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Etude des méthodes de pénalité-projection vectorielle pour les équations de Navier-Stokes avec conditions aux limites ouvertes / Study of the vector penalty-projection methods for Navier-Stokes equations with open boundary conditionsCheaytou, Rima 30 April 2014 (has links)
L'objectif de cette thèse consiste à étudier la méthode de pénalité-projection vectorielle notée VPP (Vector Penalty-Projection method), qui est une méthode à pas fractionnaire pour la résolution des équations de Navier-Stokes incompressible avec conditions aux limites ouvertes. Nous présentons une revue bibliographique des méthodes de projection traitant le couplage de vitesse et de pression. Nous nous intéressons dans un premier temps aux conditions de Dirichlet sur toute la frontière. Les tests numériques montrent une convergence d'ordre deux en temps pour la vitesse et la pression et prouvent que la méthode est rapide et peu coûteuse en terme de nombre d'itérations par pas de temps. En outre, nous établissons des estimations d'erreurs de la vitesse et de la pression et les essais numériques révèlent une parfaite concordance avec les résultats théoriques. En revanche, la contrainte d'incompressibilité n'est pas exactement nulle et converge avec un ordre de O(varepsilondelta t) où varepsilon est un paramètre de pénalité choisi assez petit et delta t le pas temps. Dans un second temps, la thèse traite les conditions aux limites ouvertes naturelles. Trois types de conditions de sortie sont étudiés et testés numériquement pour l'étape de projection. Nous effectuons des comparaisons quantitatives des résultats avec d'autres méthodes de projection. Les essais numériques sont en concordance avec les estimations théoriques également établies. Le dernier chapitre est consacré à l'étude numérique du schéma VPP en présence d'une condition aux limites ouvertes non-linéaire sur une frontière artificielle modélisant une charge singulière pour le problème de Navier-Stokes. / Motivated by solving the incompressible Navier-Stokes equations with open boundary conditions, this thesis studies the Vector Penalty-Projection method denoted VPP, which is a splitting method in time. We first present a literature review of the projection methods addressing the issue of the velocity-pressure coupling in the incompressible Navier-Stokes system. First, we focus on the case of Dirichlet conditions on the entire boundary. The numerical tests show a second-order convergence in time for both the velocity and the pressure. They also show that the VPP method is fast and cheap in terms of number of iterations at each time step. In addition, we established for the Stokes problem optimal error estimates for the velocity and pressure and the numerical experiments are in perfect agreement with the theoretical results. However, the incompressibility constraint is not exactly equal to zero and it scales as O(varepsilondelta t) where $varepsilon$ is a penalty parameter chosen small enough and delta t is the time step. Moreover, we deal with the natural outflow boundary condition. Three types of outflow boundary conditions are presented and numerically tested for the projection step. We perform quantitative comparisons of the results with those obtained by other methods in the literature. Besides, a theoretical study of the VPP method with outflow boundary conditions is stated and the numerical tests prove to be in good agreement with the theoretical results. In the last chapter, we focus on the numerical study of the VPP scheme with a nonlinear open artificial boundary condition modelling a singular load for the unsteady incompressible Navier-Stokes problem.
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Simulação numérica do escoamento bifásico em meios porosos heterogêneos empregando uma formulação semi-implícita, imitadores de fluxo e o método dos volumes finitos / Numerical simulation of two-phase flow in heterogeneous porous media applying a semi-implicit formulation, flux limiter and finite volume methodJulhane Alice Thomas Schulz 31 March 2009 (has links)
Neste trabalho apresentamos um esquema numérico para a simulação computacional de escoamentos bifásicos, água-óleo, em reservatórios de petróleo. O modelo matemático consiste em um sistema de equações diferenciais parciais não-linear nas incógnitas velocidade, pressão e saturação. Uma quebra de operadores a dois níveis possibilita uma maior eficiência ao método permitindo que a velocidade, fornecida pelo problema de velocidade-pressão, seja atualizada somente para determinados intervalos de tempo associados ao problema de transporte advectivo-difusivo em termos da saturação. O método dos volumes finitos é empregado na resolução numérica do problema de velocidade-pressão e do transporte de massa por advecção e difusão. Na solução do problema de transporte de massa utilizamos limitadores de fluxo na aproximação dos termos advectivos e diferenças centradas para os termos difusivos. O nosso simulador foi validado a partir de confrontações dos seus resultados com as soluções teóricas conhecidas para os problemas unidimensionais, equações de Burgers e de Buckley-Leverett, e com outros resultados numéricos em se tratando do escoamento bifásico água-óleo bidimensional em meios porosos heterogêneos. / A new numerical method is proposed for the solution of two-phase flow problem in petroleum reservoirs. The two-phase (water and oil) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. For computational eficiency an operator spliting technique is used; distinct time steps can be used for the computation of transport and pressure-velocity problems. The finite volume method is used in the numerical solution of the velocity-pressure and mass transport problems. A flux limiter is used for the numerical discretization of the advective terms while centered schemes are employed for the diffusion terms in the mass transport problem. In the validation of our numerical method we compared numerical and theoretical solutions for one dimensional problems, Burgers and Buckley-Leverett equations, and compared our numerical results to others, in the case of oil-water flows in two dimensions for an heterogeneous porous media.
