Publications HAL

2024

Pré-publication, Document de travail

titre: Derivation of the non-linear shallow water equations over unsaturated porous media: a discontinuous galerkin method for coarse-grained beaches
auteur: Camille Poussel, Mehmet Ersoy, Frederic Golay, Damien Sous
article: 2024
resume: This work will consider the physics of free-surface flow and groundwa- ter flow in a coupled model. Coupled models of such phenomena are not clearly justified, and there is a lack of precision in deriving such a model. The primary aim of this work is to derive a coupled model of Shallow Wa- ter Equations (SWE) and Richards’ Equation (RE) using asymptotic con- siderations. The numerical coupling chosen for the unified model will be explained as a parallel coupling. Additionally, numerical considerations on how to solve this model using Discontinuous Galerkin (DG) methods will be provided. Furthermore, explanations will be given about how informa- tion is exchanged between the two models, which are time-synchronized. The solution of RE coupled with SWE using the mentioned procedure with DG formulation is implemented in RIVAGE (an in-house numerical code based on discontinuous Galerkin method), which is then tested on a numerical problem and validated against an experimental benchmark.
typdoc: Pré-publication, Document de travail
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titre: Estimation of optimal penalization parameters and convergence of the non-linear solver for a Richards' equation-based model for variably-saturated groundwater flows based on an IIPG Discontinuous Galerkin method
auteur: Camille Poussel, Mehmet Ersoy, Frederic Golay, Damien Sous
article: 2024
resume: In this article, we study the convergence of an IIPG (Incomplete Interior Penalty Galerkin) Discontinuous Galerkin numerical method for the Richards equation. The Richards equation is a degenerate parabolic nonlinear equation for modeling flows in porous media with variable saturation. The numerical solution of this equation is known to be difficult to calculate numerically, due to the abrupt displacement of the wetting front, mainly as a result of highly non-linear hydraulic properties. As time scales are slow, implicit numerical methods are required and the convergence of nonlinear solvers is very sensitive. We propose an original method to ensure convergence of the numerical solution to the exact Richards solution, using a technique of auto-calibration of the penalty parameters derived from the Galerkin Discontinuous method. The method is constructed using non-linear 1D and 2D general elliptic problems. We show that the numerical solution converges toward the unique solution of the continuous problem under certain conditions on the penalty parameters. Then, we numerically demonstrate the efficiency and robustness of the method through test cases with analytical solutions, laboratory test cases, and large-scale simulations.
typdoc: Pré-publication, Document de travail
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titre: WETTING AND DRYING TREATMENTS WITH MESH ADAPTATION FOR SHALLOW WATER EQUATIONS USING A RUNGE-KUTTA DISCONTINUOUS GALERKIN METHOD
auteur: Camille Poussel, Mehmet Ersoy, Frederic Golay
article: 2024
resume: This work is devoted to the numerical simulation of Shallow Water Equations involving dry areas, a moving shoreline and in the context of mesh adaptation. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares three treatments, one based on Slope Modification, one based on p-adaptation and the last one based on eXtended Finite Element methods and mesh adaptation.
typdoc: Pré-publication, Document de travail
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2023

Article dans une revue

titre: A Richards' equation-based model for wave-resolving simulation of variably-saturated beach groundwater flow dynamics
auteur: Jean-Baptiste Clément, Damien Sous, Frédéric Bouchette, Frédéric Golay, Mehmet Ersoy
article: Journal of Hydrology, 2023, 619, pp.129344. ⟨10.1016/j.jhydrol.2023.129344⟩
resume: This study introduces a model based on Richards' equation to describe variably-saturated beach groundwater flow. The surface wave propagation is computed by the phase-resolving non-hydrostatic SWASH code. The SWASH data are used to make a suitable dynamic boundary condition at the beach face to force Richards' equation. The latter is solved by a weighted discontinuous Galerkin method together with adaptive mesh refinement. The model is validated by comparison with a laboratory experiment of a transient water table recharge problem. Then, the BARDEX II prototype-scale experiment is considered to assess the model abilities for beach groundwater dynamics. The barrier beach is studied for three cases with different lagoon levels. Steady-state results with no-wave conditions show excellent agreement. Transient waves simulations are evaluated in terms of pressure heads, saturations, water table position and groundwater velocities for timeaveraged, swash-resolving and spectral analysis. Results bring interesting insights about beach groundwater modelling by comparison with the experimental data as well as a Darcy's equation-based model. A first investigation is carried out to assess the groundwater effect on the bed sediment dynamics through the modification of sediment relative weight.
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.jhydrol.2023.129344
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Communication dans un congrès

titre: A Level Set approach for non-spherical DEM in YADE
auteur: Jérôme Duriez, Stéphane Bonelli, Frederic Golay, Cedric Galusinski
article: 9th International Conference on Discrete Element Methods (DEM9), Sep 2023, Erlangen, Germany
resume: For the purpose of capturing realistic particle shapes in DEM, a Level Set (LS) approach (Kawamoto et al., 2016) can be chosen whereby particle's surface is implicitly defined as the zero-level set of a discrete distance-to-surface field. The latter can be obtained for virtually any shape thanks to e.g., Fast Marching Method algorithms, conferring an interesting versatility to the approach. As a second key ingredient, a surface discretization in terms of vertices is also defined from the distance field and ray tracing methods in order to execute contact detection through a master-slave algorithm whereby surface vertices of one Discrete Element are tested against the distance field of another. After implementation in the YADE open-source code (Duriez & Galusinski, 2021), the LS method is herein discussed considering different kinds of shape. The spherical case is first revisited as it enables one to validate the implementation by comparing to a classical DEM reference and measure its computational costs (Duriez & Bonelli, 2021). The LS approach is then illustrated to require around 100 times more memory (for storing the distance field, mostly) and time (for looping over surface vertices during the contact algorithm) than classical DEM. OpenMP parallelization is nevertheless shown to be beneficial for effectively reducing time costs and memory costs could also be optimized (Duriez & Galusinski, 2020). Then, a direct application of the LS approach is proposed to convex superquadrics (superellipsoids). Describing non-convex rock aggregates from 3D scans is also discussed.
typdoc: Communication dans un congrès
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Proceedings/Recueil des communications

titre: Runge-Kutta Discontinuous Galerkin Method Applied to Shallow Water Equations
auteur: Camille Poussel, Mehmet Ersoy, Frederic Golay, Yolhan Mannes
article: Topical Problems of Fluid Mechanics 2023, Institute of Thermomechanics of the Czech Academy of Sciences; CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics, pp.152-159, 2023, ⟨10.14311/TPFM.2023.021⟩
resume: This work is devoted to the numerical simulation of Shallow Water Equations using Runge-Kutta Discontinuous Galerkin methods. Such methods were implemented in the framework of adaptive mesh refinement method using a block-based approach. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Increasing the order of approximation, spurious oscillations appear and are addressed using moment limiters. Finally, the solver is validated with a one-dimensional dam-break problem and its behavior is tested solving a two-dimensional benchmark.
typdoc: Proceedings/Recueil des communications
DOI: DOI : 10.14311/TPFM.2023.021
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2022

