O objetivo desta dissertação de mestrado é estudar técnicas numéricas para simular escoamentos incompressíveis multifásicos e implementar uma ferramenta computacional utilizando malhas hierárquicas e discretizações por diferenças finitas. São apresentados a formulação matemática e o desenvolvimento do método numérico, levando em consideração o caráter multifásico do escoamento. Foi adotado o modelo de força superficial contínua e a representação da interface foi feita pelo método de acompanhamento de fronteira. São expostos todos os testes realizados durante o desenvolvimento da ferramenta para checar cada etapa do método. Finalmente, testes visando verificar o código foram feitos e os resultados obtidos foram considerados satisfatórios para a verificação da ferramenta aqui desenvolvida. / The objective of this masters degree essay is to study numerical techniques to simulate incompressible multiphase flows and to implement a computational tool using hierachical meshes and discretizations by finite diferences. We introduce the mathematical formulation and the development of the numerical method, for the multiphase flow problem. A continuum surface force model is employed with the interface representation by the front tracking method. We show all tests performed to verify each stage of the methods development. Finally, results obtained in classical benchmark flow tests show good agreement with previous published results, corroborating the validity of this newly developed numerical tool.

Introdução: O uso de telas de polipropileno para reforço em cirurgias para correção de prolapso vaginal apresenta taxas de complicação de até 25%. Trata-se de doença de alta prevalência, acometendo até 30% das mulheres, cujas opções atuais de tratamento foram reduzidas após a descontinuação da fabricação dos reforços tradicionais por diversos fabricantes. Uma alternativa é a utilização de matrizes sintéticas de outros materiais e com outras configurações, possibilitando inclusive cultura de células em seu leito. A eletrofiação possibilita a produção e reprodução em larga escala dessas matrizes a partir de polímeros solúveis expostos a um campo elétrico. Objetivos: Estabelecer parâmetros de produção de matrizes com fibras híbridas e randômicas através de eletrofiação, demonstrar sua reprodutibilidade e implantar tal tecnologia em solo brasileiro. Testar as seguintes características teóricas das matrizes híbridas produzidas com acido polilático (PLLA): maior força tênsil nos testes biomecânicos e biocompatibilidade mantida para cultura celular. Estudar a influência da cultura de células-tronco mesenquimais derivadas de adipócitos (CTDA) sobre as propriedades mecânicas das matrizes estudadas. Avaliar a influência da hidrólise na perda de força tênsil das matrizes em experimentos de até 90 dias. Métodos: Foram produzidas matrizes de PLLA dissolvidos em diclorometano (DCM) nas configurações de fibras randômicas, alinhadas e um novo método foi desenvolvido para produção de matrizes híbridas. Foram realizados microscopia eletrônica, testes biomecânicos, testes de atividade metabólica e biocompatibilidade com cultivo de células-tronco derivadas de adipócitos, além de testes de degradação em meio de cultura por 90 dias para comparar as matrizes. Análise de variância (ANOVA) com teste de Tukey foram utilizados para comparação dos resultados obtidos nos experimentos quando aplicáveis. Resultados: A produção de matrizes híbridas foi possível ajustando-se os parâmetros de eletrofiação. Imagens de microscopia comprovaram o alinhamento e hibridização das fibras. Testes uniaxiais mostraram que as matrizes híbridas foram 3 a 4 vezes mais resistentes a tração do que as matrizes randômicas (p < 0,0001) preservando sua biocompatibilidade e afinidade celular. A incorporação de células às matrizes híbridas e o experimento de degradação mostraram quedas nas propriedades mecânicas de força tênsil máxima das matrizes híbridas a partir de 14 dias em meio de cultura, mas sempre se mantendo acima das propriedades dos tecidos nativos pelo período estudado de até 90 dias. Conclusões: Foi possível o desenvolvimento de nova técnica de eletrofiação para produção de matrizes híbridas de fibras alinhadas e randômicas com maior força tênsil, ainda sim mantendo sua afinidade celular. Tais matrizes enfraqueceram no período de 90 dias estudado, sem contudo apresentar valores abaixo dos fisiológicos, mostrando-se como opção promissora para substituição de telas de polipropileno em clínica. Estudos com