The numerics of hyperbolic conservation laws, e.g., the Euler equations of gas dynamics, shallow water equations and MHD equations, is non-trivial due to the convective terms being highly non-linear and equations being coupled. Many numerical methods have been developed to solve these equations, out of which central schemes and upwind schemes (such as Flux Vector Splitting methods, Riemann solvers, Kinetic Theory based Schemes, Relaxation Schemes etc.) are well known. The majority of the above mentioned schemes give rise to very dissipative solutions. In this thesis, we propose novel low dissipative numerical algorithms for some hyperbolic conservation laws representing fluid flows. Four different and independent numerical methods which give low diffusive solutions are developed and demonstrated. The first idea is to regulate the numerical diffusion in the existing dissipative schemes so that the smearing of solution is reduced. A diffusion regulator model is developed and used along with the existing methods, resulting in crisper shock solutions at almost no added computational cost. The diffusion regulator is a function of jump in Mach number across the interface of the finite volume and the average Mach number across the surface. The introduction of the diffusion regulator makes the diffusive parent schemes to be very accurate and the steady contact discontinuities are captured exactly. The model is demonstrated in improving the diffusive Local Lax-Friedrichs (LLF) (or Rusanov) method and a Kinetic Scheme. Even when employed together with accurate methods of Roe and Osher, improvement in solutions is demonstrated for multidimensional problems. The second method, a Central Upwind-Biased Scheme (CUBS), attempts to reorganize a central scheme such that information from irrelevant directions is largely reduced and the upwind biased information is retained. The diffusion co-efficient follows a new format unlike the use of maximum characteristic speed in the Local Lax-Friedrichs method and the scheme results in improved solutions of the flow features. The grid-aligned steady contacts are captured exactly with the reorganized format of diffusion co-efficient. The stability and positivity of the scheme are discussed and the procedure is demonstrated for its ability to capture all the features of solution for different flow problems. Another method proposed in this thesis, a Central Rankine-Hugoniot Solver, attempts to integrate more physics into the discretization procedure by enforcing a simplified Rankine-Hugoniot condition which describes the jumps and hence resolves steady discontinuities very accurately. Three different variants of the scheme, termed as the Method of Optimal Viscosity for Enhanced Resolution of Shocks (MOVERS), based on a single wave (MOVERS-1), multiple waves (MOVERS-n) and limiter based diffusion (MOVERS-L) are presented. The scheme is demonstrated for scalar Burgers equation and systems of conservation laws like Euler equations, ideal Magneto-hydrodynamics equations and shallow water equations. The new scheme uniformly improves the solutions of the Local Lax-Friedrichs scheme on which it is based and captures steady discontinuities either exactly or very accurately. A Grid-Free Central Solver, which does not require a grid structure but operates on any random distribution of points, is presented. The grid-free scheme is generic in discretization of spatial derivatives with the location of the mid-point between a point and its neighbor being used to define a relevant coefficient of numerical dissipation. A new central scheme based on convective-pressure splitting to solve for mid-point flux is proposed and many test problems are solved effectively. The Rankine-Hugoniot Solver, which is developed in this thesis, is also implemented in the grid-free framework and its utility is demonstrated. The numerical methods presented are solved in a finite volume framework, except for the Grid-Free Central Solver which is a generalized finite difference method. The algorithms developed are tested on problems represented by different systems of equations and for a wide variety of flow features. The methods presented in this thesis do not need any eigen-structure and complicated flux splittings, but can still capture discontinuities very accurately (sometimes exactly, when aligned with the grid lines), yielding low dissipative solutions. The thesis ends with a highlight on the importance of developing genuinely multidimensional schemes to obtain accurate solutions for multidimensional flows. The requirement of simpler discretization framework for such schemes is emphasized in order to match the efficacy of the popular dimensional splitting schemes.

