Tesis sobre el tema "Couplage des équations de Maxwell et de Boltzmann"
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Baranger, Céline. "Modélisation, étude mathématique et simulation des collisions". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2004. http://tel.archives-ouvertes.fr/tel-00008826.
Texto completoLe premier résultat que nous présentons est consacré à l'étude mathématique d'un couplage entre une équation cinétique de type Vlasov et les équations d'Euler isentropiques. Ces équations modélisent un spray fin. Nous démontrons l'existence en temps petit d'une solution régulière pour le couplage Vlasov-Euler isentropique.
Ensuite, nous présentons les équations précises relatives à la modélisation des collisions, coalescences et fragmentations dans un spray.
Nous décrivons par la suite la simulation numérique du couplage fluide-cinétique dans un code industriel (Commissariat à l'Énergie Atomique), en particulier l'ajout des phénomènes de collisions.
Un deuxième modèle de fragmentation est également présenté. Ce modèle est plus pertinent dans les cas où les particules de la phase dispersée ont un grand nombre de Weber.
Enfin, nous présentons un résultat concernant une estimation explicite de trou spectral pour l'opérateur de Boltzmann avec potentiels durs linéarisé, et pour l'opérateur de Landau avec potentiels durs linéarisé.
Papon, Laurence. "Approximation paraxiale des équations de Vlasov-Maxwell et applications". Paris 6, 1993. http://www.theses.fr/1993PA066619.
Texto completoSirbu, Marina. "Couplage des équations de Maxwell avec l'équation de Boltzmann en 3D : appliqué à la modélisation d'un photocommutateur THz". Paris 11, 2005. http://www.theses.fr/2005PA112255.
Texto completoThis PhD thesis presents the coupling between the Boltzmann transport equations and the electromagnetic field equations in a photoconductive switch generating THz signals. First, the transport equations are solved in the drift diffusion approximation. Then, a more complex resolution is made with a Monte Carlo based model. The photoconductive switch is located is coplanar wave guide whose dimensions are comparables with the existents structures. The numerical constraints come from the time dependant resolution, the necessarily space mesh, the simulation domain dimensions, boundary conditions and non linearity introduced by the time and space coefficients variation. The 3D equation system is solved with the variable space step FDTD (Finite Difference Time Domain) method, which allows a sufficiently refined mesh inside the switch. We have studied the photoconductive switch response when a femto second optic excitation is applied. We have shown the electromagnetic field implication in the device response origin. We also made a parametric analysis identifying the main parameters controlling the electromagnetic THz pulse. There is a good agreement between the modelling results and the experimental data. The Monte Carlo method allows taking into account the inertial effects between the electromagnetic field variation and the carrier response. This method is still in developing phase, but we have obtained good preliminary results
Ast, Isabelle d'. "Calcul parallèle en mécanique des fluides et problèmes spécifiques au couplage magnétohydrodynamique". Toulouse, INPT, 1995. http://www.theses.fr/1995INPT041H.
Texto completoBarthelmé, Régine. "Le problème de conservation de la charge dans le couplage des équations de Vlasov et de Maxwell". Université Louis Pasteur (Strasbourg) (1971-2008), 2005. https://publication-theses.unistra.fr/public/theses_doctorat/2005/BARTHELME_Regine_2005.pdf.
Texto completoGatard, Ludovic. "Méthodes d'équations intégrales de frontière d'ordre élevé pour les équations de Maxwell : couplage de la méthode de discrétisation microlocale et de la méthode multipôle rapide FMM". Bordeaux 1, 2007. http://www.theses.fr/2007BOR13416.
Texto completoHamiaz, 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/.
Texto completoThis 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
Balin, Nolwenn. "Etude de méthodes de couplage pour la résolution des équations de Maxwell : application au calcul de la signature radar d’aéronefs par hybridation de méthodes exactes et asymptotiques". Toulouse, INSA, 2005. http://www.theses.fr/2005ISAT0012.
