Дисертації з теми "Schémas préservant la structure"
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Alama, Bronsard Yvonne. "Schémas numériques pour les équations dispersives non linéaires : analyse à faible régularité, cadre aléatoire et préservation de symétries." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS065.
The work presented in this thesis belongs to the field of numerical analysis, and builds on tools stemming from the study of partial differential equations (PDEs). We focus on time discretizations to nonlinear dispersive equations. The aim is to reduce the smoothness assumptions on the design and analysis of numerical methods, in order to treat low-regularity dynamics.Part I of the thesis develops novel low-regularity schemes, suited for general bounded domains. Chapter 2 presents first and second order convergence results for the Gross-Pitaevskii equation, when both the initial data and the potential are non-smooth. Chapter 3 generalizes the construction of these schemes to higher order and to a general class of nonlinear evolution equations with potentials.Part II of the thesis consists of Chapter 4, which considers higher-order constructions for randomized initial conditions. Part III of the thesis considers the long-time properties and invariants of the equation, and deals with structure-preserving schemes. We first introduce in Chapter 5 a novel symmetric time integrator for the nonlinear Schr ̈odinger equation. We give fractional convergence rates as a function of the Sobolev regularity of the initial data. Chapter 6 extends the latter work by constructing higher order symmetric integrators for a general class of dispersive equations. All these new symmetric schemes exhibit excellent structure preservation and convergence properties, which are witnessed in numerical experiments.The higher order extensions of Chapters 3, 4, 6 follow new techniques based on decorated tree series, inspired by singular stochastic PDEs via the theory of Regularity Structures
Falissard, Fabrice. "Schémas numériques préservant la vorticité en aérodynamique compressible." Phd thesis, Paris, ENSAM, 2006. http://pastel.archives-ouvertes.fr/pastel-00002056.
Blachère, Florian. "Schémas numériques d'ordre élevé et préservant l'asymptotique pour l'hydrodynamique radiative." Thesis, Nantes, 2016. http://www.theses.fr/2016NANT4020/document.
The aim of this work is to design a high-order and explicit finite volume scheme for specific systems of conservation laws with source terms. Those systems may degenerate into diffusion equations under some compatibility conditions. The degeneracy is observed with large source term and/or with late-time. For instance, this behaviour can be seen with the isentropic Euler model with friction or with the M1 model for radiative transfer, or with the radiation hydrodynamics model. We propose a general theory to design a first-order asymptotic preserving scheme (in the sense of Jin) to follow this degeneracy. The scheme is proved to be stable and consistent under a classical hyperbolic CFL condition in both hyperbolic and diffusive regimes, for any 2D unstructured mesh. Moreover, we justify that the developed scheme also preserves the set of admissible states in all regimes, which is mandatory to conserve physical solutions. This construction is achieved by using the non-linear scheme of Droniou and Le Potier as a target scheme for the diffusive equation, which gives the form of the global scheme for the complete system of conservation laws. Then, the high-order scheme is constructed with polynomial reconstructions and the MOOD paradigm as a limiter. The main difficulties are the preservation of the set of admissible states in both regimes on unstructured meshes and to deal with the high-order polynomial reconstruction in the diffusive limit without losing the asymptotic preserving property. Numerical results are provided to validate the scheme in all regimes, with the first and high-order versions
Duarte, Denio. "Une méthode pour l'évolution de schémas XML préservant la validité des documents." Phd thesis, Tours, 2005. http://tel.archives-ouvertes.fr/tel-00009693.
L'utilisateur donne au système ce qu'il souhaite comme nouveau document devant être accepté par le schéma.
À partir de ce document, le système construit des schémas candidats, qui d'une part préservent la validité de la base de documents et, d'autre part augmentent la classe de documents acceptée par le schéma.
L'approche est implantée par un algorithme appelé GREC.
Cet algorithme utilise l'automate d'arbre A qui accepte le langage défini par le schéma pour trouver les informations nécessaires à la modification.
Plus précisément, il utilise les expressions régulières des règles de transitions de A pour proposer les candidats.
Ainsi, les modifications sont faites sur les graphes qui représentent les automates d'états finis construits à partir des expressions régulières concernées.
Les expressions régulières engendrées par GREC représentent des schémas présentés à l'utilisateur afin qu'il choisisse le plus adapté à la sémantique de son application.
Hoarau, Emma. "Mise en évidence de la brisure de symétrie des schémas numériques pour l'aérodynamique et développement de schémas préservant ces symétries." Paris 6, 2009. http://www.theses.fr/2009PA066650.