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Simulação numérica do escoamento bifásico em meios porosos heterogêneos empregando uma formulação semi-implícita, imitadores de fluxo e o método dos volumes finitos / Numerical simulation of two-phase flow in heterogeneous porous media applying a semi-implicit formulation, flux limiter and finite volume methodJulhane Alice Thomas Schulz 31 March 2009 (has links)
Neste trabalho apresentamos um esquema numérico para a simulação computacional de escoamentos bifásicos, água-óleo, em reservatórios de petróleo. O modelo matemático consiste em um sistema de equações diferenciais parciais não-linear nas incógnitas velocidade, pressão e saturação. Uma quebra de operadores a dois níveis possibilita uma maior eficiência ao método permitindo que a velocidade, fornecida pelo problema de velocidade-pressão, seja atualizada somente para determinados intervalos de tempo associados ao problema de transporte advectivo-difusivo em termos da saturação. O método dos volumes finitos é empregado na resolução numérica do problema de velocidade-pressão e do transporte de massa por advecção e difusão. Na solução do problema de transporte de massa utilizamos limitadores de fluxo na aproximação dos termos advectivos e diferenças centradas para os termos difusivos. O nosso simulador foi validado a partir de confrontações dos seus resultados com as soluções teóricas conhecidas para os problemas unidimensionais, equações de Burgers e de Buckley-Leverett, e com outros resultados numéricos em se tratando do escoamento bifásico água-óleo bidimensional em meios porosos heterogêneos. / A new numerical method is proposed for the solution of two-phase flow problem in petroleum reservoirs. The two-phase (water and oil) flow problem is governed by a pressure-velocity equation coupled to a saturation equation. For computational eficiency an operator spliting technique is used; distinct time steps can be used for the computation of transport and pressure-velocity problems. The finite volume method is used in the numerical solution of the velocity-pressure and mass transport problems. A flux limiter is used for the numerical discretization of the advective terms while centered schemes are employed for the diffusion terms in the mass transport problem. In the validation of our numerical method we compared numerical and theoretical solutions for one dimensional problems, Burgers and Buckley-Leverett equations, and compared our numerical results to others, in the case of oil-water flows in two dimensions for an heterogeneous porous media.
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Méthodes numériques pour l'équation de Vlasov réduite / Numerical methods for the reduced Vlasov equationPham, Thi Trang Nhung 19 December 2016 (has links)
Beaucoup de méthodes numériques ont été développées pour résoudre l'équation de Vlasov, car obtenir des simulations numériques précises en un temps raisonnable pour cette équation est un véritable défi. Cette équation décrit en effet l'évolution de la fonction de distribution de particules (électrons/ions) qui dépend de 3 variables d'espace, 3 variables de vitesse et du temps. L'idée principale de cette thèse est de réécrire l'équation de Vlasov sous forme d'un système hyperbolique par semi-discrétisation en vitesse. Cette semi-discrétisation est effectuée par méthode d'éléments finis. Le modèle ainsi obtenu est appelé équation de Vlasov réduite. Nous proposons différentes méthodes numériques pour résoudre efficacement ce modèle: méthodes des volumes finis, méthodes semi-Lagrangiennes et méthodes Galerkin discontinus. / Many 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.
