.

The research objective is to propose a wall law based on deep learning algorithms applicable within the framework of Reynolds-Averaged-Navier-Stokes (RANS) simulations, outperforming conventional models in terms of accuracy and generality. In addition, the exploratory nature of this study aims to identify input quantities that would enable more reliable modeling of boundary layer development. A novel approach inspired by the Dirichlet-to-Neumann map is proposed, directly imposing viscous flow across the interface between the modeled region and RANS calculations. This involves a model composed of two interconnected neural networks: the first estimating viscous shear stress, and the second evaluating the wall-normal derivative of the velocity field. Both neural networks are trained using dimensionless data extracted from RANS simulations of flow over 2D bumps. Evaluating the model's performance involves comparing simulations with wall modeling to fully-solved calculations for flow configurations (over bumbs and airfoils) not encountered during neural network training. The robustness and accuracy of the wall model are evident in testing, demonstrating an ability to reproduce the friction coefficient with only a minimal error across all tested cases.

wall law

8.5 Projection-based model order reduction for parametric quasi-static nonlinear mechanics using an open-source industrial code

Participants: Eki Agouzal, Michel Bergmann, Tommaso Taddei.

In 11, we proposed a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables; the methodology is integrated in the industrial finite element code Code Aster. We developed an adaptive algorithm based on a POD-Greedy strategy, and we developed an hyper-reduction strategy based on an element-wise empirical quadrature, in order to speed up the assembly costs of the ROM by building an appropriate reduced mesh. We introduced a cost-efficient error indicator which relies on the reconstruction of the stress field by a Gappy-POD strategy. We presented numerical results for a three-dimensional elastoplastic system in order to illustrate and validate the methodology.

This approach was then extended to a multi-modeling industrial test-case 25. More specifically, we looked at a standard section of a power plant containment, consisting of reinforced concrete. Such numerical simulations involve a multi-modeling approach: a three-dimensional nonlinear thermo-hydro-visco-elastic rheological model is used for concrete; and prestressing cables are described by a one-dimensional linear thermo-elastic behavior. The methodology is validated on the fields and quantities of interest specific to engineers for this type of problem, on a mesh used in real-world engineering simulations.

8.6 Efficient Simulation of Wave Energy Converters

Participants: Beatrice Battisti, Michel Bergmann, Umberto Bosi, Giovanni Bracco, Martin Parisot.

In response to the evolving energy landscape, the marine sector is exploring wave energy converters (WECs) for clean energy generation. The deployment of WECs in farms is crucial for achieving commercial-scale production, necessitating preliminary numerical simulations due to complex hydrodynamics. Although conventional high-fidelity simulations are resource-intensive, they are essential for accurately capturing the complexities of highly nonlinear phenomena.

On the one hand, Beatrice Battisti (PhD student), Giovanni Bracco and Michel Bergmann works on a methodology that integrates a high-fidelity solver (CFD) for the near-field representation of floaters with a Reduced-Order Model (ROM) for far-field wave propagation. Information exchange between the two models occurs bidirectionally. From the CFD to the ROM models, information passes through the violet zones in Figure 13: a minimization problem is solved to determine the ROM solution that best approximates the high-fidelity solution in that region. Subsequently, the ROM solution is transmitted to the CFD as high-fidelity boundary conditions, considering the incoming wave. Through testing under various flow conditions and with a floating body, this methodology demonstrates accurate flow reconstruction and a comprehensive description of floater dynamics. In Figure 14, translations and forces acting on the body are depicted. The coupled model results (hf+POD) are illustrated for an in-sample reconstruction and an out-of-sample case, where snapshots from simulations of two different waves are utilized to obtain results for the test wave. The reference is the outcome from the high-fidelity simulation of the test wave across the entire domain (HF). The coupled model significantly reduces computational costs, thereby streamlining optimization and design processes for wave energy converter farms. One paper is in preparation.

On the other hand, Umberto Bosi (post-doc), Michel Bergmann and Martin Parisot (Inria CARDAMOM) proposed a novel approach to simulate wave energy converters and their interactions with wave dynamics (paper in preparation). It couples a low performance, high fidelity Navier Stokes (NS) model that simulated the converter with the faster performances of asymptotic models such as Boussinesq (B) models for wave propagation. This approach allows to well capture the highly nonlinear and complex effects close to the structure thanks to the NS model and efficiently propagate the waves between structures such that even wave energy converters farm can be simulated precisely. They have demonstrated that their coupling approach, inspired by the perfectly matched layer technique, permits the transmission of waves from the B domain to the NS one without loss of informations. Moreover, reproducing the experiences of Beji and Battjes (1993) and Liu et al. (2019) of wave passing over a submerged hill, they have shown that the resulting waves preserve more informations on nonlinearities that a non coupled Boussinesq model.

