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Un nouveau modèle SPH incompressible : vers l’application à des cas industriels / A new incompressible SPH model : towards industrial applicationsLeroy, Agnes 17 November 2014 (has links)
Cette thèse a pour objet le développement d'un modèle numérique de simulation des fluides fondé sur la méthode Smoothed Particle Hydrodynamics (SPH). SPH est une méthode de simulation numérique sans maillage présentant un certain nombre d'avantages par rapport aux méthodes Eulériennes. Elle permet notamment de modéliser des écoulements à surface libre ou interfaces fortement déformées. Ce travail s'adresse principalement à quatre problématiques liées aux fondements de la méthode SPH : l'imposition des conditions aux limites, la prédiction précise des champs de pression, l'implémentation d'un modèle thermique et la réduction des temps de calcul. L'objectif est de modéliser des écoulements industriels complexes par la méthode SPH, en complément de ce qui peut se faire avec des méthodes à maillage. Typiquement, les problèmes visés sont des écoulements 3-D à surface libre ou confinés, pouvant interagir avec des structures mobiles et/ou transporter des scalaires, notamment des scalaires actifs (e.g. température). Dans ce but, on propose ici un modèle SPH incompressible (ISPH) basé sur une représentation semi-analytique des conditions aux limites. La technique des conditions aux limites semi-analytiques permet d'imposer des conditions sur la pression de manière précise et physique, contrairement à ce qui se fait avec des conditions aux limites classiques en SPH. Un modèle k-epsilon a été incorporé à ce nouveau modèle ISPH, à partir des travaux de Ferrand et al. (2013). Un modèle de flottabilité a également été ajouté, reposant sur l'approximation de Boussinesq. Les interactions entre flottabilité et turbulence sont prises en compte. Enfin, une formulation pour les frontières ouvertes dans le nouveau modèle est établie. La validation du modèle en 2-D a été réalisée sur un ensemble de cas-tests permettant d'estimer les capacités de prédiction du nouveau modèle en ce qui concerne les écoulements isothermes et non-isothermes, laminaires ou turbulents. Des cas confinés sont présentés, ainsi que des écoulements à surface libre (l'un d'eux incluant un corps solide mobile dans l'écoulement). La formulation pour les frontières ouvertes a été testée sur un canal de Poiseuille plan laminaire et sur deux cas de propagation d'une onde solitaire. Des comparaisons sont présentées avec des méthodes à maillage, ainsi qu'avec un modèle SPH quasi-incompressible (WCSPH) avec le même type de conditions aux limites. Les résultats montrent que le modèle permet de représenter des écoulements dans des domaines à géométrie complexe, tout en améliorant la prédiction des champs de pression par rapport à la méthode WCSPH. L'extension du modèle en trois dimensions a été réalisée dans un code massivement parallèle fonctionnant sur carte graphique (GPU). Deux cas de validation en 3-D sont proposés, ainsi que des résultats sur un cas simple d'application en 3-D / In this work a numerical model for fluid flow simulation was developed, based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a meshless Lagrangian Computational Fluid Dynamics (CFD) method that offers some advantages compared to mesh-based Eulerian methods. In particular, it is able to model flows presenting highly distorted free-surfaces or interfaces. This work tackles four issues concerning the SPH method : the imposition of boundary conditions, the accuracy of the pressure prediction, the modelling of buoyancy effects and the reduction of computational time. The aim is to model complex industrial flows with the SPH method, as a complement of what can be done with mesh-based methods. Typically, the targetted problems are 3-D free-surface or confined flows that may interact with moving solids and/or transport scalars, in particular active scalars (e.g. the temperature). To achieve this goal, a new incompressible SPH (ISPH) model is proposed, based on semi-analytical boundary conditions. This technique for the representation of boundary conditions in SPH makes it possible to accurately prescribe consistent pressure boundary conditions, contrary to what is done with classical boundary conditions in SPH. A k-epsilon turbulence closure is included in the new ISPH model. A buoyancy model was also added, based on the Boussinesq approximation. The interactions between buoyancy and turbulence are modelled. Finally, a formulation for open boundary conditions is proposed in this framework. The 2-D validation was performed on a set of test-cases that made it possible to assess the prediction capabilities of the new model regarding isothermal and non-isothermal flows, in laminar or turbulent regime. Confined cases are presented, as well as free-surface flows (one of them including a moving body in the flow). The open boundary formulation was tested on a laminar plane Poiseuille flow and on two cases of propagation of a solitary wave. Comparisons with mesh-based methods are provided with, as well as comparisons with a weakly-compressible SPH (WCSPH) model using the same kind of boundary conditions. The results show that the model is able to represent flows in complex boundary geometries, while improving the pressure prediction compared to the WCSPH method. The extension of the model to 3-D was done in a massively parallel code running on a Graphic Processing Unit (GPU). Two validation cases in 3-D are presented, as well as preliminary results on a simple 3-D application case