Communication dans un congrès

titre: Field testing of the overflow erosion of Rhone river levees
auteur: Christophe Picault, Fabrice Crampette, Stéphane Bonelli, Sylvie Nicaise, Naïm Chaouch, Faustine Byron, Yves Grémeaux, Alexis Doghmane, Mathys Garoui, Jordan Herbeck, Frederic Golay
article: 4th Int Seminar on Dam Protections against Overtopping, Nov 2022, Madrid, Spain. pp.1-13
resume: It is important to quantify the soil resistance against erosion caused by the overflow of dikes and levees. Small-scale tests are not recommended, as they do not provide a correct representation of the actual soil in place and do not take into account the geometry of the structure. For this reason, the National Research Institute for Agriculture, Food and Environment (INRAE) developed an on-site overflow device in 2015. The procedure followed is based on ASTM-D6460 standard. Two tests were performed in May 2022 on a Compagnie Nationale du Rhône (CNR) dike near Avignon (France). The dike is 6.2 m high; the core is mainly made of sandy silts. The toe is covered by a gravel shoulder which forms a berm. The first test was carried out on the intact soil: the core covered by a natural grass on the upper part, and the gravel fill without grass in the lower part of the slope. The test consisted of carrying out a flow in a channel of 1 m wide and 25 m long, in 12 steps of 30 min (6 hours of flow in total). The second test was carried out on the soil stripped of the vegetation cover in order to study the soil of the upper part of the embankment, made up of compacted sandy silt and sandy gravel. The test consisted of carrying out a flow in a 60 cm wide and 20 m long channel, in 9 steps of 30 min (4.5 hours of flow in total). The test campaigns were carried out with flows ranging from 12 to 140 l/s per linear meter, corresponding to a crest water depth ranging from 4 to 18 cm. On test 1, no significant erosion of the natural grass cover was observed. A small erosion pit 20 cm deep was observed on the compacted gravel berm surface. A scour hole of approximately 1.10 m in depth for a volume of 4.2 m 3 was observed in the downstream gravel fill that cover the lower part of the embankment. On test 2, the compacted sandy silt layer was eroded a few centimeters by the surface flow. The sandy gravel layer was eroded from the first flow (5.7 cm of water height at the crest), which led to the beginning of a breach (deepening) over 10 m long, of 1.30 m maximum depth, 1.80 m maximum width and 9 m 3 of eroded soil. The first result of these in situ overflow tests is that not all of these observations were predictable from the erosion tests previously performed in the laboratory and in situ (Jet and Het erosion tests). The second result is the remarkable resistance of the natural grass cover.
typdoc: Communication dans un congrès
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titre: Modélisations numériques discrètes de matériaux granulaires à partir d'une description Level Set des particules
auteur: Jérôme Duriez, Cédric Galusinski, Frederic Golay, Stéphane Bonelli
article: 25e Congrès Français de Mécanique (CFM 2022), Aug 2022, Nantes, France
typdoc: Communication dans un congrès
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titre: A DISCRETE ELEMENT METHOD FOR GRANULAR SOLIDS WITH A LEVEL SET SHAPE DESCRIPTION
auteur: Jérôme Duriez, Cedric Galusinski, Frederic Golay, Stéphane Bonelli
article: The 8th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2022), Jun 2022, Oslo, Norway
typdoc: Communication dans un congrès
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titre: DEM capabilities with Polyhedral and Level Set shape descriptors
auteur: Jérôme Duriez, Tarek Mohamed, Stéphane Bonelli, Frederic Golay, Cedric Galusinski
article: IRN GeoMech workshop on hydromechanical instabilities, May 2022, Aix-en-Provence, France
resume: Geometrically realistic particles are getting more and more available in discrete (DEM) simulations thanks to a variety of dedicated DEM implementations, enabling one to properly address the known influence of particle shape in geomechanics [1]. In addition to the multi-sphere approach, whereby an appropriate number of overlapping spheres are clumped together and act as one rigid body, one can mention the possibility to define a particle's surface as a polyhedra with its set of vertices, edges and facets or through a Level Set description [2]. The latter relies on a discrete field for the signed distance function to the surface at hand, whose zero level set implicitly describes that surface. For the purpose of contact treatment, a surface discretization in terms of boundary nodes is deduced from the distance field and also enters the method as a second ingredient.
typdoc: Communication dans un congrès
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Poster de conférence

titre: Numerical simulation of flows in unsaturated porous media by an adaptive discontinuous Galerkin method: application to La Verne dam
auteur: Jean-Baptiste Clément, Frederic Golay, Damien Sous, Mehmet Ersoy
article: Topical Problems of Fluid Mechanics 2022, Feb 2022, Prague, Czech Republic. 2022
resume: Richards' equation is used to simulate flows in unsaturated porous media but it remains challenging to solve cost-effectively for complex cases. An adaptive strategy is proposed to deal with sharp wetting fronts. It is based on weighted discontinuous Galerkin methods and adaptive mesh refinement. The reservoir impoundment of La Verne dam is a demanding case because there are several materials, stiff hydraulic properties, dynamic boundary condition and seepage. The comparison of results with experimental data highlights the potential of the solving strategy.
typdoc: Poster de conférence
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2021

