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Bernis, Laurent. "Etude mathématique d'équations aux dérivées partielles issues de la physique des plasmas (Vlasov-Poisson et Vlasov-Poisson-Boltzmann)". Orléans, 2006. http://www.theses.fr/2006ORLE2040.
Pełny tekst źródłaMadaule, Éric. "Schémas numériques adaptatifs pour les équations de Vlasov-Poisson". Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0112/document.
Pełny tekst źródłaMany numerical experiments are performed on the Vlasov-Poisson problem since it is a well known system from plasma physics and a major issue for future simulation of large scale plasmas. Our goal is to develop adaptive numerical schemes using discontinuous Galerkin discretisation combined with semi-Lagrangian description whose mesh refinement based on multi-wavelets. The discontinuous Galerkin formulation enables high-order accuracy with local data for computation. It has recently been widely studied by Ayuso de Dioset al., Rossmanith et Seal, etc. in an Eularian framework, while Guo, Nair and Qiu or Qiu and Shu or Bokanowski and Simarta performed semi-Lagrangian time resolution. We use multi-wavelets framework for the adaptive part. Those have been heavily studied by Alpert et al. during the nineties and the two thousands. Some works merging multi-scale resolution and discontinuous Galerkin methods have been described by Müller and his colleagues in 2014 for non-linear hyperbolic conservation laws in the finite volume framework. In the framework of relativistic Vlasov equation, Besse, Latu, Ghizzo, Sonnendrücker and Bertrand presented the advantage of using adaptive meshes. While they used wavelet decomposition, which requires large data stencil, multi-wavelet decomposition coupled to discontinuous Galerkin discretisation only requires local stencil. This favours the parallelisation but, at the moment, semi-Lagrangian remains an obstacle to highly efficient distributed memory parallelisation. Although most of our work is done in a 1d × 1v phase space, we were able to obtain a few results in a 2d × 2v phase space
Madaule, Éric. "Schémas numériques adaptatifs pour les équations de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2016. http://www.theses.fr/2016LORR0112.
Pełny tekst źródłaMany numerical experiments are performed on the Vlasov-Poisson problem since it is a well known system from plasma physics and a major issue for future simulation of large scale plasmas. Our goal is to develop adaptive numerical schemes using discontinuous Galerkin discretisation combined with semi-Lagrangian description whose mesh refinement based on multi-wavelets. The discontinuous Galerkin formulation enables high-order accuracy with local data for computation. It has recently been widely studied by Ayuso de Dioset al., Rossmanith et Seal, etc. in an Eularian framework, while Guo, Nair and Qiu or Qiu and Shu or Bokanowski and Simarta performed semi-Lagrangian time resolution. We use multi-wavelets framework for the adaptive part. Those have been heavily studied by Alpert et al. during the nineties and the two thousands. Some works merging multi-scale resolution and discontinuous Galerkin methods have been described by Müller and his colleagues in 2014 for non-linear hyperbolic conservation laws in the finite volume framework. In the framework of relativistic Vlasov equation, Besse, Latu, Ghizzo, Sonnendrücker and Bertrand presented the advantage of using adaptive meshes. While they used wavelet decomposition, which requires large data stencil, multi-wavelet decomposition coupled to discontinuous Galerkin discretisation only requires local stencil. This favours the parallelisation but, at the moment, semi-Lagrangian remains an obstacle to highly efficient distributed memory parallelisation. Although most of our work is done in a 1d × 1v phase space, we were able to obtain a few results in a 2d × 2v phase space
Devaux, Stéphane. "Etude cinétique de l’interaction plasma-paroi en présence d’un champ magnétique". Thesis, Nancy 1, 2007. http://www.theses.fr/2007NAN10087.
