Dissertations / Theses on the topic 'Méthodes de maillage non adaptées'
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Ramière, Isabelle. "Méthodes de domaine fictif pour des problèmes elliptiques avec conditions aux limites générales en vue de la simulation numérique d'écoulements diphasiques." Phd thesis, Université de Provence - Aix-Marseille I, 2006. http://tel.archives-ouvertes.fr/tel-00122916.
Full textL'originalité de ces méthodes consiste à utiliser le maillage du domaine fictif, généralement non adapté à la géométrie du domaine physique, pour définir une frontière immergée approchée sur laquelle seront appliquées les conditions aux limites immergées. Un même schéma numérique générique permet de traiter toutes les conditions aux limites générales. Ainsi, contrairement aux approches classiques de domaine fictif, ces méthodes ne nécessitent ni l'introduction d'un maillage surfacique de la frontière immergée ni la modification locale du schéma numérique. Deux modélisations de la frontière immergée sont étudiées. Dans la première modélisation, appelée interface diffuse, la frontière immergée approchée est l'union des mailles traversées par la frontière originelle. Dans la deuxième modélisation, la frontière immergée est approchée par une interface dite fine s'appuyant sur les faces de cellules du maillage. Des conditions de transmissions algébriques combinant les sauts de la solution et du flux sont introduites sur cette interface fine. Pour ces deux modélisations, le problème fictif à résoudre ainsi que le traitement des conditions aux limites immergées sont détaillés. Un schéma aux éléments finis Q1 est utilisé pour valider numériquement le modèle à interface diffuse alors qu'un nouveau schéma aux volumes finis est développé pour le modèle à interface fine et sauts immergés. Chaque méthode est combinée avec un algorithme de raffinement de maillage multi-niveaux (avec résidu de solution ou du flux) autour de la frontière immergée afin d'améliorer la précision de la solution obtenue.
Parallèlement, une analyse théorique de convergence en maillage non adapté au domaine physique a été effectuée pour une méthode d'éléments finis Q1. Cette étude démontre l'ordre de convergence des méthodes de domaine fictif mises en place.
Parmi les nombreuses applications industrielles possibles, une simulation sur une maquette d'échangeur de chaleur dans les centrales nucléaires permet d'apprécier la performance des méthodes mises en oeuvre.
Corti, Daniele Carlo. "Numerical methods for immersed fluid-structure interaction with enhanced interfacial mass conservation." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS176.
Full textThe present thesis is dedicated to the modeling, numerical analysis, and simu- lation of fluid-structure interaction problems involving thin-walled structures immersed in incompressible viscous fluid. The underlying motivation behind this work is the simulation of the fluid-structure interaction phenomena involved in cardiac valves. From a methodological standpoint, special focus is placed on unfitted mesh methods that guarantee accuracy without compromising computational complexity. An essential aspect is ensuring mass conservation across the fluid-structure interface. An extension of the unfitted mesh Nitsche-XFEM method reported in Alauzet et al. (2016) to three dimensions is first pro- posed, addressing both fully and partially intersected fluid domains. To achieve this, a robust general tessellation algorithm has been developed without relying on black-box mesh generators. Additionally, a novel approach for enforcing continuity in partially intersected domains is introduced. However, in situations involving contact phenomena with multiple interfaces, the computational implementation becomes exceedingly complex, particularly in 3D. Subsequently, an innovative low-order fictitious domain method is introduced, which mitigates inherent mass conservation issues arising from continuous pressure approximation by incorporating a single velocity constraint. A comprehensive a priori error analysis for a Stokes problem with a Dirichlet constraint on an immersed interface is provided. Finally, this fictitious domain approach is formulated within a fluid-structure interaction framework with general thin-walled solids and successfully applied to simulate the dynamics of the aortic valve
Leterrier, Nikos. "Discrétisation spatiale en maillage non-structuré de type général." Paris 6, 2003. http://www.theses.fr/2003PA066192.
Full textSchönfeld, Thilo. "Méthodes de raffinement adaptatif de maillage pour le calcul des écoulements non-visqueux tridimensionnels." Toulouse, INPT, 1993. http://www.theses.fr/1993INPT052H.
Full textBurbeau, Anne. "Méthodes de Galerkine discontinu d'ordre élevé pour la simulation instationnaire en maillage non structuré." Bordeaux 1, 2000. http://www.theses.fr/2000BOR10608.
Full textMer, Katherine. "Modèles de viscosités du quatrième ordre pour l'advection-diffusion en maillage non-structuré." Nice, 1996. http://www.theses.fr/1996NICE5048.
Full textGendre, Félix. "Développement de méthodes de Boltzmann sur réseau en maillages non-uniformes pour l'aéroacoustique automobile." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0196/document.
Full textThe main goal of this work is to study the capacities of the Lattice Boltzmann Method in a constrained numerical framework : that of numerical simulation in automotive aeroacoustics with non-uniform meshes, at high Reynolds number and non egligible Mach number (Ma > 0.1). The industrial problem is the computation of the interior aerodynamic noise, which includes as its first decisive step the computation of the unsteady wall pressure field on the car windows. It was observed that a lack of precision on the weak acoustic part of the total pressure field on the driver-side window, which is most probably due to errors at mesh refinement interfaces, caused an overestimation of the interior noise. We first present a coherent and unified construction of the Lattice BoltzmannMethod from the Boltzmann equation, in an athermal weakly compressible framework. Then, we study in details the aeroacoustic properties of the LBM by reviewingall the main families of collisional operators that exist in the literature. A variant of multiple relaxation time operator that can be used for aeroacoustics is presented and tested. A simplified alternative selective filter, fast and compact, is developped and numerically validated. The problem of non-uniform meshes is discussed. An exhaustive review of the LBM studies that have been carried out within that framework shows that none of them corresponds to our constraints. Alternative transition nodes algorithms are developed. Finally, all the developed models of this work are applied to industrial cases
Poret, Maud. "Méthodes en maillages mobiles auto-adaptatifs pour des systèmes hyperboliques en une et deux dimensions d'espace." Phd thesis, Ecole des Ponts ParisTech, 2005. http://pastel.archives-ouvertes.fr/pastel-00001053.