animais são necessários para confirmar essa hipótese / Introduction: Traditional reinforcement techniques for pelvic organ prolapse use mainly polypropylene meshes with complication rates up to 25%. It is a common disease with prevalence up to 30%, with reduced options of treatment after withdrawing of major companies from this market. An alternative is the use of synthetic matrices from other materials with other configurations, possibly with cell culture added. Electrospinning is a reproducible technique that uses solved polymers exposed to intense electric field to produce sheets like that. Objectives: Establish parameters to electrospin hybrid and random fibres and setup this technology in Brazil. Prove following theoretical characteristics of hybrid poly- L-lactide (PLLA) matrices: higher tensile strength in biomechanical tests with comparable biocompatibility. Study adipose derived stem cells (ADSC) culture impact over biomechanical properties of these matrices. Check hydrolysis influences on tensile strength up to 90 days. Methods: PLLA solved in dichloromethane (DCM) was electrospun in random fibres, align fibres and a novel method was developed to produce hybrid fibres. Electron microscopy (SEM), biomechanical tests, metabolic activity and biocompatibility with adipose-derived stem cells and additionally, degradation test up to 90 days in culture medium were performed to compare matrices. ANOVA with Tukey test of differences was used to compare experiment results. Results: The production of hybrid matrices was possible adjusting electrospinning parameters, SEM confirmed fibre\'s alignment and hybridization, uniaxial tests showed that hybrid matrices were 3 to 4 times stronger than random ones (p < 0,0001) maintaining its biocompatibility and cell affinity. Both cell incorporation to hybrid matrices and degradation experiment showed mechanical properties drop (ultimate tensile strength) after 14 days in culture medium but always keeping it above physiologic range up to 90 days studied. Conclusions: Development of new technique of electrospinning of hybrid matrices of align and random fibres was possible, with higher tensile strength and keeping the same cell affinity. These matrices showed drop in mechanical strength along 90 days of study but always above the natural tissues range being a promising option to polypropylene meshes in clinic. Further studies with animals are needed to confirm this hypothesis

As análises de erros são conduzidas antes de qualquer projeto a ser desenvolvido. A necessidade do conhecimento do comportamento do erro numérico em malhas estruturadas e não-estruturadas surge com o aumento do uso destas malhas nos métodos de discretização. Desta forma, o objetivo deste trabalho foi criar uma metodologia para analisar os erros de discretização gerados através do truncamento na Série de Taylor, aplicados às equações de Poisson e de Advecção-Difusão estacionárias uni e bidimensionais, utilizando-se o Método de Volumes Finitos em malhas do tipo Voronoi. A escolha dessas equações se dá devido a sua grande utilização em testes de novos modelos matemáticos e função de interpolação. Foram usados os esquemas Central Difference Scheme (CDS) e Upwind Difference Scheme(UDS) nos termos advectivos. Verificou-se a influência do tipo de condição de contorno e a posição do ponto gerador do volume na solução numérica. Os resultados analíticos foram confrontados com resultados experimentais para dois tipos de malhas de Voronoi, uma malha cartesiana e outra triangular comprovando a influência da forma do volume finito na solução numérica obtida. Foi percebido no estudo que a discretização usando o esquema CDS tem erros menores do que a discretização usando o esquema UDS conforme literatura. Também se percebe a diferença nos erros em volumes vizinhos nas malhas triangulares o que faz com que não se tenha uma uniformidade nos gráficos dos erros estudados. Percebeu-se que as malhas cartesianas com nó no centróide do volume tem menor erro de discretização do que malhas triangulares. Mas o uso deste tipo de malha depende da geometria do problema estudado / The analyses of errors are conducted before any project to be developed. The necessity of studying the behavior of the numerical error on structured and unstructured grids comes up with the increasing use of these methods of discretization meshes. Thus, the objective was to create a methodology to analyze the errors generated by discretization of the truncation in the Taylor series, applied