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Développement d’un schéma aux volumes finis centré lagrangien pour la résolution 3D des équations de l’hydrodynamique et de l’hyperélasticité / Development of a 3D cell-centered Lagrangian scheme for the numerical modeling of the gas dynamics and hyperelasticity systemsGeorges, Gabriel 19 September 2016 (has links)
La Physique des Hautes Densités d’Énergies (HEDP) est caractérisée par desécoulements multi-matériaux fortement compressibles. Le domaine contenant l’écoulementsubit de grandes variations de taille et est le siège d’ondes de chocs et dedétente intenses. La représentation Lagrangienne est bien adaptée à la descriptionde ce type d’écoulements. Elle permet en effet une très bonne description deschocs ainsi qu’un suivit naturel des interfaces multi-matériaux et des surfaces libres.En particulier, les schémas Volumes Finis centrés Lagrangiens GLACE (GodunovtypeLAgrangian scheme Conservative for total Energy) et EUCCLHYD (ExplicitUnstructured Cell-Centered Lagrangian HYDrodynamics) ont prouvé leur efficacitépour la modélisation des équations de la dynamique des gaz ainsi que de l’élastoplasticité.Le travail de cette thèse s’inscrit dans la continuité des travaux de Maireet Nkonga [JCP, 2009] pour la modélisation de l’hydrodynamique et des travauxde Kluth et Després [JCP, 2010] pour l’hyperelasticité. Plus précisément, cettethèse propose le développement de méthodes robustes et précises pour l’extension3D du schéma EUCCLHYD avec une extension d’ordre deux basée sur les méthodesMUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) et GRP(Generalized Riemann Problem). Une attention particulière est portée sur la préservationdes symétries et la monotonie des solutions. La robustesse et la précision duschéma seront validées sur de nombreux cas tests Lagrangiens dont l’extension 3Dest particulièrement difficile. / High Energy Density Physics (HEDP) flows are multi-material flows characterizedby strong shock waves and large changes in the domain shape due to rarefactionwaves. Numerical schemes based on the Lagrangian formalism are good candidatesto model this kind of flows since the computational grid follows the fluid motion.This provides accurate results around the shocks as well as a natural tracking ofmulti-material interfaces and free-surfaces. In particular, cell-centered Finite VolumeLagrangian schemes such as GLACE (Godunov-type LAgrangian scheme Conservativefor total Energy) and EUCCLHYD (Explicit Unstructured Cell-CenteredLagrangian HYDrodynamics) provide good results on both the modeling of gas dynamicsand elastic-plastic equations. The work produced during this PhD thesisis in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamicpart and the work of Kluth and Després [JCP, 2010] for the hyperelasticitypart. More precisely, the aim of this thesis is to develop robust and accurate methodsfor the 3D extension of the EUCCLHYD scheme with a second-order extensionbased on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws)and GRP (Generalized Riemann Problem) procedures. A particular care is taken onthe preservation of symmetries and the monotonicity of the solutions. The schemerobustness and accuracy are assessed on numerous Lagrangian test cases for whichthe 3D extensions are very challenging.
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Simulação Numérica de Escoamento Bifásico em reservatório de Petróleo Heterogêneos e Anisotrópicos utilizando um Método de Volumes Finitos “Verdadeiramente” Multidimensional com Aproximação de Alta OrdemSOUZA, Márcio Rodrigo de Araújo 22 September 2015 (has links)
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Previous issue date: 2015-09-22 / Anp / Sob certas hipóteses simplificadoras, o modelo matemático que descreve o escoamento
de água e óleo em reservatórios de petróleo pode ser representado por um sistema não linear
de Equações Diferenciais Parciais composto por uma equação elíptica de pressão (fluxo) e
uma equação hiperbólica de saturação (transporte). Devido a complexidades na modelagem
de ambientes deposicionais, nos quais são incluídos camadas inclinadas, canais, falhas e poços
inclinados, há uma dificuldade de se construir um modelo que represente adequadamente
certas características dos reservatórios, especialmente quando malhas estruturadas são usadas
(cartesianas ou corner point). Além disso, a modelagem do escoamento multifásico nessas
estruturas geológicas incluem descontinuidades na variável e instabilidades no escoamento,
associadas à elevadas razões de mobilidade e efeitos de orientação de malha. Isso representa
um grande desafio do ponto de vista numérico. No presente trabalho, uma formulação fundamentada
no Método de Volumes Finitos é estudada e proposta para discretizar as equações
elíptica de pressão e hiperbólica de saturação. Para resolver a equação de pressão três formulações
robustas, com aproximação dos fluxos por múltiplos pontos são estudadas. Essas formulações
são abeis para lidar com tensores de permeabilidade completos e malhas poligonais
arbitrárias, sendo portanto uma generalização de métodos mais tradicionais com aproximação
do fluxo por apenas dois pontos. A discretização da equação de saturação é feita com duas
abordagens com característica multidimensional. Em uma abordagem mais convencional, os
fluxos numéricos são extrapolados diretamente nas superfícies de controle por uma aproximação
de alta resolução no espaço (2ª a 4ª ordem) usando uma estratégia do tipo MUSCL. Uma
estratégia baseada na Técnica de Mínimos Quadrados é usada para a reconstrução polinomial.