Bulteau, Solène. "Développement et analyse de schémas numériques préservant les régimes asymptotiques de diffusion linéaire et non linéaire." Thesis, Nantes, 2019. http://www.theses.fr/2019NANT4046.
The aim of this work is to build and analyse schemes able to discretize the solutions of hyperbolic systems of conservation laws endowed with a source term. The main property required here is the preservation of the asymptotic behaviour, in other words the schemes must stay accurate in the diffusive regime, namely the long time and stiff source term regime. This manuscript is divided in two parts. The first one is dedicated to the presentation of a rigourous numerical convergence result for a scheme discretizing the solutions of the p-system. The convergence rate obtained is explicitly exhibited and coincides with the results obtained in the continuous and semi-discrete frameworks. The second part is devoted to the development of asymptotic preserving schemes and two methods are proposed. The first one is a generalization of the perturbed HLL method introduced by Berthon and Turpault in order to treat source terms of quadratic form and the second one is able to preserve both all the steady states and the diffusive limit
Bennoune, Mounir. "Approximation numérique de quelques équations cinétiques préservant leurs asymptotiques fluides." Toulouse 3, 2009. http://thesesups.ups-tlse.fr/845/.
This thesis is a contribution in the development of asymptotic preserving numerical schemes for kinetic equations. This work contains two parts. The first one is concerned with the development of numerical schemes for like Boltzmann kinetic equations, which are able to preserve the Euler limit as well as the compressible Navier-Stokes asymptotics (which is not a limit) near the hydrodynamical regime. Our strategy consists in rewriting the kinetic equation as a coupled system of kinetic part and macroscopic one, by using the micro-macro decomposition of the distribution function as a sum of its corresponding (Maxwellian) equilibrium distribution plus the deviation. The simulations are performed for the one-dimensional BGK model, and then extended for this model in higher velocity dimension. The second part is concerned with the construction of asymptotic preserving scheme in the diffusion limit for the Kac's equation. This model is much simpler that the Boltzmann equation (it is one dimensional), but it has the same quadratic structure, while the models used in the previous part were only relaxation operators. However, contrary to the Boltzmann equation, the natural fluid limit of the Kac model is a non linear diffusion equation. We also construct in this part a deterministic velocity discretization for the collisional operator. Such discretization is based on a simple new formulation of the Kac operator. Several simulations are presented in order to illustrate the efficiency of our approach
Delhem, Romain. "Verbes labiles et schémas de complémentation en anglais." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUL068.
Within a constructionist framework, this thesis studies English labile verbs, which can enter into various syntactic configurations without changing form. A study of their complementation shows that categorizing them into semantic families is relevant but not sufficient to explain their behavior. The thesis defends a syncretic approach to verb complementation to that accounts for its important productivity and its sometimes arbitrary limits. It is shown that all verbs have a default syntactic configuration, which is not meaningful and which simply allows the verb to express its arguments in an unmarked way, in accordance with certain principles of conceptual coherence. Conversely, when the complementation of the verb has an identifiable semantic contribution, the existence of fully meaningful patterns of complementation is posited. These are defined as sets of complements, whose meaning is distinct from that of the verb with which they are associated and is found regularly with verbs of diverse categories. It is shown that patterns of complementation should be considered fully-fledged English linguistic units. This implies that synchronically, these patterns are mentally stored by speakers rather than the result of a process of analogy with existing constructions. Their status as linguistic units makes it possible to study their meaning in the same way as more classical lexical units. Although most of them are polysemic, some patterns of complementation exhibit uses that are difficult to link semantically and must therefore be viewed as homonyms
Ben, Kahla Haithem. "Sur des méthodes préservant les structures d'une classe de matrices structurées." Thesis, Littoral, 2017. http://www.theses.fr/2017DUNK0463/document.