Full textColle, Anthony. "Méthodes numériques sans maillage pour la résolution de la fragmentation en dynamique rapide." Electronic Thesis or Diss., Toulouse, INSA, 2019. http://www.theses.fr/2019ISAT0052.
Full textIn Aeronautics, Defense and Space, dynamic fragmentation is a process generated by extreme loadings. Among the Lagrangian approaches, classically used for the modeling of such events, we focus here on the meshless method called SPH. Unlike grid-based methods, SPH is built on a set of interpolation points disregarding any connectivity which makes it naturally well suited to handle material failure. However, standard SPH schemes suffer from instabilities questioning their accuracy and activating non-physical processes such as numerical fragmentation. A new robust SPH scheme called γ-SPH-ALE is then proposed in this work. It is built in an ALE context and includes a stabilizing low-Mach scheme inherited from Finite Volume methods. Through a nonlinear stability analysis, CFL conditions are identified on the scheme parameters. A strong mathematical background is then built ensuring the scheme conservativity, robustness, stability and consistency. To our knowledge, this type of nonlinear analysis has never been performed on a SPH-ALE scheme. Finally, the implementation of γ-SPH-ALE on various academic fragmentation test cases demonstrates particularly its capability to prevent spurious oscillations to appear in elastic waves, as well as to solve the so-called tensile instability, major issues of standard SPH methods. Also, taking advantage of GPU parallelization, these results are achieved in reduced computation times with respect to conventional CPU implementations
Zaytsev, Victor. "Méthodes stochastiques pour la modélisation d'incertitudes sur les maillages non structurés." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEM094/document.
Full textSimulations of physical phenomenon often require discretizing the medium with a mesh. An example of this type of simulation is the simulation of fluid flow through a porous medium and the evaluation of the geomechanical stress in the petroleum reservoir. The studied medium is often not homogeneous and applying a homogeneity hypothesis can lead to incorrect simulation results. That makes simulation of heterogeneities important for this kind of problems.This thesis is devoted to geostatistical simulations of heterogeneities on unstructured grids using methods of non-linear geostatistics. The objective of this work is the development of algorithms for simulating heterogeneities directly on unstructured grids without using intermediate fine scale regular grids and upscaling. We present two theoretical models for geostatistical simulations of continuous parameters on unstructured grids which are different generalizations of the Discrete Gaussian model (DGM) – DGM 1 and DGM 2. The proposed theoretical models enable converting the problem of geostatistical simulation on an unstructured grid into the well-studied problem of simulating multivariate Gaussian random vectors followed by application of block-dependent transformation functions. The problem of simulating facies is also addressed in this work, for which generalizations of pluri-Gaussian and truncated Gaussian simulation models for unstructured grids are proposed.An application of the proposed methods is demonstrated on a case study X, which is an offshore gas reservoir with a tartan-meshed grid
Hoang, Thi Quynh Van. "Maillage cartésien non-conforme pour la méthode TLM : application à la conception de rectennas compactes." Nice, 2012. http://www.theses.fr/2012NICE4045.
Full textThe work presented in this thesis is divided into two parts. The first part is devoted to the development of a computational electromagnetic code based on the TLM method (Transmission Line Matrix) to simulate structures with multi-scale aspects, requiring multigrids-subgrids locally refined. This leads to solve a simultaneous spatial and time domain coupling problem. As it was proved to be very effective for spatial domain coupling, the technique using transformers introduced by Wlodarczyk is implemented. Actual work is focussed on the time domain coupling to allow using the maximum time step in each sub grid. Interpolation techniques such as Taylor second order and cubic Spline and also a prediction technique inspired from the Prony-Pisarenko method for power spectral density estimation were implemented and evaluated. The second part is devoted to the design of rectennas. Such non linear and multi-scale structures, integrating Schottky diodes, are key elements of wireless power transmission or energy harvesting systems. It is demonstrated that modelling rectennas with a global circuit-electromagnetic simulation tool in time domain as with TLM provides a substantial advantage compared to commercial simulation softwares that requires various experimental adjustments, rendering complex the design process. It becomes then possible to accurately predict the conversion efficiency of an entire rectenna. The design and complete experimental characterization of two compact rectennas operating at 2. 45GHz are finally presented
Tampango, Yendoubouam. "Développement d'une méthode sans maillage basée sur les approximations de Taylor." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0322/document.
Full textIn these last decades, new numerical methods known as « meshless methods » have been developped. Contrary to the FEM, these methods uses only a set of nodes in the domain, without need of any mesh. Until now, any of these methods has convinced users of FEM. In this paper, we present a new meshless method using Taylor series expansion. In this method, the PDE is solved quasi exactly in the domain and the boundary conditions are applied by using a least square method. Then only the boundary discretisation is needed so the proposed method is a « true boundary meshless method ». This technique has been proposed for the first time by S. Zeze in his PhD thesis. The study of some linear problems has shown that this technique leads to a very good accuracy and that the convergence can be improved by increasing approximation degree. Our work is a continuation of S. Zeze work, and it consists to make the proposed method more robust and to extend its range of application. For that, we first make an analysis of the series computed by the method. The aim of this analysis was to evaluate the domain of validity of these series. This analysis showed that, for some problems, an accuracy cannot be obtained without splitting the domain in subdomains and making a resolution by subdomains. Therefore the second part of our work was to define a technique which will ensure the continuity at the interface between subdomains, in the case of a resolution by subdomains. The last part of our work was dedicated to non-linear problems. We establish an algorithm to show how the proposed method can deal with nonlinear-problems
Eddhahak-Ouni, Anissa. "Modélisation de l'usure superficielle dans les contacts roulants : mise en place des méthodes adaptées au cas non stationnaire des contacts came galet." Université de Marne-la-Vallée, 2006. http://www.theses.fr/2006MARN0300.
