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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
31

SOLUÇÃO DE PROBLEMAS EM SEMIESPAÇO NA DINÂMICA DE GASES RAREFEITOS BASEADA EM MODELOS CINÉTICOS / SOLUTION OF PROBLEMS IN HALF SPACE IN THE RAREFIED GAS DYNAMICS BASED KINETIC MODELS

Cromianski, Solange Regina 28 February 2012 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The method discrete ordinates is used to solve problems involving rarefied gas dynamics. In this work, a version of the analytical method discrete ordinates (ADO) is used to solve problems in a semi-infinite. The complete analytical development, in cartesian coordinates, the solution of the Thermal-Slip and Viscous-Slip problems is presented, for four kinetic models: BGK model, S model, Gross Jackson model and MRS model in a unified approach. In addition, to describe the interaction between gas and surface, we use the Cercignani-Lampis boundary condition defined in terms of the coefficients of accommodation of tangential momentum and energy accommodation coefficient kinetic corresponding the velocity normal. Numerical results are presented, where we obtain quantities of interest, such as: velocity profile and heat flow profile, which were implemented computationally through the FORTRAN program. / O método de ordenadas discretas é utilizado na solução de alguns problemas envolvendo a dinâmica de gases rarefeitos. Neste trabalho, uma versão analítica do método de ordenadas discretas (ADO) é usada para resolver problemas em meio semiinfinito. O desenvolvimento analítico completo, em coordenadas cartesianas, da solução dos problemas Deslizamento Térmico e Deslizamento Viscoso é apresentada, para quatro modelos cinéticos: modelo BGK, modelo S, modelo Gross Jackson e modelo MRS em uma abordagem unificada. Além disso, para descrever o processo de interação entre o gás e a parede utiliza-se o núcleo de Cercignani-Lampis definido em termos do coeficiente de acomodação do momento tangencial e do coeficiente de acomodação da energia cinética correspondendo a velocidade normal. Resultados numéricos são apresentados, onde obtém-se grandezas de interesse, tais como: perfil de velocidade e perfil de fluxo de calor, os quais foram implementados computacionalmente através do programa FORTRAN.
32

FORMULACÃO UNIFICADA PARA MODELOS CIN�ETICOS DERIVADOS DA EQUAÇÃO DE BOLTZMANN COM CONDIÇÕES DE CONTORNO GENERALIZADAS / UNIFIED FORMULATION FOR KINETIC MODELS DERIVATIVES OF BOLTZMANN EQUATION WITH GENERALIZED BOUNDARY CONDITIONS

