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[pt] Esta tese propõe um método meshfree adaptativo de advecção para problemas de fluxo bifásico de fluidos incompressíveis e imiscíveis em meios porosos heterogêneos tridimensionais. Este método se baseia principalmente na combinação do método Semi-Lagrangeano adaptativo com interpolação local meshfree usando splines poliharmônicas como funções de base radial. O método proposto é uma melhoria e uma extensão do método adaptativo meshfree AMMoC proposto por Iske e Kaser (2005) para modelagem 2D de reservatórios de petróleo. Inicialmente este trabalho propõe um modelo em duas dimensões, contribuindo com uma melhoria significativa no cálculo do Laplaciano, utilizando os métodos meshfree de Hermite e Kansa. Depois, o método é ampliado para três dimensões (3D) e para um meio poroso heterogêneo. O método proposto é testado com o problema de five spot e os resultados são comparados com os obtidos por sistemas bem conhecidos na indústria de petróleo. / [en] This thesis proposes an adaptive meshfree advection method for two-phase flow problems of incompressible and immiscible fluids through three-dimensional heterogeneous porous media. This method is based mainly on a combination of adaptive semi-Lagrangian method with local meshfree interpolation using polyharmonic splines as radial basis functions. The proposed method is an improvement and extension of the adaptive meshfree advection scheme AMMoC proposed by Iske and Kaser (2005) for 2D oil reservoir modeling. Initially this work proposes a model in two dimensions, contributing to a significant improvement in the calculation of the Laplacian, using the meshfree methods of Hermite and Kansa. Then, the method is extended to three dimensions (3D) and a heterogeneous porous medium. The proposed method is tested with the five spot problem and the results are compared with those obtained by well-known systems in the oil industry.

This thesis deals with simulation and rendering of fluid based volumetric effects, especially effect of fire and smoke. Computations are accelerated on graphics card using modern graphics API with motivation to achieve realistic visual results as well as physically correct calculations. Implemented volumetric effects are distributed as dynamic library which allows addition of these effects to existing applications.

Das thermische Verhalten von Werkzeugmaschinen verursacht geometrische Abweichungen an Werkstücken. In vielen Forschungsarbeiten wurden wertvolle Beiträge zu deren Verbesserung veröffentlicht. Dabei kommt die Finite-Elemente (FE)- Simulation zum Einsatz. Für diese ist unter anderem der Wärmeübergangskoeffizient als Randparameter notwendig. Insbesondere für Hohlräume, beispielsweise unter der Maschinenverkleidung, gibt es keine Methode diesen schnell zu berechnen. Die vorliegende Arbeit liefert umfangreiche Untersuchungen zu den thermischen Vorgängen in Hohlräumen und deren Auswirkungen auf die thermischen Verlagerungen an Werkzeugmaschinen. Dafür erarbeitet diese Arbeit eine Methode, um Metamodelle für die schnelle Berechnung des Wärmeübergangskoeffizienten in Hohlräumen zu erstellen. Mögliche Hohlraumkonfigurationen werden dafür kategorisiert und für messtechnische Untersuchungen ein Versuchsstand konzipiert. Der Einfluss des Mikroklimas auf die thermischen Verlagerungen wird analysiert. Dabei wird der Einfluss von Konvektion und Strahlung, der Maschinenverkleidung und des Öffnens der Arbeitsraumtüre untersucht. In dieser Arbeit werden zwei Metamodelle erstellt, für einen Hohlraum mit einer Seitenwand als Wärmequelle und für einen Hohlraum mit mittig platzierter Wärmequelle. Die Anwendung der Metamodelle wird mit der thermischen FE-Simulation einer Werkzeugmaschine erläutert und eine Hilfestellung für die Übertragung auf weitere Werkzeugmaschinen gegeben. / The thermal behavior of machine tools causes most of the geometric errors on workpieces. In recent years, many authors published valuable contributions to the analysis, correction and compensation of the thermal behavior of machine tools. One way is the finite element simulation, where the heat transfer coefficient is needed as an input parameter. In particular, for enclosures, for example under the machine housing, there is no method to calculate this coefficient quickly. As state of the art the heat transfer coefficient is received from a computation-intensive fluid simulation of the enclosure. The present work provides investigations of enclosures, the microclimate in enclosures, its effect on the thermal errors of machine tools and finally a method to develop metamodels for the fast calculation of the heat transfer coefficient in enclosures and to use them in the finite element simulation. Possible enclosure configurations are categorized and a test stand is designed for metrological investigations. In basic investigations the thermal processes in different enclosures are analyzed. The influence of the microclimate on thermal errors of machine tools is analyzed in experiments. The influence of convection and radiation, the machine housing and the opening of the working room door are examined. In this work two metamodels are developed. One for an enclosure with a side wall as a heat source and one for an enclosure with a centrally placed heat source. The application of the metamodels is explained in the thermal finite element simulation of a machine tool.

