This thesis presents numerical techniques for solving problems of incompressible flow coupled to scalar transport equations using finite element discretizations in space. The two applications considered in this thesis are multi-phase flow, modeled by level set or phase field methods, and planetary mantle convection based on the Boussinesq approximation. A systematic numerical study of approximation errors in evaluating the surface tension in finite element models for two-phase flow is presented. Forces constructed from a gradient in the same discrete function space as used for the pressure are shown to give the best performance. Moreover, two approaches for introducing contact line dynamics into level set methods are proposed. Firstly, a multiscale approach extracts a slip velocity from a micro simulation based on the phase field method and imposes it as a boundary condition in the macro model. This multiscale method is shown to provide an efficient model for the simulation of contact-line driven flow. The second approach combines a level set method based on a smoothed color function with a the phase field method in different parts of the domain. Away from contact lines, the additional information in phase field models is not necessary and it is disabled from the equations by a switch function. An in-depth convergence study is performed in order to quantify the benefits from this combination. Also, the resulting hybrid method is shown to satisfy an a priori energy estimate. For the simulation of mantle convection, an implementation framework based on modern finite element and solver packages is presented. The framework is capable of running on today's large computing clusters with thousands of processors. All parts in the solution chain, from mesh adaptation over assembly to the solution of linear systems, are done in a fully distributed way. These tools are used for a parallel solver that combines higher order time and space discretizations. For treating the convection-dominated temperature equation, an advanced stabilization technique based on an artificial viscosity is used. For more efficient evaluation of finite element operators in iterative methods, a matrix-free implementation built on cell-based quadrature is proposed. We obtain remarkable speedups over sparse matrix-vector products for many finite elements which are of practical interest. Our approach is particularly efficient for systems of differential equations.

This study focuses ontransient heat flow behavior in which centralizing energy on themetal makes metal surface come to aheat molten state with centralized heat source . This flow field is two-dimensional transient model, using Phase-field method and Two-phase flow to simulatemetal surface. In this study is under considerations of the mass conservation equation, momentum equation, energy equation and the level-set equation, regardless of the impact due to the concentration diffusion. At last it will show the flow of the molten zone caused by temperature, and the flows in molten zone forced by thermocapillary which is caused byvariation of temperature.

Steadily increasing heat dissipation in electronic devices has generated renewed interest in direct immersion cooling. The ideal heat transfer fluid for direct immersion cooling applications should be chemically and thermally stable, and compatible with the electronic components. These constraints have led to the use of Novec fluids and fluroinerts as coolants. Although these fluids are chemically stable and have low dielectric constants, they are plagued by poor thermal properties. These factors necessitate the development of new heat transfer fluids with improved heat transfer properties and applicability. Computer Aided Molecular Design (CAMD) approach was used in this work to systematically design novel heat transfer fluids that exhibit significantly better properties than those of current high performance electronic coolants. The candidate fluids generated by CAMD were constrained by limiting their boiling points, latent heat of vaporization and thermal conductivity. The selected candidates were further screened using a figure of merit (FOM) analysis. Some of the fluids/additives that have been identified after the FOM analysis include C₄H₅F₃O, C₄H₄F₆O, C₆H₁₁F₃, C₄ H₁₂O₂Si, methanol, and ethoxybutane. The heat transfer performance of these new fluids/fluid mixtures was analyzed through pool boiling and flow boiling experiments. All the fluid mixtures tested showed an improvement in the critical heat flux (CHF) when compared to the base fluid (HFE 7200). A pool boiling model was developed using the phase field method available in COMSOL. Although these simulations are computationally expensive, they provide an alternate solution to evaluate several candidate fluids generated using the CAMD approach.