Article dans une revue

titre: An adaptive strategy for discontinuous Galerkin simulations of Richards’ equation: application to multi-materials dam wetting
auteur: Jean-Baptiste Clément, Frederic Golay, Mehmet Ersoy, Damien Sous
article: Advances in Water Resources, 2021, 151, pp.103897. ⟨10.1016/j.advwatres.2021.103897⟩
resume: Numerical solution of Richards’ equation remains challenging to get robust, accurate and cost-effective results, particularly for moving sharp wetting fronts. An adaptive strategy for both space and time is proposed to deal with 2D sharp wetting fronts associated with varying and possibly vanishing diffusivity caused by nonlinearity, heterogeneity and anisotropy. Adaptive time stepping makes nonlinear convergence reliable and backward difference formula provides high-order time scheme. Adaptive mesh refinement tracks wetting fronts with an a posteriori error indicator. The novelty of this paper consists in using this technique in combination with a weighted discontinuous Galerkin framework to better approximate steep wetting fronts by a discontinuity. The potential of the overall approach is shown through various examples including analytical and laboratory benchmarks and simulation of full-scale multi-materials dam wetting experiment.
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.advwatres.2021.103897
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2020

Article dans une revue

titre: Wave-driven Groundwater Flows in Sandy Beaches: A Richards Equation-based Model
auteur: Jean-Baptiste Clément, Damien Sous, Frederic Golay, Mehmet Ersoy
article: Journal of Coastal Research, 2020, Proceedings from the 16th International Coastal Symposium, Special issue 95, pp.1047-1051. ⟨10.2112/SI95-204.1⟩
resume: A groundwater model is developed to simulate flows under the swash zone of sandy beach. Variably saturated beach is described by Richards equation, which is solved by the Rivage code thanks to a discontinuous Galerkin method. The SWASH code is used to simulate wave propagation in nearshore waters and compute suitable boundary conditions at the beachface to force Richards equation. An idealized case is considered to investigate the beach groundwater response to the action of swash cycles associated with long IG-like waves: infiltration/ exfiltration, water table, hydraulic head and pore velocities are outlined. A good qualitative agreement is found with observations from experimental studies in the literature.
typdoc: Article dans une revue
DOI: DOI : 10.2112/SI95-204.1
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Communication dans un congrès

titre: Adaptive Discontinuous Galerkin Method for Richards Equation
auteur: Jean-Baptiste Clément, Frederic Golay, Mehmet Ersoy, Damien Sous
article: Topical Problems of Fluid Mechanics 2020, Feb 2020, Prague, Czech Republic. pp.27-34, ⟨10.14311/TPFM.2020.004⟩
resume: This paper deals with the numerical simulation of time-dependant flows in partially saturated porous media modelled by Richards equation. A Discontinuous Galerkin method together with an implicit scheme are used to approximate the solution. The mathematical framework and a procedure for solving this nonlinear equation are presented. In particular, treatment of seepage boundary condition and adaptive time step are underlined. An adaptive mesh refinement technique is also outlined in order to capture wetting front efficiently. Some numerical simulations are performed to illustrate the performance of the method.
typdoc: Communication dans un congrès
DOI: DOI : 10.14311/TPFM.2020.004
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2019

Communication dans un congrès

titre: Simulation numérique d’un essai de surverse
auteur: Sophie Jeuck, Gregory Charrier, Frederic Golay, Stéphane Bonelli
article: Digues Maritimes et Fluviales de Protection contre les Inondations, 2019, Mar 2019, Aix-en-Provence, France. ⟨10.5281/zenodo.2530076⟩
resume: Nous considérons une digue en terre soumise à un écoulement de surverse. La modélisation physique et numérique d’un tel phénomène est en général un compromis entre pertinence physique, précision numérique et temps de calcul. Nous nous sommes attachés à l’analyse de l’écoulement à surface libre caractéristique d’une surverse, éludant momentanément les phénomènes d’érosion et de transport sédimentaire qui seront inclus ultérieurement par couplage. L’hydrodynamique complexe associée à la surverse est traitée grâce à un modèle bi-fluide Eulérien à faible nombre de Mach. Ce modèle bi-fluide, non visqueux et faiblement compressible est physiquement plus pertinent que des modèles de type Saint-Venant généralement utilisés. En effet, on observe dans l’écoulement des jets et des recirculations plus facilement appréhendés par un modèle diphasique. Ce modèle est évidemment moins riche qu’un modèle de Navier-Stokes avec ou sans turbulence, mais sa formulation permet des simulations tridimensionnelles beaucoup plus économes en temps de calcul pour une représentation hydrodynamique réaliste. En effet, la formulation hyperbolique du problème à résoudre autorise l’utilisation d’un solveur volumes finis explicite parallèle rapide. Ce solveur bénéficie d’un outil de raffinement dynamique de maillage par blocs sur critère de production numérique d’entropie, qui permet d’optimiser le nombre d’inconnues, et donc le temps de calcul, tout en augmentant la précision de la simulation dans les zones d’intérêt. Ce modèle est appliqué à l’étude de la surverse d’une digue expérimentale. Le parement aval de la digue est considéré lisse ou bien avec un profil en marches représentatif des observations expérimentales. Grâce au raffinement dynamique de maillage, l’établissement de l’écoulement est simulé rapidement. Puis, lorsque l’écoulement stationnaire est atteint, les hauteurs et champs de vitesse sont confrontés avec succès à quelques mesures expérimentales. Ces résultats sont également comparés avec des simulations réalisées avec un code commercial utilisant un modèle Navier-Stokes diphasique avec turbulence k-ωSST.
typdoc: Communication dans un congrès
DOI: DOI : 10.5281/zenodo.2530076
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titre: Discontinuous Galerkin Method for Steady-State Richards Equation
auteur: Jean-Baptiste Clément, Mehmet Ersoy, Frederic Golay, Damien Sous
article: Topical Problems of Fluid Mechanics 2019, Feb 2019, Prague, Czech Republic. pp.53-62, ⟨10.14311/TPFM.2019.008⟩
resume: This work is devoted to the numerical simulation of flows in partially saturated porous media. We describe the Richards equation governing the subsurface flow and discuss its range of applicability. A discontinuous Galerkin formulation is used to approximate the steady-state Richards equation. To this end, we present the mathematical framework and a procedure for solving the nonlinear equation. Numerical tests are carried out to highlight properties of the discontinuous Galerkin method and a test case is compared to experimental data to validate the model.
typdoc: Communication dans un congrès
DOI: DOI : 10.14311/TPFM.2019.008
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2018