Pełny tekst źródłaIn fusion devices, the region of plasma directly in contact with a material surface (limiter, divertor) can erode the surface and release impurities, which mirgrate toward the bulk plasma and deteriorate its confinement. In this thesis, we studied the plasma-wall interaction using a Vlasov-Poisson model. This kinetic model allowed us to investigate the three different regions (Debye sheath, magnetic and collisional presheaths) that compose the transition between a low-pressure plasma and a wall when a tilted magnetic field is present. Particular attention was devoted to the physical properties of ions entering the Debye sheath and the role of ion-neutral collisions on the Bohm criterion. Moreover, we showed that, in the presence of a tilted magnetic field, the ion distribution function is significantly distorted from its Maxwellian shape in the bulk plasma, thus requiring a fully kinetic study. Using the computed ion distributions on the wall, we estimated the wall sputtering rate in terms of the magnetic field strength and angle of incidence. We showed in particular that, for grazing incidence, the sputtering rate is reduced because of two effects: first, the ion flux is spread over a larger area and, second, the grazing magnetic field limits the kinetic energy of ion population. As plasmas are generally composed of more than one species, we extended our model to simulate an argon-helium plasma. Our study focussed on the Bohm criterion at the Debye sheath entrance and its modifications brought by the introduction of a second ion species
Saidi, Karima. "Stabilisation d’une classe d’EDP non linéaire. Application à l’équation de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0225.
Pełny tekst źródłaThe work presented in this thesis concerns the stabilization of a class of nonlinear partialdifferential equations. It is a discretized model of the Vlasov-Poisson equation describing the spatial and temporal evolution, in a plasma, of a distribution function of charged particles. In a first step, we addressed the stabilization of the dynamical systems in fixed time (i.e. stabilization in finite time with a uniformly bounded). Criteria relaxing existing results in the literature have been established. Indeed, we have shown that, for a dynamical system, the combination of slow stability (in the polynomial sense) and fast stability (in the finite time sense) leads to a stability in fixed time. Various applications on the discretized Vlasov-Poisson system also concern the double integrator system with observer and the bilinear systems in infinite dimension where for each of these systems, the stabilizing feedback and/or observers in fixed time are constructed and numerically tested. In a second step, we are interested in the small time stabilization of time varying dynamical systems. In fact, the notion of small time is commonly used in theory of controllability. For stabilization, this small time is located between finite time and the fixed time. We have developed theoretical results based on the energy method guaranteeing the disappearance of the solution in small time. This is obtainedby means of a time excitation of a positive function not integrable in the sense of Lebesgue. Then, we have applied our results on model examples such as the transport equation with boundary control, the wave equation subject to a boundary control of the Wentzell type. Also, for finite and infinite dimensional bilinear systems which are, in addition, typical discretized Vlasov-Poisson models. For each system, we have elaborated its feedback whose construction is based on the integration of temporal and uniform excitations
Cisse, Amadou. "Observation et commande d'une classe d'équations aux dérivées partielles couplées : Application à l'équation de Vlasov-Poisson". Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0234.
Pełny tekst źródłaThis subject of research, addresses the problem of the observation and control of a class of nonlinear Partial Differential Equations (PDEs) in finite and infinite dimension. One of the main motivations concerns the application of these approaches to the Vlasov-Poisson equation (VP) in dimension 1Dx1D. The latter describes the evolution of the distribution function of charged particles in a fusion plasma.Most of the work in the literature on the Vlasov-Poisson equations concerns the analysis and discretisation of these equations, but very few results exist on the control and even fewer on the observation. It deals on the one hand with the observer synthesis, the stabilization by state feedback of the control and the observer-based stabilization under LMI conditions of the discretized system obtained by the discontinuous Galerkin method. And on the other hand by the design of state observer in infinite dimension by the technique of backstepping
Le, Bourdiec Solène. "Méthodes déterministes de résolution des équations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen". Phd thesis, Ecole Centrale Paris, 2007. http://tel.archives-ouvertes.fr/tel-00146258.
Pełny tekst źródłaLe travail de cette thèse a consisté à concevoir un schéma numérique original pour la résolution du système d'équations modélisant ces interactions : les équations de Vlasov-Maxwell relativistes. Notre choix s'est orienté vers des méthodes d'intégration directe. Nous proposons trois nouvelles méthodes spectrales pour discrétiser en impulsion les équations : une méthode de Galerkin et deux méthodes de type collocation. Ces approches sont basées sur des fonctions de Hermite qui ont la particularité de dépendre d'un facteur d'échelle permettant d'obtenir une bonne résolution en vitesse.