Dans ce travail de thèse, nous nous sommes intéressés à la simulation de l’évolution de la microstructure d’un polymère. Plus précisément, nous avons étudié le changement de la morphologie du polyéthylène téréphthalate (PET) sous l’effet de différents mécanismes. Ces simulations sont réalisées par la méthode des champs de phase. Il s’agit d’une méthode basée sur l’équation de Cahn-Hilliard ou l’équation de Ginzburg-Landau. Elle utilise un paramètre d’ordre pour décrire l’état du matériau, des variables thermodynamiques et cinématiques. Ainsi on peut décrire l’évolution d’une microstructure sans suivre l’interface et ainsi reproduire l’évolution de la structure cristalline sphérolitique qui apparait lors d’une cristallisation induite par la température. Dans le cadre d’un changement de morphologie induit par la température, le calcul par champ de phase a été simulé par la méthode de différences finies et la méthode d’éléments finis. Le coefficient cinétique a été identifié à partir de données expérimentales de la littérature. En introduisant un modèle du champ de phases multiples (the MPF model) on a aussi simulé l’évolution de plusieurs sphérolites et gérer la jonction lorsque deux sphérolites se rencontrent. La croissance et la jonction des sphérolite a été modélisée par la méthode d’éléments finis : elle reproduit parfaitement l’évolution expérimentale de cristallisation isotherme d’un polymère. En comparant ces résultats avec le modèle macroscopique d’Avrami, une évaluation de la constante d'Avrami, K(T), a été discutée en fonction des fluctuations des conditions initiales (positions et taille des germes).Dans le cadre de la cristallisation induite par la déformation mécanique, nous avons couplé le champ de phase aux équations de la mécanique pour un comportement viscoélastique différent pour chaque phase. L’influence, sur la cristallisation et l’orientation, de la déformation, de la vitesse de sollicitation, du contraste entre les phases sont étudiées et comparées qualitativement aux observations expérimentales. Il s’agit d’une étude préliminaire qui devra être poursuivie et affinée afin de prédire une morphologie plus réaliste / In this thesis work, we are interested in simulating the evolution of the microstructure of a polymer. In particular, we have studied in the morphology change of polyethylene terephthalate (PET) under different mechanisms. These simulations carried out by the phase field simulation. This method based on the Cahn-Hilliard equation or the Ginzburg-Landau equation. It uses an order parameter to describe the state of material, thermodynamic and kinetic variables. Thus we can describe the microstructure evolution without tracking the interface (which would require complex remeshing) and reproduce the evolution of the crystalline structure within the polymers, for example the growth of spherulites which appear during crystallization induced by temperature. Within the scope the morphology changing by the temperature, the evolution of phase field simulation is performed by the finite difference method and the finite element method. The kinetic coefficient is adjusted in order to fit the experiment data in of the literature. We introduce the multiphase field model (the MPF model) in order to simulate the evolution of several spherulites and to describe the junction of spherulites. The growth and junction of spherulites have been modeled by the finite element method and nicely reproduced in comparing the experimental evolution of isothermal crystallization of a polymer. Comparing these results with the Avrami macroscopic model, an evaluation of the Avrami constant, K (T), was discussed according to the fluctuations of the initial conditions (positions and size of the germs).In the following part, we study the crystallization induced by mechanical deformation. We are interested in the viscoelastic model to simulate the induced crystallization of PET in plane stress. The phase field model coupled to mechanics will be presented. Different viscoelastic behaviors have been considered for each phase. The influence on crystallization and orientation of the deformation, the stress velocity and the contrast between the phases are studied and compared qualitatively with the experimental observations. This is a preliminary study that will have to be continued in order to predict a more realistic morphology

In this thesis, a robust, reliable and efficient isogeometric analysis framework is presented that allows for an adaptive spatial discretization of non-linear and time-dependent multi-field problems. In detail, B\'ezier extraction of truncated hierarchical B-splines is proposed that allows for a strict element viewpoint, and in this way, for the application of standard finite element procedures. Furthermore, local mesh refinement and coarsening strategies are introduced to generate graded meshes that meet given minimum quality requirements. The different strategies are classified in two groups and compared in the adaptive isogeometric analysis of two- and three-dimensional, singular and non-singular problems of elasticity and the Poisson equation. Since a large class of boundary value problems is non-linear or time-dependent in nature and requires incremental solution schemes, projection and transfer operators are needed to transfer all state variables to the new locally refined or coarsened mesh. For field variables, two novel projection methods are proposed and compared to existing global and semi-local versions. For internal variables, two different transfer operators are discussed and compared in numerical examples. The developed analysis framework is than combined with the phase-field method. Numerous phase-field models are discussed including the simulation of structural evolution processes to verify the stability and efficiency of the whole adaptive framework and to compare the projection and transfer operators for the state variables. Furthermore, the phase-field method is used to develop an unified modelling approach for weak and strong discontinuities in solid mechanics as they arise in the numerical analysis of heterogeneous materials due to rapidly changing mechanical properties at material interfaces or due to propagation of cracks if a specific failure load is exceeded. To avoid the time consuming mesh generation, a diffuse representation of the material interface is proposed by introducing a static phase-field. The material in the resulting transition region is recomputed by a homogenization of the adjacent material parameters. The extension of this approach by a phase-field model for crack propagation that also accounts for interface failure allows for the computation of brittle fracture in heterogeneous materials using non-conforming meshes.