Rosa, Cinara Ewerling da 28 February 2012 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this paper, we present numerical results obtained from the FORTRAN language for physical quantities of interest such as velocity profile, pro�le, heat ow rate, particle ow rate,heat ux and pressure tensor component. The gas ow occur in the direction parallel to thesurface the gas is confined because of a constant gradient of pressure and a constant gradient of temperature are represented by Poiseuille Problem and Problem Creep Thermal, respectively. It also considers the Couette Problem where the gas moves from the motion of the plates in opposite directions. In order to describe the gas-surface interaction we use the kernel of Cercignani-Lamp, which as opposed to core scattering Maxwell has two accommodation coeficients to represent the physical properties of gas, leaving this interaction closer to reality. From the simplification of the Boltzmann equation has the kinetic theory for rarefied gas dynamics, which is developed analytically in a uni�ed approach to the BGK Model, S Model, Gross-Jackson (GJ) Model and MRS Model. Thus, we seek to model that most closely approximates the veracity, comparing the numerical values generated by the models and the linearized Boltzmann equation through numerical analysis, graphics and mathematical statistics with the procedure of the variance of two factors made by Friedman. A version of the analytical method of discrete ordinates (ADO) is used to solve the problems of Poiseuille, Creep Thermal and Couette for two plates infinte paralalelas with different chemical constitutions Boundary Conditions for the Cercignani-Lampis. / Neste trabalho, são apresentados resultados numéricos obtidos a partir da linguagem FORTRAN para quantidades físicas de interesse como perfil de velocidade, perfil fluxo de calor, taxa fluxo de partícula, taxa fluxo de calor e componente tensor de pressão. O fluxo gasoso ocorre na direção paralela a superfície que o gás esta confinado devido a um gradiente constante de pressão e um gradiente constante de temperatura que são representados pelo Problema de Poiseuille e Problema Creep térmico respectivamente. Além disso, também considera-se o Problema de Couette onde o gás se move a partir do movimento das placas em sentidos opostos. A �fim de descrever a interação gás-superfície utiliza-se o núcleo de Cercignani-Lampis, que ao contrário do núcleo de espalhamento de Maxwell tem dois coeficientes de acomodação para representar as propriedades físicas do gás, deixando esta interação mais próxima da realidade. A partir da simplificação da Equação de Boltzmann tem-se a teoria cinética para a dinâmica de gases rarefeito, que é desenvolvida analiticamente em uma abordagem unificada para o Modelo BGK, Modelo S, Modelo Gross-Jackson (GJ) e Modelo MRS. Dessa maneira, busca-se o modelo que mais se aproxima da veracidade, comparando os valores numéricos gerados pelos modelos e a Equação Linearizada de Boltzmann através de análises numéricas, gráficas e de matemática estatística com o procedimento da variância de dois fatores de Friedman por postos. Uma versão analítica do método de ordenadas discretas (ADO) é usada para resolver os Problemas de Poiseuille, Creep Térmico e Couette para duas placas paralalelas infintas com constituições químicas diferentes para Condições de Contorno de Cercignani-Lampis.
33

Estudo cinético do processo de digestão anaeróbia de resíduos sólidos vegetais / Kinetics study of the process of anaerobic digestion of vegetable residual solids