Full textWear simulation in rolling contact is considered one of the major concerns of designers and industrialists. In order to extend the life time of their mechanical systems, a wear prediction tool has to be developed. The aim of this research is to develop a simplified approach for the description of wear evolution in cam’s track of the plastic bottles blowing machines manufactured by Sidel. Thecycloid shape of the opening/closing cam governs the roller movement and consequently the system kinematics. Thus, roller rotation velocity and normal contact load cam/roller are not stationary, so it’s of interest to be able to describe these transient phenomena as well as the worn profiles of the contacting bodies during time. First, we start the study by presenting a simplified approach for the resolution of the rolling contact problem in steady state. The method reliability is proved when compared with the exact theory and tested on several critical cases. Second, we extend this approach to transient case by taking into account the dynamic feature of both solids. This transient model is fast, its results show a good agreement with the reality. The industrial example of the moulds opening/closing system of the blowing machines is treated making the hypothesis of components stiffness and perfect joints. The Archard’s law is used with a modified version to describe the evolution of worn cam profile versus rollers passages. In the end of this work and in order to describe phenomena in a more realistic way, we investigated the influence of components flexibility in the modelling. Numerical results of non linear dynamic equations are compared with the stiff model to conclude on the effect of the flexibility on the system dynamic response
Mamaghani, Magnolia. "Suivi de fronts par des méthodes de raffinement de maillage adaptatif et application à la simulation du procédé de récupération Steam Assited Gravity Drainage." Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2010. http://tel.archives-ouvertes.fr/tel-00740906.
Full textLéger, Raphaël. "Couplage pour l'aéroacoustique de schémas aux différences finies en maillage structuré avec des schémas de type éléments finis discontinus en maillage non structuré." Thesis, Paris Est, 2011. http://www.theses.fr/2011PEST1030/document.
Full textThis thesis aims at studying coupling techniques between Discontinuous Galerkin (DG) and finite difference (FD) schemes in a non-structured / Cartesian hybrid-mesh context,in the framework of Aeroacoustics computations. The idea behind such an approach is the possibility to locally take advantage of the qualities of each method. In other words, the goal is to be able to deal with complex geometries using a DG scheme on a non-structured mesh in their neighborhood, while solving the rest of the domain using a FD scheme on a cartesian grid, in order to alleviate the needs in computational resources. More precisely, this work aims at designing an hybridization algorithm between these two types of numerical schemes, in the framework of the approximation of the solutions of the Linearized Euler Equations. Then, the numerical behaviour of hybrid solutions is cautiously evaluated. Due to the fact that no theoretical result seems achievable at the present time, this study is mainly based on numerical experiments. What's more, the interest of such an hybridization is illustrated by its application to an acoustic propagation computation in a realistic case
Canouet, Nicolas. "Méthodes de Galerkin Discontinu pour la résolution du système de Maxwell sur des maillages localement raffinés non-conformes." Phd thesis, Ecole des Ponts ParisTech, 2003. http://pastel.archives-ouvertes.fr/pastel-00000555.
Full textBonilla, Matthieu. "Contribution à l'étude des méthodes d'analyse électromagnétique temporelle des dispositifs micro-ondes et non linéaires." Paris 6, 2002. http://www.theses.fr/2002PA066043.
Full textMamaghani, Magnolia. "Suivi de fronts par des méthodes de raffinement de maillage adaptatif et application à la simulation du procédé de récupération Steam Assited Gravity Drainage." Phd thesis, Clermont-Ferrand 2, 2010. http://www.theses.fr/2010CLF22014.
Full textPaxion, Sébastien. "Développement d'un solveur multigrille non-structuré parallèle pour la simulation de flammes laminaires en chimie et transport complexes." Châtenay-Malabry, Ecole centrale de Paris, 1999. http://www.theses.fr/1999ECAP0681.
Full textFahs, Hassan. "Méthodes de type Galerkin discontinu d'ordre élevé pour la résolution numérique des équations de Maxwell instationnaires sur des maillages simplexes non-conformes." Phd thesis, Université de Nice Sophia-Antipolis, 2008. http://tel.archives-ouvertes.fr/tel-00359874.
Full textAfin d'améliorer la précision et la vitesse de convergence des méthodes GDDT précédentes, on étudie une famille de schémas saute-mouton d'ordre
arbitrairement élevé. Ces schémas temporels nous assurent sur tout maillage la conservation d'un équivalent discret de l'énergie électromagnétique ainsi que la stabilité des méthodes GDDT résultantes sous une condition de type CFL. On réalise aussi une étude de convergence /hp a priori/ ainsi qu'une étude de convergence de l'erreur sur la divergence. Des expériences numériques montrent que pour un maillage donné, le schéma saute-mouton du quatrième ordre est moins coûteux en temps de calcul et plus précis que le schéma saute-mouton du second ordre, en dépit d'une complexité arithmétique accrue.
De plus, on obtient une convergence exponentielle avec le schéma saute-mouton du quatrième ordre.
El, Alaoui Lakhnati Linda. "Analyse d'esrreur a priori et a posteriori pour des méthodes d'éléments finis mixtes non-conformes." Marne-la-vallée, ENPC, 2005. https://pastel.archives-ouvertes.fr/pastel-00001267.
Full textGorsse, Yannick. "Approximation numérique sur maillage cartésien de lois de conservation : écoulements compressibles et élasticité non linéaire." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2012. http://tel.archives-ouvertes.fr/tel-00796722.
Full textEl, Alaoui Lakhnati Linda. "Analyse d'erreur a priori et a posteriori pour des méthodes d'éléments finis mixtes non-conformes." Phd thesis, Ecole des Ponts ParisTech, 2005. http://pastel.archives-ouvertes.fr/pastel-00001267.
Full textEl, Khaoulani Rachid. "Prédiction fiable de l'endommagement ductile par la méthode des éléments finis mixtes : endommagement non local et adaptation de maillage." Phd thesis, École Nationale Supérieure des Mines de Paris, 2010. http://pastel.archives-ouvertes.fr/pastel-00566805.
