Le modèle multi-fluide permet de décrire par une approche Eulérienne les sprays polydispersés et apparaît donc comme une méthode indiquée pour les applications de combustion diphasique. Sa pertinence pour la simulation à l’échelle d’applications industrielles est évaluée dans ce travail, par sa mise en oeuvre dans des configurations bi-dimensionnelle et tri-dimensionnelle plus représentatives de ce type de simulations. Cette évaluation couple une étude de faisabilité en terme de coût de calcul avec une analyse de la précision obtenue, par des comparaisons avec les résultats de méthodes de références pour la description des sprays. Afin de définir une telle référence, une hiérarchisation des modèles de spray est proposée dans ce travail, soulignant les niveaux de modélisation associée aux diverses méthodes. Une première configuration d’écoulements tourbillonnaires est utilisée pour caractériser la méthode multi-fluide. L’étude de la structure mathématique du système de lois de conservation permet d’analyser la formation de singularités et de fournir les outils permettant d’évaluer leur impact sur la modélisation. Cette étude permet également de dériver un schéma numérique robuste et efficace pour des configurations bi- et tri-dimensionnelle. La description des dynamiques de gouttes conditionnées par la taille est évaluée dans ces configurations tourbillonnaires au moyen de comparaisons quantitatives, sur des champs instantanés, où le multi-fluide est confronté à une méthode Lagrangienne, ainsi qu’à des résultats expérimentaux. Afin d’évaluer le comportement de la méthode multi-fluide dans des configurations plus représentatives des problématiques industrielles, le solveur MUSES3D est développé, permettant, entre autres, une évaluation fine des méthodes de résolution des sprays. Une implémentation originale de la méthode multi-fluide, conciliant généricité et efficacité pour le calcul parallèle, est réalisée. Le couplage de ce solveur avec le code ASPHODELE, développé au CORIA, permet d’effectuer une évaluation opérationnelle des approches Euler/Lagrange et Euler/Euler pour la description des écoulements diphasiques à inclusions dispersées. Finalement, le comportement de la méthode multi-fluide dans des jets bi-dimensionnels et dans une turbulence homogène isotrope tri-dimensionnelle permet de montrer sa précision pour la description de la dynamique de sprays évaporant dans des configurations plus complexes. La résolution de la polydispersion du spray permet de décrire précisément la fraction massique de combustible en phase vapeur, un élément clé pour les applications de combustion. De plus, l’efficacité du calcul parallèle par décomposition de domaine avec la méthode multi-fluide permet d’envisager son utilisation à l’échelle d’applications industrielles. / The multi-fluid model, providing a Eulerian description of polydisperse sprays, appears as an interesting method for two-phase combustion applications. Its relevance as a numerical tool for industrial device simulations is evaluated in this work. This evaluation assesses the feasibility of multi-fluid simulations in terms of computational cost and analyzes their precision through comparisons with reference methods for spray resolution. In order to define such a reference, the link between the available methods for spray resolution is provided, highlighting their corresponding level of modeling. A first framework of 2-D vortical flows is used to assess the mathematical structure of the multi-fluid model governing system of equations. The link between the mathematical peculiarities and the physical modeling is provided, and a robust numerical scheme efficient for 2-D/3-D configurations is designed. This framework is also used to evaluate the multi-fluid description of evaporating spray sizeconditioned dynamics through quantitative, time-resolved, comparisons with a Lagrangian reference and with experimental data. In order to assess the multi-fluid efficiency in configurations more representative of industrial devices, a numerical solver is designed, providing a framework devoted to spray method evaluation. An original implementation of the multifluid method, combining genericity and efficiency in a parallel framework, is achieved. The coupling with a Eulerian/Lagrangian solver for dispersed two-phase flows, developed at CORIA, is conducted. It allows a precise evaluation of Euler/Lagrange versus Euler/Euler approaches, in terms of precision and computational cost. Finally, the behavior of the multi-fluid model is assessed in 2D-jets and 3-D Homogeneous Isotropic Turbulence. It illustrates the ability of the method to capture evaporating spray dynamics in more complex configurations. The method is shown to describe accurately the fuel vapor mass fraction, a key issue for combustion applications. Furthermore, the method is shown to be efficient in domain decomposition parallel computing framework, a key issue for simulations at the scale of industrial devices.