The classical linear algebra methods, for calculating eigenvalues and eigenvectors of a matrix, or lower-rank approximations of a solution, etc....do not consider the structures of matrices. Such structures are usually destroyed in the numerical process. Alternative structure-preserving methods are the subject of an important interest mattering to the community. This thesis establishes a contribution in this field. The SR decomposition is usually implemented via the symplectic Gram-Schmidt algorithm. As in the classical case, a loss of orthogonality can occur. To remedy this, we have proposed two algorithms RSGSi and RMSGSi, where the reorthogonalization of a current set of vectors against the previously computed set is performed twice. The loss of J-orthogonality has significantly improved. A direct rounding error analysis of symplectic Gram-Schmidt algorithm is very hard to accomplish. We managed to get around this difficulty and give the error bounds on the loss of the J-orthogonality and on the factorization. Another way to implement the SR decomposition is based on symplectic Householder transformations. An optimal choice of free parameters provided an optimal version of the algorithm SROSH. However, the latter may be subject to numerical instability. We have proposed a new modified version SRMSH, which has the advantage of being numerically more stable. By a detailes study, we are led to two new variants numerically more stables : SRMSH and SRMSH2. In order to build a SR algorithm of complexity O(n³), where 2n is the size of the matrix, a reduction to the condensed matrix form (upper J-Hessenberg form) via adequate similarities is crucial. This reduction may be handled via the algorithm JHESS. We have shown that it is possible to perform a reduction of a general matrix, to an upper J-Hessenberg form, based only on the use of symplectic Householder transformations. The new algorithm, which will be called JHSH algorithm, is based on an adaptation of SRSH algorithm. We are led to two news variants algorithms JHMSH and JHMSH2 which are significantly more stable numerically. We found that these algortihms behave quite similarly to JHESS algorithm. The main drawback of all these algorithms (JHESS, JHMSH, JHMSH2) is that they may encounter fatal breakdowns or may suffer from a severe form of near-breakdowns, causing a brutal stop of the computations, the algorithm breaks down, or leading to a serious numerical instability. This phenomenon has no equivalent in the Euclidean case. We sketch out a very efficient strategy for curing fatal breakdowns and treating near breakdowns. Thus, the new algorithms incorporating this modification will be referred to as MJHESS, MJHSH, JHM²SH and JHM²SH2. These strategies were then incorporated into the implicit version of the SR algorithm to overcome the difficulties encountered by the fatal breakdown or near-breakdown. We recall that without these strategies, the SR algorithms breaks. Finally ans in another framework of structured matrices, we presented a robust algorithm via FFT and a Hankel matrix, based on computing approximate greatest common divisors (GCD) of polynomials, for solving the problem pf blind image deconvolution. Specifically, we designe a specialized algorithm for computing the GCD of bivariate polynomials. The new algorithm is based on the fast GCD algorithm for univariate polynomials , of quadratic complexity O(n²) flops. The complexitiy of our algorithm is O(n²log(n)) where the size of blurred images is n x n. The experimental results with synthetically burred images are included to illustrate the effectiveness of our approach
Mokrane, Abdellah. "Sur la structure de la cohomologie cristalline logarithmique des schémas semi-stables." Paris 11, 1992. http://www.theses.fr/1992PA112041.
Habacha, Hamada Anja. "Reconnaissance de symboles techniques et analyse contextuelle de schémas." Vandoeuvre-les-Nancy, INPL, 1993. http://docnum.univ-lorraine.fr/public/INPL_T_1993_HABACHA_HAMADA_A.pdf.
Chabassier, Juliette. "Modélisation et simulation numérique d'un piano par modèles physiques." Palaiseau, Ecole polytechnique, 2012. https://theses.hal.science/docs/00/67/88/18/PDF/These.pdf.
The purpose of this study is the time domain modeling and numerical simulation of a piano. We aim at explaining the vibratory and acoustical behavior of the piano, by taking into account the main elements that contribute to sound production. The soundboard is modeled as a bidimensional thick, orthotropic, heterogeneous, frequency dependant damped plate, using Reissner Mindlin equations. The vibroacoustics equations allow the soundboard to radiate into the surrounding air, in which we wish to compute the complete acoustical field around the perfectly rigid rim. The soundboard is also coupled to the strings at the bridge, where they form a slight angle from horizontal. Each string is modeled by a one dimensional damped system of equations, taking into account not only the transversal waves excited by the hammer, but also the stiffness thanks to shear waves, as well as the longitudinal waves arising from geometric nonlinearities. The hammer is given an initial velocity that projects it towards a choir of strings, before being repelled. The interacting force is a nonlinear function of the hammer compression. The final piano model that will be discretized is a coupled system of partial differential equations, each of them exhibiting specific difficulties (nonlinear nature of the string system of equations, frequency dependant damping of the soundboard, great number of unknowns required for the acoustic propagation), in addition to couplings' inherent difficulties. On the one hand, numerical stability of the discrete scheme can be compromised by nonlinear and coupling terms. A very efficient way to guarantee this stability is to construct a numerical scheme which ensures the conservation (or dissipation) of a discrete equivalent of the continuous energy, across time steps. A major contribution of this work has been to develop energy preserving schemes for a class of nonlinear systems of equations, in which enters the string model. On the other hand, numerical efficiency and computation time reduction require that the unknowns of each problem's part, for which time discretization is specific, hence different, be updated separately. To achieve this artificial decoupling, adapted Schur complements are performed after Lagrange multipliers are introduced. The potential of this time domain piano modeling is emphasized by realistic numerical simulations. Beyond greatly replicating the measurements, the program allows us to investigate the influence of physical phenomena (string stiffness or nonlinearity), geometry or materials on the general vibratory behavior of the piano, sound included. Spectral enrichment, " phantom partials " and nonlinear precursors are clearly revealed when large playing amplitudes are involved, highlighting how this approach can help better understand how a piano works
Dakin, Gautier. "Couplage fluide-structure d'ordre (très) élevé pour des schémas volumes finis 2D Lagrange-projection." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066404/document.