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Otimização de medidas de gerenciamento de fluxo de tráfego aéreo para múltiplos elementos regulados. / Optimization of air traffic management measures for multiple regulated elements.Koroishi, Giovanna Ono 02 May 2019 (has links)
O Serviço de Gerenciamento de Fluxo de Tráfego Aéreo (ATFM) estabelece um controle de fluxo seguro, ordenado e eficiente de acordo com a capacidade da infraestrutura e dos serviços de controle. O Gerenciamento ´e realizado com o auxílio de sistemas automatizados. Tais sistemas implementam programas que ajustam a demanda de voos à capacidade do espaço aéreo. Algoritmos simples podem sugerir medidas ATFM para solucionar a saturação em um conjunto restrito de elementos regulados (aeródromos, regiões do espaço aéreo, fixos ou aerovias). A natureza interconectada dos elementos regulados, que compõem o fluxo de tráfego aéreo, demanda uma abordagem mais abrangente para atingir o uso ótimo desses recursos, uma vez que outros problemas podem surgir quando a otimização local é aplicada a um elemento sem levar em conta seus elementos relacionados. Nem sempre há a necessidade do planejamento estratégico ser um ótimo global, uma vez que cenários viáveis e sub-ótimos encontrados com menor custo computacional podem representar soluções satisfatórias. O aumento da demanda do tráfego aéreo, no entanto, tem fomentado a aplicação de programas de geração de medidas ATFM mais complexos. Esta pesquisa implementou um programa de otimização global para a geração de medidas ATFM em cenários de larga escala do mundo real. O problema ´e modelado como um problema de programa¸c~ao inteira e o modelo adotado ´e abrangente, pois prevê atraso em solo, em voo, alteração de velocidade e rerroteamento. O programa é capaz de balancear o fluxo atendendo restrições de capacidade dos aeródromos e dos setores. Além disso, foi desenvolvida uma interface de visualização e edição de dados para os cenários estudados. Dados de voos no espaço aéreo brasileiro foram processados e utilizados para testar a solução implementada e mostraram a viabilidade do método. A utilização de um programa de otimização que leva em conta mais restrições potencialmente irá contribuir com o aumento de eficiência no uso da infraestrutura e do espaço aéreo de forma segura. / The Air Traffic Flow Management Service (ATFM) establishes a secure, orderly and efficient flow control according to the capacity of the infrastructure and control services. The Management is performed with the aid of automated systems. Such systems implement programs that adjust the flight demand to the airspace capacity. Simple algorithms might suggest ATFM measures to resolve saturation in a restricted set of regulated elements (aerodromes, airspace regions, fixes or airways). The interconnected nature of the regulated elements that make up the air traffic flow requires a more comprehensive approach to achieve optimum use of these resources, since other problems can arise when local optimization is applied to an element without regard to its related elements. There is not always a need for strategic planning to be a global optimum, since feasible and sub-optimal scenarios encountered at lower computational cost might represent satisfactory solutions. The increase in air traffic demand, however, has encouraged the application of programs to generate more complex ATFM measures. This research implemented a global optimization program for the generation of ATFM measures in large-scale real-world scenarios. The problem is modeled as an integer programming problem and the adopted model is comprehensive, since it provides ground and airborne delays, change of speed and re-routing. The program is able to balance the flow by meeting capacity constraints of the aerodromes and sectors. In addition, a visualization and data editing interface was developed for the studied scenarios. Flight data in Brazilian airspace were processed and used to test the implemented solution and the viability of the method was shown. The use of an optimization program that takes into account more constraints will potentially contribute to increase the efficiency in use of infrastructure and airspace in a secure manner.