to the equations of Poisson and Advection-Diffusion stationary and uni and bi-dimensional, using the Finite Volume Method on Voronoi mesh. The choice of these equations is due to its wide use in testing new mathematical models and interpolation function. The schemes used were the Central Difference Scheme (CDS) and the Upwind Difference Scheme (UDS) in the advective terms. There was the influence of boundary condition and position of the generator in the numerical solution of the volume. The analytical results were compared with experimental results for two types of Voronoi meshes, a Cartesian mesh and a triangular shape showing the influence of finite volume in the numerical solution obtained. It was perceived that the discretization in the study using the CDS scheme has smaller errors than the discretization scheme using the UDS as literature. Also notice the difference in the errors in neighboring volumes in triangular meshes which means that there has been no uniformity in the graphs of errors studied. It was noticed that the Cartesian meshes with node at the centroid of the volume is smaller than discretization error triangular meshes. But using this type of meshes depends on the geometry of the problem studied

Moldagem por injeção é um dos mais importantes processos industriais para produção de produtos plásticos finos. Esse processo é dividido essencialmente em quatro estágios: plastificação, preenchimento, empacotamento e resfriamento. O escoamento de um fluido caracterizado por alta viscosidade em uma cavidade estreita é um problema tipicamente encontrado em processos de moldagem por injeção.Neste caso, o escoamento pode ser descrito por uma formulação conhecida como aproximação de Hele-Shaw. Tal formulação pode ser derivada das equações de conservação tridimensionais usando um número de suposições a respeito do polímero injetado e da geometria da cavidade do molde, juntamente com a integração e o acoplamento das equações da conservação da quantidade de movimento e da continuidade. Essa formulação, referindo às limitações da geometria do molde como sendo canais estreitos e quase sem curvatura, é comumente denominada formulação 2 1/2D. Neste trabalho, é apresentada uma técnica para a simulação da fase de preenchimento de um processo de moldagem por injeção, usando essa formulação 2 1/2D, com um método de volumes finitos e malhas não estruturadas. O modelo de Cross modificado com dependência da temperatura de Arrhenius é empregado para descrever a viscosidade do polímero fundido. O campo de distribuição de temperatura é tridimensional e é resolvido usando um esquema semi-Lagrangeano baseado em volumes finitos. As malhas não estruturadas utilizadas são geradas por triangulação de Delaunay e o método numérico implementado usa a estrutura de dados topológica SHE - Singular Handle Edge, que é capaz de lidar com condições de contorno e singularidades, aspectos comumente encontrados em simulações numéricas de escoamento de fluidos. / Injection molding is one of the most important industrial processes for the manufacturing of thin plastic products. This process can be divided into four stages: plastic melting, filling, packing and cooling phases. The flow of a fluid characterized by high viscosity in a narrow gap is a problem typically found in injection molding processes. In this case, the flow can be described by a formulation known as Hele-Shaw approach. Such formulation can be btained from the three-dimensional conservation equation using a number of assumptions regarding the injected polymer and the geometry of the mold, together with the integration and the coupling of the momentum and continuity equations. This approach, referring to limitations of the mould geometry to narrow, weakly curved channels, is usually called 2 1/2D approach. In this work a technique for the simulation of the filling stage of the injection molding process, using this 2 1/2D approach, with a finite volume method and unstructured meshes, is presented. The modified-Cross model with Arrhenius temperature dependence is employed to describe the viscosity of the melt. The temperature field is 3D and it is solved using a semi-Lagrangian scheme based on the finite volume method. The employed unstructured meshes are generated by Delaunay triangulation and the implemented numerical method uses the topological data structure SHE - Singular Handle Edge, capable to deal with boundary conditions and singularities, aspects commonly found in numerical simulation of fluid flow.