Silva, Wellington Regis 27 July 2009 (has links)
Made available in DSpace on 2015-05-14T13:21:51Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1010298 bytes, checksum: a5a24de3f4abc4b3987d2584b46eea8f (MD5) Previous issue date: 2009-07-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The waste from fruit and vegetables and the discharge of domestic and industrial wastewaters in an unacceptable way cause serious problems for the majority of cities in Brazil and the rest of the world. The residues from fruit and vegetables and domestic and industrial wastewater could be treated jointly by the process of anaerobic digestion resulting in the production of energy and a reduction in negative environmental impacts. The principal objective of this work was to study the kinetics of the process of anaerobic biostabilization of vegetable residual solids (RSV), treated at different concentrations of total solids with the view to optimizing energy production and anaerobic biostabilization. To execute this study a completely mixed, compartmentalized anaerobic reactor comprising three compartments separated by glass plates with unit volumes of 25 litres, was designed, installed and monitored,. The resulting products from anaerobic biostabiliztion in the form of semi-solids were monitored weekly except for pH, total alkalinity and volatile fatty acids which jointly with biogas production were monitored twice weekly during a the total monitoring period of 294 days. The work was divided into two stages. In the first stage a substrate comprising twelve different types of vegetable solid waste with a total solids concentration equal to 75, 4 g/L was used. In the second stage the concentration of total solids applied to compartments C1, C2 and C3 were 40, 22.6 and 23.2 g/L respectively, with the with the level of humidity being adjusted by the addition of domestic sewage. The maximum percentage of methane in the biogas was 61.5% obtained in the first compartment (C1) of the reactor during the second experimental stage. The maximum kinetic constants for bioconversion (k) for COD total and soluble, TKN and sulphate during the first stage were respectively 3.86 x 10-2, 3.01 x 10-2, 4.75 x 10-2 and 2.13 x 10-2d-1. During the second stage of the study the values maximum obtained were 1.28 x 10-2, 1.90 x 10-2, 2.90 x 10-2 and 3.22 x 10-2d-1, for COD total and soluble, TKN and sulphate respectively. / O desperdício de frutas e verduras e o lançamento de águas residuárias domésticas ou industriais de forma inadequada representam sérios problemas para maioria das cidades do Brasil e do mundo. Os resíduos de frutas e verduras e as águas residuárias domésticas e industriais podem ser tratados de forma conjugada pelo processo de digestão anaeróbia, resultando no aproveitamento energético e na redução de impactos ao meio ambiente. O objetivo principal deste trabalho foi o estudo cinético do processo de bioestabilização anaeróbia de resíduos sólidos vegetais (RSV), tratados com diferentes concentrações de sólidos totais, visando o aproveitamento do potencial energético e consequentemente a bioestabilização anaeróbia do material orgânico. Para realização deste trabalho foi projetado, construído, instalado e monitorado um reator anaeróbio compartimentado de mistura completa, contendo três câmaras individuais de reação, construídas com placas de vidro, com volumes unitários de 25 litros. Os produtos resultantes do processo de bioestabilização anaeróbia que se encontravam na forma semi-sólida foram monitorados semanalmente, exceto pH, alcalinidade total e ácidos graxos voláteis que juntamente com o biogás foram monitorados duas vezes por semana; o período total de monitoração foi de 294 dias. O trabalho foi dividido em duas etapas. Na primeira etapa, o substrato constituído por doze diferentes tipos de (RSV) foi digerido a uma concentração de sólidos totais igual a 75,4 g/L. Para realização da segunda etapa, a concentração de sólidos totais aplicada às câmaras C1, C2 e C3 foram de 40; 22,8 e 23,2 g/L respectivamente, haja vista o teor de umidade do substrato preparado ter sido ajustado com adição esgoto doméstico. A porcentagem máxima de metano contido no biogás foi de 61,5%, obtida para primeira câmara de reação, no decorrer da segunda etapa. A produção máxima de biogás foi de 56 litros, também obtida na primeira câmara C1, ao longo da segunda etapa. Os valores máximos das constantes cinéticas de bioconversão (k) obtidos no decorrer da primeira etapa para DQOt, DQOs, NTK e sulfato foram respectivamente 3,86.10-2, 3,01.10-2, 4,75.10-2 e 2,13.10-2d-1. Durante a segunda etapa do trabalho os valores máximos obtidos foram de 1,28.10-2, 1,90.10-2, 2,90.10-2 e 3,22.10-2d-1 para DQOt, DQOs, NTK e sulfato, respectivamente.
34

Efficient Asymptotic Preserving Schemes for BGK and ES-BGK models on Cartesian grids / Schémas préservant la limite asymptotique pour les modèles BGK et ES-BGK sur grilles cartésiennes