This work is devoted to the construction of stable and high-order numerical methods in order to simulate fluid - rigid body interactions. In this manuscript, a bibliographic overview is done, which highlights theoretical results about hyperbolic system of conservation laws, as well as the methods available in the literature for the hydrodynamics simulation and the numericalboundary treatment. A high-order accurate scheme is proposed on staggered Cartesian grids to approximate the solution of Euler equations in 1D and 2D. The scheme relies on Lagrange-remap formalism, and although formulated in internal energy, ensures both conservation and weak consistency thanks to an internal energy corrector. In the same time, the study of high-order numerical boundary treatment for linear hyperbolic system is done. It highlights the necessity to focus especially on the linear stability of the effective scheme. Starting from the linear results, the numerical boundary treatment with imposed normal velocity is done for Euler equations in 1D and 2D. Last, the coupling between a compressible fluid and a rigid body is realized, using the designed procedure for numerical boudary treatment
Chabassier, Juliette. "Modélisation et simulation numérique d'un piano par modèles physiques." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00690351.
Fedele, Baptiste. "Étude mathématique et numérique d'équations cinétiques et fluides multi-échelles pour la description d'un plasma de fusion." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30097.
This thesis deals with the mathematical modeling and the numerical simulation of several evolution equations with a stiff term which model phenomena coming from plasma physics and fluid mechanics. Thermonuclear plasmas are a highly unstable and anisotropic medium, where the occurrence of several interesting mathematical problems. The first part concerns toy-models obtained from the anisotropic Vlasov equation. The aim is to develop numerical methods (in particular asymptotic-preserving schemes) which resolve efficiently these problems, in the aim to pass then to more complex physical models. In particular, this work has permitted to highlight both advantages and drawbacks of the developed numerical schemes depending on the considered problem. The second part is dedicated to the study of more complex models, in particular to the Vlasov-Poisson system. From a numerical point of view, an AP scheme is developed, based on a Micro-Macro decomposition coupled with a regularization technique. Thanks to this scheme, it is possible to attain the BGK waves, solution of the Vlasov-Poisson equation, in few time iterations, avoiding thus an important accumulation of numerical errors. The last part focus on the study of a Vorticity-Poisson system, coming from fluid mechanics. In particular, two characteristics flows of this system are investigated : the so-called Taylor-Green and Kolmogorov flows. The first one permits mainly to validate our numerical procedure, similar to that evocated in the last part. However, the Kolmogorov flow is more deeply studied. It can lead to an unstable flow under certain conditions. An analytical result for the linear instability is given, linking the growth rate of the instability phase with the aspect ratio of the domain. Then, both non-linear and saturation phases are numerically investigated. In particular, the special AP-properties of our scheme permit us to attain in only few iterations a new equilibrium of the instability
Chauvat, Yann. "Le phénomène de "carbuncle" : analyse d'une pathologie des schémas numériques à capture de choc." Toulouse, ENSAE, 2005. http://www.theses.fr/2005ESAE0015.
Braud, Laurent. "The structure of orders in the pushdown hierarchy." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00587409.
Boukadida, Thameur. "Convergence de schémas numériques adaptés à la convection non linéaire bidimensionnelle : application à des couplages de modes en plasma." Bordeaux 1, 1988. http://www.theses.fr/1988BOR10569.
Guisset, Sébastien. "Modélisation et méthodes numériques pour l'étude du transport de particules dans un plasma chaud." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0117/document.