Communication dans un congrès

titre: Monolithic Fluid Structure Interaction Model, Application to Water Entry Problem
auteur: Frederic Golay
article: Topical Problems of Fluid Mechanics 2018, Feb 2018, Prague, Czech Republic. ⟨10.14311/TPFM.2018.016⟩
resume: We consider the interaction between an air-water flow and a rigid structure using a fast accurate numerical model. Following the 3D low Mach compressible Euler model previously developed and validated, a compressible fluid-structure interaction model is proposed. In the context of a fictitious domain, a volumic penalization is applied inside the body to ensur a rigidity constraint through a penalized velocity in order to get the correct motion of the rigid body. The accuracy of this simple model is improved using block-based adaptive mesh refinement technique. The improvement and the validity of our fluid-structure interaction procedure is investigated through the numerical simulation of the water entry of a cylinder freely falling and impacting the water. This test case is compared to experimental data and other numerical simulations.
typdoc: Communication dans un congrès
DOI: DOI : 10.14311/TPFM.2018.016
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2017

Communication dans un congrès

titre: Adaptive Mesh Refinement Method Applied to Shallow Water Model: A Mass Conservative Projection
auteur: Kévin Pons, Frederic Golay, R. Marcer
article: Topical Problems of Fluid Mechanics 2017, Feb 2017, Prague, Czech Republic. ⟨10.14311/TPFM.2017.032⟩
resume: In the tsunami waves context, efficient numerical methods are necessary to simulate multiscales events. One way to reduce the computational cost is to use an adaptive mesh refinement method on unstructured meshes. This approach is used in this paper with a finite volume scheme solving the multi-dimensional Saint-Venant system. The adaptive mesh refinement method follows a block-based decomposition (called BB-AMR), which allows quick meshing and easy parallelization. One step of the AMR method is the so-called projection step where the new mesh values have to be defined from the old ones. For vertically integrated model the bathymetry variation during the projection step plays a crucial role on the mass conservation. To avoid large deficit or excess of mass a special attention is given to the projection step. Finally a 3D test case simulation is compared to experimental results to illustrated the quasi conservation of the mass with an appropriated projection method.
typdoc: Communication dans un congrès
DOI: DOI : 10.14311/TPFM.2017.032
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2016

Article dans une revue

titre: Numerical investigation of BB-AMR scheme using entropy production as refinement criterion
auteur: Thomas Altazin, Mehmet Ersoy, Frederic Golay, Damien Sous, Lyudmyla Yushchenko
article: International Journal of Computational Fluid Dynamics, 2016, ⟨10.1080/10618562.2016.1194977⟩
resume: In this work, a parallel finite volume scheme on unstructured meshes is applied to fluid flow for multidimensional hyperbolic system of conservation laws. It is based on a block-based adaptive mesh refinement strategy which allows quick meshing and easy parallelisation. As a continuation and as an extension of a previous work, the useful numerical density of entropy production is used as mesh refinement criterion combined with a local time-stepping method to preserve the computational time. Then, we numerically investigate its efficiency through several test cases with a confrontation with exact solution or experimental data.
typdoc: Article dans une revue
DOI: DOI : 10.1080/10618562.2016.1194977
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Communication dans un congrès

titre: A 3D unified model to Fluid-Structure Interaction with Block Based Adaptive Mesh Refinement
auteur: Thomas Altazin, Frederic Golay, Philippe Fraunié
article: Topical problems of fluid mechanics, Feb 2016, prague, Czech Republic
resume: We propose to bring a better understanding of the interaction between an air-water flow and a floating structure by means of a fast accurate numerical model. Following the 3D low Mach compressible Euler model developed in [14] and previous works from [20], [11] and [13], we are now interested in simulating the motion of a floating structure in an air-water flow. In the context of a fictitious domain, a volumic penalization is applied inside the body to ensure a rigidity constraint through a penalized velocity in order to get the correct motion of the rigid body. The tracking of the solid is insured by the reconstruction of a Heaviside function thanks to a ray-casting algorithm. The validity of our fluid-structure interaction (FSI) procedure is investigated through some examples.
typdoc: Communication dans un congrès
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Pré-publication, Document de travail

titre: Adaptive mesh refinement method. Part 2: Application to tsunamis propagation
auteur: Kévin Pons, Richard Marcer, Mehmet Ersoy, Frederic Golay, Richard Marcer Principia
article: 2016
resume: Numerical simulations of multi dimensional large scale fluid-flows such as tsunamis, are still nowadays a challenging and a difficult problem. To this purpose, a parallel finite volume scheme on adaptive unstructured meshes for multi dimensional Saint-Venant system is presented. The adaptive mesh refinement method is based on a block-based decomposition (called BB-AMR) which allows quick meshing and easy parallelization. The main difficulty addressed here concerns the selection of the mesh refinement threshold which is certainly the most important parameter in the AMR method. Usually, the threshold is calibrated according to the test problem to balance the accuracy of the solution and the computational cost. To avoid " hand calibration " , we apply an automatic threshold method based on the decreasing rearrangement function of the mesh refinement criterion. This method is applied and validated successfully to the one and two dimensional non homogeneous Saint-Venant system through several tsunamis propagation test cases.
typdoc: Pré-publication, Document de travail
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2015