Full textSchwartz, Martin. "Contribution à la résolution de problèmes tridimensionnels de fissuration fragile. Vers l'utilisation d'un modèle non-local de comportement élastique." Thesis, Université de Lorraine, 2012. http://www.theses.fr/2012LORR0031/document.
Full textIn this thesis, we have developed a numerical tool, based on a classical boundary elements method, which allows a conventional analysis of a stationary crack in a 3D specimen under complex mechanical loading. In order to assess the impact of the microstructure on the brittle fracture, we were interested in non local models of behavior. First, we have adopted the non local elastic model due to Eringen. This refined constitutive equation allows to account for long range interactions in the description of the elastic behavior in the vicinity of the crack front. Unlike the traditional approach, this type of model leads to a finite stress field at the crack front. Moreover, the stress is locally maximal ahead of the front. These interesting results indicate that it is possible to predict the stability and direction of crack propagation in a simple and more naturel way by using stress based criteria. The implemented numerical strategy can handle cases of crack in tension or compression, under shear stress or mixed loadings. Having clearly highlighted the interest of non local models, we have adopted the improved version of Eringen elastic model as proposed by Polizzotto. This elastic model is applicable to finite domains and requires a specific numerical treatment. The basis of such a numerical strategy initiated by R. Kouitat has been established. The method couples the conventional boundary element method with local point interpolation of a strong form differential equation. Promising results are obtained and show that with such modeling of material behavior, it is possible to describe the irreversible process of fracturing in a similar way as plasticity
Drui, Florence. "Modélisation et simulation Eulériennes des écoulements diphasiques à phases séparées et dispersées : développement d’une modélisation unifiée et de méthodes numériques adaptées au calcul massivement parallèle." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLC033/document.
Full textIn an industrial context, reduced-order two-phase models are used in predictive simulations of the liquid fuel injection in combustion chambers and help designing more efficient and less polluting devices. The combustion quality strongly depends on the atomization process, starting from the separated phase flow at the exit of the nozzle down to the cloud of fuel droplets characterized by a disperse-phase flow. Today, simulating all the physical scales involved in this process requires a major breakthrough in terms of modeling, numerical methods and high performance computing (HPC). These three aspects are addressed in this thesis. First, we are interested in mixture models, derived through Hamilton’s variational principle and the second principle of thermodynamics. We enrich these models, so that they can describe sub-scale pulsations mechanisms. Comparisons with experimental data in a context of bubbly flows enables to assess the models and the methodology. Based on a geometrical study of the interface evolution, new tracks are then proposed for further enriching the mixture models using the same methodology. Second, we propose a numerical strategy based on finite volume methods composed of an operator splitting strategy, approximate Riemann solvers for the resolution of the convective part and specific ODE solvers for the source terms. These methods have been adapted so as to handle several difficulties related to two-phase flows, like the large acoustic impedance ratio, the stiffness of the source terms and low-Mach issues. Moreover, a cell-based Adaptive Mesh Refinement (AMR) strategy is considered. This involves to develop refinement criteria, the setting of the solution values on the new grids and to adapt the standard methods for regular structured grids to non-conforming grids. Finally, the scalability of this AMR tool relies on the p4est AMR library, that shows excellent scalability on several thousands cores. A code named CanoP has been developed and enables to solve fluid dynamics equations on AMR grids. We show that CanoP can be used for future simulations of the liquid atomization
Shi, Yu-E. "Résolution numérique des équations de Saint-Venant par la technique de projection en utilisant une méthode des volumes finis dans un maillage non structuré." Phd thesis, Caen, 2006. http://www.theses.fr/2006CAEN2045.
Full textRecently, several Unstructured Finite-Volumes Methods (UFVM) have been developed to solve Navier-Stokes flows, but there do not exist so many applications of UFVM to the shallow-water problems. The principal difficulty, encountered in the applications of such models, is related to the irregular variation of bed elevation with the presence of wet/dry zones in a complex geometry. This dissertation presents the development of a 2-D numerical model, named ECOMOD-UFVM, which is based on the solving of the Saint-Venant equations by a projection technique coupled with a UFVM. The UFVM will allow a numerical modelling, which can perfectively adapt to the geometry very complex in the coastal and estuarine zones. Initially, in the framework of this thesis, a second order scheme of ULSS (Upwind Least Squares Scheme) is introduced in the code to handle the convection terms in order to prevent undesirable numerical oscillations and diffusions. Ten benchmarked test cases proposed in the existing studies were carried out: shallow water flows; dam-break flows. The results of the case-tests are satisfactory and allow us to make with confidence the passage into two real natural applications: dam-break of Malpasset (France) and flash flood in the city of Dongchuan (China). The results obtained confirm the reliability, the precision, the stability and the robustness of the developed UMVF model in solving the Saint-Venant equations, describing all kinds of flows: slow, fast and torrential on any type of the bottom: wet/dry, flat or great slopes, regular or very irregular
Cayot, Pierre. "Schémas numériques d'ordre élevé pour la simulation des écoulements turbulents sur maillage structuré et non structuré." Phd thesis, Toulouse, INPT, 2016. http://oatao.univ-toulouse.fr/16624/1/Cayot_Pierre.pdf.
Full textGhozzi, Yosr. "Simulation numérique des problèmes mécaniques non linéaires par approche mixte MEF-MESHLESS." Thesis, Troyes, 2014. http://www.theses.fr/2014TROY0006/document.