[pt] Este trabalho apresenta um método para extração de malhas poligonais adaptativas em multi-resolução, a partir de objetos volumétricos. As principais aplicações da extração de malhas estão ligadas à área médica, dinâmica de fluidos, geociências, meteorologia, dentre outras. Nestas áreas os dados podem ser representados como objetos volumétricos. Nos dados volumétricos as informações estão representadas implicitamente, o que dificulta o processamento direto dos objetos que se encontram representados dentro do volume. A extração da malha visa obter uma representação explícita dos objetos, de modo a viabilizar o processamento dos mesmos. O método apresentado na tese procura extrair a malha a partir de processos de Simplicação e Refinamento. Durante a simplificação é extraída uma representação super amostrada do objeto (na mesma resolução do volume inicial), a qual é simplificada de modo a se obter uma malha base ou malha grossa, em baixa resolução, porém contendo a topologia correta do objeto. A etapa de refinamento utiliza a transformada de distâ ncia para obter uma representação da malha em multi-resolução, ou seja, a cada instante é obtida uma malha de maior resolução que vai se adaptando progressivamente à geometria do objeto. A malha final apresenta uma série de propriedades importantes, como boa razão de aspecto dos triângulos, converge para a superfície do objeto, pode ser aplicada tanto a objetos com borda quanto a objetos sem borda, pode ser aplicada tanto a superfície conexas quanto a não conexas, dentre outras. / [en] This work presents a method for extracting multiresolution adaptive polygonal meshes, from volumetric objects. Main aplications of this work are related to medical area, fluid dynamics, geosciences, metheorology and others. In these areas data may be represented as volumetric objects. Volumetric datasets are implicit representations of objects, so it s very dificult to apply directly any process to these objects. Mesh extraction obtains an explicit representation of the objetc, such that it s easier to process directly the objects. The presented method extracts the mesh from two main processes: Simplification and Refinement. The simplification step extracts a supersampled representation of the object (in the same volume resolution), and simplifies it in such a way to obtain a base mesh (or coarse mesh), in a low resolution, but containing the correct topology of the object. Refinement step uses the distance transform to obtain a multiresolution representation of the mesh, it means that at each instant it s obtained an adaptive higher resolution mesh. The final mesh presents a set of important properties, like good triangle aspect ratio, convergency to the object surface, may be applied as to objects with boundary and as to objects with multiple connected components, among others properties.

Este trabalho apresenta uma análise comparativa com três tipos de ligações entre paredes de alvenaria estrutural submetidas a ações verticais. O primeiro tipo de ligação é feito através de amarração direta de paredes de alvenaria. O segundo por amarração indireta solidarizada por telas metálicas e o terceiro, também com amarração indireta, porém, enrijecida por grampos metálicos ancorados em furos grauteados. O estudo é baseado em resultados obtidos por meio de um programa experimental realizado no laboratório de estruturas da EESC-USP. Os modelos utilizados são paredes em formato H, com cinco fiadas, em escala reduzida 1:3, os quais foram propostos por Capuzzo Neto (2005). A partir da análise experimental é obtida a resistência ao cisalhamento da interface no plano vertical de ligação entre a parede central e o flange todos os modelos ensaiados. Conclui-se que os modelos com amarração direta possuem maiores resistências ao cisalhamento, o que reforça o fenômeno da interação de paredes submetidas a ações verticais, além de apresentarem forma de ruptura caracterizada como frágil. Os modelos com amarração indireta, tanto com telas quanto com grampos, possuem resistências ao cisalhamento aproximadamente igual a 60% da encontrada para amarração direta, contudo, apresentam ruptura dúctil, com destaque para a ligação com grampos. / This work presents a comparative analysis of three types of connections between structural masonry walls under vertical loads. The first type is a set of running bond interconnected masonry walls. The second connection is obtained by means of steel meshes and the third, also stack bond, is hardened by metallic staples anchored in grouted holes. The study is based on an experimental program carried out in the laboratory of structures of the EESC-USP. The test specimens are H shaped third scale walls, with five courses, as proposed by Capuzzo Neto (2005). The experimental analysis allows for the evaluation of the shear strength of the vertical interface between the central wall and the flanges. The study shows that the models with running bond provide the largest shear strength, which corroborates the phenomenon of the walls’ interaction under vertical loads, and a fragile failure type. Both the stack bond specimens present a shear strength of roughly 60% of the running bond type, with ductile failure, specially for the stapled connection.