Nous présentons dans ce manuscript les calculs conduisant à la discrétisation et à la résolution du problème de Vlasov-Poisson monodimensionnel ainsi que les résultats numériques obtenus. Puis nous étudions les extensions possibles des méthodes au problème complet relativiste. Afin de réduire les temps de calcul, une parallélisation et une optimisation des algorithmes ont été mises en \oe uvre. Enfin, les calculs de validation du code 1Dx-3Dv, à partir d'instabilités de types Weibel et whistlers, à une ou deux espèces d'électrons, sont détaillés.
Giorgi, Pierre-Antoine. "Analyse mathématique de modèles cinétiques en physique des plasmas". Electronic Thesis or Diss., Aix-Marseille, 2019. http://www.theses.fr/2019AIXM0609.
Pełny tekst źródłaThis thesis deals with the study of some kinetic models encountered in plasma physics.The first model considered is a 1D Vlasov-Poisson system representing the dynamics of two species of particles (ions and electrons) in a bounded set, x ∈ (0,1), with direct reflection boundary conditions. In the linear case, generalized characteristics are defined, ensuring the time s=0 to be reached after a finite number of bounces, the problematic case being when the electric field points outward of the boundary. Then, for initial conditions even in the velocity variable, a global continuous solution is built by means of generalized characteristics and a fixed point argument. Local uniqueness of a continuous solution is shown, in a frame where two successive bounces at the same boundary cannot occur. The second model was obtained as the limit of a Vlasov-Poisson system in the finite Larmor radius regime.For solutions satisfying a decay assumption, a Wasserstein stability estimate is proven, and a new proof of the existence of such solutions is given. The advection field is then Lipschitz continuous. Finally, numerical simulations are performed to investigate the kinetic response of electrons to an external drive. A beating between two waves, one at the external frequency, the other at the Landau frequency, is revealed
Herda, Maxime. "Analyse asymptotique et numérique de quelques modèles pour le transport de particules chargées". Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1165/document.
Pełny tekst źródłaThis thesis is devoted to the mathematical study of some models of partial differential equations from plasma physics. We are mainly interested in the theoretical study of various asymptotic regimes of Vlasov-Poisson-Fokker-Planck systems. First, in the presence of an external magnetic field, we focus on the approximation of massless electrons providing reduced models when the ratio me{mi between the mass me of an electron and the mass mi of an ion tends to 0 in the equations. Depending on the scaling, it is shown that, at the limit, solutions satisfy hydrodynamic models of convection-diffusion type or are given by Maxwell-Boltzmann-Gibbs densities depending on the intensity of collisions. Using hypocoercive and hypoelliptic properties of the equations, we are able to obtain convergence rates as a function of the mass ratio. In a second step, by similar methods, we show exponential convergence of solutions of the Vlasov-Poisson-Fokker-Planck system without magnetic field towards the steady state, with explicit rates depending on the parameters of the model. Finally, we design a new type of finite volume scheme for a class of nonlinear convection-diffusion equations ensuring the satisfying long-time behavior of discrete solutions. These properties are verified numerically on several models including the Fokker-Planck equation with magnetic field
Filbet, Francis. "Contribution à l'analyse et la simulation numérique de l'équation de Vlasov". Nancy 1, 2001. http://docnum.univ-lorraine.fr/public/SCD_T_2001_0068_FILBET.pdf.
Pełny tekst źródłaMouton, Alexandre. "Approximation multi-échelles de l'équation de Vlasov". Phd thesis, Université de Strasbourg, 2009. http://tel.archives-ouvertes.fr/tel-00411964.
Pełny tekst źródłaA ce jour, la notion de convergence 2-échelles introduite par G. Allaire et G. Nguetseng est un des outils permettant de dériver rigoureusement des limites multi-échelles, ce qui nous permet d'obtenir des modèles limites qu'il est possible de discrétiser avec une méthode numérique usuelle : nous parlons alors d'une méthode numérique 2-échelles.