Full textIn this work, we implement a development of mixed discretization MEF-Meshless for solving strongly nonlinear mechanical problem. Particular attention is given to the construction of the shape functions by diffuse approximation. In order to deal with problems of solid mechanics with large strain, we develop a so-called “mixed” numerical method combining both Meshless to discretize areas of high deformation gradient, and Finite Element Method (MEF) for non-concerned areas. We ensure coupling between both discretization methods through the implementation of specific techniques, including the continuity and consistency of the field and the choice of the appropriate method of numerical integration. We test later the reliability and performance of the model by the introduction of a comparative study with a standard FEM model designed for the same numerical conditions to evaluate numerical techniques attributed to our “mixed” model. We develop, thereafter, a model of behavior through a large strain description. We adopt spatial discretization elements “assumed strain” and a suitable time discretization. To validate our “mixed” model, we perform a comparative study of nonlinear simple calculation examples
Mounier, Marie. "Résolution des équations de Maxwell-Vlasov sur maillage cartésien non conforme 2D par un solveur Galerkin discontinu." Thesis, Strasbourg, 2014. http://www.theses.fr/2014STRAD028/document.
Full textThis thesis deals with the study of a numerical method to simulate a plasma. We consider a set of particles whose displacement is governed by the Vlasov equation and which creates an electromagnetic field thanks to Maxwell equations. The numerical resolution of the Vlasov-Maxwell system is performed by a Particle In Cell (PIC) method. The resolution of Maxwell equations needs a sufficiently fine mesh to correctly simulate the multi scaled problems that we have to face. Yet, a uniform fine mesh of the whole domain has a prohibitive cost. The novelty of this thesis is a PIC solver on locally refined Cartesian meshes : non conforming meshes, to guarantee the good modeling of the physical phenomena and to avoid too large CPU time. We use the Discontinuous Galerkin in Time Domain (DGTD) method which has the advantage of a great flexibility in the choice of the mesh and which is a high order method. A fundamental point in the study of PIC solvers is the respect of the charge conserving law. We propose two approaches to tackle this point. The first one deals with augmented Maxwell systems, that we have adapted to non conforming meshes. The second one deals with an original method of preprocessing of the calculation of the current source term
Li, Yue. "Modélisation des phénomènes électromagnétiques caractérisant des structures composites complexes : application à l’évaluation non destructive." Nantes, 2012. http://archive.bu.univ-nantes.fr/pollux/show.action?id=970a22ed-e6af-4d0d-8cf8-eafcf4a8a5cb.
Full textThe carbon fiber composite materials (CFCM) are widely used in the industrial and domestic sectors thanks to their advantages: light weight, corrosion resistance and mechanical strength. This work focuses on building a model to simulate the Non-destructive Testing (NDT) problems on CFCM. The objective of this thesis is to determine the distribution of eddy currents and the impedance of the system. Based on the formulation T-Omega, a simplified T-iterative formulation who limits the area of study to the MCFC workpiece is developed using the Finite Volume Method (FVM). This numerical method allows dealing with the defect in the CFCM. The developed model allows solving the 3D problems of highly anisotropic materials. In addition, this model allows making different meshes by regions to reduce the matrix system size. This means that a method of non-conforming mesh is included in the program and adapted to the NDT of CFCM. Finally, the fabrication of the CFCM plates are realized, which helps us to understand the nature of CFCM. The simulation results are validated by the experimental ones
Horstmann, Tobias. "Méthodes numériques hybrides basées sur une approche Boltzmann sur réseau en vue de l'application aux maillages non-uniformes." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEC027/document.
Full textDespite the inherent efficiency and low dissipative behaviour of the standard lattice Boltzmann method (LBM) relying on a two step stream and collide algorithm, a major drawback of this approach is the restriction to uniform Cartesian grids. The adaptation of the discretization step to varying fluid dynamic scales is usually achieved by multi-scale lattice Boltzmann schemes, in which the computational domain is decomposed into multiple uniform subdomains with different spatial resolutions. For the sake of connectivity, the resolution factor of adjacent subdomains has to be a multiple of two, introducing an abrupt change of the space-time discretization step at the interface that is prone to trigger instabilites and generate spurious noise sources that contaminate the expected physical pressure signal. In the present PhD thesis, we first elucidate the subject of mesh refinement in the standard lattice Boltzmann method and point out challenges and potential sources of error. Subsequently, we propose a novel hybrid lattice Boltzmann method (HLBM) that combines the stream and collide algorithm with an Eulerian flux-balance algorithm that is obtained from a finite-volume discretization of the discrete velocity Boltzmann equations. The interest of a hybrid lattice Boltzmann method is the pairing of efficiency and low numerical dissipation with an increase in geometrical flexibility. The HLBM allows for non-uniform grids. In the scope of 2D periodic test cases, it is shown that such an approach constitutes a valuable alternative to multi-scale lattice Boltzmann schemes by allowing local mesh refinement of type H. The HLBM properly resolves aerodynamics and aeroacoustics in the interface regions. A further part of the presented work examines the coupling of the stream and collide algorithm with a finite-volume formulation of the isothermal Navier-Stokes equations. Such an attempt bears the advantages that the number of equations of the finite-volume solver is reduced. In addition, the stability is increased due to a more favorable CFL condition. A major difference to the pairing of two kinetic schemes is the coupling in moment space. Here, a novel technique is presented to inject the macroscopic solution of the Navier-Stokes solver into the stream and collide algorithm using a central moment collision. First results on 2D tests cases show that such an algorithm is stable and feasible. Numerical results are compared with those of the previous HLBM
Shi, Yu-E. "Résolution numérique des équations de Saint-Venant par la technique de projection en utilisant une méthode des volumes finis dans un maillage non structuré." Phd thesis, Université de Caen, 2006. http://tel.archives-ouvertes.fr/tel-00130539.
Full textAnsanay-Alex, Guillaume. "Un schéma éléments finis non-conformes / volumes finis pour l'approximation en maillages non-structurés des écoulements à faible nombre de Mach." Phd thesis, Université de Provence - Aix-Marseille I, 2009. http://tel.archives-ouvertes.fr/tel-00483598.
Full textTavé, Cédric. "Construction simple de schémas distribuant le résidu non-oscillants et d'ordre élevé pour la simulation d'écoulements stationnaires sur maillages triangulaires et hybrides." Bordeaux 1, 2007. http://www.theses.fr/2007BOR13496.