Em uma segunda abordagem, uma variação de uma esquema numérico Verdadeiramente Multidimensional
é proposto. Esse esquema diminui o efeito de orientação de malha, especialmente
para malhas ortogonais, mesmo embora alguma falta de robustez possa ser observada
pra malhas excessivamente distorcidas. Nesse tipo de formulação, os fluxos numéricos são
calculados de uma forma multidimensional. Consiste em uma combinação convexa de valores
de saturação ou fluxo fracionário, seguindo a orientação do escoamento através do domínio
computacional. No entanto, a maioria dos esquemas numéricos achados na literatura tem
aproximação apenas de primeira ordem no espaço e requer uma solução implícita de sistemas
algébricos locais. Adicionalmente, no presente texto, uma forma modificada desses esquemas
“Verdadeiramente” Multidimensionais é proposta em um contexto centrado na célula. Nesse
caso, os fluxos numéricos multidimensionais são calculados explicitamente usando aproximações
de alta ordem no espaço. Para o esquema proposto, a robustez e o caráter multidimensional
também leva em conta a distorção da malha por meio de uma ponderação adaptativa. Essa
ponderação regula a característica multidimensional da formulação de acordo com a distorção
da malha. Claramente, os efeitos de orientação de malha são reduzidos. A supressão de oscilações
espúrias, típicas de aproximações de alta ordem, são obtidas usando, pela primeira vez
no contexto de simulação de reservatórios, uma estratégia de limitação multidimensional ou
Multidimensional Limiting Process (MLP). Essa estratégia garante soluções monótonas e podem
ser usadas em qualquer malha poligonal, sendo naturalmente aplicada em aproximações
de ordem arbitrária. Por fim, de modo a garantir soluções convergentes, mesmo para problemas
tipicamente não convexos, associados ao modelo de Buckley-Leverett, uma estratégia
robusta de correção de entropia é empregada. O desempenho dessas formulações é verificado
com a solução de problemas relevantes achados na literatura. / Under certain simplifying assumptions, the problem that describes the fluid flow of oil
and water in heterogeneous and anisotropic petroleum reservoir can be described by a system
of non-linear partial differential equations that comprises an elliptic pressure equation (flow)
and a hyperbolic saturation equation (transport). Due to the modeling of complex depositional
environments, including inclined laminated layers, channels, fractures, faults and the geometrical
modeling of deviated wells, it is difficult to properly build and handle the Reservoir
Characterization Process (RCM), particularly by using structured meshes (cartesian or corner
point), which is the current standard in petroleum reservoir simulators. Besides, the multiphase
flow in such geological structures includes the proper modeling of water saturation
shocks and flow instabilities associated to high mobility ratios and Grid Orientation Effects
(GOE), posing a great challenge from a numerical point of view. In this work, a Full Finite
Volume Formulation is studied and proposed to discretize both, the elliptic pressure and the
hyperbolic saturation equations. To solve the pressure equation, we study and use three robust
Multipoint Flux Approximation Methods (MPFA) that are able to deal with full permeability
tensors and arbitrary polygonal meshes, making it relatively easy to handle complex geological
structures, inclined wells and mesh adaptivity in a natural way. To discretize the saturation
equation, two different multidimensional approaches are employed. In a more conventional
approach, the numerical fluxes are extrapolated directly on the control surfaces for a higher
resolution approximation in space (2nd to 4th order) by a MUSCL (Monotone Upstream Centered
Scheme for Conservation Laws) procedure. A least squares based strategy is employed
for the polynomial reconstruction. In a second approach, a variation of a “Truly” Multidimensional
Finite Volume method is proposed. This scheme diminishes GOE, especially for orthogonal
grids, even though some lack of robustness can be observed for extremely distorted
meshes. In this type of scheme, the numerical flux is computed in each control surface in a
multidimensional way, by a convex combination of the saturation or the fractional flow values,
following the approximate wave orientation throughout the computational domain. However,
the majority of the schemes found in literature is only first order accurate in space and
demand the implicit solution of local conservation problems. In the present text, a Modified
Truly Multidimensional Finite Volume Method (MTM-FVM) is proposed in a cell centered
context. The truly multidimensional numerical fluxes are explicitly computed using higher
order accuracy in space. For the proposed scheme, the robustness and the multidimensional
character of the aforementioned MTM-FVM explicitly takes into account the angular distortion
of the computational mesh by means of an adaptive weight, that tunes the multidimensional
character of the formulation according to the grid distortion, clearly diminishing GOE.