Nesta tese é apresentado um esquema novo de alta resolução upwind (denominado TDPUS-C3) para reconstrução de fluxos numéricos para leis de conservação não lineares e problemas relacionados em DFC. O esquema é baseado nos critérios de estabilidade CBC e TVD e desenvolvido utilizando condições de diferenciabilidade \'C POT. 3\'. Além disso, é realiozada a implementação da associação do esquema TDPLUS-C3 com a modelagem de turbulência RNG \'\\kappa - \\epsilon\'. O propósito é obter soluções numéricas de sistemas hiperbólicos de leis de conservação para dinâmica dos gases e equações de Navier-Stokes para escoamento incompreensível de fluidos newtonianos e não newtonianos (viscoelásticos). Fazendo o uso do esquema TDPUS-C3, a precisão global dos métodos numéricos é verificada acessando o erro em problemas teste (benchmark) 1D e 2D. Um estudo comparativo entre os resultados do esquema TDPUS-C3 e os esquemas upwind convencionais para leis de conservação hiperbólicas complexas é também realizado. A Associação das modelagens numéricas (upwinding mais RNG \'\\kappa - \\epsilon\') é , então, examinada na simulação de escoamentos turbulentos de fluidos newtonianos envolvendo superfícies livres móveis, usando a metodologia URANS. No geral, em termos do comportamento global, concordância satisfatória é observada / In this thesis, a new high-resolution upwind scheme (named TDPUS-C3) for reconstruction of numerical fluxes for nonlinear conservation laws and related CFD problems in presented. The scheme is based on CBC and TVD stability criteria and developed by employing differentiability condictions (\'C POT. 3\'). In additon, the implementation of an association of the TDPUS-C3 scheme with the RNG \'\\kappa - \\epsilon\' turbulence modelling is also performed. The purpose is to obtain numerical solutions of systems of hyperbolic conservation laws for gas dynamics and Navier-Stokes equations for incompressible flow of Newtonian and non-Newtonian (viscoelstic) fluids. By using the TDPUS-C3 scheme, the global accuracy of the numerical methods is verified by assessing the error on 1D and 2D benchmark test cases. A comparative study between the TDPUS-C3 scheme and convectional upwind schemes to solve standard and complex hyperbolic conservation laws is also accomplished. The association of the numerical modelling (upwinding plus RNG \'\\kappa - epsilon\') is then examined in the simulation of turbulent Newtonian fluid flows involving moving free surfaces, by using URANS methodology. Overall, satisfactory agreement is found in terms of the overall behaviour

Este trabalho estuda o fenômeno de evaporação rápida em jatos de líquidos superaquecidos ou metaestáveis numa região 2D. O fenômeno se inicia, neste caso, quando um jato na fase líquida a alta temperatura e pressão, emerge de um diminuto bocal projetando-se numa câmara de baixa pressão, inferior à pressão de saturação. Durante a evolução do processo, ao cruzar-se a curva de saturação, se observa que o fluido ainda permanece no estado de líquido superaquecido. Então, subitamente o líquido superaquecido muda de fase por meio de uma onda de evaporação oblíqua. Esta mudança de fase transforma o líquido superaquecido numa mistura bifásica com alta velocidade distribuída em várias direções e que se expande com velocidades supersônicas cada vez maiores, até atingir a pressão a jusante, e atravessando antes uma onda de choque. As equações que governam o fenômeno são as equações de conservação da massa, conservação da quantidade de movimento, e conservação da energia, incluindo uma equação de estado precisa. Devido ao fenômeno em estudo estar em regime permanente, um método de diferenças finitas com modelo estacionário e esquema de MacCormack é aplicado. Tendo em vista que este modelo não captura a onda de choque diretamente, um segundo modelo de falso transiente com o esquema de \"shock-capturing\": \"Dispersion-Controlled Dissipative\" (DCD) é desenvolvido e aplicado até atingir o regime permanente. Resultados numéricos com o código ShoWPhasT-2D v2 e testes experimentais foram comparados e os resultados numéricos com código DCD-2D v1 foram analisados. / This study analyses the rapid evaporation of superheated or metastable liquid jets in a two-dimensional region. The phenomenon is triggered, in this case, when a jet in its liquid phase at high temperature and pressure, emerges from a small aperture nozzle and expands into a low pressure chamber, below saturation pressure. During the evolution of the process, after crossing the saturation curve, one observes that the fluid remains in a superheated liquid state. Then, suddenly the superheated liquid changes phase by means of an oblique evaporation wave. This phase change transforms the liquid into a biphasic mixture at high