Angular moments models represent alternative descriptions situated in between the kinetic and the fluid models. In this work, angular moments models based on an entropy minimisation principle are considered for plasma physics applications. This manuscript is organised in three parts. The first one is a contribution to plasma physics modelling within the formalism of angular moments models. The validity domain of angular moments models in collisionless regimes is studied. It is also shown that the collisional operators proposed for the M1 angular moments model enable to recover accurate plasma transport coefficients. The second part of this document deals with the derivation of numerical methods for the long timescales particle transport. Appropriate asymptotic-preserving numerical schemes are designed for the M1 angular moments model and numerical validations are performed. The third part represents a first important step toward multi-species modelling. The M1 angular moments model in a moving frame is introduced and applied to rarefied gas dynamics. The model properties are highlighted, a numerical scheme is proposed and a numerical validation is carried out
Landajuela, Larma Mikel. "Coupling schemes and unfitted mesh methods for fluid-structure interaction." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066053/document.
This thesis is devoted to the numerical approximation of mechanical systems involving the interaction of a deformable thin-walled structure with an internal or surrounding incompressible fluid flow. In the first part, we introduce two new classes of explicit coupling schemes using fitted meshes. The methods proposed combine a certain Robin-consistency in the system with (i) a projection-based time-marching in the fluid or (ii) second-order time-stepping in both the fluid and the solid. The stability properties of the methods are analyzed within representative linear settings. This part includes also a comprehensive numerical study in which state-of-the-art coupling schemes (including some of the methods proposed herein) are compared and validated against the results of an experimental benchmark. In the second part, we consider unfitted mesh formulations. The spatial discretization in this case is based on variants of Nitsche’s method with cut elements. We present two new classes of splitting schemes which exploit the aforementioned interface Robin-consistency in the unfitted framework. The semi-implicit or explicit nature of the splitting in time is dictated by the order in which the spatial and time discretizations are performed. In the case of the coupling with immersed structures, weak and strong discontinuities across the interface are allowed for the velocity and pressure, respectively. Stability and error estimates are provided within a linear setting. A series of numerical tests illustrates the performance of the different methods proposed
Nouveau, Léo. "Adaptive residual based schemes for solving the penalized Navier Stokes equations with moving bodies : application to ice shedding trajectories." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0410/document.
The prediction of solid motion evolving in a fluid presents a real interest for engineering application such as ice accretion on aerodynamics bodies.In this context, considering de-icing systems, the ice shedding trajectory is needed to prevent the risk of collision/ingestion of the ice in/with some sensitive part of the aircraft. This application raises many challenges from a numerical point of view, especially concerning mesh generation/adaptation as the solid moves in the computational domain. To handle this issue, in this work the solids are known implicitly on the mesh via a level set function. An immersed boundary method, called penalization, is employed to impose the wall boundary conditions. To improve the resolution of these boundaries, the equations are solved on adaptive unstructured grids. This allows to have are finement close to the solid boundary and thus increases the solid definition,leading to a more accurate imposition of the wall conditions. To save computational time, and avoid costly remeshing/interpolation steps, the strategy chosen for unsteady simulations is to use a constant connectivity mesh adaptation,also known as r-adaptation
Moubachir, Marwan. "Contrôle des phénomènes d'interaction fluide-structure, application à la stabilité aéroélastique." Phd thesis, Ecole Nationale des Ponts et Chaussées, 2002. http://tel.archives-ouvertes.fr/tel-00350505.
Sarazin, Desbois Céline. "Méthodes numériques pour des systèmes hyperboliques avec terme source provenant de physiques complexes autour du rayonnement." Phd thesis, Université de Nantes, 2013. http://tel.archives-ouvertes.fr/tel-00814182.
Liang, Yan. "Mise en œuvre d'un simulateur en OCCAM pour la conception d'architectures parallèles à base d'une structure multiprocesseur hiérarchique." Compiègne, 1989. http://www.theses.fr/1989COMPD176.