9.1 Bilateral contracts with industry

• Contrat accompagnement Cifre Ingeliance (M. Truel) - du 01/05/2023 au 30/04/2026
• Contrat accompagnement EDF (E. Agouzal) - du 01/04/2021 au 30/03/2024
• Contrat accompagnement IFPEN (C. Le Guern) - du 01/12/2021 au 30/11/2024

10.1 International initiatives

10.2 International research visitors

10.3 European initiatives

10.4 National initiatives

• ANR (national agency for research funding) DRAGON2.
  • Principal investigators: Michel Bergmann.
  • Partners: CNRS/Université de Poitiers/Inria. 27 k€+ 1 PhD.
  • Summary: The goal is study the aquatic swimming a several snakes using biomimetism and bioinspiration. In this project, we have experimental data for snake swimming, and we are building a numerical twin to compute integral quantities like the efficiency. Reinforcement learning is also considered to optimize the snake swimming.
• ANR (national agency for research funding) RedLum.
  • Principal investigators: Tommaso Taddei.
  • Partners: Team ACTA at INRAE Rennes.
  • Summary: REDLUM is a joint project between the team ACTA at INRAE Rennes and the team MEMPHIS at Inria Bordeaux; the project will fund a PhD thesis in October 2024: the selected student will join team MEMPHIS in Bordeaux and will work closely with the other partners of the project. The objective of REDLUM is to develop a model reduction procedure for turbulent flows with unknown boundary conditions; the ultimate goal is to devise a rapid and reliable simulation tool to tackle real-time data assimilation tasks in agricultural sciences. The distinctive methodological feature of the approach that we wish to develop is a stochastic closure model to adequately approximate the dynamics of the low-dimensional coherent structures of the system.
• Inria Exploratory Action: AM2OR (Adaptive meshes for model order reduction).
  • Principal investigators: Nicolas Barral (Inria team: Cardamom), Tommaso Taddei. 14 k€+ 1 PhD + 1 PostDoc.
  • Summary: Mesh adaptation and model order reduction both aim at reducing significantly the computational cost of numerical simulations by taking advantage of the solution's features. Model order reduction is a method that builds lighter surrogate models of a system's response over a range of parameters, which is particularly useful in the solution of design and optimization inverse problems. Reduced-order models rely on a high-fidelity (e.g., finite element) approximation that should be sufficiently accurate over the whole range of parameters considered: in presence of structures such as shocks and boundary layers, standard mesh refinement techniques would lead to high-fidelity models of intractable size. In this project, we propose a novel adaptive procedure to simultaneously construct a high-fidelity mesh (and associated discretisation) and a reduced-order model for a range of parameters, with particular emphasis on inverse problems in computational fluid dynamics.

10.5 Regional initiatives

Chaire Onera-Nouvelle Aquitaine PROpulsion Verte (PROVE)

• Duration: 2022-2027

• Summary: The Chair is dedicated to the development of reduced models at the crossroads between PDE modelling and machine learning, with application to aerodynamics for propulsion. The Chair has 6 PhD students, 2 post-docs and a budget for research activities (internships, missions). 4 theses have already been launched. The Chair has a budget of 1.2M€.

  The project is led by Dr. Denis Sipp at ONERA and Prof. Angelo Iollo at INRIA Bordeaux.