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Le calcul scientifique parallèle est un domaine en plein essor qui permet à la fois d’augmenter la vitesse des longs traitements, de traiter des problèmes de taille plus importante ou encore des problèmes plus précis. Ce domaine permet donc d’aller plus loin dans les calculs scientifiques, d’obtenir des résultats plus pertinents, car plus précis, ou d’étudier des problèmes plus volumineux qu’auparavant. Dans le monde plus particulier de la simulation numérique scientifique, la résolution d’équations aux dérivées partielles (EDP) est un calcul particulièrement demandeur de ressources parallèles. Si les ressources matérielles permettant le calcul parallèle sont de plus en plus présentes et disponibles pour les scientifiques, à l’inverse leur utilisation et la programmation parallèle se démocratisent difficilement. Pour cette raison, des modèles de programmation parallèle, des outils de développement et même des langages de programmation parallèle ont vu le jour et visent à simplifier l’utilisation de ces machines. Il est toutefois difficile, dans ce domaine dit du “parallélisme implicite”, de trouver le niveau d’abstraction idéal pour les scientifiques, tout en réduisant l’effort de programmation. Ce travail de thèse propose tout d’abord un modèle permettant de mettre en oeuvre des solutions de parallélisme implicite pour les simulations numériques et la résolution d’EDP. Ce modèle est appelé “Structured Implicit Parallelism for scientific SIMulations” (SIPSim), et propose une vision au croisement de plusieurs types d’abstraction, en tentant de conserver les avantages de chaque vision. Une première implémentation de ce modèle, sous la forme d’une librairie C++ appelée SkelGIS, est proposée pour les maillages cartésiens à deux dimensions. Par la suite, SkelGIS, et donc l’implémentation du modèle, est étendue à des simulations numériques sur les réseaux (permettant l’application de simulations représentant plusieurs phénomènes physiques). Les performances de ces deux implémentations sont évaluées et analysées sur des cas d’application réels et complexes et démontrent qu’il est possible d’obtenir de bonnes performances en implémentant le modèle SIPSim. / Parallel scientific computations is an expanding domain of computer science which increases the speed of calculations and offers a way to deal with heavier or more accurate calculations. Thus, the interest of scientific computations increases, with more precised results and bigger physical domains to study. In the particular case of scientific numerical simulations, solving partial differential equations (PDEs) is an especially heavy calculation and a perfect applicant to parallel computations. On one hand, it is more and more easy to get an access to very powerfull parallel machines and clusters, but on the other hand parallel programming is hard to democratize, and most scientists are not able to use these machines. As a result, high level programming models, framework, libraries, languages etc. have been proposed to hide technical details of parallel programming. However, in this “implicit parallelism” field, it is difficult to find the good abstraction level while keeping a low programming effort. This thesis proposes a model to write implicit parallelism solutions for numerical simulations such as mesh-based PDEs computations. This model is called “Structured Implicit Parallelism for scientific SIMulations” (SIPSim), and proposes an approach at the crossroads of existing solutions, taking advantage of each one. A first implementation of this model is proposed, as a C++ library called SkelGIS, for two dimensional Cartesian meshes. A second implementation of the model, and an extension of SkelGIS, proposes an implicit parallelism solution for network-simulations (which deals with simulations with multiple physical phenomenons), and is studied in details. A performance analysis of both these implementations is given on real case simulations, and it demonstrates that the SIPSim model can be implemented efficiently.

Nous nous intéressons à l'utilisation d'approximations de rang faible pour réduire le coût des solveurs creux directs multifrontaux. Parmi les différents formats matriciels qui ont été proposés pour exploiter la propriété de rang faible dans les solveurs multifrontaux, nous nous concentrons sur le format Block Low-Rank (BLR) dont la simplicité et la flexibilité permettent de l'utiliser facilement dans un solveur multifrontal algébrique et généraliste. Nous présentons différentes variantes de la factorisation BLR, selon comment les mises à jour de rang faible sont effectuées, et comment le pivotage numérique est géré. D'abord, nous étudions la complexité théorique du format BLR qui, contrairement à d'autres formats comme les formats hiérarchiques, était inconnue jusqu'à présent. Nous prouvons que la complexité théorique de la factorisation multifrontale BLR est asymptotiquement inférieure à celle du solveur de rang plein. Nous montrons ensuite comment les variantes BLR peuvent encore réduire cette complexité. Nous étayons nos bornes de complexité par une étude expérimentale. Après avoir montré que les solveurs multifrontaux BLR peuvent atteindre une faible complexité, nous nous intéressons au problème de la convertir en gains de performance réels sur les architectures modernes. Nous présentons d'abord une factorisation BLR multithreadée, et analysons sa performance dans des environnements multicœurs à mémoire partagée. Nous montrons que les variantes BLR sont cruciales pour exploiter efficacement les machines multicœurs en améliorant l'intensité arithmétique et la scalabilité de la factorisation. Nous considérons ensuite à la factorisation BLR sur des architectures à mémoire distribuée. Les algorithmes présentés dans cette thèse ont été implémentés dans le solveur MUMPS. Nous illustrons l'utilisation de notre approche dans trois applications industrielles provenant des géosciences et de la mécanique des structures. Nous comparons également notre solveur avec STRUMPACK, basé sur des approximations Hierarchically Semi-Separable. Nous concluons cette thèse en rapportant un résultat sur un problème de très grande taille (130 millions d'inconnues) qui illustre les futurs défis posés par le passage à l'échelle des solveurs multifrontaux BLR. / We investigate the use of low-rank approximations to reduce the cost of sparse direct multifrontal solvers. Among the different matrix representations that have been proposed to exploit the low-rank property within multifrontal solvers, we focus on the Block Low-Rank (BLR) format whose simplicity and flexibility make it easy to use in a general purpose, algebraic multifrontal solver. We present different variants of the BLR factorization, depending on how the low-rank updates are performed and on the constraints to handle numerical pivoting. We first investigate the theoretical complexity of the BLR format which, unlike other formats such as hierarchical ones, was previously unknown. We prove that the theoretical complexity of the BLR multifrontal factorization is asymptotically lower than that of the full-rank solver. We then show how the BLR variants can further reduce that complexity. We provide an experimental study with numerical results to support our complexity bounds. After proving that BLR multifrontal solvers can achieve a low complexity, we turn to the problem of translating that low complexity in actual performance gains on modern architectures. We first present a multithreaded BLR factorization, and analyze its performance in shared-memory multicore environments on a large set of real-life problems. We put forward several algorithmic properties of the BLR variants necessary to efficiently exploit multicore systems by improving the arithmetic intensity and the scalability of the BLR factorization. We then move on to the distributed-memory BLR factorization, for which additional challenges are identified and addressed. The algorithms presented throughout this thesis have been implemented within the MUMPS solver. We illustrate the use of our approach in three industrial applications coming from geosciences and structural mechanics. We also compare our solver with the STRUMPACK package, based on Hierarchically Semi-Separable approximations. We conclude this thesis by reporting results on a very large problem (130 millions of unknowns) which illustrates future challenges posed by BLR multifrontal solvers at scale.

Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.

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.

Formulamos um modelo simplificado para o estudo do processo de injeção de solvente em reservatórios de petróleo, onde o fluido injetado (um ácido) tem a capacidade de dissolver parcialmente a matriz sólida. Como hipóteses principais, consideramos que o solvente e o soluto (componente químico que constitui o meio poroso) são espécies totalmente miscíveis, a viscosidade da mistura solvente + soluto não varia com a concentração de soluto, há significativa transferência de massa entre as fases e a permeabilidade do meio poroso varia linearmente com a porosidade. O modelo é formado por duas Equações Diferenciais Parciais, uma do tipo Convecção-Difusão a outra é do tipo Convecção-Reação. Para resolução numérica, desenvolvemos uma metodologia que denominamos de EPEC (Explícita Porosidade e Explícita Concentração). Tal metodologia se baseia em um limitador de fluxo do tipo TVD e em diferenças finitas centradas de segunda ordem. Em adição, o EPEC emprega uma técnica de separação de operadores. Deste modo, em cada passo de tempo, realizamos inicialmente o cálculo explícito da porosidade seguido do cálculo explícito da concentração do solvente. Assim, obtemos um desacoplamento natural das equações que descrevem o problema. Resultados de simulações são apresentados para um meio poroso bidimensional, após sessenta dias de injeção de solvente. / We formulate a simplified Model to study the process of solvent injection in petroleum Reservoir, where the injected fluid (an acid) can partially dissolve a solid matrix. As prime hypotheses, we considered that solvent an soluble component are completely mixed, the viscosity of the fluid does not vary with the concentration of the soluble component, theres significant transfer of mass between the parts and, the permeability of media porous changes linearly with porosity. The model is formed by two Partial Differential Equation, one is convection-diffusion type and another is a convection-reaction type. The Numerical Resolution weve developed a method called EPEC (Explicit Porosity Explicit Concentration). Such methodology is based upon a Limiting of Flow of TVD type and, used Centered Finite Differences of second order. In addition, the EPEC use a operators separation technique. This way, every time, first we clearly calculate the porosity and then the concentration of solvent is calculated. Thus we obtain a natural decoupling of the equations that describe the problem. Simulation results are presented to a two dimensional media porous after sixty days of solvent injection.

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.

Submitted by Pedro Silva Filho (pfsilva@ipen.br) on 2017-11-22T16:34:17Z No. of bitstreams: 0 / Made available in DSpace on 2017-11-22T16:34:17Z (GMT). No. of bitstreams: 0 / A cultura de segurança na área nuclear é definida como o conjunto de características e atitudes da organização e dos indivíduos que fazem que, com uma prioridade insuperável, as questões relacionadas à proteção e segurança nuclear recebam a atenção assegurada pelo seu significado. Até o momento, não existem instrumentos validados que permitam avaliar a cultura de segurança na área nuclear. Em vista disso, os resultados da definição de estratégias para o seu fortalecimento e o acompanhamento do desempenho das ações de melhorias tornam-se difíceis de serem avaliados. Este trabalho teve como objetivo principal desenvolver e validar um instrumento para a avaliação da cultura de segurança de organizações nucleares, utilizando o Instituto de Pesquisas Energéticas e Nucleares como unidade de pesquisa e coleta de dados. Os indicadores e variáveis latentes do instrumento foram definidos utilizando como referência modelos de avaliação de cultura de segurança da área da saúde e área nuclear. O instrumento de coleta de dados proposto inicialmente foi submetido à avaliação por especialistas da área nuclear e, posteriormente, ao pré-teste com indivíduos que pertenciam à população pesquisada. A validação do modelo foi feita por meio da modelagem por equações estruturais utilizando o método de mínimos quadrados parciais (Partial Least Square - Structural Equation Modeling PLS-SEM), no software SmartPLS. A versão final do instrumento foi composta por quarenta indicadores distribuídos em nove variáveis latentes. O modelo de mensuração apresentou validade convergente, validade discriminante e confiabilidade e, o modelo estrutural apresentou significância estatística, demonstrando que o instrumento cumpriu adequadamente todas as etapas de validação. / Tese (Doutorado em Tecnologia Nuclear) / IPEN/T / Instituto de Pesquisas Energéticas e Nucleares - IPEN-CNEN/SP