Bernard, Florian 09 March 2015 (has links)
Dans cette thèse, nous nous sommes intéressés à des écoulements complexes où les régimes hydrodynamique et raréfiés coexistent. On retrouve ce type d'écoulements dans des applications industrielles comme les pompes à vide ou encore les rentrées de capsules spatiales dans l'atmosphère, lorsque la distance entre les molécules de gaz devient si grande que le comportement microscopique des molécules doit être pris en compte. Pour ce faire, nous étudions 2 modèles de l'équation de Boltzmann, le modèle BGK et le modèle ES-BGK. Dans un premier temps, nous développons une nouvelle condition au bord permettant une transition continue de la solution du régime raréfié vers le régime hydrodynamique. Cette nouvelle condition permettant de préserver l'asymptotique vers les équations d'Euler compressible est ensuite incluse dans une méthode de frontière immergée pour traiter, à une précision raisonnable (ordre 2), le cas de solides immergés dans un écoulement, sur grilles cartésiennes. L'utilisation de grillescartésiennes permet une parallélisation aisée du code de simulation numérique afin d'obtenir une réduction considérable du temps de calcul, un des principaux inconvénients des modèles cinétiques. Par la suite, une approche dites aux grilles locales en vitesses est présentée réduisant également le temps de calcul de manière importante (jusqu'à 80%). Des simulations 3D sont également présentées montrant l'efficacité des méthodes. Enfin, le transport passive de particules solides dans un écoulement raréfié est étudié avec l'introduction d'un modèle de type Vlasov couplé au modèle cinétique. Grâce à une résolution basée sur des méthodes de remaillage, la pollution de dispositif optiques embarqués sur des satellites dues à des particules issues de la combustion incomplète dans les moteurs contrôlant d'altitude est étudiée. / This work is devoted to the study of complex flows where hydrodynamic and rarefled regimes coexist. This kind of flows are found in vacuum pumps or hypersonic re-entries of space vehicles where the distance between gas molecules is so large that their microscopicbehaviour differ from the average behaviour of the flow and has be taken into account. We then consider two modelsof the Boltzmann equation viable for such flows: the BGK model dans the ES-BGK model.We first devise a new wall boundary condition ensuring a smooth transition of the solution from the rarefled regime to the hydrodynamic regime. We then describe how this boundary condition (and boundary conditions in general) can be enforced with second order accuracy on an immersed body on Cartesian grids preserving the asymptotic limit towards compressible Euler equations. We exploit the ability of Cartesian grids to massive parallel computations (HPC) to drastically reduce the computational time which is an issue for kinetic models. A new approach considering local velocity grids is then presented showing important gain on the computational time (up to 80%). 3D simulations are also presented showing the efficiency of the methods. Finally, solid particle transport in a rarefied flow is studied. The kinetic model is coupled with a Vlasov-type equation modeling the passive particle transport solved with a method based on remeshing processes. As application, we investigate the realistic test case of the pollution of optical devices carried by satellites due to incompletely burned particles coming from the altitude control thrusters
35

Kinetic modeling of the transient flows of the single gases and gaseous mixtures

Ho, Minh Tuan 30 September 2015 (has links)
Un gaz à l'intérieur d’un microsystème ou d’un milieu poreux est dans un état hors équilibre, car le libre parcours moyen des molécules est comparable à la dimension caractéristique du milieu. Ce même état degaz, appelé raréfié, se retrouve en haute altitude ou dans un équipement de vide à basse pression. Ces gaz raréfiés suivent des types d’écoulements qui peuvent être décrits par des modèles cinétiques dérivés de l'équation de Boltzmann. Dans ce travail nous présentons les principaux modèles et leurs mises en oeuvre numériquepour la simulation des écoulements de gaz raréfiés. Parmi les modèles utilisés nous présentons les deux modèles complets de l'équation de Boltzmann, le modèle de Shakhov(S-model) pour un gaz monoatomique et le modèle de McCormack pour un mélange de gaz toujours monoatomiques. La méthode des vitesses discrètes est utilisée pour la discrétisation numérique dans l'espace des vitesses moléculaires et le schéma de type TVD est mis en œuvre dans l'espace physique. L’aspect original de ce travail se situe sur les régimes transitoires et, en particuliersur les comportements non-stationnaires des transferts de chaleur et de masse. Cependant, pour certaines configurations nous considérons uniquement les conditions stationnaires des écoulements et un schéma implicite est développé afin de réduire le coût de calcul. En utilisant ces approches numériques, nous présentons les résultats pour plusieurs types d’écoulements non-stationnaires, de gaz raréfiés monoatomiqueset de mélanges binaires de gaz monoatomiques. / A gas inside the microsystems or the porous media is in its non-equilibrium state, due to the fact that the molecular mean free path is comparable to the characteristic dimension of the media. The same state of a gas, called rarefied, is found at high altitude or in the vacuum equipment working at low pressure. All these types of flow can be described by the kinetic models derived from the Boltzmann equation. This thesis presents the development of the numerical tools for the modeling and simulations of the rarefied gas flows. The two models of the full Boltzmann equation, the Shakhov model (S-model) for the single gas and the McCormack model for the gas mixture, are considered. The discrete velocity method is used to the numerical discretization in the molecular velocity space and the TVD-like scheme is implemented in the physical space. The main aspect of this work is centered around the transient properties of the gas flows and, especially, on the transient heat and mass transfer behaviors. However, for some configurations only steady-state solutions are considered and the implicit scheme is developed to reduce the computational cost. Using the proposed numerical approach several types of the transient rarefied single gas flows as well as the binary mixture of the monoatomic gases are studied.
36