Full textFoerster, Evelyne. "Évaluation des Méthodes Meshfree pour les Simulations Géomécaniques en Transformations Finies." Phd thesis, Ecole Centrale Paris, 2003. http://tel.archives-ouvertes.fr/tel-00649662.
Full textLaurent, Jean-Baptiste. "Raffinements locaux auto-adaptatifs dans une méthode Galerkin discontinu pour la résolution des équations de Maxwell." Toulouse 3, 2013. http://thesesups.ups-tlse.fr/2012/.
Full textThis thesis is devoted to study some keypoints in order to propose a self-adaptive refinement method for the numerical resolution of time-domain Maxwell's equations with a discontinuous Galerkin scheme. We first put into light numerically an instability phenomenon due to the interpolation operator taking account for the modification of the approximation space from one step to another. This is explained in the 1D case. Then, a new operator is proposed and shown to retrieve asymptotically consistency and stability for the scheme. This has thus been extended to the 3D case. Second part of this work deals with non-conformity on mesh (in the finite element sense) or non-uniform polynomial order applied to the discontinuous Galerkin scheme. To avoid spurious waves that can be excited in such case, we aim at recover the solution from a conformal space. This is done by creating a cleaning operator that allows us to keep the benefits of our original scheme. Explicitation of this operator is given on the 2D Transverse Magnetic Maxwell's equations. Finally, the last part implements and analyses a self-adaptive refinement strategy in the 1D case, to draw conclusions in the future 3D application
Vu, Do Huy Cuong. "Méthodes numériques pour les écoulements et le transport en milieu poreux." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112348/document.
Full textThis thesis bears on the modelling of groundwater flow and transport in porous media; we perform numerical simulations by means of finite volume methods and prove convergence results. In Chapter 1, we first apply a semi-implicit standard finite volume method and then the generalized finite volume method SUSHI for the numerical simulation of density driven flows in porous media; we solve a nonlinear convection-diffusion parabolic equation for the concentration coupled with an elliptic equation for the pressure. We apply the standard finite volume method to compute the solutions of a problem involving a rotating interface between salt and fresh water and of Henry's problem. We then apply the SUSHI scheme to the same problems as well as to a three dimensional saltpool problem. We use adaptive meshes, based upon square volume elements in space dimension two and cubic volume elements in space dimension three. In Chapter 2, we apply the generalized finite volume method SUSHI to the discretization of Richards equation, an elliptic-parabolic equation modeling groundwater flow, where the diffusion term can be anisotropic and heterogeneous. This class of locally conservative methods can be applied to a wide range of unstructured possibly non-matching polyhedral meshes in arbitrary space dimension. As is needed for Richards equation, the time discretization is fully implicit. We obtain a convergence result based upon a priori estimates and the application of the Fréchet-Kolmogorov compactness theorem. We implement the scheme and present numerical tests. In Chapter 3, we study a gradient scheme for the Signorini problem. Gradient schemes are nonconforming methods written in discrete variational formulation which are based on independent approximations of the functions and the gradients. We prove the existence and uniqueness of the discrete solution as well as its convergence to the weak solution of the Signorini problem. Finally we introduce a numerical scheme based upon the SUSHI discretization and present numerical results. In Chapter 4, we apply a semi-implicit scheme in time together with a generalized finite volume method for the numerical solution of density driven flows in porous media; it comes to solve nonlinear convection-diffusion parabolic equations for the solute and temperature transport as well as for the pressure. We compute the solutions for a specific problem which describes the advance of a warm fresh water front coupled to heat transfer in a confined aquifer which is initially charged with cold salt water. We use adaptive meshes, based upon square volume elements in space dimension two
Gobé, Alexis. "Méthodes Galerkin discontinues pour la simulation de problèmes multiéchelles en nanophotonique et applications au piégeage de la lumière dans des cellules solaires." Thesis, Université Côte d'Azur, 2020. http://www.theses.fr/2020COAZ4011.
Full textThe objective of this thesis is the numerical study of light trapping in nanostructured solar cells. Climate change has become a major issue requiring a short-term energy transition. In this context, solar energy seems to be an ideal energy source. This resource is both globally scalable and environmentally friendly. In order to maximize its penetration, it is needed to increase the amount of light absorbed and reduce the costs associated with cell design. Light trapping is a strategy that achieves both of these objectives. The principle is to use nanometric textures to focus the light in the absorbing semiconductor layers. In this work, the Discontinuous Galerkin Time-Domain (DGTD) method is introduced. Two major methodological developments are presented, allowing to better take into account the characteristics of solar cells. First, the use of a local approximation order is proposed, based on a particular order distribution strategy. The second development is the use of hybrid meshes mixing structured hexahedral and unstructured tetrahedral elements. Realistic cases of solar cells from the literature and collaborations with physicists in the field of photovoltaics illustrate the contribution of these developments. A case of inverse optimization of a diffraction grating in a solar cell is also presented by coupling the numerical solver with a Bayesian optimization algorithm. In addition, an in-depth study of the solver's performance has also been carried out with methodological modifications to counter load balancing problems. Finally, a more prospective method, the Multiscale Hybrid-Mixed method (MHM) specialized in solving very highly multiscale problems is introduced. A multiscale time scheme is presented and its stability is proven
Langenais, Adrien. "Adaptation des méthodes et outils aéroacoustiques pour les jets en interaction dans le cadre des lanceurs spatiaux." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEC003/document.