velocity pointing toward different directions, with increasing supersonic velocity as an expansion process takes place to the chamber back pressure, after going through a compression shock wave. The equations which govern this phenomenon are: the equations of conservation of mass, momentum and energy and an equation of state. Due to its steady state process, the numerical simulation is by means of a finite difference method using the McCormack method of Discretization. As this method does not capture shock waves, a second finite difference method is used to reach this task, the method uses the transient equations version of the conservation laws, applying the Dispersion-Controlled Dissipative (DCD) scheme. Numerical results using the code ShoWPhasT-2D v2 and experimental data have been compared, and the numerical results from the DCD-2D v1 have been analysed.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-02T18:09:12Z No. of bitstreams: 1 deniseschimitzdecarvalhotristao.pdf: 734334 bytes, checksum: 9fda9bda660d5bfec3204e328fe66d1c (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-06T19:58:58Z (GMT) No. of bitstreams: 1 deniseschimitzdecarvalhotristao.pdf: 734334 bytes, checksum: 9fda9bda660d5bfec3204e328fe66d1c (MD5) / Made available in DSpace on 2017-03-06T19:58:58Z (GMT). No. of bitstreams: 1 deniseschimitzdecarvalhotristao.pdf: 734334 bytes, checksum: 9fda9bda660d5bfec3204e328fe66d1c (MD5) Previous issue date: 2013-08-30 / O desenvolvimento de modelos matemáticos e métodos computacionais para a simulação de escoamentos em meios porosos é de grande interesse, devido à sua aplicação em diversas áreas da engenharia e ciências aplicadas. Em geral, na simulação numérica de um modelo de escoamento em meios porosos, são adotadas estratégias de desacoplamento dos sistemas de equações diferenciais parciais que o compõem. Este estudo recai sobre esquemas numéricos para leis de conservação hiperbólicas, cuja aproximação é não-trivial. Os esquemas de volumes finitos de alta resolução baseados no algoritmo REA (Reconstruct, Evolve, Average) têm sido empregados com considerável sucesso para a aproximação de leis de conservação. Recentemente, esquemas centrais de alta ordem, baseados nos métodos de Lax-Friedrichs e de Rusanov (Local Lax-Friedrichs) têm sido apresentados de forma a reduzir a excessiva difusão numérica característica destes esquemas de primeira ordem. Nesta dissertação apresentamos o estudo e a aplicação de esquemas de volumes finitos centrais de alta ordem para equações hiperbólicas que aparecem na modelagem de escoamentos em meios porosos. / The development of mathematical models and computational methods for the simulation of flow in porous media has a great interest because of its applications in engineering and other sciences. In general, in order to solve numerically the flow model in porous media the system of partial differential equations are decoupled. This study focus on the numerical schemes for the hyperbolic conservation laws, which solution is non-trivial. The finite volume schemes based on high order algorithm REA (Reconstruct, Evolve, Average) have been used with considerable success for the numerical solution of the conservation laws. Recently, high-order central schemes, based on the methods of Lax-Friedrichs and Rusanov (Local Lax-Friedrichs) have been presented, they reduce the excessive numerical diffusion presented in the first order schemes. In this dissertation we present the study and application of the high-order finite volume central schemes for hyperbolic equations as appear in the porous media flow modeling.

L’objectif principal de cette thèse concerne l’étude, la conception et la mise en œuvre numérique de schémas volumes finis associés aux solveurs de type Godunov. On s’intéresse à des systèmes hyperboliques de lois de conservation non linéaires, avec une attention particulière sur les équations d’Euler et les équations MHD idéale. Tout d’abord, nous dérivons un solveur de Riemann simple et véritablement multidimensionnelle, pouvant s’appliquer à tout système de lois de conservation. Ce solveur peut être considéré comme une généralisation 2D de l’approche HLL. Les ingrédients de base de la dérivation sont : la consistance avec la formulation intégrale et une utilisation adéquate des relations de Rankine-Hugoniot. Au final nous obtenons des expressions assez simples et applicables dans les contextes des maillages structurés et non structurés. Dans un second temps, nous nous intéressons à la préservation, au niveau discret, de la contrainte de divergence nulle du champ magnétique pour les équations de la MHD idéale. Deux stratégies sont évaluées et nous montrons comment le solveur de Riemann multidimensionnelle peut être utilisé pour obtenir des simulations