The simulation has become an indispensable phase for conception of parallel processing systems, and enables to avoid construction of expensive prototypes. In this paper, a parallel process-oriented simulator written in OCCAM language has been developed. Our objective is to conceive a simulator adapted to a network of transputers for prototyping parallel processing systems by connecting directly the serial transputer channels. As a simulation example, a parallel processor system (coprocessor) based on hierarchical structure : master-slave has been realized at the processor-memory-switch level. The performance analysis is obtained via two queuing models : the former as independent M/M/1 systems and the latter as a M/M/s system. The experimental performance is measured respectively based on the independent tasks and the sequential tasks. The comparison of analytic and experimental results enables us to constate the advantage and limit of the coprocessor and to encourage us to its implementation
Burel, Aliénor. "Contributions à la simulation numérique en élastodynamique : découplage des ondes P et S, modèles asymptotiques pour la traversée de couches minces." Phd thesis, Université Paris Sud - Paris XI, 2014. http://tel.archives-ouvertes.fr/tel-01060178.
Sabat, Macole. "Modèles euleriens et méthodes numériques pour la description des sprays polydisperses turbulents." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLC086.
In aeronautical combustion chambers, the ability to simulate two-phase flows gains increasing importance nowadays since it is one of the elements needed for the full understanding and prediction of the combustion process. This matter is motivated by the objective of improving the engine performance and better predicting the pollutant emissions. On the industrial scale, the description of the fuel spray found downstream of the injector is preferably done through Eulerian methods. This is due to the intrinsic statistical convergence of these methods, their natural coupling to the gas phase and their efficiency in terms of High Performance Computing compared to Lagrangian methods. In this thesis, the use of Kinetic-Based Moment Method with an Anisotropic Gaussian (AG) closure is investigated. By solving all velocity moments up to second order, this model reproduces statistically the main features of small scale Particles Trajectories Crossing (PTC). The resulting hyperbolic system of equations is mathematically well-posed and satisfies the realizability properties. This model is compared to the first order model in the KBMM hierarchy, the monokinetic model MK which is suitable of low inertia particles. The latter leads to a weakly hyperbolic system that can generate δ-shocks. Several schemes are compared for the resolution of the hyperbolic and weakly hyperbolic system of equations. These methods are assessed based on their ability to handle the naturally en- countered singularities due to the moment closures, especially without globally degenerating to lower order or violating the realizability constraints. The AG is evaluated for the Direct Numerical Simulation of 3D turbulent particle-laden flows by using ASPHODELE solver for the gas phase, and MUSES3D solver for the Eulerian spray in which the new model is implemented. The results are compared to the reference Lagrangian simulation as well as the MK results. Through the qualitative and quantitative results, the AG is found to be a predictive method for the description of moderately inertial particles and is a good candidate for complex simulations in realistic configurations where small scale PTC occurs. Finally, within the framework of industrial turbulence simulations a fully kinetic Large Eddy Simulation formalism is derived based on the AG model. This strategy of directly applying the filter on the kinetic level is helpful to devise realizability conditions. Preliminary results for the AG-LES model are evaluated in 2D, in order to investigate the sensitivity of the LES result on the subgrid closures
Betina, Adel. "Structure locale des variétés p-adiques de Hecke-Hilbert aux points classiques de poids 1." Thesis, Lille 1, 2016. http://www.theses.fr/2016LIL10036/document.
We show that the Eigenvariety attached to Hilbert modular forms over a totally real field F is smooth at the points corresponding to certain classical weight one theta series and we give a precise criterion for etaleness over the weight space at those points. In the case where the theta series has real multiplication, we construct a non-classical overconvergent generalised eigenform and compute its Fourier coefficient in terms of p-adic logarithms of algebraic numbers. When F = Q, we complete the work of Bellaïche-Dimitrov at the points where the Eigencurve is smooth but not etale over the weight space by giving a precise criterion for the ramication index to be 2. Our approach uses deformations and pseudo-deformations of Galois representations
Liu, Ning. "Modélisation Hamiltonienne à ports et commande distribuée de structures flexibles : application aux endoscopes biomédicaux à actionneurs à base de polymère électro-actif." Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCD054.
This thesis deals with the multiphysical modeling and the distributed control of flexible structures actuated by Ionic Polymer Metal Composite (IPMC) actuators. We firstly propose a model for the IPMC actuator using infinite dimensional port-Hamiltonian formulations in order to tackle the multiphysical and multiscale couplings. Lagrange multipliers are used to handle the mechanical constraints appearing in the actuator. The mechanical structure of the flexible structure is then modeled in 1D with beam models and in 2D with a thin shell model. Secondly, two structure preserving discretization methods are presented and extended to infinite dimensional dissipative port-Hamiltonian system with distributed input. The proposed IPMC actuator model is then discretized using the structure preserving finite differences method on staggered grids and validated on experimental data. Thirdly, we propose an in-domain distributed control law on a simplified model i.e. the vibrating string actuated with patches, that allows to shape the total energy of the system and to inject damping in order to stabilize the overall system with predefined performances
Ghanem, Assaf. "Contributions à la modélisation avancée des machines tournantes en dynamique transitoire dans le cadre Arlequin." Thesis, Lyon, INSA, 2013. http://www.theses.fr/2013ISAL0006.