Understanding of the shape and size of different features of human body from the scanned data is necessary for automated design and evaluation of product ergonomics. The traditional method of finding required body dimensions by manual measurements (Anthropometry) has many sociological, logistical and technical drawbacks such as prolonged time, skilled researcher for consistency and accuracy of measurements, undesirable physical contact between the subject and the researcher, required presence of people from different demographic categories or travel of researcher with equipments. If these di- mensions are extracted from the stored digital human models, above drawbacks can be eliminated. With the emergence of laser based 3d scanners, it is now possible generate a large database of surface models of humans from different demographic backgrounds but the automatic processing of 3d meshes is under development. Though some commercial packages are available for extraction of a limited number of dimensions from full body scans, mostly belonging to topologically separable body parts like hands and legs, the dimensions associated with head and face are particularly not available in public domain. The processing of surface models of head and face from the automatic measurement point of view is also not discussed in literature though this type of data has many practical applications like ergonomic design of close-fitting products like respiratory masks,ophthalmic frames (spectacles), helmets and similar head-mounted devices; Creation of a facial feature database for face modeling coding and reconstruction and for use in forensic sciences; Automated anthropological surveys and Medical growth analysis and aesthetic surgery planning. Hence, in this thesis, a computational framework is developed for automatic detection, recognition and measurement of important facial features namely eyes, eyebrows, nose, mouth and moustache (if applicable) from scanned head and shoulder polyhedral models. After preprocessing the scanned mesh manually to fill holes and remove singular vertices, discrete differential geometric operators were implemented to compute surface normals and curvatures. Mean curvature magnitude was used as the primary metric to segment the mesh using morphological watershed algorithms which treat the mesh as a height map and separate the regions according to the water catchment basins. After visualization it was hypothesized that the important facial features consist of relatively high curvature regions and based on this hypothesis a much faster approach was then employed based on mathematical morphology to group the high curvature vertices into regions based on adjacency. The important feature regions isolated this way were then identified and labeled to be belonging to different facial features by a decision tree based on their relative spatial disposition. Adaptive selection of parameters was incorporated later to ensure robustness of this algorithm. Critical points of these identified features are recognized as the standard landmarks associated with those primary facial features. A number of clinically identified landmarks lie on the facial mid-line. An efficient algorithm is proposed for detection and processing of the mid-line using a point sampling technique which is fast and has immunity to noise in the data. An algorithm to find shortest path between two vertices while traveling along the edges is implemented to measure on-surface distances and to isolate the nose. Complete program comprising of curvature and surface normal computations, seg- mentation and identification of 6 important features, facial mid-line processing, detection of total 17 landmarks and shortest path computations to separate nose takes about 2 minutes to work including visualization on a full resolution mesh of typically 2,15,521 Vertices and 4,30,560 Faces. The algorithm was tested successfully on more than 40 faces with minor exceptions. The results match human perception. The computed measurements were also compared with the physical measurements for a few subjects, the measurements were found to be in good agreement and satisfactory for its usage in product ergonomics and clinical applications.