robustes à divergence numérique nulle. Deux autres points sont abordés dans cette thèse : la méthode de relaxation pour un système Euler-Poisson pour des écoulements gravitationnels en astrophysique, la formulation volumes finis en coordonnées curvilignes. Tout au long de la thèse, les choix numériques sont validés à travers de nombreux résultats numériques. / The main objective of this thesis concerns the study, design and numerical implementation of finite volume schemes based on the so-Called Godunov-Type solvers for hyperbolic systems of nonlinear conservation laws, with special attention given to the Euler equations and ideal MHD equations. First, we derive a simple and genuinely two-Dimensional Riemann solver for general conservation laws that can be regarded as an actual 2D generalization of the HLL approach, relying heavily on the consistency with the integral formulation and on the proper use of Rankine-Hugoniot relations to yield expressions that are simple enough to be applied in the structured and unstructured contexts. Then, a comparison between two methods aiming to numerically maintain the divergence constraint of the magnetic field for the ideal MHD equations is performed and we show how the 2D Riemann solver can be employed to obtain robust divergence-Free simulations. Next, we derive a relaxation scheme that incorporates gravity source terms derived from a potential into the hydrodynamic equations, an important problem in astrophysics, and finally, we review the design of finite volume approximations in curvilinear coordinates, providing a fresher view on an alternative discretization approach. Throughout this thesis, numerous numerical results are shown.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-01-13T13:25:29Z No. of bitstreams: 1 pavelzenonsejaspaz.pdf: 1021401 bytes, checksum: 6c80da770310ced9141a330e3a4d4f9b (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-01-25T17:32:38Z (GMT) No. of bitstreams: 1 pavelzenonsejaspaz.pdf: 1021401 bytes, checksum: 6c80da770310ced9141a330e3a4d4f9b (MD5) / Made available in DSpace on 2016-01-25T17:32:38Z (GMT). No. of bitstreams: 1 pavelzenonsejaspaz.pdf: 1021401 bytes, checksum: 6c80da770310ced9141a330e3a4d4f9b (MD5) Previous issue date: 2015-08-28 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho apresentamos um estudo analítico sobre a recuperação de óleo pesado utilizando injeção de água, que é aquecida por meio de ondas eletromagnéticas de alta freqüência. Recentemente, foi feito um experimento (descrito em [12]), onde a água foi injetada num meio poroso, aquecida por meio de ondas eletromagnéticas. Os resultados do experimento mostram que o aquecimento mediante ondas EM melhora o deslocamento do óleo pela água. Desta maneira, apresenta-se a injeção de água com aquecimento por ondas EM como um método viável na recuperação de óleo. Consideraremos um modelo matemático simples descrevendo o experimento mencionado acima, que consiste de duas leis de balanço, uma para a energia e outra para a massa da água. O objetivo do trabalho é usar o Princípio de Duhamel e a Teoria das Leis de Conservação para encontrar soluções semi-analíticas deste modelo simplificado. Segundo [8], utilizamos o Princípio para achar a solução da equação de balanço de energia do tipo Convecção-Reação-Difusão para o problema de transporte de calor num meio poroso na presença de uma fonte de ondas eletromagnéticas. A equação de balanço para a massa da água é uma equação diferencial parcial não linear de primeira ordem do tipo Buckley-Leverett (Veja [4] e [7]). Ela será resolvida usando a Teoria das Leis de Conservação. Segundo [15], a solução deste problema contém ondas de rarefação e choque. / In this work, we present the results obtained by analytical study of heavy oil recovery by water flooding and electromagnetic (EM) heating of high frequency. Recently, an experiment was made, where water was injected into a porous medium, warmed by means of electromagnetic waves. The experiment results show that EM heating improves the displacement of oil by water. Thus, the water flooding combined with EM heating is a viable method for oil recovery. We consider a simple mathematical model describing this experiment consisting of two balance laws for energy and water mass. The goal is to use Duhamel’s Principle and the Theory of Conservation Laws to find semi-analytical solutions of this simplified model. We use the principle solve the energy balance equation of convection-reaction-diffusion type for heat transport problem in a porous medium in the presence of a source of electromagnetic waves. The balance equation for the mass of water is a nonlinear partial differential equation of first order of Buckley-Leverett type. It is solved using the Theory of Conservation Laws.