Rotating machinery are subjected to specific vibratory phenomena related to various sources of excitation arising from rotation, vibration / rotation movements coupling, symmetry of the periodic or quasi-periodic structures, and internal and external damping. This work focuses on developing a methodology for coupling beam and 3D models for advanced dynamic analysis of rotating machinery. The Arlequin method is a multi-scale computation strategy allowing the coupling of numerical models of different nature through a technique of superposition. The extension of this method to the dynamics of rotating machinery framework offers the possibility of a better treatment of the energy aspects and wave propagation through the overlapping zone. To this end, several points are discussed. The first one concerns writing the Arlequin formalism in a transient dynamic regime for a 1D-3D coupling. Using the continuous and discrete formulations, questions regarding coupling different integration schemes and heterogeneous time scales are studied based on the total energy conservation of the coupled sub-domains. In the second point, a multi-scheme integration method based on a weighting partition of unity function of the Newmark’s scheme parameters in the gluing zone is proposed. It ensures the energy balance of the overall system and the continuity of kinematic quantities at the interface. This approach is then generalized to a multi-scheme / multi-scale framework. Based on displacement continuity in the recovering area, this new formalism allows the numerical integration with different time scales and heterogeneous time schemes while preserving the overall energy balance. The last point deals with two main components. In the first phase, a mixed formulation aiming at rotating machinery applications where a rotating and a fixed frame coexist is developed. In the second phase, the multi-scheme / multi-scale framework is extended and applied to the mixed formulation in order to obtain a general approach for analyzing advanced modeling of rotating machinery. The relevance of this work is illustrated by a representative application of rotating machines
Martin, Xavier. "Modélisation d'écoulements fluides en milieu encombré d'obstacles." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4759/document.
This document focuses on the modeling of compressible flows in one-dimensional (1D) pipes with variable cross-section, and in two or three-dimensional domains containing many small obstacles. The basic motivation is urged by the modeling of flows in the coolant circuit of pressurised water reactors (PWR). Thus this work aims at providing a new formulation for such a variety of flows. The basic idea consists in using an integral approach that is applied to the governing set of partial differential equations. Here the keystone is the conservative Euler set of equations, including mass, momentum and energy balance for any equation of state.Hence, the first chapter investigates the case of one-dimensional pipes with continuous or discontinuous cross-section. Once the 1D+ integral formulation has been presented, numerical results are compared with : (i) the classical Well-Balanced (WB) approach, and (ii) the reference solution obtained with a multi-dimensional code with huge mesh refinement.The second and third chapters provide some new insight on the numerical modeling of compressible flows in domains obstructed with many tubes. The integral formulation is derived, and numerical schemes are detailed, in order to handle fluid/fluid interfaces and wall boundaries. Schemes may be explicit (chapter 2), or implicit (chapter 3). A few analytic test cases are investigated. Focus is made on the flow incoming a region containing many tiny and aligned tubes. Here again, a comparison with the reference "fluid" solution is achieved; results are also compared with those arising from the WB approach, and with those coming from the 1D+ integral approach proposed in the first chapter
Boilevin-Kayl, Ludovic. "Modeling and numerical simulation of implantable cardiovascular devices." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS039.