Full textDuring a space launch, the noise from hot supersonic jets, generated by rocket engines at liftoff and interacting with the launch pad, is harmful to the launcher and in particular its payload. Consequently, space actors are seeking to strengthen their understanding and control of this acoustic environment through numerical methods and tools, among the others. However, they do not dispose of a comprehensive numerical strategy that can simultaneously take into account accurate noise generation, nonlinear acoustic propagation, complex installation effects and realistic geometries, which are inherent to space applications. For this purpose, the present study consists in setting up and validating a numerical simulation methodology using a Navier-Stokes − Euler two-way coupling approach, then applying it to realistic cases of supersonic jet noise in order to improve prediction capabilities and contribute to the understanding of the noise generation mechanisms in such jets. The Navier-Stokes solver is based on an LES method on unstructured mesh and the acoustic solver on a high-order discontinuous Galerkin method on unstructured mesh. The methodology is first assessed on academic cases to validate the use of the two-way coupling. After preliminary computations, the methodology is applied to the simulation of the noise from a supersonic free jet at Mach 3.1. A geometric turbulence tripping method is implemented via a step at the nozzle wall. The computation leads to noise predictions very close to the experimental measurements performed at the MARTEL test bench and highlights significant nonlinear effects as well as a quite particular Mach waves radiation mechanism. Targeting even more realistic cases, the entire numerical approach is finally successfully adapted to the simulation of the noise from a supersonic jet configuration including a flame trench. In the future, it may be extended to configurations with clustered reactive jets, water injection devices or even at full scale
Hamiaz, Adnane. "Étude d'une méthode volumes finis pour la résolution d'un modèle non linéaire d'un couplage Maxwell/plasma dans le domaine temporel." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1711/.
Full textThis thesis presents the study of an efficient numerical method to solve the Maxwell equations coupled with a fluid plasma model. The document is split into five chapters where we introduce the formulation of the physical model, a mathematical study to demonstrate the existence and uniqueness of a solution for the problem, numerical approximations of the equations, simulations and validations on 3D and 2D examples and a prospective work on a finite volume method with adaptative mesh for the 1D case. The accent is continuously put on the choice of the most efficient numerical approximation to solve the coupled problem. In this work, we exhibit the drawbacks of the finite difference method usually employed in this context. To overcome these drawbacks, we propose a method based upon a finite volume scheme which allows the capability to use local refinements. Then, to increase the gain in time CPU and memory storage, we introduce a local time-stepping scheme
Desobry, David. "Génération de maillages hexaédriques pour des simulations de grandes déformations." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0163.
Full textThis thesis focuses on the development of hexahedral meshing methods suitable for large deformation simulations in non-linear mechanics. Domain parameterization methods based on frame fields are used to generate high-quality hexahedral meshes aligned with the domain boundaries. However, during large deformations, the mesh quality may degrade and potentially block the simulation. This thesis explores the idea of determining an optimal connectivity for the mesh elements while taking into account the anticipated deformations.In 2D, a complete pipeline is developed to tackle this challenge by combining previous work and scientific contributions. In 3D, contributions are made to approach this objective, particularly by controlling the boundary valences of hexahedral meshes produced from frame fields. The different parts of the thesis address the steps of large deformation numerical simulations, the advantages of global parameterization methods, the results of simulations on industrial 2D meshes, and contributions to improving the flexibility and robustness of the hexahedral meshing process.The ultimate goal is to reduce the time spent by engineers in generating an adequate mesh for a simulation by considering a priori information on the deformation to which the mesh and the object will be subjected
Cheaytou, Rima. "Etude des méthodes de pénalité-projection vectorielle pour les équations de Navier-Stokes avec conditions aux limites ouvertes." Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4715.
Full textMotivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem
Duran, Arnaud. "Numerical simulation of depth-averaged flows models : a class of Finite Volume and discontinuous Galerkin approaches." Thesis, Montpellier 2, 2014. http://www.theses.fr/2014MON20066/document.
Full textThis work is devoted to the development of numerical schemes to approximatesolutions of depth averaged flow models. We first detail the construction of Finite Volume approaches for the Shallow Water system with source terms on unstructured meshes. Based on a suitable reformulation of the equations, we implement a well-balanced and positive preserving approach, and suggest adapted MUSCL extensions. The method is shown to handle irregular topography variations and demonstrates strong stabilities properties. The inclusion of friction terms is subject to a thorough analysis, leading to the establishment of some Asymptotic Preserving property through the enhancement of another recent Finite Volume scheme.The second aspect of this study concerns discontinuous Galerkin Finite Elementmethods. Some of the ideas advanced in the Finite Volume context areemployed to broach the Shallow Water system on triangular meshes. Numericalresults are exposed and the method turns out to be well suited to describe a large variety of flows. On these observations we finally propose to exploit its features to extend the approach to a new family of Green-Nadghi equations. Numerical experiments are also proposed to validate this numerical model
Layouni, Siham. "Etude d'une méthode de volumes finis pour la résolution des équations de Maxwell en deux dimensions d'espace sur des maillages quelconques et couplage avec l'équation de Vlasov." Toulouse 3, 2008. http://thesesups.ups-tlse.fr/562/.
Full textWe develop and study a finite volume method to solve the bidimensional nonstationary Maxwell equations on arbitrary (non-conforming, non-convex, flat. . . ) meshes. We start by the construction of the scheme, which is based on the use of the DDFV discrete operators and a pertinent choice to discretize initial and boundary conditions. Then, we prove that the scheme locally preserves the divergence condition, that a discrete electromagnetic energy is conserved or decreasing (depending on boundary conditions) and that it is positive under a CFL condition. We also show the stability of the scheme under a CFL condition and its convergence for regular and non-regular fields. Then, these results are numerically validated with some tests using different types of meshes. We verify, also, that the use of non-conforming meshes doesn't amplify parasitic reflections. Finally, we coupled the scheme with a PIC method to solve the Maxwell-Vlasov system. We calculate the current density using a generalization of Buneman's method to arbitrary meshes and we prove that discrete charge equations, and thus Gauss' law, are conserved. The coupled problem is numerically validated and the simulation of Landau damping confirms the electric energy decrease with a precision depending on the number of particles per cell
Clément, Jean-Baptiste. "Simulation numérique des écoulements en milieu poreux non-saturés par une méthode de Galerkine discontinue adaptative : application aux plages sableuses." Electronic Thesis or Diss., Toulon, 2021. http://www.theses.fr/2021TOUL0022.
