1,721,036 research outputs found
Modélisation et analyse numérique de problèmes de réaction-diffusion provenant de la solidification d'alliages binaires
Get PDFIn this work, we are interested in elaborating models and numerical methods in order to study some phenomena which arise in the solidification of binary alloys. We propose two distinct models based on the mass and energy conservation laws as well as on classical thermodynamics. The first model is based on the irreversible process theory and therefore requires the computation of the entropy of the system to complete the description. To obtain this quantity, we develop a formalism and a method which yields numerical results. This construction is made so that the entropy function inherits some interesting mathematical properties from physical requirements. These properties allow us to elaborate and analyze mathematically an original scheme using a time discretization depending on a real parameter to solve the solidification problem. In particular, we are able to prove that the scheme is stable for all values of the time step if the parameter is chosen correctly. Furthermore, we give some numerical results to support the theory. The second model, called phase-field model, is used to describe dendrites' formation during the solidification of binary alloys. The nature of the problem constrains us to use very fine meshes in some physical regions. To reduce the number of discrete unknowns, we develop an adaptive mesh strategy based on an ad-hoc error estimator. We make numerical tests showing that the method converges on regular meshes and that the estimator is in good agreement with the true error. We also show that the mesh refinement strategy gives good results in academic and physical cases.AS
Modélisation et analyse numérique de couches limites réactives d'air
Get PDFThe objective of this work is the numerical simulation of the reactive laminar boundary layer which occurs in a neighbourhood of a body moving in the air. We have investigated the modelling of the reactive boundary layer when, the "chemical equilibrium" hypothesis concerning the chemical reactions occuring in the air is satisfied, and when the chemical reaction rates are finite. We have made a mathematical study of the simplified problems coming from the modelling of the reactive boundary layer. We recall the method to state the conservation equations which are written for the ten functions representing the five mass fractions of the chemical species constituting the air, the mean density of the air, the temperature of the air, the mean velocity and the pressure. Then we consider the chemical reactions occuring in the air, and we propose a mode1 for the production terms of the chemical species. In the case where the "chemical equilibrium" is satisfied, we investigate the regularity of the functions representing the mass fractions of the chemical species. Finally, we state a relation which allows us to consider the free enthalpy function as a Lyapounov's function for the equations of conservation of the species when the species diffusion is neglected. The reactive boundary layer equations are semi-linear partial differential equations of parabolic type which degenerate on the part of the boundary of the domain corresponding to the moving body. When considering simplified problems derived from the reactive boundary layer equations, we investigate the type of degeneration taking place in these equations and we state convergence results and error estimates for the approximation of these problems with finite difference methods. In the case where the diffusion of the chemical species is neglected, we have investigated the asymptotic behavior of the functions representing the mass fractions of the species when approaching the body. Finally, we propose an algorithm to compute numerically the reactive boundary layer equations.AS
Simulation numérique des équilibres d'un plasma dans un tokamak : modélisation et étude mathématiques
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Simulation numérique du mouvement des fluides dans une cellule de Hall-Héroult
No full textThis work aims to investigate, by means of numerical simulation, the evolution of free surface flow in aluminium production cells, and especially the magnetohydrodynamic instabilities. We design a numerical method combining a level-set technique together with a finite element discretization, in order to solve the non-stationnary Navier-Stokes equations and the equation for the motion of the free surface. Our numerical experiments confirms results obtained by other authors and we study the evolution of instabilities calculated by a stationary program, ALUCELL.AS
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Modélisation mathématique et simulation numérique des phénomènes dynamiques et thermiques apparaissant dans un glacier
No full textIn this work, two problems linked to glacier modeling are investigated. We propose an optimisation method for studying the flow of the ice and we present a numerical study about glacier thermal phenomena. In the first chapter of this thesis, we expose the models of these two problems. On one hand, we note that the boundary conditions on the bedrock are misunderstood, which explains it is difficult to obtain an accurate simulation of the motion of the ice. Also we establish a mathematical model where the bedrock boundary conditions depend on a control parameter. The aim of this study is to minimize a cost functional describing the difference between the computed velocity at the surface and the measure done. We study the cost functional with respect to the control parameter and we detail an optimisation method to solve the optimal control problem. On the other hand, we introduce two thermodynamical model governing the temperature and the water content field. The models correspond to a Stefan problem for the temperature and a convection-diffusion equation for the water content. The second chapter deals with the numerical resolution of the optimisation problem. First, a Finite Element Method (FEM) is described to solve the partial differential equations. Then, the algorithms used for the optimal control problem are detailed. Finally, this techniques are applied on two glaciers : Griesgletcher for 2D and Storglaciaren for 3D. The third chapter deals with the numerical resolution of the temperature and the water content models. A FEM is used for each problem. Concerning the temperature problem, the Stefan problem is numerically solved and the results allow to detect a free surface between the temperated ice and the cold ice. The water content field is also simulated. Numerical results are discussed on the Storglaciaren.AS
Analyse numérique d'une méthode intégrale frontière sans singularité : application à l'électromagnétisme
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