Article dans une revue

titre: Validation of CFD models for tsunami simulation. TANDEM Projec
auteur: Richard Marcer, Kévin Pons, Camille Journeau, Frederic Golay
article: Revue Paralia, 2015, 8 (4), pp.6. ⟨10.5150/revue-paralia.2015.n04⟩
typdoc: Article dans une revue
DOI: DOI : 10.5150/revue-paralia.2015.n04
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titre: Block-based adaptive mesh refinement scheme using numerical density of entropy production for three-dimensional two-fluid flows
auteur: Frederic Golay, Mehmet Ersoy, Lyudmyla Yushchenko, Damien Sous
article: International Journal of Computational Fluid Dynamics, 2015, ⟨10.1080/10618562.2015.1012161⟩
resume: In this work, we present a fast and parallel finite volume scheme on unstructured meshes applied to complex fluid flow. The mathematical model is based on a three-dimensional compressible low Mach two-phase flows model, combined with a linearised ‘artificial pressure’ law. This hyperbolic system of conservation laws allows an explicit scheme, improved by a block-based adaptive mesh refinement scheme. Following a previous one-dimensional work, the useful numerical density of entropy production is used as mesh refinement criterion. Moreover, the computational time is preserved using a local time-stepping method. Finally, we show through several test cases the efficiency of the present scheme on two- and three-dimensional dam-break problems over an obstacle.
typdoc: Article dans une revue
DOI: DOI : 10.1080/10618562.2015.1012161
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titre: Entropy production and mesh refinement – Application to wave breaking
auteur: Lyudmyla Yushchenko, Frederic Golay, Mehmet Ersoy
article: Mechanics & Industry, 2015, 16 (3), pp.5. ⟨10.1051/meca/2015003⟩
resume: We propose an adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). Thus it is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solutions remain smooth. Nevertheless, due to the CFL stability condition the time step is restricted and leads to time consuming simulations. Therefore, we propose a local time stepping algorithm. This approach is validated in the case of classical 1D numerical tests. Then, we present a 3D application. Indeed, according to an eulerian bi-fluid formulation at low Mach, an hyperbolic system of conservation laws allows an easily parallelization and mesh refinement by “blocks”.
typdoc: Article dans une revue
DOI: DOI : 10.1051/meca/2015003
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titre: Modélisation numérique de l'érosion pendant un essai d'érosion de conduit
auteur: Florian Mercier, Stéphane Bonelli, Frederic Golay, F. Anselmet, P. Philippe, R. Borghi
article: Acta Geotechnica, 2015, 10 (3), pp.319-332. ⟨10.1007/s11440-014-0349-5⟩
resume: This study focuses on the numerical modelling of concentrated leak erosion of a cohesive soil by a turbulent flow in axisymmetrical geometry, with application to the Hole Erosion Test (HET). The numerical model is based on adaptive remeshing of the water/soil interface to ensure accurate description of the mechanical phenomena occurring near the soil/water interface. The erosion law governing the interface motion is based on two erosion parameters: the critical shear stress and the erosion coefficient. The model is first validated in the case of 2D piping erosion induced by a laminar flow. Then, the numerical results are compared with the interpretation model of the Hole Erosion Test. Three HETs performed on different soils are modelled with a rather good accuracy. Lastly, a parametric analysis of the influence of the erosion parameters on erosion kinetics and evolution of channel diameter is conducted. Finally, after this validation by comparison with both the experimental results and the interpretation of Bonelli et al. [2], our model is now able to reproduce accurately the erosion of a cohesive soil by a concentrated leak. It also gives access to a detailed description of all the averaged hydrodynamic flow quantities. This detailed description is essential in order to achieve a better understanding of the erosion processes.
typdoc: Article dans une revue
DOI: DOI : 10.1007/s11440-014-0349-5
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Communication dans un congrès

titre: Discrete Duality Finite Volume applied to soil erosion
auteur: Jalal Lakhlili, Cedric Galusinski, Frederic Golay
article: congres français de mécanique, Aug 2015, Lyon, France
typdoc: Communication dans un congrès
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titre: Calculs CFD de propagation et d’impact de vague en zone côtière Projet TANDEM
auteur: Kévin Pons, Camille Journeau, Richard Marcer, Frederic Golay
article: Rencontres Universitaires de Génie Civil, May 2015, Bayonne, France
resume: RÉSUMÉ. Dans le cadre du projet TANDEM -Tsunamis en Atlantique et MaNche : Définition des Effets par Modélisation- une première phase de l'étude a pour but (pour Principia) de qualifier différents modèles CFD (Computational Fluid Dynamics) 3D pour la simulation de tsunamis. Un premier modèle (code EOLE) résout un écoulement bi-fluide 3D couplé avec une méthode de reconstruction de type VOF, sur des maillages structurés multi-blocs. Un autre modèle (code EOLENS) basé sur une approche de capture d'interface, utilise des maillages non-structurés. Cet article présente, pour différents cas tests académiques de propagation de vagues et de run-up en zone côtière, des comparaisons entre simulations et données expérimentales. Les résultats obtenus sur ces cas-tests sont dans l'ensemble satisfaisants et démontrent tout le potentiel de ces deux codes pour simuler en situation réelle l'impact côtier 3D d'un tsunami.
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titre: Discrete Duality Finite Volume applied to soil erosion
auteur: Jalal Lakhlili, Cedric Galusinski, Frederic Golay
article: Topical Problems of Fluid Mechanics, Feb 2015, prague, Czech Republic. pp.97-104
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2014

Article dans une revue

titre: 2D axisymmetrical numerical modelling of the erosion of a cohesive soil by a submerged turbulent impinging jet
auteur: Fabienne Mercier, Frederic Golay, Stéphane Bonelli, Fabien Anselmet, Roland Borghi, Pierre Philippe
article: European Journal of Mechanics - B/Fluids, 2014, 45, pp.36-50. ⟨10.1016/j.euromechflu.2013.12.001⟩
resume: This study focuses on 2D Computational Fluid Dynamics (CFD) numerical modelling of the erosion of a cohesive soil by a circular impinging turbulent jet. Initially, the model is validated in the case of a non erodible flat plate. Several turbulence models are compared to experimental results and to simplified formulas available in the literature. The results obtained show that the Reynolds Stress Model (RSM) is in good agreement with the semi-empirical results in the literature. Nonetheless, the RSM cannot be used with successive remeshings, due to its convergence issues. The shear stress at the wall is well-described by the k-ε model while the pressure is better-described by the k-ω model. The numerical model of erosion is based on adaptive remeshing of the water/soil interface to ensure the good precision of the mechanical values at the wall. The two erosion parameters are the critical shear stress and the erosion coefficient. The results obtained are compared with the semi-empirical model interpreting the Jet Erosion Test. The k-ε model underestimates the shear stress and does not allow simulation of the entire erosion process, whereas the results obtained with the k-ω model agree well with the semi-empirical model and experimental data. A study of the influence of erosion parameters on erosion kinetics and scouring depth shows that the shape and depth of scouring are influenced solely by the critical shear stress while the duration of scouring depends on both erosion parameters. Further research is nonetheless required to better understand the erosion mechanisms in the stagnation zone.
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.euromechflu.2013.12.001
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titre: Comparaison de simulations CFD avec des résultats expérimentaux de Jet Erosion Test
auteur: Florian Mercier, Stéphane Bonelli, P. Pinettes, Frederic Golay, F. Anselmet, P. Philippe
article: Journal of Hydraulic Engineering, 2014, 33 p. ⟨10.1061/(ASCE)HY.1943-7900.0000829⟩
resume: The Jet Erosion Test (JET) is an experimental device increasingly used to quantify the resistance of soils to erosion. This resistance is characterised by two geotechnical parameters: the critical shear stress and the erosion coefficient. The JET interpretation model of Hanson and Cook (2004) provides an estimation of these erosion parameters. But Hanson's model is simplified, semi-empirical and several assumed hypotheses can be discussed. Our aim is to determine the relevance of the JET interpretation model. Therefore, we developed a numerical model able to predict the erosion of a cohesive soil by a turbulent flow. Our numerical model is first validated on a benchmark: erosion of an erodible pipe by a laminar flow. The numerical results are satisfactorily compared with the theoretical solution. Then, three JETs are modelled numerically, with values of erosion parameters obtained experimentally. A parametric study is also conducted to validate the accuracy of the numerical results and a good agreement is observed. The erosion parameters found experimentally permit to predict numerically the evolution of the erosion pattern within good accuracy. This result contributes to the validation of the JET's semi-empirical model. The numerical model also gives a complete description of the flow, including vortices which can be observed in the cavity created by erosion. The whole erosion pattern evolution is given by the numerical results. Our numerical model gives information that is not available otherwise.
typdoc: Article dans une revue
DOI: DOI : 10.1061/(ASCE)HY.1943-7900.0000829
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Communication dans un congrès