Full textFlows in unsaturated porous media are modelled by the Richards' equation which is a degenerate parabolic nonlinear equation. Its limitations and the challenges raised by its numerical solution are laid out. Getting robust, accurate and cost-effective results is difficult in particular because of moving sharp wetting fronts due to the nonlinear hydraulic properties. Richards' equation is discretized by a discontinuous Galerkin method in space and backward differentiation formulas in time. The resulting numerical scheme is conservative, high-order and very flexible. Thereby, complex boundary conditions are included easily such as seepage condition or dynamic forcing. Moreover, an adaptive strategy is proposed. Adaptive time stepping makes nonlinear convergence robust and a block-based adaptive mesh refinement is used to reach required accuracy cost-effectively. A suitable a posteriori error indicator helps the mesh to capture sharp wetting fronts which are also better approximated by a discontinuity introduced in the solution thanks to a weighted discontinuous Galerkin method. The approach is checked through various test-cases and a 2D benchmark. Numerical simulations are compared with laboratory experiments of water table recharge/drainage and a largescale experiment of wetting, following reservoir impoundment of the multi-materials La Verne dam. This demanding case shows the potentiality of the strategy developed in this thesis. Finally, applications are handled to simulate groundwater flows under the swash zone of sandy beaches in comparison with experimental observations
Durochat, Clément. "Méthode de type Galerkin discontinu en maillages multi-éléments (et non-conformes) pour la résolution numérique des équations de Maxwell instationnaires." Thesis, Nice, 2013. http://www.theses.fr/2013NICE4005.
Full textThis thesis is concerned with the study of a Discontinuous Galerkin Time-Domain method (DGTD), for the numerical resolution of the unsteady Maxwell equations on hybrid tetrahedral/hexahedral in 3D (triangular/quadrangular in 2D) and non-conforming meshes, denoted by DGTD-PpQk method. Like in several studies on various hybrid time domain methods (such as a combination of Finite Volume with Finite Difference methods, or Finite Element with Finite Difference, etc.), our general objective is to mesh objects with complex geometry by tetrahedra for high precision and mesh the surrounding space by square elements for simplicity and speed. In the discretization scheme of the DGTD method considered here, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered approximation for the surface integrals. Time integration of the associated semi-discrete equations is achieved by a second or fourth order Leap-Frog scheme. After introducing the historical and physical context of Maxwell equations, we present the details of the DGTD-PpQk method. We prove the L2 stability of this method by establishing the conservation of a discrete analog of the electromagnetic energy and a sufficient CFL-like stability condition is exhibited. The theoritical convergence of the scheme is also studied, this leads to a-priori error estimate that takes into account the hybrid nature of the mesh. Afterward, we perform a complete numerical study in 2D (TMz waves), for several test problems, on hybrid and non-conforming meshes, and for homogeneous or heterogeneous media. We do the same for the 3D implementation, with more realistic simulations, for example the propagation in a heterogeneous human head model. We show the consistency between the mathematical and numerical results of this DGTD-PpQk method, and its contribution in terms of accuracy and CPU time
Dugois, Kévin. "Simulation à l’échelle microscopique et analyse macroscopique de l’imprégnation d’un matériau composite par un fluide chargé en particules." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0011/document.
Full textIn order to improve thermo-mechanical behavior of tubine blades in SAFRAN engines plane, a new composite material is necessary. The manufacturing process to obtain this composite is intricate and requires a two steps fluid densification process. This thesis focuses on numerical simulation of the first one called Slurry Cats/APS. In this step, suspended particles are introducted and captured in the reinforcement. For that purpose,we carry out a model at fiber scale, using Navier-Stokes equations in incompressible and monophasic formulation, Phillips equations [Phillips et al., 1992] and a rheological law [Krieger, 1972]. After validation step consisting in a comparison of computational results with experiments [Hampton et al., 1997] and theorical law [Belfort et al., 1994], this model has been used to simulate flow around geometries similar to those encountered in our composite material
Moussaed, Carine. "Modèles variationnels dynamique et hybride pour la simulation numérique d'écoulements turbulents." Thesis, Montpellier 2, 2013. http://www.theses.fr/2013MON20130/document.
Full textThis work is a contribution to the numerical simulation of turbulent flows with the aim of industrial application. At first, we focus on a new combination "VMS-LES/dynamic procedure" for the simulation of flows around circular and square cylinders. The VMS-LES approach adopted in this work is original in using an averaging procedure over agglomerated finite volumes in order to separate the scales, the dynamic approach being the one introduced by Germano in LES. A RANS/VMS-LES hybrid approach is then evaluated on the circular cylinder test case at high Reynolds numbers. This approach introduces a hybridization parameter which privileges the RANS model or the VMS-LES model according to the grid resolution. Finally, the performance of a two-level Schwarz algorithm, which uses the deflation and balancing methods, are examined in terms of efficiency and scalability in the context of VMS-LES simulations
Dudouit, Yohann. "Spatio-temporal refinement using a discontinuous Galerkin approach for elastodynamic in a high performance computing framework." Thesis, Bordeaux, 2014. http://www.theses.fr/2014BORD0248/document.
Full textThis thesis studies local mesh refinement both in time and space for the second order elastodynamic equation in a high performance computing context. The objective is to develop numerical methods to treat small heterogeneities that have global impact on wave propagation. We use an internal penalty discontinuous Galerkin finite element approach for its flexibity and parallelization capabilities. The elasto-acoustic finite element formulation we discuss is elasto-acoustic in order to handle local acoustic heterogeneities. We also propose an optimized penalty term more suited to the elastodynamic equation that results in better CFL condition. We improve a second order PML formulation with an original time discretization that results in a more stable formulation. Using the p-adaptivity and nonconforming mesh capabilities of discontinuous Galerkin methods combined with a local time stepping method, we greatly reduce the high computational cost of local refinements. These methods have been implemented in C++, using template metaprogramming, in a distributed memory (MPI) and shared memory (OpenMP) parallel code. Finally, we show the potential of our methods on validation test cases and on more realistic test cases with medium including hydrofractures