11.1 Promoting scientific activities

11.2 Teaching - Supervision - Juries

11.3 Popularization

12.1 Major publications

• 1 articleE.E. Abbate, A.A. Iollo and G.G. Puppo. An all-speed relaxation scheme for gases and compressible materials.Journal of Computational Physics3512017, 1-24HALDOI
• 2 articleL.Luis Benetti Ramos, O.Olivier Marquet, M.Michel Bergmann and A.Angelo Iollo. Fluid--solid Floquet stability analysis of self-propelled heaving foils.Journal of Fluid Mechanics9102021, A28HALDOI
• 3 articleM.M. Bergmann, C.-H.Charles-Henri Bruneau and A.A. Iollo. Enablers for robust POD models.Journal of Computational Physics22822009, 516--538
• 4 articleM.M. Bergmann, J.J. Hovnanian and A.A. Iollo. An accurate cartesian method for incompressible flows with moving boundaries.Communications in Computational Physics1552014, 1266--1290back to text
• 5 articleM.M. Bergmann and A.A. Iollo. Bioinspired swimming simulations.Journal of Computational Physics3232016, 310 - 321
• 6 articleM.M. Bergmann and A.A. Iollo. Modeling and simulation of fish-like swimming.Journal of Computational Physics23022011, 329 - 348
• 7 articleF.F. Bernard, A.A. Iollo and G.G. Puppo. Accurate Asymptotic Preserving Boundary Conditions for Kinetic Equations on Cartesian Grids.Journal of Scientific Computing2015, 34
• 8 articleA.A. Bouharguane, A.A. Iollo and L.L. Weynans. Numerical solution of the Monge--Kantorovich problem by density lift-up continuation.ESAIM: Mathematical Modelling and Numerical Analysis4961577November 2015
• 9 articleA.A. De Brauer, A.A. Iollo and T.T. Milcent. A Cartesian Scheme for Compressible Multimaterial Models in 3D.Journal of Computational Physics3132016, 121-143back to text
• 10 articleF.F. Luddens, M.M. Bergmann and L.L. Weynans. Enablers for high-order level set methods in fluid mechanics.International Journal for Numerical Methods in Fluids79December 2015, 654-675

12.2 Publications of the year

12.3 Cited publications

• 32 articleP.P. Angot, C.-H.Charles-Henri Bruneau and P.P. Fabrie. A penalization method to take into account obstacles in a incompressible flow.Numerische Mathematik8141999, 497-520back to text
• 33 articleP.P.T. Barton, D.D. Drikakis, E.E. Romenski and V.V.A. Titarev. Exact and approximate solutions of Riemann problems in non-linear elasticity.Journal of Computational Physics228182009, 7046-7068back to text
• 34 articleA. D.A. De Brauer, A.A. Iollo and T.T. Milcent. A Cartesian scheme for compressible multimaterial models in 3D.Journal of Computational Physics3132016, 121-143URL: http://www.sciencedirect.com/science/article/pii/S0021999116000966DOIback to text
• 35 articleB.B Cantwell and D.D Coles. An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder.Journal of fluid mechanics1361983, 321--374back to text
• 36 articleA.Andrea Ferrero, T.Tommaso Taddei and L.Lei Zhang. Registration-based model reduction of parameterized two-dimensional conservation laws.Journal of Computational Physics4572022, 111068URL: https://www.sciencedirect.com/science/article/pii/S0021999122001309DOIback to text
• 37 articleA. I.A. Iollo G. Ravon and C.C. Caradu. Automatic Rigid Registration of Aortic Aneurysm Arterial System.March 2022HALback to text
• 38 articleS.S.L. Gavrilyuk, N.N. Favrie and R.R. Saurel. Modelling wave dynamics of compressible elastic materials.Journal of Computational Physics22752008, 2941-2969back to text
• 39 bookS.S.K. Godunov. Elements of continuum mechanics.Nauka Moscow1978back to text
• 40 articleA.Angelo Iollo, G.Giulia Sambataro and T.Tommaso Taddei. An adaptive projection-based model reduction method for nonlinear mechanics with internal variables: Application to thermo-hydro-mechanical systems.International Journal for Numerical Methods in Engineering123122022, 2894-2918URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6964DOIback to text
• 41 articleA.Angelo Iollo and T.Tommaso Taddei. Mapping of coherent structures in parameterized flows by learning optimal transportation with Gaussian models.Journal of Computational Physics4712022, 111671URL: https://www.sciencedirect.com/science/article/pii/S0021999122007343DOIback to textback to textback to textback to text
• 42 phdthesisX.X Jin. Construction d'une chaîne d'outils numériques pour la conception aérodynamique de pales d'éoliennes.Université de Bordeaux2014back to text
• 43 articleG.G.H. Miller and P.P. Colella. A Conservative Three-Dimensional Eulerian Method for Coupled Solid-Fluid Shock Capturing.Journal of Computational Physics18312002, 26-82back to text
• 44 bookJ. A.J. A. Sethian. Level Set Methods and Fast Marching Methods.Cambridge University Press, Cambridge, UK1999back to text
• 45 articleT.Tommaso Taddei. A registration method for model order reduction: data compression and geometry reduction.SIAM Journal on Scientific Computing4222020, A997--A1027back to text
• 46 articleT.Tommaso Taddei and L.Lei Zhang. Registration-based model reduction in complex two-dimensional geometries.submitted to Journal of Scientific Computing2021back to text
• 47 articleT.Tommaso Taddei and L.Lei Zhang. Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs.ESAIM: Mathematical Modelling and Numerical Analysis (accepted)2020back to textback to text