Étude cinétique de réactions de pyrolyse et de combustion d'hydrocarbures cycliques par les approches de chimie quantique / Kinetic study of pyrolysis and oxidation reactions of cyclic hydrocarbons by quantum chemistry approaches

Sirjean, Baptiste 04 December 2007 (has links)
Les carburants dérivés du pétrole constituent la première source mondiale énergétique et leur approvisionnement constitue un défi actuel majeur impliquant des enjeux économiques et environnementaux cruciaux. Une des voies les plus efficaces pour peser simultanément sur ces deux enjeux passe par la diminution de la consommation en carburant. La simulation numérique constitue dès lors un outil précieux pour améliorer et optimiser les moteurs et les carburants. Les modèles chimiques détaillés sont nécessaires pour comprendre les phénomènes d’auto-inflammation et caractériser la nature et les quantités de polluants émis. Ces modèles mettent en jeu un nombre très important d’espèces et de réactions élémentaires, pour une espèce donnée et pour lesquelles la détermination des données thermodynamiques et cinétiques est un problème crucial. La chimie quantique constitue un outil précieux permettant d’une part de déterminer de façon précise les données thermocinétiques pour bon nombre de systèmes chimiques et d’autre part de mieux comprendre la réactivité de ces systèmes. Dans ce travail, les réactions unimoléculaires de décomposition d’hydrocarbures monocycliques et polycycliques (amorçages, réactions moléculaires, ß-scissions, formations d’éthers cycliques) ont été étudiées à l’aide des méthodes de la chimie quantique. Un mécanisme détaillé de pyrolyse d’un alcane polycyclique a été développé à partir des données thermodynamiques et cinétiques et des corrélations entre structure et réactivité déterminées pour les cyclanes à partir des calculs quantiques. Les simulations effectuées à partir de ce modèle sont en très bon accord avec les résultats expérimentaux de la littérature / Petroleum fuels are the world’s most important primary energy source and the need to maintain their supply is a major actual challenge involving both economical and environmental features. Decreasing fuels consumption is one of the more efficient ways to reconcile the goals of energy price and environmental protection. Numerical simulations become therefore a very important tool to optimize fuels and motors. Detailed chemical kinetic models are required to reproduce the reactivity of fuels and to characterize the amount of emitted pollutants. Such models imply a very large number of chemical species and elementary reactions, for a given species, and the determination of thermodynamic and kinetic data is a critical problem. Nowadays, quantum chemistry methods are able to calculate accurately thermodynamic data for a large number of chemical systems and to elucidate the reactivity of these systems. In this work we have used quantum chemistry to study the unimolecular reactions (initiation, molecular reactions, ß-scissions, cyclic ethers formations) involved in the decomposition of monocyclic and polycyclic hydrocarbons. From the results of quantum chemical calculations, a detailed chemical kinetic mechanism of the pyrolysis of a polycyclic alkane has been developed and validated against experimental data
37

The Inactivation Mechanisms of Shaker IR and Kv2.1 Potassium Channels: Lessons from Pore Mutation