L'objectif de cette thèse est de développer une méthode semi-lagrangienne 2 échelles sur un modèle de type Vlasov gyrocinétique afin de simuler un plasma soumis à un champ magnétique fort du même type que ceux utilisés pour le projet ITER. Cependant, comme les phénomènes physiques à simuler sont assez complexes et comme nous ne savons que peu de choses sur le comportement d'une méthode numérique 2-échelles sur un modèle non-linéaire, il convient de procéder par étapes avant de développer une telle méthode sur un modèle gyrocinétique.
Dans une première partie, nous construisons une méthode de volumes finis 2-échelles sur les équations d'Euler 1D isentropiques faiblement compressibles. Bien que ce modèle soit assez différent d'un modèle de type Vlasov, il n'en est pas moins un cadre de travail relativement simple pour étudier le comportement d'une méthode numérique 2-échelles face à un modèle non-linéaire.
Dans une seconde partie, nous nous basons sur le modèle limite développé par E. Frénod, F. Salvarani et E. Sonnendrücker afin de construire une méthode semi-lagrangienne 2-échelles pour simuler des faisceaux de particules en géométrie axisymétrique. Même si le modèle de Vlasov axisymétrique utilisé est différent d'un modèle gyrocinétique, il constitue un contexte idéal pour établir les bases d'une méthode semi-lagrangienne 2 échelles.
Enfin, dans une troisième partie, nous utilisons la convergence 2-échelles afin d'améliorer les résultats de convergence faible-* établis par M. Bostan en 2007, et nous proposons une méthode semi-lagrangienne en avant permettant de valider numériquement ces résultats.
Pham, Thi Trang Nhung. "Méthodes numériques pour l'équation de Vlasov réduite". Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAD051/document.
Pełny tekst źródłaMany numerical methods have been developed in order to selve the Vlasov equation, because computing precise simulations in a reasonable time is a real challenge. This equation describes the time evolution of the distribution function of charged particles (electrons/ions), which depends on 3 variables in space, 3 in velocity and time. The main idea of this thesis is to rewrite the Vlasov equation in the form of a hyperbolic system using a semi-discretization of the velocity. This semi-discretization is achieved using the finite element method. The resulting model is called the reduced Vlasov equation. We propose different numerical methods to salve this new model efficiently: finite volume methods, semi-Lagrangian methods and discontinuous Galerkin methods
Bourne, Emily. "Non-uniform numerical schemes for the modelling of turbulence in the 5D GYSELA code". Electronic Thesis or Diss., Aix-Marseille, 2022. http://www.theses.fr/2022AIXM0412.
Pełny tekst źródłaThis thesis lies within the context of fusion plasma simulations and it has a double objective: (i) develop new scalable numerical methods, adapted to the semi-lagrangian scheme used in the 5D gyrokinetic GYSELA code, capable of solving the problem of large fluctuations and temperature variations at the edge of the plasma, and (ii) take into account more realistic magnetic configurations than the concentric circles currently simulated by the code. I present a new approach for quadrature using splines, which limits the condition number for the procurement of such quadrature coefficients. I present a local spline method where derivatives are transported between patches, and show its stability for semi-lagrangian advection. The semi-lagrangian method based on non-uniform splines on a Vlasov-Poisson 1D-1V model is used for studies of the plasma sheath. The existing VOICE code (which is a mini version of GYSELA), designed to study such problems, has been modified and optimised on a GPU to operate on a non-uniform mesh. Co-variant and contra-variant transformation matrices of a new realistic magnetic configuration were derived and implemented in the code to allow the 5D Vlasov equations to take into account new geometry. The inclusion of this new magnetic configuration has been successfully numerically validated on the linear benchmarks used for GAM studies. In parallel, a test platform for the 2D Poisson solver was developed in order to numerically compare this spline finite elements solver to two other multi-grid solvers: (i) a solver using finite volumes on a uniform cartesian mesh with embedded boundaries, and (ii) a solver using finite differences on a logical mesh
Han-Kwan, Daniel. "Contribution à l'étude mathématique des plasmas fortement magnétisés". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2011. http://tel.archives-ouvertes.fr/tel-00615169.
Pełny tekst źródłaCampos, Serrano Juan. "Modèles attractifs en astrophysique et biologie : points critiques et comportement en temps grand des solutions". Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00861568.
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