Neste trabalho apresenta-se um novo esquema prático tipo upwind de alta resolução, denominado EPUS (Eight-degree Polynomial Upwind Scheme), para resolver numericamente equações de conservação TVD e é implementado no contexto do método das diferenças finitas. O desempenho do esquema é investigado na resolução de sistemas hiperbólicos de leis de conservação e escoamentos incompressíveis complexos com superfícies livres. Os resultados numéricos mostraram boa concordãncia com outros resultados numéricos e dados experimentais existentes / Is this work a new practical high resolution upwinding scheme, called EPUS (Eight-degree Polynomial Upwind Scheme), for the numerical solution of transient convection-dominated conservation equations is present. The scheme is based on TVD stability criterion and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving hyperbolic systems of conservation laws and complex incompressible flows with free surfaces. The numerical results displayed good agreement with other existing numerical and experimental data

Esta dissertação trata da solução numérica de problemas em dinâmica dos fluidos usando dois novos esquemas upwind de alta resolução, denominados FDPUS-C1 (Five-Degree Polynomial Upwind Scheme of \' C POT. 1\' Class) e SDPUS-C1 (Six-Degree Polynomial Upwind Scheme of \'C POT.1\' Class), para a discretização de termos convectivos lineares e não-lineares. Os esquemas são baseados nos critérios de estabilidade TVD (Total Variation Diminishing) e CBC (Convection Boundedness Criterion) e são implementados, nos contextos das metodologias de diferenças finitas e volumes finitos, no ambiente de simulação Freeflow (an integrated simulation system for Free surface Flow) para escoamentos imcompressíveis 2D, 2D-1/2 e 3D, ou no código bem conhecido CLAWPACK ( Conservation LAW PACKage) para problemaw compressíveis 1D e 2D. Vários testes computacionais são feitos com o objetivo de verificar e validar os métodos numéricos contra esquemas upwind populares. Os novos esqumas são então aplicados na resolução de uma gama ampla de problemas em CFD (Computational Fluids Dynamics), tais como propagação de ondas de choque e escoamentos incompressíveis envolvendo superfícies livres móveis. Em particular, os resultados numéricos para leis de conservação hiperbólicas 2D e equações de Navier-Stokes incompressíveis 2D, 2D-1/2 e 3D demosntram que esses novos esquemas convectivos tipo upwind polinomiais funcionam muito bem / This dissertation deals with the numerical solution of fluid dynamics problems using two new high resolution upwind schemes,. namely FDPUS-C1 and SDPUS-C1, for the discretization of the linear and non-linear convection terms. The Schemes are based on TVD and DBC stability criteria and are implemented in the context of the finite difference and finite volume methodologies, either into the Freeflow code for 2D, 2D-1/2 and 3D incompressible flows or in the well-known CLAWPACK code for 1D and 2D compressible flows. Several computational tests are performed to verify and validate the numerical methods against other popularly used upwind schemes. The new schemes are then applied to solve a wide range of problems in CFD, such as shock wave propagation and incompressible fluid flows involving moving free msurfaces. In particular, the numerical results for 2D hyperbolic conservation laws and 2D, 2D-1/2 and 3D incompressible Navier-Stokes eqautions show that new polynomial upwind convection schemes perform very well

Três esquemas de captura de descontinuidade são apresentados para simular hiperbólicos de leis de conservação e equações de Navier-Stokes incompressíveis, a saber: FDHERPUS (Five Degree Hermite Upwind Scheme); RUS (Rational Upwind Scheme); e CSPUS (Cubic Spline Polynomial Upwind Scheme). Esses esquemas são baseados nos critérios de estabilidade CBC e TVD e implementados nos contextos das metodologias diferenças finitas e volumes finitos. A precisão local dos esquemas é verificada acessando o erro e a taxa de convergência em problemas testes de referência. Um estudo comparativo entre os esquemas estudados (incluido o WENO5) e o esquema bem estabelecido de van Albada, para resolver leis de conservação lineares e não lineares, é também realizado. O esquema de convecção que fornece melhores resultados em leis de conservação hiperbólicas é então examinado na simulação de escoamentos de fluidos newtonianos com superfícies livres móveis de complexidade crescente; resultados satisfatórios têm sido observados em termos do comportamento global / Three shock capturing schemes for numerical solution of hyperbolic conservation laws and incompressible Navier-Stokes equations are presented, namely: FDHERPUS (Five Degree Hermite Polynomial Upwind Scheme); RUS (Rational Upwind Scheme); and CSPUS ( Cubic Spline Polynomial Upwind Scheme). These schemes are based on CBC and TVD stability criteria and implemented in the context of finite volume methodologies. The local observed accuracy of the schemes is verified by assessing the error and convergence rate on benchmark test cases. A comparative study between the schemes (including WENO5) and the well established van. Albada scheme to solve standard linear and nonlinear hyperbolic conservation laws is also accomplished. The scheme that has provided better results in hyperbolic conservation laws is then examined in the simulation of Newtonian moving free surface flows of increasing complexity, satisfactory agreement has been observed in terms of the overall behavior

In a preamble, a quick summary of the line of thought from Noether's theorems to modern views on conserved charges in gauge theories is attempted. Most of the background material needed for the thesis is set out through a small survey of the literature. Emphasis is put on the concepts more than on the formalism, which is relegated to the appendices.<p><p>The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism.<p>The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described.<p><p><p>The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished