O presente trabalho consiste no desenvolvimento de um código computacional baseado no método dos elementos finitos (MEF), para análise bidimensional de interação fluido-estrutura. Desenvolve-se um código bidimensional para dinâmica de fluidos compressíveis, viscosos ou não, em formulação Euleriana, com base no algoritmo CBS – characteristic based split. Então o código desenvolvido é adaptado para poder ser acoplado a um programa de formulação Lagrangeana para análise dinâmica de estruturas, o que é feito através do emprego da descrição Lagrangeana - Euleriana arbitrária (ALE). Por fim procede-se o acoplamento com um código para análise de estruturas, de formulação posicional e não linear geométrica, baseado no método dos elementos finitos. / The present work consists of the development of a computational code based on the element finite method for fluid-structure interaction analysis. A two-dimensional fluid dynamic Eulerian code is developed based on the CBS algorithm – characteristic based split. Then, the computational code is modified to be coupled with a Lagrangean structures dynamical code by using the arbitrary Lagrangean – Eulerian description (ALE). At the end, the coupling is made with a positional nonlinear geometrical structural dynamics code based on the finite element method.

Um dos grandes desafios da engenharia atualmente é viabilizar soluções computacionais que reduzam o tempo de processamento e forneçam respostas ainda mais precisas. Frequentemente surgem propostas com as mais diversas abordagens que exploram novas formas de resolver tais problemas ou tentam, ainda, melhorar as soluções existentes. Uma das áreas que se dedica a propor tais melhorias é a computação paralela e de alto desempenho - HPC (High Performance Computing). Técnicas que otimizem o tempo de processamento, algoritmos mais eficientes e computadores mais rápidos abrem novos horizontes possibilitando realizar tarefas que antes eram inviáveis ou levariam muito tempo para serem concluídas. Neste projeto propõe-se a implementação computacional de uma arquitetura de computação paralela com o intuito de resolver, de forma mais eficiente, em comparação com a arquitetura sequencial, problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura e que também seja possível estender esta arquitetura para a resolução de outros problemas relacionados com o Método dos Elementos Finitos. O objetivo deste trabalho é desenvolver um algoritmo computacional eficiente em linguagem de programação científica C++ e CUDA - de propriedade da NVIDIAr - tendo como base trabalhos anteriores desenvolvidos no LMC (Laboratório de Mecânica Computacional) e, posteriormente, com a arquitetura desenvolvida, executar e investigar problemas de Dinâmica dos Fluidos e Interação Fluido-Estrutura (aplicando o método dos Elementos Finitos com Fronteiras Imersas e a solução direta do sistema de equações lineares com PARDISO) com o auxílio dos computadores do LMC. Uma análise de sensibilidade para cada problema é realizada de forma a encontrar a melhor combinação entre o número de elementos da malha de elementos finitos e o speedup, e posteriormente é feita uma análise comparativa de desempenho entre a arquitetura paralela a sequencial. Com uma única GPU conseguiu-se uma considerável redução no tempo para o assembly das matrizes globais e no tempo total da simulação. / One of the biggest challenges of engineering is enable computational solutions that reduce processing time and provide more accurate numerical solutions. Proposals with several approaches that explore new ways of solving such problems or improve existing solutions emerge. One of the biggest areas dedicated to propose such improvements is the parallel and high performance computing. Techniques that improve the processing time, more efficient algorithms and faster computers open up new horizons allowing to perform tasks that were previously unfeasible or would take too long to complete. We can point out, among several areas of interest, Fluid Dynamics and Interaction Fluid-Structure. In this work it is developed a parallel computing architecture in order to solve numerical problems more efficiently, compared to sequential architecture (e.g. Fluid Dynamics and Fluid-Structure Interaction problems) and it is also possible to extend this architecture to solve different problems (e.g. Structural problems). The objective is to develop an efficient computational algorithm in scientific programming language C ++, based on previous work carried out in Computational Mechanics Laboratory (CML) at Polytechnic School at University of São Paulo, and later with the developed architecture, execute and investigate Fluid Dynamics and Fluid-Structure Interaction problems with the aid of CML computers. A sensitivity analysis is executed for different problems in order to assess the best combination of elements quantity and speedup, and then a perfomance comparison. Using only one GPU, we could get a 10 times speedup compared to a sequential software, using the Finite Element with Immersed Boundary Method and a direct solver (PARDISO).

Au cours de cette thèse, nous nous sommes intéressés à la modélisation des interactions fluide-structure entre un fluide visqueux, incompressible et une structure pouvant être déformable. Après avoir présenté les différentes approches possibles de modélisation, nous introduisons une nouvelle méthode de type frontière immergée : la méthode IPC ("Image Point Correction"). Combinant approches Ghost-Cell et Pénalisation, cette méthode mixte du second degré globalement et localement en vitesse, est validée sur différents cas tests (comparaisons des coefficients aérodynamiques pour des cylindres fixes ou mobiles, sédimentation 2D d'un cylindre). Nous avons ensuite appliqué la méthode IPC à la simulation de la nage. Dans un premier temps, le solveur 2D a été couplé avec un algorithme d'optimisation mathématique afin de déterminer la loi de nage optimale pour une géométrie de poisson donnée. Puis, dans un second temps, nous avons simulé la nage 3D après reconstruction approchée de la géométrie, basée sur des images du nageur. Enfin, grâce à l'outil du squelette, une reconstruction réaliste du poisson est proposée. / The aim of this thesis is to investigate the modeling of fluid-structure interactions. The fluid is viscous and incompressible, and the structure is subject to an imposed deformation. After a survey of the different existing approachs to model fluid-structure interactions, we introduce a new immersed boundary method: the IPC method (”Image Point Correction”). This ap-proach merges Ghost-Cell and Penalty concepts. It is globally and locally second order in velocity, and it is validated through several canonical simulations. Then, we apply the IPC method to fish-like swimming. First, the 2D solver is paired up with a mathematical optimization algorithm to determine the optimal swimming law for a given fish geometry. Secondly, we simulate a 3D swimmer after performing an approximated reconstruction of the geometry based on actual fish pictures. Finally, thanks to the skeleton approach, a realistic reconstruction of the fish is exposed.

Le but de cette étude est d’étudier l’utilisation d’interactions fluide-structure (FSI) pour améliorer le transfert de chaleur et les performances de mélange dans des échangeurs-réacteurs multifonctionnels, et d’évaluer des configurations pour lesquelles l’objectif est de produire et de maintenir un régime dynamique auto-entretenu d’oscillations des générateurs de tourbillons flexibles. Dans un premier temps, deux études numériques ont été réalisées pour des écoulements laminaires bidimensionnels. Les résultats montrent qu’un minimum de trois générateurs de tourbillons alternés est nécessaire pour produire une instabilité qui engendre les oscillations de larges amplitudes. L’ajout de deux promoteurs coplanaires en amont déstabilise l’écoulement en créant des forces périodiques agissant sur les générateurs de tourbillons en aval. Il en résulte une augmentation de la vitesse réduite qui impose un blocage en fréquence des oscillations des générateurs de tourbillons en aval. Dans cette configuration, des oscillations de larges amplitudes sont obtenues pour uniquement deux générateurs de tourbillons en aval. Les oscillations des générateurs de tourbillons produisent une vorticité intense qui a une incidence positive que le transfert de chaleur et sur le mélange. Dans un second temps, une configuration tridimensionnelle HEV incluant des générateurs de tourbillons trapézoïdaux flexibles orientés a 45◦ vers l’amont est étudiée par simulations numériques. Une analyse FFT réalisée sur les coefficients issus d’une analyse POD montre un pic fréquentiel correspondant aux formations et lâchers tourbillonnaires périodiques. Cette fréquence dominante correspond bien au mode propre d’oscillation des générateurs de tourbillons et engendre ainsi de larges amplitudes d’oscillations. / The aim of this study is to investigate the use of fluid-structure interaction (FSI) to improve heat transfer and mixing performances in multi-functional heat exchangers/reactors, and to evaluate configuration designs where the main target is to produce and maintain self-sustained oscillations of flexible vortex generators. At first, two dimensional laminar flow studies are numerically investigated. The results show that a minimum of three alternating flaps is needed to produce an instability that leads to large displacement oscillations. However, the introduction of two co-planar flaps upstream destabilizes the flow by creating periodic forces that act on the alternating downstream flaps. Hence, this results in artificially increasing the reduced velocity that will induce the alternating flaps to be in a lock-in state. Thus in this case, large displacement amplitudes are created with two alternating flaps only. The free flaps oscillations produce vortices of higher strength which have a positive impact on heat transfer and mixing. Secondly, a three dimensional HEV configuration with flexible trapezoidal vortex generators inclined with an angle of 45◦ with respect to the wall and reversed opposite to the flow direction is numerically investigated. Fast Fourier Transformation is applied on the temporal variation of the Proper Orthogonal Decomposition (POD) coefficientswhich displays a dominant peak in the flow and corresponds to the vortices periodic formation and detachment. This dominant frequency synchronizes well with the structural oscillation frequency and the fundamental frequency of the tabs reaching a lock-in state and leading to large oscillation amplitudes.

Heart disease is the leading cause of death in the world. Therefore, numerous studies are undertaken to identify indicators which can be applied to discover cardiac dysfunctions at an early age. Among others, the fluid dynamics of the blood flow (hemodymanics) is considered to contain relevant information related to abnormal performance of the heart.This thesis presents a robust framework for numerical simulation of the fluid dynamics of the blood flow in the left ventricle of a human heart and the fluid-structure interaction of the blood and the aortic leaflets.We first describe a patient-specific model for simulating the intraventricular blood flow. The motion of the endocardial wall is extracted from data acquired with medical imaging and we use the incompressible Navier-Stokes equations to model the hemodynamics within the chamber. We set boundary conditions to model the opening and closing of the mitral and aortic valves respectively, and we apply a stabilized Arbitrary Lagrangian-Eulerian (ALE) space-time finite element method to simulate the blood flow. Even though it is difficult to collect in-vivo data for validation, the available data and results from other simulation models indicate that our approach possesses the potential and capability to provide relevant information about the intraventricular blood flow.To further demonstrate the robustness and clinical feasibility of our model, a semi-automatic pathway from 4D cardiac ultrasound imaging to patient-specific simulation of the blood flow in the left ventricle is developed. The outcome is promising and further simulations and analysis of large data sets are planned.In order to enhance our solver by introducing additional features, the fluid solver is extended by embedding different geometrical prototypes of both a native and a mechanical aortic valve in the outflow area of the left ventricle.Both, the contact as well as the fluid-structure interaction, are modeled as a unified continuum problem using conservation laws for mass and momentum. To use this ansatz for simulating the valvular dynamics is unique and has the expedient properties that the whole problem can be described with partial different equations and the same numerical methods for discretization are applicable.All algorithms are implemented in the high performance computing branch of Unicorn, which is part of the open source software framework FEniCS-HPC. The strong advantage of implementing the solvers in an open source software is the accessibility and reproducibility of the results which enhance the prospects of developing a method with clinical relevance. / <p>QC 20171006</p>

La prédiction de mouvement de solide évoluant dans un fluide présente un réel intérêt pour des applications industrielles telle que l’accrétion de glace sur des surfaces aérodynamiques. Dans ce contexte, en considérant des systèmes de dégivrage, la prévision des trajectoire de glace est nécessaire pour éviter des risques de collision/ingestion de glace sur/dans des zones sensibles de l’avion. Ce type d’application soulève de nombreux challenges d’un point de vue numérique, en particulier concernant la génération/l’adaptation de maillage au cours du mouvement du solide dans le domaine. Pour gérer ces difficultés, dans cette étude, les solides sont définis de manière implicite via une fonction level set. Une méthode de type frontière immergée, appelée Pénalization, est utilisée pour imposer les conditions de bords. Pour améliorer la précision de l’interface, les équations sont résolues sur des maillages non structurés adaptatifs. Cela permet d’obtenir un raffinement proche des bords du solide et ainsi d’améliorer sa définition, permettant un meilleure impositions des conditions de bord. Pour économiser du temps de calcul, et éviter de coûteuses étapes de remaillage/interpolation, la stratégie adoptée pour les simulations instationnaires est d’utiliser une adaptation de maillage à connectivité constante, aussi appelée r-adaptation. / The prediction of solid motion evolving in a fluid presents a real interest for engineering application such as ice accretion on aerodynamics bodies.In this context, considering de-icing systems, the ice shedding trajectory is needed to prevent the risk of collision/ingestion of the ice in/with some sensitive part of the aircraft. This application raises many challenges from a numerical point of view, especially concerning mesh generation/adaptation as the solid moves in the computational domain. To handle this issue, in this work the solids are known implicitly on the mesh via a level set function. An immersed boundary method, called penalization, is employed to impose the wall boundary conditions. To improve the resolution of these boundaries, the equations are solved on adaptive unstructured grids. This allows to have are finement close to the solid boundary and thus increases the solid definition,leading to a more accurate imposition of the wall conditions. To save computational time, and avoid costly remeshing/interpolation steps, the strategy chosen for unsteady simulations is to use a constant connectivity mesh adaptation,also known as r-adaptation

Dans cette thèse, une nouvelle méthode de frontières immergées a été développée pour la simulation d'interaction fluide-structure, appelée la méthode de frontières immergées mobiles (en langage anglo-saxon: MIBM). L'objectif principal de cette nouvelle méthode est de déplacer arbitrairement les solides à géométrie complexe dans un fluide visqueux incompressible, sans remailler le domaine fluide. Cette nouvelle méthode a l'avantage d'imposer la condition de non-glissement à l'interface d'une manière exacte via une force sans introduire des constantes artificielles modélisant la structure rigide. Cet avantage conduit également à la satisfaction de la condition CFL avec un pas de temps plus grand. Pour un calcul précis de la force induite par les frontières mobiles, un système linéaire a été introduit et résolu par la méthode de gradient conjugué. La méthode proposée peut être intégrée facilement dans des solveurs résolvant les équations de Navier-Stokes. Dans ce travail la MIBM a été mise en œuvre en couplage avec un solveur fluide utilisant une méthode de projection adaptée pour obtenir des solutions d'ordre deux en temps et en espace. Le champ de pression a été obtenu par l'équation de Poisson qui a été résolue à l'aide de la méthode du gradient conjugué préconditionné par la méthode multi-grille. La combinaison de ces deux méthodes a permis un gain de temps considérable par rapport aux méthodes classiques de la résolution des systèmes linéaires. De plus le code de calcul développé a été parallélisé sur l'unité graphique GPU équipée de la bibliothèque CUDA pour aboutir à des hautes performances de calcul. Enfin, comme application de nos travaux sur la MIBM, nous avons étudié le couplage "fort" d'interaction fluide-structure (IFS). Pour ce type de couplage, un schéma implicite partitionné a été adopté dans lequel les conditions à l'interface sont satisfaites via un schéma de type "point fixe". Pour réduire le temps de calcul inhérent à cette application, un nouveau schéma de couplage a été proposé pour éviter la résolution de l'équation de Poisson durant les itérations du "point fixe". Cette nouvelle façon de résoudre les problèmes IFS a montré des performances prometteuses pour des systèmes en IFS complexe. / In this thesis a novel non-body conforming mesh formulation is developed, called the moving immersed boundary method (MIBM), for the numerical simulation of fluid-structure interaction (FSI). The primary goal is to enable solids of complex shape to move arbitrarily in an incompressible viscous fluid, without fitting the solid boundary motion with dynamic meshes. This novel method enforces the no-slip boundary condition exactly at the fluid-solid interface with a boundary force, without introducing any artificial constants to the rigid body formulation. As a result, large time step can be used in current method. To determine the boundary force more efficiently in case of moving boundaries, an additional moving force equation is derived and the resulting system is solved by the conjugate gradient method. The proposed method is highly portable and can be integrated into any fluid solver as a plug-in. In the present thesis, the MIBM is implemented in the fluid solver based on the projection method. In order to obtain results of high accuracy, the rotational incremental pressure correction projection method is adopted, which is free of numerical boundary layer and is second order accurate. To accelerate the calculation of the pressure Poisson equation, the multi-grid method is employed as a preconditioner together with the conjugate gradient method as a solver. The code is further parallelized on the graphics processing unit (GPU) with the CUDA library to enjoy high performance computing. At last, the proposed MIBM is applied to the study of two-way FSI problem. For stability and modularity reasons, a partitioned implicit scheme is selected for this strongly coupled problem. The interface matching of fluid and solid variables is realized through a fixed point iteration. To reduce the computational cost, a novel efficient coupling scheme is proposed by removing the time-consuming pressure Poisson equation from this fixed point interaction. The proposed method has shown a promising performance in modeling complex FSI system.

Fluid-structure interaction (FSI) as the name suggests, is the study of dynamic interaction of both fluid and structure motions. Fluid-structure interaction exists in almost all engineering and science fields. Moreover, the random loading caused by fluid motions in uncertain environment conditions present new challenges to the designers. The objective of the present research work is to develop efficient and robust finite element models to solve fluid structure interaction problems effectively. A key advantage of the displacement based FE M is the flexibility and easiness in modifying the existing efficient numerical solvers, and can also be extended easily to a number of problems. The research work carried out in this thesis can be divided into three parts. In the first part, development of displacement based Lagrangian FE models for acoustic fluids is presented. Here, the displacement fields of the 2-D and 3-DFEs are derived based on the consistently assumed constrained strain fields satisfying irrotationality and incompressibility constraints simultaneously. These elements’ behaviour, in terms of number of zero energy modes, non-zero spurious modes, and the integration order is studied. The inf-sup test is carried out on all the elements to examine the performance of each formulated element. Next, a new class of FEs based on Legendre polynomials is presented. The node point locations in this case are obtained by calculating the zero’s of equation(1- ξ2)L’n(ξ) =0,where,Ln is the Legendre polynomial of order n in one dimension. In the second part, the development of a spectral layer element for studying wave propagation in acoustic fluids is presented. Laplace transform based spectral finite element formulation is developed for studying acoustic wave propagation. The partial differential equations(PDE)are converted to ordinary differential equations(ODE) by taking Laplace transform. The Laplace damping parameter is introduced for easy handling of the numerical Laplace transform(NLT).This Laplace damping parameter removes the “wraparound”problem which is present in shortwave guides due to periodicity of the Fourier transform. Later, a technique is developed through which SFEM stiffness matrix can be added to the FEM dynamic stiffness matrix in the frequency domain. Finally, Uncertainty analysis is carried out to understand the effect of randomness in the design parameters on the system response variability. Here, standard uncertainty analysis procedure called Monte Carlo simulation (MCS) is considered first and later Polynomial chaos expansion(PCE). In this analysis, the gravitational forces, bulk modulus of the fluid, and Young’s modulus of the structure are considered as random input variables in the study. The randomness in the system output is measured in terms of coefficient of variation for each random variable considered.

Cette thèse est dédiée à la simulation numérique des systèmes mécaniques impliquant l'interaction entre une structure mince déformable et un fluide incompressible interne ou qui l'entoure.Dans la première partie, nous introduisons deux nouvelles classes de schémas de couplage explicites en utilisant des maillages compatibles. Les méthodes proposées combinent une certaine consistance Robin dans le système avec (i) un schéma à pas fractionnaire pour le fluide ou (ii) une discrétisation temporelle d'ordre deux pour le fluide et le solide. Les propriétés de stabilité des méthodes sont analysées dans un cadre linéaire représentatif. Cette partie inclut aussi une étude numérique exhaustive dans laquelle plusieurs schémas de couplage (dont certains proposés ici) sont comparés et validés avec des résultats expérimentaux. Dans la seconde partie, nous considérons des maillages non compatibles. La discrétisation spatiale est basée, dans ce cas là, sur des variantes de la méthode de Nitsche avec éléments coupés. Nous présentons deux nouveaux types de schémas de découplage qui exploitent la susmentionée condition de Robin en utilisant des maillages incompatibles. Le caractère semi-implicite ou explicite du couplage en temps dépend de l'ordre dans lequel les discrétisations spatiales et temporelles sont effectuées. Dans le cas d'un couplage avec des structures immergées, la vitesse et la pression discrètes permettent des discontinuités faibles et fortes à travers l'interface, respectivement. Des estimations de stabilité et d'erreur sont fournies dans un cadre linéaire. Une série de tests numériques illustre la performance des différentes méthodes proposées. / This thesis is devoted to the numerical approximation of mechanical systems involving the interaction of a deformable thin-walled structure with an internal or surrounding incompressible fluid flow. In the first part, we introduce two new classes of explicit coupling schemes using fitted meshes. The methods proposed combine a certain Robin-consistency in the system with (i) a projection-based time-marching in the fluid or (ii) second-order time-stepping in both the fluid and the solid. The stability properties of the methods are analyzed within representative linear settings. This part includes also a comprehensive numerical study in which state-of-the-art coupling schemes (including some of the methods proposed herein) are compared and validated against the results of an experimental benchmark. In the second part, we consider unfitted mesh formulations. The spatial discretization in this case is based on variants of Nitsche’s method with cut elements. We present two new classes of splitting schemes which exploit the aforementioned interface Robin-consistency in the unfitted framework. The semi-implicit or explicit nature of the splitting in time is dictated by the order in which the spatial and time discretizations are performed. In the case of the coupling with immersed structures, weak and strong discontinuities across the interface are allowed for the velocity and pressure, respectively. Stability and error estimates are provided within a linear setting. A series of numerical tests illustrates the performance of the different methods proposed.

Tato disertační práce se zabývá experimentálním a výpočtovým výzkumem přídavných účinků od proudu kapaliny na obtékaný hydraulický profil. Dynamická odezva profilu byla analyzována pro dva typy buzení: buzení odtržením mezní vrstvy a Kármánových vírů a dále buzení pomocí externího budiče připojeného k lopatce. Experimentální měření dynamické odezvy profilu na oba typy buzení bylo provedeno pro lopatku umístěnou v kavitujícím a nekavitujícím proudění. Získané výsledky byly použity pro verifikaci přídavných účinků stanovených s využitím numerického modelování.