Texto completoThis thesis is concerned with the numerical simulation of the scattering of an electromagnetic wave by air-breathing aircraft, represented by a deep and narrow cavity within a large perfectly conducting structure. Due to the size and the complexity of this object, the classical methods (full-wave and asymptotic) cannot be successfully applied. The aim of this study is to develop a new hybrid method to solve this kind of problem. The methods have first been developed and validated in the 2D case and then extended to the 3D case. At first, for the treatment of the cavity, a new substructuring domain decomposition method based on a boundary element formulation and a frontal forward substitution was developed. After this step, the remaining equations are set on the aperture of the cavity and the rest of the boundary of the structure. Next, to reduce the size of the resulting external problem, we use a Schwarz method associated with an overlapping boundary decomposition well-suited for the boundary integral equations. Finally, for the part of the boundary that does not cover the aperture of the cavity, we introduce an asymptotic method, based on the radiation of equivalent currents by a Generalized Ray Expansion process. The use of the previous algorithm ensures a strong coupling between the subdomains. We have mathematically established the stability and solvability of the cavity factorization method. We have also numerically demonstrated the efficiency of these three elementary steps and of the whole hybridization process
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/.
Texto completoWe 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
Godinho, Pereira David. "Contribution à l'étude des équations de Boltzmann, Kac et Keller-Segel à l'aide d'équations différentielles stochastiques non linéaires". Phd thesis, Université Paris-Est, 2013. http://tel.archives-ouvertes.fr/tel-00975091.
Texto completoZaki, Abdou. "Modélisation d’antennes de type circuit imprimé méthode purement surfacique et couplage avec des éléments finis : Application à l’imagerie par résonance magnétique". Cergy-Pontoise, 2006. http://biblioweb.u-cergy.fr/theses/06CERG0350.pdf.
Texto completoMy subject relates to the study of some problems of antennas LTED used in IRM. They are dielectric cover partially by a very fine layer of metal. We proposed three formulations based on methods of the surface types. It is a method which associates finite elements in the dielectric one and a simple cutting on metal. It makes it possible to reduce the number of unknown factors considerably. A complete study of each formulation was proposed and compared with another method which associates finished Elements and integral methods for some types of antennas
Garnier, Romain. "Contribution à la résolution des équations de Maxwell dans les structures périodiques par la méthode des éléments finis". Phd thesis, Toulouse 3, 2013. http://thesesups.ups-tlse.fr/1944/.
Texto completoElectromagnetic periodic structures are of great interest. These structures act as frequency filters and allow the manufacturing of meta-materials which appear to be composite and artificial. They exhibit electromagnetic properties that are unusual to natural materials such as band gaps. This allows new devices to guide, focus or stop the propagation. This is for example useful to avoid coupling between various radiating elements via the characterization of the surface waves which propagate at the interface between air and the periodic structure. This thesis provides a description of the finite element method dedicated to the characterization of periodic structures. Numerical modelling results in eigenvalue problems of large sizes. It involves solving linear systems compounds of sparse matrices. A method is therefore discussed for solving this type of problem, optimizing and combining different algorithms. Before discussing the different aspects of the developed method, we establish an exhaustive list of all the existing methods by stating their advantages and drawbacks. We note that the finite element method can handle a wide range of periodic structures in three dimensions without limitation on their shape. We present different formulations of this method. Then the algorithmic aspects of the method are detailed. We show that an analysis of the resolution settings can impact the physical interpretations of the results. Finally we show the performance of our tool on classical validation results from the bibliography and we discuss the characterization of surface waves. Therefore, the study of a patch antenna array included in metal cavities is conducted. To conclude we can say that the studies conducted in this thesis have resulted in the production of a code used in an environment calculation initially present at ONERA
Garnier, Romain. "Contribution à la résolution des équations de Maxwell dans les structures périodiques par la méthode des éléments finis". Phd thesis, Université Paul Sabatier - Toulouse III, 2013. http://tel.archives-ouvertes.fr/tel-00878558.
Texto completoGiraudon, Cyril. "Contribution à la simulation électromagnétique dans le domaine temporel : Approches électromagnétique et informatique". Limoges, 2002. http://www.theses.fr/2002LIMO0019.
Texto completoCambon, Sebastien. "Méthode d'éléments finis d'ordre élevé et d'équations intégrales pour la résolution de problème de furtivité radar d'objets à symétrie de révolution". Thesis, Toulouse, INSA, 2012. http://www.theses.fr/2012ISAT0047/document.