No description available.

Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys. / QC 20100622

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T14:38:55Z No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:42:47Z (GMT) No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) / Made available in DSpace on 2018-01-23T13:42:47Z (GMT). No. of bitstreams: 1 danielmoutinhodesouza.pdf: 14087574 bytes, checksum: 14fbe9db31be8496c781a98af92ca3fd (MD5) Previous issue date: 2017-08-28 / A fibrilação ventricular é uma arritmia cardíaca listada como uma das principais causas de morte no mundo industrializado, por isso, a importância do estudo do comportamento elétrico cardíaco. O equipamento mais indicado para tentar reverter este quadro de arritmia é o desfibrilador, que submete o tórax do paciente a um campo elétrico de alta energia. Entretanto essa técnica pode causar efeitos graves como queimaduras e dor intensa. Técnicas menos agressivas vêm sendo estudadas e consideram, por exemplo, protocolos com múltiplos estímulos de baixa energia. Observou-se que, nessas estratégias alternativas, a rede vascular cardíaca pode ter papel importante com relação ao padrões espaço-temporais gerados pelos estímulos. Nesta mesma direção, este trabalho apresenta um estudo computacional sobre a influência da rede vascular durante estímulos por campo elétrico em tecidos cardíacos. O fenômeno é capturado por um sistema não-linear de equações diferenciais parciais. Para resolver este modelo numericamente os Métodos de Volumes Finitos (MVF) e de Phase-Field (MPF) foram combinados buscando assim a caracterização geométrica de vasos arteriais durante simulações de desfibrilação de tecido cardíaco. Os resultados obtidos sugerem que os métodos usados (MVF+MPF) são adequados para o estudo de protocolo para desfibrilação cardíaca. / The ventricular fibrillation is a cardiac arrhythmia listed as one of the leading causes of death within the industrialized world, hence the study of cardiac electrical behavior is an important research area. The most used equipment for the reversal of this condition is the defibrillator, which subjects the patient's chest to a high-energy electric field. However, it can have serious effects such as burns and severe pain. Less aggressive techniques have been studied and considered, for example, protocols with multiple low energy stimuli. It was observed that, in this alternative technique, the cardiac vascular network may play an important role in relation to the spatial-temporal patterns generated by the stimuli. This work presents a computational study about the influence of the vascular network during electrical field stimuli in cardiac tissues. The phenomenon is described by a nonlinear system of partial differential equations. To solve this model numerically the Finite Volume Method (FVM) and the Phase-Field Method (PFM) were combined, thus seeking a better geometric characterization of arterial vessels during simulations of cardiac tissue defibrillation. The results obtained in this work suggest that these methods (FVM + PFM) are suitable for the protocol study for cardiac defibrillation.