Jamieson, Quentin 11 June 2014 (has links)
No description available.
38

Photocatalytic degradation of dyes and pesticides in the presence of ions

Pete, Kwena Yvonne 03 1900 (has links)
M. Tech. (Department of Chemical Engineering, Faculty of Engineering and Technology), Vaal University of Technology / Water pollution caused by organic and inorganic contaminants represents an important ecological and health hazard. Simultaneous treatment of organic and inorganic contaminants had gradually gained great scientific interest. Advanced oxidation processes such as photocatalysis, using TiO2 as a photocatalyst, have been shown to be very robust in the removal of biorecalcitrant pollutants. These methods offer the advantage of removing the pollutants, in contrast to conventional techniques. At present, the main technical challenge that hinder its commercialization remained on the post-recovery of the photocatalyst particles after water treatment. Supporting of the photocatalyst on the adsorbent surface is important as it assists during the filtration step, reducing losses of the materials and yielding better results in degrading pollutants. To overcome this challenge, in this study composite photocatalysts of TiO2/zeolite and TiO2/silica were prepared and investigated to explore the possible application in the simultaneous removal of organic and inorganic compounds from contaminated water. The main objective of this study was to investigate the heterogeneous photocatalytic degradation of organic compounds in the presence of metal ions using composite photocatalysts. The Brunauer–Emmett–Teller (BET), Scanning Electron Microscopy and Energy Dispersive X-ray (SEM-EDX), Raman spectroscopy (RS) and zeta potential (ZP) analyses were used to characterize the prepared composite photocatalysts. The successive composite photocatalysts were used in a semi-batch reactor under an irradiation intensity of 5.5 mW/m2 (protected by a quartz sleeve) at 25 ± 3°C for the photocatalytic degradation of synthetic textile (methyl orange) and agricultural (atrazine) wastewater in the presence of ions. The effect of operating parameters such as TiO2 composition on supporting material, particle size, composite photocatalyst loading, initial pollutant concentration and pH were optimized. The effects of inorganic salts and humic acid on dye and pesticides degradation were also studied, respectively. The performance of the photocatalyst reactor was evaluated on the basis of color removal, metal ion reduction, total organic carbon (TOC) reduction, intermediates product analysis and modeling of kinetics and isotherms. Different kinetic and isotherm models were introduced and applied in this work. Important aspects such as error functions with the optimal magnitude were used for the selection of the best suitable model. / European Union. City of Mikkeli, Finland. Water Research Commission (RSA)
39

Etude numérique et modélisation du modèle d'Euler bitempérature : point de vue cinétique. / Numerical approximation and modelling of the bitemperature Euler model : a kinetic viewpoint.