Texto completoIn this thesis, we are interested in modeling diffraction of electromagnetic waves by axisymmetric and highly heterogeneous objects. Our method consists in a coupling between partial differential equations and integral equations. This idea is mainly interesting for two reasons : heterogeneities are handled naturally in the formulation and integral equations give an analytical representation of solutions outside the object based on surface currents.These advantages allow us to limit the domain of simulation to the object itself. In addition,using Fourier series combined with the rotational invariance property of the object, the 3D problem is reduced to a countable set of 2D problems. The study of these problems is split into several parts. Each part has to deal with aspecific problem as for example the numerical integration of singular integrals which is difficult to achieve. As a first step, we study time-harmonic Maxwell’s equations in a bounded domain for which we develop a new high-order finite element method and present its efficiency and accuracy on many examples. Secondly, we consider the diffraction of plane waves by perfect electric conductors to analyse integral equations for these kind of object.The boundary finite element method applied is defined by extension of the previous one via tangential trace operator. Then, we solve the coupled problem using a well chosen formulation based on the previous studies for which our finite element method is naturally adapted by construction. In order to evaluate its efficiency, a comparison is performed between our program « AxiMax » and one based on a purely 3D model. To conclude, in the last two chapters, we present the numerical integration method and the multi-processing algorithm developed in AxiMax. In all cases, we put forward the fact that our finite element method provides accurate results depending on the quality of the simulation parameters
Dellacherie, Stéphane. "Contribution à l'analyse et à la simulation numériques des équations cinétiques décrivant un plasma chaud". Phd thesis, Université Paris-Diderot - Paris VII, 1998. http://tel.archives-ouvertes.fr/tel-00479816.
Texto completoNtovoris, Eleftherios. "Contribution à la théorie des EDP non linéaires avec applications à la méthode des surfaces de niveau, aux fluides non newtoniens et à l'équation de Boltzmann". Thesis, Paris Est, 2016. http://www.theses.fr/2016PESC1057/document.
Texto completoThis thesis consists of three different and independent chapters, concerning the mathematical study of three distinctive physical problems, which are modelled by three non- linear partial differential equations. These equations concern the level set method, the theory of incompressible flow of non-Newtonian materials and the kinetic theory of rare- fied gases. The first chapter of the thesis concerns the dynamics of moving interfaces and contains a rigorous justification of a numerical procedure called re-initialization, for which there are several applications in the context of the level set method. We apply these results for first order level set equations. We write the re-initialization procedure as a splitting algorithm and study the convergence of the algorithm using homogenization techniques in the time variable. As a result of the rigorous analysis, we are also able to introduce a new method for the approximation of the distance function in the context of the level set method. In the case where one only looks for a level set function with gradient bounded from below near the zero level, we propose a simpler approximation. In the general case where the zero level might present changes of topology we introduce a new notion of relaxed limits. In the second chapter of the thesis, we study a free boundary problem arising in the study of the flow of an incompressible non-Newtonian material with Drucker-Prager plasticity on an inclined plane. We derive a subdifferential equation, which we reformulate as a variational problem containing a term with linear growth in the gradient variable, and we study the problem in an unbounded domain. We show that the equations are well posed and satisfy some regularity properties. We are then able to connect the physical parameters with the abstract problem and prove some quantitative properties of the solution. In particular, we show that the solution has compact support and the support is the free boundary. We also construct explicit solutions of an ordinary differential equation, which we use to estimate the free boundary. The last chapter of the thesis is dedicated to the study of infinite energy solutions of the homogeneous Boltzmann equation with Maxwellian molecules. We obtain new results concerning the existence of eternal solutions in the space of probability measure with infinite energy (i.e. the second order moment is infinite). These solutions describe the asymptotic behaviour of other infinite energy solutions but could also be useful in the study of intermediate asymptotic states of solutions with finite but arbitrarily large energy. We use harmonic analysis tools to study the equation, where the velocity variable is expressed in the Fourier space. Finally, a logarithmic scaling of the time variable allows to determine the correct asymptotic scaling of the solutions