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[en] CAPITAL FLOWS AND ECONOMIC GROWTH: THE ROLE OF FINANCIAL DEPTH AND THE EXCHANGE RATE CHANNEL / [pt] FLUXOS DE CAPITAIS E CRESCIMENTO ECONÔMICO: O PAPEL DO APROFUNDAMENTO FINANCEIRO E O CANAL DO CÂMBIOANDRE DINIZ JUNQUEIRA 03 September 2008 (has links)
[pt] O objetivo deste trabalho é investigar empiricamente uma
possível relação de causalidade entre fluxos de capitais (e
abertura financeira de um modo geral) e o crescimento
econômico de longo prazo dos países. Utilizando uma amostra
de 70 países para o período de 1970-2004 foram realizadas
uma série de estimações econométricas em painel em vista de
se medir o impacto de um fluxo mais elevado de capitais
sobre a produtividade das economias. Uma vez que a
literatura documenta uma possível assimetria neste efeito,
no sentido de que capitais externos devem ser benéficos
somente para países que já possuem uma capacidade absorciva
mínima, ou seja, que são capazes de converter de forma
eficaz esses capitais para investimentos produtivos que
alavancam o crescimento, utilizamos termos de interações
nas regressões. Mais especificamente testou-se o papel que
o aprofundamento financeiro de um país, medido como a razão
do volume de crédito doméstico privado sobre o PIB,
desempenha nesta relação entre fluxos de capitais e
crescimento. Os resultados obtidos indicam que, para
economias com razão crédito/PIB maior que um nível de
threshold que varia entre 25 e 30%, o impacto de
maiores fluxos de capitais é positivo e significante. Para
abaixo desse threshold o impacto é negativo.
Uma vez que fluxos excessivos de capitais externos exercem
forte pressão de apreciação da taxa real de câmbio de um
país, e que tal apreciação pode ser maléfica ao
crescimento da produtividade uma vez que impõe perdas
significantes aos setores de bens tradables, pode ocorrer
que países com baixo aprofundamento financeiro cresceram a
taxas menores em resultado de maiores fluxos de capitais
devido a uma apreciação excessiva do câmbio real. No
entanto, as estimações das regressões entre desalinhamentos
da taxa real de câmbio e crescimento apontam um efeito
significante e negativo do ponto de vista estatístico,
porém insignificante do ponto de vista econômico. / [en] The objective of this paper is to investigate empirically a
possible causal relation between capital flows (and
financial openess in a widely fashion) and long run
economic growth. With a sample of 70 countries in the
period ranging from 1970 to 2004 we estimated econometric
panels to test for the presence of a productivity growth
enhancing effect of higher capital flows. Since the
literature points out an assimetric effect in the sense
that foreign capital is desirable only for countries which
have attained a certain level of absorptive capacity, that
means, which are more able to convert them to productive
capital, interactive terms were included in the
regressions. More specifically, we tested the role of the
financial depth, measured as the ratio of domestic private
credit over GDP, on the relationship between capital flows
and growth. The results obtained show that economies which
have already attained a certain ratio of credit over GDP
greater than a threshold that varies between 25% and 30%
has a positive and significant impact of capital flows on
growth. Below this threshold, this impact is negative.
Since excessive capital flows exerts a pressure of strong
appreciation of the real exchange rate of a country and
that appreciation may be negative to productivity growth
since it imposes significant losses to tradables sectors,
it is possible that countries with a low financial depth
had grown less because of the effects of appreciation of
the exchange rate caused by capital flows. However, the
regression estimates between real exchange rate
misalignments and growth show a negative significant effect
by a statistical standpoint but insignificant by an
economic standpoint.
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Using dynamic programming and unsupervised learning to optimize material flow in assembly line supermarket : A case study of Volvo Powertrain at SkövdeAli, Muzdalifa January 2019 (has links)
Replenishment is an important process in automotive industries. It is the process by which parts required at assembly lines are stored and organized in assembly lines supermarket. Over many years replenishment have been done with the aim of positively impacting the varying demand frequency of articles in multi flows mixed-model assembly lines (MMALs) operating in just-in-time (JIT) fashion. However, a series of successive replenishment actions have negative impacts on the number of reallocation movements of parts within volume flows of supermarkets especially within a context of multi-flows supermarkets (MFSs). The cost of movements of parts within the supermarket has not been taken into consideration in previous replenishment methods. This is a significant problem since both un-optimized reallocation movements, and articles misplacement resolutions lead to production halts which cost assembly plants valuable time and money. Therefore, this research study proposes a replenishment method that optimizes flow of material within multi-flow assembly lines supermarkets and hence reduces the cost due to reallocation movement of multi-flow assembly lines supermarkets. The proposed method has been evaluated in the context of Volvo automobile engine assembly plant in Skövde. The proposed replenishment method has been evaluated by conducting an experiment using real-world data for the assembly plant in context. Performance metrics such as accuracy, F1-score, precision, sensitivity, and specificity were used to demonstrate the utility and validity of the proposed method. The evaluation results showed that the proposed method for optimizing material flow in supermarkets performed better than the existing method. In addition to utility, the proposed method provides contribution to knowledge by providing means for the industry to adopt replenishment method that takes into consideration the cost of reallocation movements of the parts within the supermarket.