Prigent, Corentin 24 October 2019 (has links)
Dans divers domaines de la physique, certains phénomènes sont modélisés par des systèmes hyperboliques non-conservatifs. En particulier, dans le domaine de la physique des plasmas, dont l'un des champs d'application majeur est la Fusion par Confinement Inertiel, le système d'Euler bi-température, modélisant les phénomènes de transport de particules chargées, en est un exemple. La difficulté de l'étude de ces systèmes réside dans la présence de termes non-conservatifs, qui empêchent la définition classique des solutions faibles. Pour parvenir à une définition de ce type de solutions, on a recours à l'emploi de systèmes cinétiques sous-jacents. Dans ce manuscrit, on s'intéresse à l'étude numérique de ces systèmes cinétiques pour la résolution du système d'Euler bi-température.Ce manuscrit se divise en deux parties. La première partie contient l'étude numérique du système d'Euler bi-température. Dans un premier chapitre, on résout numériquement les équations en dimension 1 d'espace par le biais d'un système sous-jacent issu de la physique des plasmas: le système de Vlasov-BGK-Ampère. On présente une méthode numérique préservant l'asymptotique pour ce système sous-jacent et on montre, par des simulations numériques, que le schéma limite obtenu donne des résultats consistants avec Euler bi-température. Dans un second chapitre, on résout le même modèle en dimension 2 d'espace par un système sous-jacent de type BGK discret. On démontre une inégalité d'entropie pour les solutions issues du modèle sous-jacent, ainsi qu'une inégalité discrète de dissipation d'entropie pour le schéma.Dans la deuxième partie de ce manuscrit, on s'intéresse au développement de méthodes numériques pour quelques modèles cinétiques. On considère ici le cas des écoulements raréfiés de mélanges de gaz, dans l'optique d'une application aux cas des plasmas. Premièrement, on présente un schéma cinétique adaptatif et dynamique en vitesse pour les gaz inertes. Par l'emploi de lois de conservation discrètes, la solution est approchée sur un ensemble de vitesses discrètes local et dynamique. Dans un second temps, on propose une extension de cette méthode visant à améliorer les performances de celle-ci. Puis, ces deux versions de la méthode sont comparées à la méthode classique sur grille fixe uniforme sur une série de cas tests.Enfin, dans le dernier chapitre, on propose une méthode numérique pour la résolution d'une extension de ces équations, prenant en compte la présence de réactions chimiques au sein du mélange. Le contexte considéré est celui des réactions chimiques bi-moléculaires réversibles lentes. La méthode proposée, de type implicite-explicite, est linéaire, stable et conservative. / In various domains of physics, several phenomena can be modeled via the use of nonconservative hyperbolic systems. In particular, in plasma physics, in the process of developping and understanding the phenomena leading to Inertial Confinement Fusion, the bi-temperature Euler sytem can be used to model particle transport phenomena in a plasma. The difficulty of the mathematical study of such systems dwells in the presence of so-called non-conservative products, which prevent the classical definition of weak solutions via distribution theory. To attempt to define these quantities, it is useful to supplement the hyperbolic system with an underlying kinetic model. In this work, the objective is the numerical study of such kinetic systems in order to solve the bi-temperature Euler system.This manuscript is split in two parts. The first one contains the study of the bi-temperature Euler system. In the first chapter, this system in dimension 1 is solved by the use of an underlying kinetic model sprung from plasma physics: the Vlasov-BGK-Ampère system. An asymptotic-preserving numerical method is introduced, and it is shown that the scheme obtained in the limit is consistant with a scheme for teh bi-temperature Euler system. In the following chapter, the same hyperbolic model in dimension 2 is studied, this time via a discrete-BGK type underlying model. An entropy inequality is proved for solutions coming from the kinetic model, as well as a discrete entropy dissipation inequality.In the second part of the manuscript, we are interested in the development of numerical schemes for gas mixture rarefied flows. Firstly, an adaptive kinetic scheme is introduced for inert gas mixtures. By the use of discrete conservation laws, the solution is approximated on a set of discrete velocities that depends on space, time and species. Secondly, an extension of the method is proposed in order to improve the efficiency of the first method. Finally, the two methods are compared to the classical fixed grid method on a series of test cases.In the last chapter, a numerical method is proposed for rarefied flows of reacting mixtures. The setting considered is the case of slow bimolecular reversible chemical reactions. The method introduced is an explicit-implicit treatment of the relaxation operator, which is shown to be stable, linear and conservative.
40

Keller-Segel-type models and kinetic equations for interacting particles : long-time asymptotic analysis

Hoffmann, Franca Karoline Olga January 2017 (has links)
This thesis consists of three parts: The first and second parts focus on long-time asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling approaches. (1) Keller–Segel-type aggregation-diffusion equations: We study a Keller–Segel-type model with non-linear power-law diffusion and non-local particle interaction: Does the system admit equilibria? If yes, are they unique? Which solutions converge to them? Can we determine an explicit rate of convergence? To answer these questions, we make use of the special gradient flow structure of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the asymptotic behaviour of solutions. (2) Hypocoercivity techniques for a fibre lay-down model: We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in non-woven textile production. Further, we prove convergence to equilibrium with an explicit rate. This part of the thesis is an extension of previous work which considered the case of a stationary conveyor belt. Adding the movement of the belt, the global equilibrium state is not known explicitly and a more general hypocoercivity estimate is needed. Although we focus here on a particular application, this approach can be used for any equation with a similar structure as long as it can be understood as a certain perturbation of a system for which the global Gibbs state is known. (3) Scaling approaches for collective animal behaviour models: We study the multi-scale aspects of self-organised biological aggregations using various scaling techniques. Not many previous studies investigate how the dynamics of the initial models are preserved via these scalings. Firstly, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local kinetic 1D and 2D models to simpler models existing in the literature. Secondly, we investigate how some of the kinetic spatio-temporal patterns are preserved via these scalings using asymptotic preserving numerical methods.

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