When solving partial differential equations using finite difference methods on structured meshes, adaptive refinement can be used to increase the accuracy of the solution in an efficient manner. When implementing solvers using structured adaptive mesh refinement for modern parallel computer systems, an important task is the partitioning of the grid hierarchy over the available processors. The Meta-partitioner is an autonomic framework which can dynamically select between a large number of grid-partitioning algorithms at run time. In this thesis we investigate which modifications that are necessary in order to connect the Meta-partitioner to the existing SAMR-framework Chombo, and begin the process of performing this connection. We conclude that although significant changes to both Chombo and the Meta-partitioner are necessary, a connection definitely seams feasible. We estimate that that the major work of the connection has been done, and that with the experience gained from this project, the continuation is straightforward. We also connect a patch-based partitioning algorithm to Chombo and evaluate it for the first time as part of a real SAMR-based simulation. The results are promising and we conclude that it is a viable candidate for inclusion in the Meta-partitioner.

Three-dimensional (3-D) medical imaging creates notable opportunities as input toward engineering analyses, whether for basic understanding of the normal function or patho-physiology of an organ, or for the simulation of virtual surgical procedures. These analyses most often require finite element (FE) models to be constructed from patient-specific 3-D medical images. However, creation of such models can be extremely labor-intensive; in addition, image processing and mesh generation are often operator-dependent, lack robustness and may be of suboptimal quality. Focusing on the human aorta, the goal of the present work is to create a fast and robust methodology for quadrilateral surface and hexahedral volume meshing from 3-D medical images with minimal user input. By making use of the segmentation capabilities of the 3-D gradient vector flow field combined with original ray-tracing and orientation control algorithms, we will demonstrate that it is possible to incrementally grow a structured quadrilateral surface mesh of the inner wall of the aorta. The process does not only require minimal input from the user, it is also robust and very fast compared to existing methods; it effectively combines segmentation and meshing into one single effort. After successfully testing the methodology and measuring the quality of the meshes produced by it from synthetic as well as real medical image datasets, we will make use of the surface mesh of the inner aortic wall to derive hexahedral meshes of the aortic wall thickness and of the fluid domain inside the aorta. We will finally outline a tentative approach to merge several structured meshes to process the main branches of the aorta.

L'analyse de sensibilité pour la simulation numérique des écoulements compressibles en aérodynamique externe par rapport à la discrétisation de maillage et aux incertitudes liées à des paramètres d'entrées du modèle a été traitée 1- par le moyen des méthodes adjointes pour le calcul de gradient et 2- par approximations stochastiques non-intrusives basées sur des grilles creuses. 1- Une méthode d'adaptation de maillages goal-oriented basée sur les dérivées totales des fonctions aérodynamiques d'intérêt par rapport aux nœuds du maillage a été introduite sous une forme améliorée. La méthode s'applique au cadre de volumes finis pour des écoulements RANS pour des maillages mono-bloc et multi-bloc structurés. Des applications 2D pour des écoulements transsoniques ainsi que subsonique détaché atour d'un profil pour l'estimation du coefficient de traînée sont présentées. L'apport de la méthode proposée est vérifié. 2- Les méthodes du polynôme de chaos généralisé sous forme pseudospectrale creuse et de la collocation stochastique construite sur des grilles creuses isotropes et anisotropes sont examinées. Les maillages anisotropes sont obtenus par le biais d'une méthode adaptive basée sur l'analyse de sensibilité globale. L'efficacité des ces approximations est testée avec des fonctions test et des écoulements aérodynamiques visqueux autour d'un profil en présence d'incertitudes géométriques et opérationnelles. L'intégration des méthodes et aboutissements 1- et 2- dans une approche couplée permettrait de contrôler de façon équilibrée l'erreur déterministe/stochastique goal-oriented. / Sensitivity analysis for the numerical simulation of external aerodynamics compressible flows with respect to the mesh discretization and to the model input parametric uncertainty has been addressed respectively 1- through adjoint-based gradient computation techniques and 2- through non-intrusive stochastic approximation methods based on sparse grids. 1- An enhanced goal-oriented mesh adaptation method based on aerodynamic functional total derivatives with respect to mesh coordinates in a RANS finite-volume mono-block and non-matching multi-block structured grid framework is introduced. Applications to 2D RANS flow about an airfoil in transonic and detached subsonic conditions for the drag coefficient estimation are presented. The asset of the proposed method is patent. 2- The generalized Polynomial Chaos in its sparse pseudospectral form and stochastic collocation methods based on both isotropic and dimension-adapted sparse grids obtained through an improved dimension-adaptivity method driven by global sensitivity analysis are considered. The stochastic approximations efficiency is assessed on multi-variate test functions and airfoil viscous aerodynamics simulation in the presence of geometrical and operational uncertainties. Integration of achievements 1- and 2- into a coupled approach in future work will pave the way for a well-balanced goal-oriented deterministic/stochastic error control.

Three-dimensional (3-D) medical imaging creates notable opportunities as input toward engineering analyses, whether for basic understanding of the normal function or patho-physiology of an organ, or for the simulation of virtual surgical procedures. These analyses most often require finite element (FE) models to be constructed from patient-specific 3-D medical images. However, creation of such models can be extremely labor-intensive; in addition, image processing and mesh generation are often operator-dependent, lack robustness and may be of suboptimal quality. Focusing on the human aorta, the goal of the present work is to create a fast and robust methodology for quadrilateral surface and hexahedral volume meshing from 3-D medical images with minimal user input. By making use of the segmentation capabilities of the 3-D gradient vector flow field combined with original ray-tracing and orientation control algorithms, we will demonstrate that it is possible to incrementally grow a structured quadrilateral surface mesh of the inner wall of the aorta. The process does not only require minimal input from the user, it is also robust and very fast compared to existing methods; it effectively combines segmentation and meshing into one single effort. After successfully testing the methodology and measuring the quality of the meshes produced by it from synthetic as well as real medical image datasets, we will make use of the surface mesh of the inner aortic wall to derive hexahedral meshes of the aortic wall thickness and of the fluid domain inside the aorta. We will finally outline a tentative approach to merge several structured meshes to process the main branches of the aorta.