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The effect of Mercosur on trade : How have Mercosur effected trade between member countries?Habtu, Besrat, Ahmed, Intisar January 2019 (has links)
This thesis examines whether there is an effect of the Mercosur free trade agreement on export and import between member countries. The study uses an extended gravity model framework on a panel data between the years 1975 to 2017 for 34 countries, including the member countries. Two different regressions were run using OLS and country fixed effect. A Linder effect was also added to the regressions to further understand the impact on trade. The results show a significantly positive effect of the FTA on imports. The FTA yielded insignificant and significantly negative result for OLS and FEM respectively on exports.
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Highly-skilled migration : knowledge spillovers and regional performances / Migration hautement qualifiée : externalités de connaissances et performances régionalesNoumedem Temgoua, Claudia 02 October 2018 (has links)
Les travailleurs hautement qualifiés - scientifiques et ingénieurs en particulier - sont un atout important pour le développement d’un pays car ils sont des facteurs majeurs dans la production de connaissances. C'est ce qui justifie les efforts compétitifs déployés par plusieurs pays afin d'attirer ces travailleurs. Les pays de destination sont en général décrits comme étant les grands gagnants des migrations des travailleurs hautement qualifiés. Ce qui n'est pas le cas des pays d'origine où ces migrations sont perçues comme une perte en capital humain. Cependant, ce phénomène serait beaucoup plus complexe qu'il n'y parait. En effet, il existe d'autres facteurs inhérents à la dynamique des migrations des travailleurs hautement qualifiés qui restent soit partiellement ou totalement inexplorés dans la littérature. Ces facteurs sont liés à des éléments résultant de ces migrations et pouvant créer des retombées positives vers les pays d'origine tout en contribuant ainsi à l'innovation dans ces pays. Afin d'explorer plus en profondeur cette question, il serait nécessaire de conduire une analyse approfondie autour de la question sur la nature des liens entre migrants hautement qualifiés résidant à l'étranger d'une part et celle des liens qui lient ces migrants à leurs pays d'origine d'autre part. A travers cette analyse, nous nous proposons de contribuer au débat sur le « brain gain » en investiguant les dynamiques de diffusion des connaissances à l'intérieur du réseau des migrants hautement qualifiés dans les pays de destination, mais également vers les pays d'origine. / Highly skilled workers – scientists and engineers in particular – are an important asset for a nation in so far that they enter in the production of knowledge as highly valuable human capital. That is why many countries have been competing for attracting. Receiving countries are in general pictured as the biggest winners from highly skilled migration. While the latter is perceived as a loss for sending countries. However, the situation might not be as simplistic as it seems. Indeed, we believe there are several unexplored factors underpinning the dynamics of highly skilled migration which contribute to some positive feedback to the sending countries in terms of knowledge and innovation while spurring innovation in the destination countries. And for a better understanding of these factors, one needs to look further into the nature of the ties linking highly skilled migrants abroad on one hand and to their home countries on the other hand. With our research we intend to contribute to the brain drain – brain gain trade-off debate by investigating the dynamics of knowledge diffusion within migrants’ networks in receiving countries and more importantly to sending countries.
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[en] MODELS AND ALGORITHMS FOR CONGESTION ANALYSIS AND YARD USE DETERMINATION IN RAILWAY LOGISTICS / [pt] MODELOS E ALGORITMOS PARA ANÁLISE DE CONGESTIONAMENTO E DETERMINAÇÃO DE PARADAS NA LOGÍSTICA FERROVIÁRIARAFAEL MARTINELLI PINTO 04 December 2007 (has links)
[pt] A importância do planejamento em logística ferroviária
cresce a cada dia devido
ao alto custo dos investimentos para o aumento da sua
capacidade. Entretanto,
planejar é uma atividade que exige uma representação
suficientemente precisa
da realidade estudada. Neste contexto, os modelos de
programação matemática
apresentam-se cada vez mais adequados. Isto decorre dos
recentes avanços nos
algoritmos e computadores disponíveis para sua resolução.