In this thesis, we present an experimental and numerical study of globularization during reheating of thixocast billet having non-dendritic microstructure. The process of reheating is an important step in the semisolid processing and is essential to control its microstructure and hence its mechanical properties. Material chosen for this study is Aluminum alloy, A356. The primary focus of this study is the heat treatment below eutectic temperature i.e. transformation in solid phase. It is found that during short duration heat treatment, globularization of primary α grains and spheroidization of eutectic Si flakes take place which improves the mechanical properties of semisolid cast products significantly. A prolonged heat treatment is found to degrade the properties of castings since it enhances the porosity and coarsening of Si. The study suggests that a precise heat treatment practice can be designed to improve the semisolid microstructure. A computational model based on Phase field approach has been proposed to study this phenomena. Predictions based on this model are qualitatively compared with corresponding experimental observations. Since eutectics form an important step in multiphase solidification, an attempt has been made to develop an enthalpy based explicit micro-scale model for eutectic solidification. In this preliminary study, growth of adjacent α and β phases in a two dimensional Eulerian framework has been simulated. The model is qualitatively validated with Jackson Hunt theory. Results show expected eutectic growth. This methodology promises significant saving in computational time compared to existing numerical models.

In this thesis, micro computed tomography (μ−CT) scans of a bio-glass scaffold produced by the robocasting technique was used to create finite element method (FEM) models with the purpose of determining its mechanical strength. Prior to this, a Matlab script was used to create several simplified geometries of the scaffold in an effort to determine the importance of scaffold design parameters (such as the fiber compenetration between two adjacent printing planes) on the strength of the scaffold. Furthermore, to assess the influence of micro-structural defects such as voids and micro-cracks that are intrinsic to the robocasting manufacturing process, the total number of voids and their respective volume was calculated using the μ-CT scan imagery and fitted to a statistical distribution. The distribution of voids was then used to create several scaffold models in Matlab with either spherical or ellipsoidal voids present. In the final two models, one scaled-down and one scaled-up FEM based on μ-CT scans were investigated.To model the crack initiation, propagation and final failure, the phase-field method was used. The method was implemented by the use of a publicly available Fortran user subroutine and was edited to account for asymmetric tension/compression energy degradation. The resulting strength of the produced models have been presented as non-dimensional values. The finite element analysis (FEA) of the Matlab produced scaffolds showed that the fiber shifting between two adjacent layers, porosity, and voids of ellipsoidal shape that were perpendicular to the loading direction had the highest effect on the strength of the scaffold. The resulting normalized strength values obtained from the μ-CT models was partially validated through a comparison with the literature available.The different failure modes and overall architectural arrangement of cracks also showed promising results. / I den här uppsatsen så användes mikrotomografi (μ-CT) skanning av en bio-glas stödstruktur tillverkad av robocasting tekniken för att skapa finita element modeller med syftet att bestämma dess mekaniska styrka. Innan detta så användes ett Matlab-skript för att skapa flera förenklade geometrier av stödstrukturen i ett försök att fastställa betydelsen av viktiga designparametrar (som t.ex fiberpenetrering mellan två intilliggande plan) på stödstrukturens styrka. Vidare, för att bedöma påverkan av mikrostrukturella defekter som tomrum och mikrosprickor som är naturligt förekommande i robocasting-tillverkningsprocessen så uppmättes det totala antal hålrum och deras respektive volym med hjälp av μ-CT-skannade bilder. Denna data blev anpassad till en statistisk fördelning. Fördelningen av tomrum och mikcrosprickor användes sedan för att skapa flera modeller av stödstrukturerna i Matlab med antingen sfäriska eller ellipsoida hålrum närvarande. I de sista två modellerna undersöktes en en nedskalad och en uppskalad finita elementmodell baserad på μ-CT-skanning.För att modellera sprickinitiering, sprickpropagering och slutligen brott användes fasfältsmetoden. Fasfältsmetoden implementerades med hjälp av en för allmänheten tillgänglig Fortran användarrutin som redigerades för att ta hänsyn till en asymmetrisk energidegradering i drag-och tryck. Den resulterande styrkan hos alla modeller har presenterats som icke-dimensionella värden. Finita elementanalysen av Matlab modellerna visade att fiberskiftningen mellan två intilliggande plan, porositet och hålrum med ellipsoid form som var vinkelräta mot belastningsriktningen hade störst effekt på stödstrukturens styrka. De resulterande normaliserade styrkevärdena erhållna från μ-CTmodeller validerades delvis genom en jämförelse med tillgänglig litteratur. Dom olika felmoderna och övergripande strukturella fördelningen av sprickor visade också lovande resultat.