La conception assistée par ordinateur (CAO), les effets visuels, la robotique et de nombreux autres domaines tels que la biologie computationnelle, le génie aérospatial, etc. reposent sur la résolution de problèmes mathématiques. Dans la plupart des cas, des méthodes de calcul sont utilisées pour résoudre ces problèmes. Le choix et la construction de la méthode de calcul ont un impact important sur les résultats et l'efficacité du calcul. La structure du problème peut être utilisée pour créer des méthodes, qui sont plus rapides et produisent des résultats qualitativement meilleurs que les méthodes qui n'utilisent pas la structure. Cette thèse présente trois articles avec trois nouvelles méthodes de calcul s'attaquant à des problèmes de simulation et d'optimisation contraints par des équations aux dérivées partielles (EDP). Dans le premier article, nous abordons le problème de la dissipation d'énergie des solveurs fluides courants dans les effets visuels. Les solveurs de fluides sont omniprésents dans la création d'effets dans les courts et longs métrages d'animation. Nous présentons un schéma d'intégration temporelle pour la dynamique des fluides incompressibles qui préserve mieux l'énergie comparé aux nombreuses méthodes précédentes. La méthode présentée présente une faible surcharge et peut être intégrée à un large éventail de méthodes existantes. L'amélioration de la conservation de l'énergie permet la création d'animations nettement plus dynamiques. Nous abordons ensuite la conception computationelle dont le but est d'exploiter l'outils computationnel dans le but d'améliorer le processus de conception. Plus précisément, nous examinons l'analyse de sensibilité, qui calcule les sensibilités du résultat de la simulation par rapport aux paramètres de conception afin d'optimiser automatiquement la conception. Dans ce contexte, nous présentons une méthode efficace de calcul de la direction de recherche de Gauss-Newton, en tirant parti des solveurs linéaires directs épars modernes. Notre méthode réduit considérablement le coût de calcul du processus d'optimisation pour une certaine classe de problèmes de conception inverse. Enfin, nous examinons l'optimisation de la topologie à l'aide de techniques d'apprentissage automatique. Nous posons deux questions : Pouvons-nous faire de l'optimisation topologique sans maillage et pouvons-nous apprendre un espace de solutions d'optimisation topologique. Nous appliquons des représentations neuronales implicites et obtenons des résultats structurellement sensibles pour l'optimisation topologique sans maillage en guidant le réseau neuronal pendant le processus d'optimisation et en adaptant les méthodes d'optimisation topologique par éléments finis. Notre méthode produit une représentation continue du champ de densité. De plus, nous présentons des espaces de solution appris en utilisant la représentation neuronale implicite. / Computer-aided design (CAD), visual effects, robotics and many other fields such as computational biology, aerospace engineering etc. rely on the solution of mathematical problems. In most cases, computational methods are used to solve these problems. The choice and construction of the computational method has large impact on the results and the computational efficiency. The structure of the problem can be used to create methods, that are faster and produce qualitatively better results than methods that do not use the structure. This thesis presents three articles with three new computational methods tackling partial differential equation (PDE) constrained simulation and optimization problems. In the first article, we tackle the problem of energy dissipation of common fluid solvers in visual effects. Fluid solvers are ubiquitously used to create effects in animated shorts and feature films. We present a time integration scheme for incompressible fluid dynamics which preserves energy better than many previous methods. The presented method has low overhead and can be integrated into a wide range of existing methods. The improved energy conservation leads to noticeably more dynamic animations. We then move on to computational design whose goal is to harnesses computational techniques for the design process. Specifically, we look at sensitivity analysis, which computes the sensitivities of the simulation result with respect to the design parameters to automatically optimize the design. In this context, we present an efficient way to compute the Gauss-Newton search direction, leveraging modern sparse direct linear solvers. Our method reduces the computational cost of the optimization process greatly for a certain class of inverse design problems. Finally, we look at topology optimization using machine learning techniques. We ask two questions: Can we do mesh-free topology optimization and can we learn a space of topology optimization solutions. We apply implicit neural representations and obtain structurally sensible results for mesh-free topology optimization by guiding the neural network during optimization process and adapting methods from finite element based topology optimization. Our method produces a continuous representation of the density field. Additionally, we present learned solution spaces using the implicit neural representation.

The simulation of physical systems in the early stages of conceptual designs has shown to be a key factor for adequate decision making and avoiding big and expensive issues downstream in engineering projects. In the case of aircraft cabin design, taking into account the thermal comfort of the passengers as well as the proper air circulation and renovation can make this difference. However, current numerical fluid simulations (CFD) are too computationally expensive for integrating them in early design stages where extensive comparative studies have to be performed. Instead, Zonal Models (ZM) appear to be a fast-computation approach that can provide coarse simulations for aircraft cabin flows. In this thesis, a Zonal Model solver is developed as well as a geometry-definition and meshing framework, both in Matlab®, for performing coarse, flexible and computationally cheap flow simulations of user-defined cabin designs. On one hand, this solver consists of a Fractional Step approach for coarse unstructured bi-dimensional meshes. On the other, the cabin geometry can be introduced by hand for simple shapes, but also with Computational Aided Design tools (CAD) for more complex designs. Additionally, it can be chosen to generate the meshes from scratch or morph them from previously generated ones. / <p>The presentation was online</p>