Esta dissertação apresenta
modelos e algoritmos para o planejamento ferroviário
tático e estratégico,
isto é feito estudando o Problema de Planejamento de
Atendimento (PPA).
Primeiramente este problema é considerado assumindo que
toda a estrutura ferroviária
está definida: a malha, a tração e os vagões disponíveis,
os pátios para
carga, descarga e transbordo, suas respectivas taxas de
carga e descarga e as demandas
previstas. Em seguida, a questão adicional de determinar
os pátios onde
paradas podem ser efetuadas é considerada. Finalmente, em
uma terceira etapa,
introduz-se a capacidade de se analisar os efeitos do
congestionamento de trechos
da malha e seu impacto nos tempos de circulação e na
capacidade da estrutura
logística. Modelos são apresentados para cada um dos
níveis de complexidade
do PPA. Algoritmos exatos e heurísticos e técnicas de pré-
processamento,
foram desenvolvidos para os tratamentos dos casos obtidos.
Em todos os casos,
foi possível resolver de maneira ótima ou quase ótima em
tempo razoável,
tanto em termos acadêmicos, como para a utilização
prática. Resultados computacionais
sobre um amplo conjunto de instâncias reais são
apresentados. / [en] Planning in Railway Logistic is an activity with growing
importance. This is due
to the high costs of investment to increase the railway
capacity. Nevertheless,
planning in this context is a cumbersome task, since a
precise representation is
necessary to consider most relevant points in this
activity. Mathematical programming
is becoming one of the best ways derive precise
representations and
to solve them. This is due to the recent advances on
algorithms and computers
used in the resolution of mathematical programming
problems. This dissertation
presents models and algorithms for tactical and
strategical railway planning
what is done by studying a demand planning problem (PPA).
First, this problem
is considered assuming that all the railway structure is
defined: the network, the
locomotives and wagons available, the yards for loading
and unloading with their
respective rates, and the forecast of demands. Next, the
question of deciding the
yards to stop is considered. Finally, in a third step, the
effect of congestion in
parts of the network is introduced to the models. This
allows analyzing the variation
in the travel times and its consequence in the logistic
structure capacity.
Models are presented for all cases of the PPA. Exact and
heuristic algorithms, as
well as pre-processing techniques, are described for the
problem resolution. In all
cases, the resulting approach allowed to solve the
problems optimally or quasioptimally
in a reasonable computing time. Computational results are
presented
on a wide set of real world instances.
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Managing the bi-directional flow of materials to increase customer satisfaction and reduce cost : A case study at Sandvik Mining and Rock TechnologyCannava, Catharina January 2019 (has links)
Purpose: This thesis explores the bi-directional flows of material perceived by manufacturing firms in the supply chain and accordingly derive suggestions to properly manage these flows to increase customer satisfaction and reduce cost. Methods: A literature review was summarized in a conceptual framework. This framework was then illustrated in a case. In this case, 11 semi-structured interviews, 3 participant observations and 3 types of archival records were collected. Analysis and discussion of the preliminary conceptual framework compared to the case was the basis for the modified conceptual framework that was designed. Main findings: In general material flows downstream the supply chain, but because of quality issues, recycling or returns material need to flow upstream the supply chain. This thesis provides a holistic view of how to manage these flows with a modified conceptual framework. Academic contributions: Previously, almost no academic research has been conducted on decision variables when it comes to managing material flows upstream the supply chain. This thesis contributes to closing this gap by suggesting different actions to properly manage the bi-directional flow of material. Furthermore, previous research addressing how to manage material flows has been re-accessed and expanded. Managerial implications: By using the framework, practitioners can determine helpful activities to increase customer satisfaction and reduce cost. This means management gets directions of where to allocate their resources. Limitations: The perspective and evidence in this research are only collected from the manufacturer’s point of view, valuable insight from suppliers and customers may have been overlooked. The suggestions of how to manage the bi-directional flow of materials have not been tested and the outcome of these recommendations has not been compared to KPIs or other measurements.