titre: On the numerical modelling of the Hole Erosion Test
auteur: Fabienne Mercier, Stéphane Bonelli, Pierre Philippe, Frederic Golay, Fabien Anselmet, Patrick Pinettes, Jean Jacques Fry
article: 7th International Conference on Scour and Erosion, Dec 2014, Perth, Australia
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titre: Results of Jet Erosion Tests numerical modelling
auteur: Fabienne Mercier, Stéphane Bonelli, Pierre Philippe, Patrick Pinettes, Frederic Golay, Fabien Anselmet, Jean Jacques Fry
article: 7th International Conference on Scour and Erosion, Dec 2014, Perth, Australia
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titre: 3D entropic AMR for air-water flow
auteur: Frederic Golay
article: Topical Problems of fluid mechanics, Feb 2014, Prague, Czech Republic
resume: We use an adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). It is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solutions remain smooth. We numerically investigate the efficiency of the scheme through several 3D dam break test cases.
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2013

Article dans une revue

titre: Adaptive multi scale scheme based on numerical density of entropy production for conservation laws
auteur: Mehmet Ersoy, Frederic Golay, Lyudmyla Yushchenko
article: Central European Journal of Mathematics, 2013, 11 (8), pp.1392-1415. ⟨10.2478/s11533-013-0252-6⟩
resume: We propose a 1D adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). Thus it is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solution remains smooth. Nevertheless, due to the CFL stability condition the time step is restricted and leads to time consuming simulations. Therefore, we propose a local time stepping algorithm. We also use high order time extensions using Adams-Bashforth time integration technique as well as a second order linear reconstruction in space. We numerically investigate the efficiency of the scheme through several test cases: the Sod's shock tube problem, the Lax's shock tube problem and the Shu-Osher test problem.
typdoc: Article dans une revue
DOI: DOI : 10.2478/s11533-013-0252-6
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Communication dans un congrès

titre: Entropy production and mesh refinement – application to wave breaking
auteur: Lyudmyla Yushchenko, Frederic Golay, Mehmet Ersoy
article: 21ème Congrès Français de Mécanique, Aug 2013, Bordeaux, France. ⟨10.1051/meca/2015003⟩
resume: We propose an adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). Thus it is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solutions remain smooth. Nevertheless, due to the CFL stability condition the time step is restricted and leads to time consuming simulations. Therefore, we propose a local time stepping algorithm. This approach is validated in the case of classical 1D numerical tests. Then, we present a 3D application. Indeed, according to an eulerian bi-fluid formulation at low Mach, an hyperbolic system of conservation laws allows an easily parallelization and mesh refinement by " blocks " .
typdoc: Communication dans un congrès
DOI: DOI : 10.1051/meca/2015003
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titre: Entropy production as a mesh refinement criterion: application to wave breaking
auteur: Frederic Golay, Mehmet Ersoy, Lyudmyla Yushchenko
article: Topical Problems of Fluid Mechanics, Feb 2013, Prague, Czech Republic
resume: We propose an adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). Thus it is used as an a posteriori error which provides information on the need to refine the mesh in the regions where discontinuities occur and to coarsen the mesh in the regions where the solutions remain smooth. Nevertheless, due to the CFL stability condition the time step is restricted and leads to time consuming simulations. Therefore, we propose a local time stepping algorithm. We numerically investigate the efficiency of the scheme through several 1D test cases and 3D dam break test case.
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Rapport

titre: Adaptive scheme based on entropy production: robustness through severe test cases for hyperbolic conservation laws
auteur: Mehmet Ersoy, Frederic Golay, Lyudmyla Yushchenko
article: [Research Report] Imath. 2013
resume: In this paper, we study the robustness of the 1D adaptive numerical scheme based on numerical density of entropy production for hyperbolic conservation. In particular, we focus on vacuum states or low densities states or both in presence of strong shocks solutions to the one-dimensional gas dynamics equations for ideal gas. To this purpose, it is numerically shown that the adaptive numerical scheme is well-designed to capture accurately these type of solutions as the pressure vanishes. The efficiency of the scheme is investigated through several test cases for first and second order scheme with a MUSCL reconstruction. We focus in particular on several numerical experiments to test the ability to conserve the entropy in the adaptive framework, to capture strong discontinuities (both shocks and contact dis- continuities) as well as strong rarefactions. We also perform some numerical test case for solutions which are close to the vacuum or vanishes.
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2012