The suppression of the spurious oscillations, typical from higher order schemes, is achieved
by using for the first time in the context of reservoir simulation a Multidimensional Limiting
Process (MLP). The MLP strategy formally guarantees monotone solutions and can be used
with any polygonal mesh and arbitrary orders of approximation. Finally, in order to guarantee
physically meaningful solutions, a robust “entropy fix” strategy is employed. This produces
convergent solutions even for the typical non-convex flux functions that are associated to the
Buckley-Leverett problem. The performance of the proposed full finite volume formulation is
verified by solving some relevant benchmark problems.
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Modelagem, simulação e analise de desempenho de reatores tubulares de polimerização com deflectores angulares internosMendoza Marin, Florentino Lazaro 17 December 2004 (has links)
Orientadores: Rubens Maciel Filho, Liliane Maria Ferrareso Lona / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-04T02:31:19Z (GMT). No. of bitstreams: 1
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Previous issue date: 2004 / Resumo: O modelo determinístico e processo homopolimerização na emulsão do estireno são aplicados em reator tubular contínuo sem e com deflectores angulares internos sob condição isotérmica e não isotérmica. Os resultados de modelagem e simulação foram realizados a estado estacionário, modelo unidimensional, coordenada cilíndrica, fluxo pistão laminar completamente desenvolvido, modelo Smith-Ewart para estimar a conversão do monômero, cinética química de Arrhenius corno modelo de velocidade finita laminar para computar a geração química. O objetivo é modelar, simular e analisar o comportamento do reator de homopolimerização na emulsão do estireno com deflectores angulares inclinados internos, e comparar com reator tubular. Os métodos experimental e matemático-dedutivo foram aplicados para obter resultados, por meio de programação computacional, usando Dinâmica de Fluido Computacional através do método de volumes finitos. As seguintes variáveis como temperatura de reação constante e variável, reator tubular sem e com deflectores, temperatura de alimentação, diâmetro de reator, processo adiabático e exotérmico, calor de reação constante e velocidade axial completamente desenvolvida foram investigados. Os efeitos de conversão de monômero, área transversal interna, temperatura axial, concentração do polímero, radicais e iniciador, outros corno densidade de polímero e monômero, perda de carga e queda de pressão foram determinados e simulados. Os produtos foram caracterizados com Número de Partículas (nucleação homogênea e heterogênea), distribuição de peso molecular, tamanho de partículas de polímero e distribuição de viscosidade. Estes resultados foram validados com resultados da literatura sob condição igualou aproximada. Os resultados sob condições não isotérmicas foram melhores que os resultados isotérmicos em termos de caracterização do polímero. Isso mostra que o desenho alternativo proposto (com deflectores) permite obter o polímero com propriedades melhores em termos de número de partículas, distribuição de peso molecular, distribuição do tamanho de partículas e viscosidade / Abstract: Deterministic model and emulsion homopolymerization process of styrene are applied in continuous tubular reactor without and with internal angular baffles under isothermic and no isothermic conditions. The modeling and simulation results were approximate to steady state, one-dimensional model, cylindrical coordinate, fully developed laminar plug flow, Smith-Ewart model to estimate the monomer conversion, Arrhenius chemical kinetics as laminar finite-rate model to compute chemical source. The objective is to model, simulate and to analyze the emulsion homopolymerization reactor performance of styrene with internal-inc1ined angular baffles, and to compare with continuous tubular reactor. The experimental and mathematical-deductive methods were applied to obtain results, by means of computational programming, using Computational Fluid Dynamics (program code), finite volume method. The following variables such as constant and variable reaction temperature, tubular reactor without and with baffles, feed temperature, reactor diameter, adiabatic and exothermic process, constant reaction heat and fully developed axial velocity were investigated. The monomer conversion, internal transversal are a, axial temperature, concentration of polymer, radicals and initiator, others as density of polymer and monomer, head loss and pressure drop effects were determined and simulated. The products were characterized by partic1es number (homogeneous and heterogeneous nuc1eation), molecular weight distribution, polymer partic1es size and polymer viscosity distribution. These results were validated with literature results under same or approximate condition. The results under no isothermic conditions were better than isothermic results in terms of polymer characterization. It is shown that the proposed alternative design (with baffles) allow to obtain the polymer with better properties in terms of number of partic1es, molecular weight distribution, particle size distribution and viscosity / Doutorado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química