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Simulação numérica de escoamentos gás-sólido em leito fluidizado borbulhante utilizando a teoria cinética dos escoamentos granulares /Mineto, Andreza Tangerino. January 2009 (has links)
Orientador: Hélio Aparecido Navarro / Banca: Paulo Cesar Razuk / Banca: Luben Cabezas Gomez / Resumo: No presente trabalho desenvolve-se um estudo de modelagem matemática e simulação numérica do escoamento gás-sólido em um leito fuidizado borbulhante. É apresentado o modelo hidrodinâmico, A, para escoamentos bifásicos gás-solido considerando a Teoria Cinética dos Escoamentos Granulares. É usado o modelo Euleriano de duas fases separadas considerando a modelagem do tensor das tensões da fase sólida através do atrito entre as partículas e da teoria cinética dos escoamentos granulares. O código fonte MFIX (Multiphase Flow with Interphase eXchanges) desenvolvido no NETL (National Energy Technology Laboratory) é utilizado para as simulações numéricas. Os resultados de simulação são obtidos resolvendo a temperatura granular algebricamente ou através de uma equação diferencial parcial. Obtêm-se resultados mais realísticos no uso da EDP com condição de contorno de deslizamento parcial na parede. Uma variação no diâmetro das partículas (partículas do grupo B e do grupo A/B) é investigada, concluindo-se que deve ser acrescentado ao código MFIX outros parâmetros físico para simulações com partículas do grupo A/B. / Abstract: In the present work is described a mathematical model and numerical simulation of gas-solid flow in the bubbling fluidized bed. It is presented the hydrodynamic model, A, for gas-solid flow considering the Kinetic Theory of Granular Flows. It is used the two fluids Eulerian model where the solid phase stress tensor is modeled considering the friction between the particles and the kinetic theory of granular flows. The code MFIX (Multiphase Flow with Interphase eXchanges) developed in NETL (National Energy Tecnology Laboratory) is used for numerical simulations. The results are obtained with the compute of the granular temperature using a partial differential equation or an algebraic expression. It was obtained more realistic results when is used a PDE with boundary conditions of the partial slip. A variation in the diameter of the particles (particles in Group B and Group A/B) it is analyzed. It is also concluded that should be added to the code MFIX other physical parameters for simulations with particles of group A/B. / Mestre
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Solução numérica do modelo Giesekus para escoamentos com superfícies livres / Numerical solution of the Giesekus model for free surface flowsAraujo, Matheus Tozo de 25 September 2015 (has links)
Este trabalho apresenta um método numérico para simular escoamentos viscoelásticos bidimensionais governados pela equação constitutiva Giesekus [Schleiniger e Weinacht 1991]. As equações governantes são resolvidas pelo método de diferenças finitas numa malha deslocada. A superfície livre do fluido é modelada por partículas marcadoras possibilitando assim a sua visualização e localização. O cálculo da velocidade é efetuado por um método implícito enquanto a pressão é calculada por um método explícito. A equação constitutiva de Giesekus é resolvida pelo método de Euler modificado explícito. O método numérico desenvolvido nesse trabalho é verificado comparando-se a solução numérica com a solução analítica para o escoamento de um fluido Giesekus em um canal. Resultados de convergência são obtidos pelo uso de refinamento de malha. Os resultados alcançados incluem um estudo da aplicação do modelo Giesekus para simular o escoamento numa contração planar 4:1 e o problema de um jato incidindo sobre uma placa rígida, em que o fenômeno jet buckling é simulado. / This work presents a numerical method to simulate two-dimensional viscoelastic flows governed by the Giesekus constitutive equation [Schleiniger e Weinacht 1991]. The governing equations are solved by the finite difference method on a staggered grid. The free surface of the fluid is modeled by tracer particles thus enabling its visualization and location. The calculation of the velocity is performed by an implicit method while pressure is calculated by an explicit method. The Giesekus constitutive equation is resolved by the explicit modified Euler method. The numerical method developed in this work is verified by comparing the numerical solution with the analytical solution for the flow of a Giesekus fluid in a channel. Convergence results are obtained by the use of mesh refinement. Results obtained include a study of the application of the Giesekus model to simulate the flow through a 4:1 contraction and the problem of a jet flowing onto a rigid plate where the phenomenon of jet buckling is simulated.
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