Article dans une revue

titre: Numerical modeling of suffusion as an interfacial erosion process
auteur: Frederic Golay, Stéphane Bonelli
article: European Journal of Environmental and Civil Engineering, 2012, 15 (8), pp.1225-1241. ⟨10.1080/19648189.2011.9714850⟩
resume: Suffusion is an internal erosion process which occurs when finer soil particles are detached by seepage flow and start moving within the pore space of larger particles. Suffusion can be viewed as clay/water interface erosion. The aim of this study is to use a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process at pore scale. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level-set function. The ability of the model to predict suffusion is confirmed by several numerical simulations.
typdoc: Article dans une revue
DOI: DOI : 10.1080/19648189.2011.9714850
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Communication dans un congrès

titre: 3D parallel numerical simulation of two phase flow on unstructured grid
auteur: Frederic Golay, Alioune Nar Sambe, Damien Sous, Philippe Fraunié, Richard Marcer
article: Topical Problems of Fluid Mechanics, Feb 2012, Prague, Czech Republic
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Chapitre d'ouvrage

titre: Chapitre 6 : Erosion des géomatériaux
auteur: Stéphane Bonelli, Frederic Golay, Fabienne Mercier
article: Erosion des géomatériaux, 2012, 978-2-7462-2570-1
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titre: Erosion of geomaterials
auteur: Stéphane Bonelli, Frederic Golay, Fabienne Mercier
article: Erosion of geomaterials, pp.187-222, 2012, 978-1-8482-1351-7
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2011

Article dans une revue

titre: Two-Phase-Flow Unstructured Grid Solver: Application to Tsunami Wave Impact
auteur: Frederic Golay, Alioune Nar Sambe, Damien Sous, Philippe Fraunié, Vincent Rey, Richard Marcer, Christine Dejouette
article: International Journal of Offshore and Polar Engineering (IJOPE), 2011, 21 (3), pp.186-191
resume: This paper describes the CFD of incompressible air-water flows by solving Euler equations with a 2-phase flow model leading to a hyperbolic system of conservation laws solved with a finite volume discretization on unstructured grids. An artificial compressibility approach allows for a fully explicit scheme for an efficient parallel implementation. The numerical model is based on a low Mach number preconditioning and a 2nd-order Riemann solver. Applications to breaking waves on a 15% slope with and without the influence of macro-roughness are performed concerning impact and run-up processes on the beach.
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titre: Numerical wave breaking with macro-roughness
auteur: Alioune Nar Sambe, Damien Sous, Frederic Golay, Philippe Fraunié, Richard Marcer
article: European Journal of Mechanics - B/Fluids, 2011, 30 (6), pp.577-588. ⟨10.1016/j.euromechflu.2011.03.002⟩
resume: This paper reports on a numerical investigation of solitary wave breaking over a sloping bottom covered with macro-roughness elements. Wave breaking is simulated by solving Euler equations with a two phase incompressible flow model. The hyperbolic system of the conservation laws is solved with a finite volume discretization on an unstructured grid. An artificial compressibility approach allows the use of a fully explicit scheme for an efficient parallel implementation. The numerical model is based on a low Mach number preconditioning and a second order Riemann solver. Several test cases are performed to analyze the role played by macro-roughness on the breaking dynamics. The influence of the macro-roughness elements on the solitary long wave breaking is shown to depend on two dimensionless ratios D/A and H/A, where D, H and A are the separation distances between the macro-roughness elements, the height of the elements and the wave amplitude, respectively. Significant effects are observed for large values of D/A and H/A. The successive cycles of impact/splash-ups/rebounds are strongly impaired. Three-dimensional wave breaking simulations are presented, showing the robustness of the method for modeling complex wave-structure interactions
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.euromechflu.2011.03.002
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Communication dans un congrès

titre: Déferlement de vague : approche multi-pas
auteur: Alioune Nar Sambe, Frederic Golay, Lyudmyla Yushchenko, Damien Sous, Philippe Fraunié, Richard Marcer
article: congres français de mécanique, Aug 2011, Besançon, France
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titre: 3D Solver for Two Phases Flows Unstructured Grid: Application to Wave Impact on Structures
auteur: Alioune Nar Sambe, Frederic Golay, Richard Marcer, Damien Sous, Philippe Fraunié
article: International offshore and polar engineering, Jun 2011, Hawaia, United States
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2010

Article dans une revue

titre: Numerical modelling of interfacial soil erosion with viscous incompressible flows
auteur: Frederic Golay, Damien Lachouette, Stéphane Bonelli, Pierre Seppecher
article: Computer Methods in Applied Mechanics and Engineering, 2010, 200 (1-4), pp.383-391. ⟨10.1016/j.cma.2010.09.002⟩
resume: The aim of this study is to develop a numerical model for simulating surface erosion occurring at a fluid/soil interface subject to a flow process. Balance equations with jump relations are used. A penalization procedure including a fictitious domain method is used to compute the Stokes flow around obstacles, in order to avoid body-fitted unstructured meshes and instead use fast and efficient finite volume approximations on Cartesian meshes. The evolution of the water/soil interface is described by using a level set function. The ability of the model to predict the interfacial erosion of soils is confirmed by several numerical simulations.
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.cma.2010.09.002
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titre: Interfacial erosion: A three-dimensional numerical model
auteur: Frederic Golay, Damien Lachouette, Stéphane Bonelli, Pierre Seppecher
article: Comptes Rendus Mécanique, 2010, 338 (6), pp.333-337
resume: The aim of this study was to develop a numerical model to simulate the surface erosion occurring at a fluid/soil interface subject to a flow process. We used a penalization procedure to compute flow around obstacles. A fictitious domain method allowed the use of fast and efficient finite volumes approximations on Cartesian meshes and avoided unstructured body-fitted meshes. The water/soil interface evolution was described with a Level Set function. Several numerical simulations confirmed the model's ability to predict the interfacial erosion of soils.
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Communication dans un congrès

titre: Interfacial erosion: a three-dimensional numerical model
auteur: Frederic Golay, Damien Lachouette, Stéphane Bonelli, Pierre Seppecher, Cedric Galusinski
article: Euro Mediterranean Symposium On Advances in Geomaterial and Structures , May 2010, Djerba, Tunisia
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2009