Ce travail est une contribution à la simulation numérique d'écoulements turbulents dans un but d'application industrielle. Nous nous intéressons dans un premier temps à une nouvelle combinaison "VMS-LES/procédure dynamique" pour la simulation d'écoulements autour de cylindres circulaire et carré. L'approche VMS-LES mise en œuvre a pour originalité d'utiliser une procédure de moyennage sur des volumes finis agglomérés dans le but de séparer les échelles, l'approche dynamique étant celle introduite par Germano en LES. Une approche hybride RANS/VMS-LES est ensuite évaluée sur le problème du cylindre circulaire à des nombres de Reynolds élevés. Cette approche introduit un paramètre d'hybridation qui selon la résolution locale de grille privilège le modèle RANS ou celui VMS-LES. Enfin, les performances d'un algorithme de Schwarz deux-niveau, qui utilise les méthodes de déflation et de balancing, sont examinées d'un point de vue efficacité et scalabilité dans le cas de simulations VMS-LES. / This work is a contribution to the numerical simulation of turbulent flows with the aim of industrial application. At first, we focus on a new combination "VMS-LES/dynamic procedure" for the simulation of flows around circular and square cylinders. The VMS-LES approach adopted in this work is original in using an averaging procedure over agglomerated finite volumes in order to separate the scales, the dynamic approach being the one introduced by Germano in LES. A RANS/VMS-LES hybrid approach is then evaluated on the circular cylinder test case at high Reynolds numbers. This approach introduces a hybridization parameter which privileges the RANS model or the VMS-LES model according to the grid resolution. Finally, the performance of a two-level Schwarz algorithm, which uses the deflation and balancing methods, are examined in terms of efficiency and scalability in the context of VMS-LES simulations.

Fundação de Amparo a Pesquisa do Estado de Minas Gerais / Esta dissertação é parte de um amplo projeto de pesquisa, que visa ao desenvolvimento de uma plataforma computacional de dinâmica dos fluidos (CFD) capaz de simular a física de escoamentos que envolvem mistura de várias espécies químicas, com reação e combustão, utilizando um método hibrido Simulação de Grandes Escalas (LES) / Função Densidade Filtrada (FDF) Lagrangiana em malha adaptativa, bloco-estruturada. Uma vez que escoamentos com mistura proporcionam fenômenos que podem ser correlacionados com a combustão em escoamentos turbulentos, uma visão global da fenomenologia de mistura foi apresentada e escoamentos fechados, laminar e turbulento, que envolvem mistura de duas espécies químicas inicialmente segregadas foram simulados utilizando o código de desenvolvimento interno AMR3D e o código recentemente desenvolvido FDF Lagrangiana de composição. A primeira etapa deste trabalho consistiu na criação de um modelo computacional de partículas estocásticas em ambiente de processamento distribuído. Isto foi alcançado com a construção de um mapa Lagrangiano paralelo, que pode gerenciar diferentes tipos de elementos lagrangianos, incluindo partículas estocásticas, particulados, sensores e nós computacionais intrínsecos dos métodos Fronteira Imersa e Acompanhamento de Interface. O mapa conecta informações Lagrangianas com a plataforma Euleriana do código AMR3D, no qual equações de trans- porte são resolvidas. O método FDF Lagrangiana de composição realiza cálculos algébricos sobre partículas estocásticas e provê campos de composição estatisticamente equivalentes aos obtidos quando se utiliza o método de Diferenças Finitas para solução de equações diferenciais parciais; a técnica de Monte Carlo foi utilizada para resolver um sistema derivado de equações diferenciais estocásticas (SDE). Os resultados concordaram com os benchmarks, que são simulações baseadas em plataforma de Diferenças Finitas para solução de uma equação de transporte de composição filtrada. / This master thesis is part of a wide research project, which aims at developing a com- putational fluid dynamics (CFD) framework able to simulate the physics of multiple-species mixing flows, with chemical reaction and combustion, using a hybrid Large Eddy Simulation (LES) / Lagrangian Filtered Density Function (FDF) method on adaptive, block-structured mesh. Since mixing flows provide phenomena that may be correlated with combustion in turbulent flows, we expose an overview of mixing phenomenology and simulated enclosed, ini- tially segregated two-species mixing flows, at laminar and turbulent states, using the in-house built AMR3D and the developed Lagrangian composition FDF codes. The first step towards this objective consisted of building a computational model of notional particles transport on distributed processing environment. We achieved it constructing a parallel Lagrangian map, which can hold different types of Lagrangian elements, including notional particles, particu- lates, sensors and computational nodes intrinsic to Immersed Boundary and Front Tracking methods. The map connects Lagrangian information with the Eulerian framework of the AMR3D code, in which transport equations are solved. The Lagrangian composition FDF method performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by Finite Differences numerical solution of partially differential equations (PDE); we applied the Monte Carlo technique to solve a derived system of stochastic differential equations (SDE). The results agreed with the benchmarks, which are simulations based on Finite Differences framework to solve a filtered composition transport equation. / Mestre em Engenharia Mecânica