This thesis, taking place in the context of the Mivana project, is devoted to the modeling and to the numerical simulation of implantable cardiovascular devices. This project is led by the start-up companies Kephalios and Epygon, conceptors of minimally invasive surgical solutions for the treatment of mitral regurgitation. The design and the simulation of such devices call for efficient and accurate numerical methods able to correctly compute cardiac hemodynamics. This is the main purpose of this thesis. In the first part, we describe the cardiovascular system and the cardiac valves before presenting some standard material for the mathematical modeling of cardiac hemodynamics. Based on the degree of complexity adopted for the modeling of the valve leaflets, two approaches are identified: the resistive immersed surfaces model and the complete fluidstructure interaction model. In the second part, we investigate the first approach which consists in combining a reduced modeling of the valves dynamics with a kinematic uncoupling of cardiac hemodynamics and electromechanics. We enhance it with external physiological data for the correct simulation of isovolumetric phases, cornerstones of the heartbeat, resulting in a relatively accurate model which avoids the complexity of fully coupled problems. Then, a series of numerical tests on 3D physiological geometries, involving mitral regurgitation and several configurations of immersed valves, illustrates the performance of the proposed model. In the third and final part, complete fluid-structure interaction models are considered. This type of modeling is necessary when investigating more complex problems where the previous approach is no longer satisfactory, such as mitral valve prolapse or the closing of a mechanical valve. From the numerical point of view, the development of accurate and efficient methods is mandatory to be able to compute such physiological cases. We then consider a complete numerical study in which several unfitted meshes methods are compared. Next, we present a new explicit coupling scheme in the context of the fictitious domain method for which the unconditional stability in the energy norm is proved. Several 2D numerical examples are provided to illustrate the properties and the performance of this scheme. Last, this method is finally used for 2D and 3D numerical simulation of implantable cardiovascular devices in a complete fluid-structure interaction framework
Boujelben, Abir. "Géante éolienne offshore (GEOF) : analyse dynamique des pales flexibles en grandes transformations." Thesis, Compiègne, 2018. http://www.theses.fr/2018COMP2442.
In this work, a numerical model of fluid-structure interaction is developed for dynamic analysis of giant wind turbines with flexible blades that can deflect significantly under wind loading. The model is based on an efficient partitioned FSI approach for incompressible and inviscid flow interacting with a flexible structure undergoing large transformations. It seeks to provide the best estimate of true design aerodynamic load and the associated dynamic response of such system (blades, tower, attachments, cables). To model the structure, we developed a 3D solid element to analyze geometrically nonlinear statics and dynamics of wind turbine blades undergoing large displacements and rotations. The 3D solid bending behavior is improved by introducing rotational degrees of freedom and enriching the approximation of displacement field in order to describe the flexibility of the blades more accurately. This solid iscapable of representing high frequencies modes which should be taken under control. Thus, we proposed a regularized form of the mass matrix and robust time-stepping schemes based on energy conservation and dissipation. Aerodynamic loads are modeled by using the 3D Vortex Panel Method. Such boundary method is relatively fast to calculate pressure distribution compared to CFD and provides enough precision. The aerodynamic and structural parts interact with each other via a partitioned coupling scheme with iterative procedure where special considerations are taken into account for large overall motion. In an effort to introduce a fatigue indicator within the proposed framework, pre-stressed cables are added to the wind turbine, connecting the tower to the support and providing more stability. Therefore, a novel complementary force-based finite element formulation is constructed for dynamic analysis of elasto-viscoplastic cables. Each of theproposed methods is first validated with differents estexamples.Then,several numerical simulations of full-scale wind turbines are performed in order to better understand its dynamic behavior and to eventually optimize its operation
Zafati, Eliass. "Couches absorbantes hybrides multi-pas de temps en dynamique des sols." Thesis, Lyon, INSA, 2015. http://www.theses.fr/2015ISAL0050/document.
This thesis which deals with the study of absorbing layers for soil dynamics problems, is divided into three essential parts. The first part aims to propose a design method of absorbing layers by the Rayleigh damping to simulate wave propagation problems in infinite media. This method is based on a mathematical analysis of the wave propagation problem in a media characterized by a Rayleigh damping matrix, which allows us, firstly, to establish conditions for minimizing spurious waves at the interfaces, and another hand, to provide a simple design relationship for the absorbing domain based on the notion of the logarithmic decrement. The second part aims to apply the multi-time step strategy for wave propagation problems in 1D and 2D infinite media. The proposed approach is to integrate the physical domain by an explicit scheme and the absorbing domain by an implicit scheme and to evaluate the potential of this method by varying the time step ratio between subdomains. Special attention is given to the 1D case for which the effect of the mesh fineness, defined by the number of finite elements per wavelength, is also analyzed. Furthermore, the evolution of computing time depending on the time ratio is studied in order to estimate the gains made with respect to a reference computation achieved by a full explicit integration. The last part is dedicated to the study of the Perfectly Matched Layer (PML) as part of hybrid couplings multi-time step. This section is introduced by a stability study of temporal scheme for 1D cases. The absorbing layer PML is integrated by an implicit scheme with a time step larger than that of the domain of interest. Although this coupling methodology is very effective for the reproduction of infinite media, parametric studies show a sensitivity to the time ratio greater than that exhibited by the Rayleigh damping layers