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Modélisation de l'encrassement en régime turbulent dans un échangeur de chaleur à plaques avec un revêtement fibreux sur les parois / Numerical modeling of fouling induced by turbulent flow in a plate heat exchanger with fibrous coating on the wallsSadouk, Hamza Chérif 15 June 2009 (has links)
Les transferts de chaleur par convection forcée turbulente dans une conduite plane partiellement remplie par un milieu poreux sont étudiés numériquement. L’étude concerne l’analyse de l’encrassement dans un canal plan représentatif d’un échangeur de chaleur à plaques. Un fluide, ayant un fort pouvoir encrassant, est considéré en régime turbulent. L’objectif de cette étude est de proposer une technique qui repose sur l’utilisation de matériaux fibreux comme capteur de particules pouvant réduire les méfaits de l’encrassement. Cela consiste à essayer de réduire la résistance d’encrassement en agissant sur les propriétés thermiques du dépôt. L’étude de la cinétique de l’encrassement permet de déterminer la loi de variation de l’épaisseur du dépôt au cours du temps. Cette équation est couplée aux équations de conservation. Un modèle de conductivité thermique effective (fluide, dépôt, fibres poreuses) a été choisi et le phénomène de colmatage de la matrice poreuse est considéré. L’apport du milieu poreux sur les performances de l’échangeur est analysé / A numerical study is carried out to investigate the forced convection heat transfer induced by a turbulent flow in a parallel plate channel partly filled with a porous or fibrous material. The study involves the analysis of fouling in a plate heat exchanger, represented by a parallel plate channel with a high fouling potential liquid flow in turbulent regime. The objective is to come out with a technical solution that relies on the use of fibrous materials capability to capture deposited particles, and therefore to reduce the fouling impacts within heat exchangers. This solution focuses on reducing the fouling resistance on wall surfaces by modifying the thermal properties of the deposit. The deposit thickness evolution is obtained through a kinetics model of fouling, which is coupled to the conservation equations. An effective thermal conduction model (liquid, deposit, porous material) is selected in order to account for fouling within the porous matrix. The benefits of porous material on heat exchanger performance are analyzed
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Sur le modèle de Kerr-Debye pour la propagation des ondes électromagnétiquesKanso, Mohamed 01 October 2012 (has links)
Dans cette thèse on étudie des systèmes d’EDP non linéaires modélisant la propagation électromagnétique dans des milieux de type Kerr. On considère deux modèles. Le premier dit de Kerr-Debye, suppose un temps de réponse non nul du matériau à l’onde électromagnétique. Le second, dit de Kerr, suppose une réponse instantanée. On est ainsi confronté à des systèmes de relaxation tels que définis par Chen-Levermore-Liu (CPAM 1994). Nous établissons ici des résultats d’existence globale de solutions fortes à données petites en 3D pour le problème de Cauchy et un problème mixte. Puis nous construisons des schémas volumes finis asymptotic preserving et nous étudions leurs performances sur des cas physiques. / In this thesis, we study non-linear PDE systems modeling the electromagnetic propagation in Kerr media. We consider two models. The first one is the Kerr-Debye model, it assumes a finite response time of the medium. The second one is the Kerr model, it assumes an instantaneous response. We deal with relaxation systems as defined by Chen-Levermore-Liu (CPAM 1994). For small data, we establish results of global existence of smooth solutions in 3D for the Cauchy problem and the IBVP. Then we investigate asymptotic preserving finite volume schemes and we study their performance on physical cases.
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An artificial compressibility analogy approach for compressible ideal MHD: application to space weather simulationYalim, Mehmet S. 05 December 2008 (has links)
Ideal magnetohydrodynamics (MHD) simulations are known to have problems in satisfying the solenoidal constraint (i.e. the divergence of magnetic field should be equal to zero, $<p>ablacdotvec{B} = 0$). The simulations become unstable unless specific measures have been taken.<p><p>In this thesis, a solenoidal constraint satisfying technique that allows discrete satisfaction of the solenoidal constraint up to the machine accuracy is presented and validated with a variety of test cases. Due to its inspiration from Chorin's artificial compressibility method developed for incompressible CFD applications, the technique was named as \ / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished
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