Article dans une revue

titre: Numerical entropy production and error indicator for compressible flows
auteur: Frederic Golay
article: Comptes Rendus Mécanique, 2009, 337 (4), pp.233-237. ⟨10.1016/j.crme.2009.04.004⟩
resume: In the case of multifluid flows, it is classical to refine the mesh in order to improve the precision. As mesh refinement criterion, we propose to use the numerical entropy production. In a refinement procedure by bitree, we check the relevance of this criterion. Our objective is to validate the mesh refinement before integrating it into a three-dimensional parallel code
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.crme.2009.04.004
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2008

Article dans une revue

titre: One-dimensional modeling of piping flow erosion
auteur: Damien Lachouette, Frederic Golay, Stéphane Bonelli
article: Comptes Rendus Mécanique, 2008, 336 (9), pp.731-736. ⟨10.1016/j.crme.2008.06.007⟩
resume: A process called "piping", which often occurs in water-retaining structures (earth-dams, dykes, levees), involving the formation and progression of a continuous tunnel between the upstream and downstream sides, is one of the main cause of structure failure. Starting with the diphasic flow volume equations and the jump equations including the erosion processes, a simplified one-dimensional model for two-phase piping flow erosion was developed. The numerical simulation based on constant input and output pressures showed that the particle concentration can be a significant factor at the very beginning of the process, resulting in the enlargement of the hole at the exit. However, it was concluded that this influence is a secondary factor: the dilute flow assumption, which considerably simplifies the description, is relevant here.
typdoc: Article dans une revue
DOI: DOI : 10.1016/j.crme.2008.06.007
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Communication dans un congrès

titre: Wind-forced modulations of gravity waves
auteur: Stephane Leblanc, Hubert Branger, Marc Francius, Frederic Golay, Christian Kharif
article: Rogue wave symposium 2008, Oct 2008, Brest, France. pp.115-116
resume: The effect of wind on modulational instability of gravity waves is presented. A forced nonlinear Schödinger equation that governs the evolution in deep water of weakly nonlinear packets of surface gravity waves under wind forcing is derived. Stokes waves are shown to grow exponentially following Miles' linear mechanism, while modulational instability becomes explosive. These analytical results are completed by numerical simulations and experiments showing the amplification of modulations by wind. Therefore, we suggest that wind boosts the formation of rogue waves.
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2007

Article dans une revue

titre: Numerical schemes for low Mach wave breaking
auteur: Frederic Golay, Philippe Helluy
article: International Journal of Computational Fluid Dynamics, 2007, 21 (2), pp.69-86. ⟨10.1080/10618560701343382⟩
resume: In this work, we describe a finite volume scheme for the compu- tation of incompressible air-water flows. We use an artificial compressibility approach that permits us to use a completely explicit scheme. We describe successively the low Mach preconditioning of the scheme, the Riemann solver and the non-conservative approach that is used to suppress velocity-pressure oscillations, the second order extensions and the parallel implementation. Then it is applied to the simulation of the breaking of a wave on a 15% slope.
typdoc: Article dans une revue
DOI: DOI : 10.1080/10618560701343382
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2006

Article dans une revue

titre: Applications of the finite volumes method for complex flows : From the theory to the practice
auteur: Philippe Helluy, Frederic Golay
article: Flow, Turbulence and Combustion, 2006, 76 (4), pp.315-329
resume: In this short paper, we recall some well-known results on hyperbolic systems of conservation laws. We introduce the Godunov finite volume scheme for their approximations. We then present two recent applications to multiphase flows: the computation of a wave breaking and the construction of entropic scheme for phase transition.
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2005

Article dans une revue

titre: Numerical simulation of wave breaking
auteur: Philippe Helluy, Frederic Golay, Jean-Paul Caltagirone, Pierre Lubin, Stephane P. Vincent, Deborah Drevard, Richard Marcer, Philippe Fraunie, Nicolas Seguin, Stephan Grilli, Anne-Cecile Lesage, Alain Dervieux, Olivier Allain
article: ESAIM: Mathematical Modelling and Numerical Analysis, 2005, 39 (3), pp.591-607
resume: This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.
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titre: Numerical simulations of wave breaking
auteur: Nicolas Seguin, P. Helluy, Frederic Golay, J.P. Caltagirone, P. Lubin, Serge Vincent, D. Drevard, Richard Marcer, P. Fraunier, S. Grilli, A.C. Lesage, Alain Dervieux, O. Allain
article: ESAIM: Mathematical Modelling and Numerical Analysis, 2005, 39-3, pp.591-607
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2004

Article dans une revue

titre: Optimisation topologique de forme et raffinement de maillage
auteur: Frederic Golay
article: Revue Européenne des Éléments Finis, 2004, 13 (8), pp.881-897. ⟨10.3166/reef.13.881-897⟩
resume: We present the problem of topological optimization with fictitious materials. This approach leads to a formulation of blocking materials that is treated numerically by finite elements as a problem of non-linear elasticity. The computing time and the quality of the solution depend strongly on the mesh, because the topology is unknown and the problem is highly non-linear. For these reasons we use a local automatic mesh refinement method that allows to quickly determine an optimal topology on a coarse grid and then to refine the solution according to strong geometrical or numerical non-linearities. We test initially some refinement criteria related to the physics of the problem, such as the thickness or the thickness gradient, and then a criterion resulting from a posteriori error analysis developed by R. Verfürth.
typdoc: Article dans une revue
DOI: DOI : 10.3166/reef.13.881-897
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2001

Article dans une revue

titre: Locking materials and the topology of optimal shapes
auteur: Frederic Golay, Pierre Seppecher
article: European Journal of Mechanics - A/Solids, 2001, 20 (4), pp.631-644
resume: We study a problem of structural optimisation using the fictitious material approach. This is connected with the equilibrium of locking materials, which can be approximated by strongly non linear materials. A finite element simulation allows us to experiment with some conjectures about the topology of the optimal solutions.
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1998

Rapport

titre: Numerical simulation of a viscous compressible fluid based on a splitting method
auteur: Frederic Golay, Philippe Helluy
article: [Research Report] Université de Toulon Sud. 1998
resume: In this paper, a new approximation to solve the equations of a stationary , viscous and slightly compressible fluid is proposed. This method is based on a splitting of the equation into an elliptic and a hyperbolic part.
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1992

Article dans une revue

titre: Modélisation par éléments finis de la polymérisation de structures composites. Applications industrielles.
auteur: Frederic Golay, Olivier Débordes
article: Revue Européenne des Éléments Finis, 1992, 1, 23 p
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