In this thesis singularly perturbed convection-diffusion equations in the unit square are considered. Due to the presence of a small perturbation parameter the solutions of those problems exhibit an exponential layer near the outflow boundary and two parabolic layers near the characteristic boundaries. Discretisation of such problems on standard meshes and with standard methods leads to numerical solutions with unphysical oscillations, unless the mesh size is of order of the perturbation parameter which is impracticable. Instead we aim at uniformly convergent methods using layer-adapted meshes combined with standard methods. The meshes considered here are S-type meshes--generalisations of the standard Shishkin mesh. The domain is dissected in a non-layer part and layer parts. Inside the layer parts, the mesh might be anisotropic and non-uniform, depending on a mesh-generating function. We show, that the unstabilised Galerkin finite element method with bilinear elements on an S-type mesh is uniformly convergent in the energy norm of order (almost) one. Moreover, the numerical solution shows a supercloseness property, i.e. the numerical solution is closer to the nodal bilinear interpolant than to the exact solution in the given norm. Unfortunately, the Galerkin method lacks stability resulting in linear systems that are hard to solve. To overcome this drawback, stabilisation methods are used. We analyse different stabilisation techniques with respect to the supercloseness property. For the residual-based methods Streamline Diffusion FEM and Galerkin Least Squares FEM, the choice of parameters is addressed additionally. The modern stabilisation technique Continuous Interior Penalty FEM--penalisation of jumps of derivatives--is considered too. All those methods are proved to possess convergence and supercloseness properties similar to the standard Galerkin FEM. With a suitable postprocessing operator, the supercloseness property can be used to enhance the accuracy of the numerical solution and superconvergence of order (almost) two can be proved. We compare different postprocessing methods and prove superconvergence of above numerical methods on S-type meshes. To recover the exact solution, we apply continuous biquadratic interpolation on a macro mesh, a discontinuous biquadratic projection on a macro mesh and two methods to recover the gradient of the exact solution. Special attentions is payed to the effects of non-uniformity due to the S-type meshes. Numerical simulations illustrate the theoretical results.

The handling of gradient calculations on non-orthogonal meshes in the Finite Volume Method (FVM) is important in the modelling of complex geometries, since different implementation methods have an influence on the accuracy and the stability of the solution. The application in the current study is the numerical solution of heat conduction in a complex geometry. It finds relevance in many engineering applications such as the Micro-Channel Heat Exchanger (MCHE) that acts as a recuperator in a High Temperature Reactor (HTR) power generation cycle. A program based on the FVM was developed in Excel for the solution of the diffusion equation on a non-orthogonal mesh. A test case of heat conduction in a rectangular block, meshed with a tetrahedral mesh, was solved with the Excel code. The same test case was solved with OpenFOAM. The results of the two codes were compared. Small differences were found and their origins were traced to slightly different implementation methods. Knowledge of the differences in implementation between the two codes resulted in a better understanding of the aspects that influenced accuracy and stability. Computations on meshes with the presence of mesh skewness and non-orthogonal mesh lines at boundaries were performed and an accompanying decrease in accuracy was observed. The results showed that the standard FVM as implemented in the Excel code and in OpenFOAM will need advanced methods to compensate for mesh skewness and non-orthogonality found at boundaries. During the study, a deeper knowledge and understanding was gained of the challenge of obtaining accurate solutions of heat conduction on non-orthogonal meshes. This knowledge may lead to the overall improvement of the simulation of heat transfer models in general and for the MCHE specifically. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.

The handling of gradient calculations on non-orthogonal meshes in the Finite Volume Method (FVM) is important in the modelling of complex geometries, since different implementation methods have an influence on the accuracy and the stability of the solution. The application in the current study is the numerical solution of heat conduction in a complex geometry. It finds relevance in many engineering applications such as the Micro-Channel Heat Exchanger (MCHE) that acts as a recuperator in a High Temperature Reactor (HTR) power generation cycle. A program based on the FVM was developed in Excel for the solution of the diffusion equation on a non-orthogonal mesh. A test case of heat conduction in a rectangular block, meshed with a tetrahedral mesh, was solved with the Excel code. The same test case was solved with OpenFOAM. The results of the two codes were compared. Small differences were found and their origins were traced to slightly different implementation methods. Knowledge of the differences in implementation between the two codes resulted in a better understanding of the aspects that influenced accuracy and stability. Computations on meshes with the presence of mesh skewness and non-orthogonal mesh lines at boundaries were performed and an accompanying decrease in accuracy was observed. The results showed that the standard FVM as implemented in the Excel code and in OpenFOAM will need advanced methods to compensate for mesh skewness and non-orthogonality found at boundaries. During the study, a deeper knowledge and understanding was gained of the challenge of obtaining accurate solutions of heat conduction on non-orthogonal meshes. This knowledge may lead to the overall improvement of the simulation of heat transfer models in general and for the MCHE specifically. / Thesis (MIng (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2013.