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Fluids are important to the Visual Effects Industry but extremely hard to control and simulate because of the complexity of the governing equations. Fluid solvers can be divided into two categories, those of the Eulerian point of reference and those of the Lagrangian. Both categories have different advantages and weaknesses and hybrid methods are popular. This thesis examines Smoothed Particle Hydrodynamics, a Lagrangian method for physically based uid simulations. To allow the artist the exibility given by shorter simulation times and increased number of iterations, the performance of the solver is key. In order to maximize the speed of the solver it is implemented entirely on the GPU, including collisions, volumetric force fields, sinks and other artist tools. To understand the implementation decisions, it is important to be familiar with the CUDA programming model. Thus, a brief explanation of CUDA is given before the exact implementation of the methods are explained. The results are presented along with a performance comparison as well as a discussion of the different parameters which can be fed to the solver. Some thoughts on possible future extensions can be found in the conclusion.

Dans le cadre de la simulation numérique portant sur la prédiction de phénomènes complexes, la modélisation de la pénétration d’un corps à travers un solide reste un challenge. Ceci est d’autant plus vrai si le corps impacté comporte une épaisseur importante devant les dimensions du projectile. Notamment, dans le contexte de la biomécanique des chocs, l’investigation des traumatismes suite à une blessure par balle, par un moyen numérique, nécessite la modélisation d’une zone pouvant être de plusieurs dizaines de fois supérieure aux dimensions du projectile sur un temps extrêmement court (de l’ordre de quelques dixièmes de milli-seconde). Les méthodes numériques dites classiques comme les éléments finis sont limitées dans ce domaine, dû en particulier à des problèmes de distorsions de maillage. Ce travail de thèse tente donc d’apporter une contribution dans le cadre de la modélisation des impacts pénétrants en proposant l'utilisation d’une méthode alternative sans maillage, la méthode "Smoothed Particle Hydrodynamics" (SPH).Méthode "Smoothed Particle Hydrodynamics, Impact Pénétrant, Biomécanique, Dynamique Rapide, Axisymétrie / Numerical simulation offers the possibility to investigate complexe phenomenons by giving access to useful informations about the evolution of a material system under constraints. Nevertheless, there are some situations where classical procedures, such as the Finite Elements Method (FEM), suffers from issues (e.g. mesh distorsions). One of these situations comes from a biomechanical context, where the investigation tends to observe the penetration of a projectile through human soft tissus. In this context, the objective of this Ph.D Thesis is to evaluate the capability of one alternative method, named Smoothed Particle Hydrodynamics method (SPH), to handle such modelling configurations.Smoothed Particle Hydrodynamics method, Penetrating Impact, Biomechanics, Fast Dynamics, Axis-symmetry

Recent technological advances are based on effectively using complex multiphysics concepts. Therefore, there is an ever increasing need for accurate numerical al-gorithms of reduced complexity for solving multiphysics problems. Traditional mesh-based simulation methods depend on a neighbor connectivity information for formulation of operators like derivatives. In large deformation problems, de-pendence on a mesh could prove a limitation in terms of accuracy and cost of preprocessing. Meshless methods obviate the need to construct meshes thus al-lowing simulations involving severe geometric deformations such as breakup of a contiguous domain into multiple fragments. Smoothed Particle Hydrodynamics (SPH) is a meshless particle based Lagrangian numerical method that has the longest continuous history of development ever since it was introduced in 1977. Commensurate with the significant growth in computational power, SPH has been increasingly applied to solve problems of greater complexity in fluid mechanics, solid mechanics, interfacial flows and astrophysics to name a few. The SPH approximation of the continuity and momentum equations govern-ing fluid flow traditionally involves a stiff equation of state relating pressure and density, when applied to incompressible flow problems. Incompressible Smoothed Particle Hydrodynamics (ISPH) is a variant of SPH that replaces this weak com-pressibility approach with a pressure equation that gives a hydrostatic pressure field which ensures a divergence-free (or density invariant) velocity field. The present study explains the development of an ISPH algorithm and its implementa-tion with focus on application to free surface flows, interaction of fluid with rigid bodies and coupling of incompressible fluids with a compressible second phase. Several improvements to the exiting ISPH algorithm are proposed in this study. A semi-analytic free surface model which is more accurate and robust compared to existing algorithms used in ISPH methods is introduced, validated against experi-ments and grid based CFD results. A surface tension model with specific applica-bility to free surfaces is presented and tested using 2D and 3D simulations. Using theoretical arguments, a volume conservation error in existing particle methods in general is demonstrated. A deformation gradient based approach is used to derive a new pressure equation which reduces these errors. The method is ap-plied to both free surface and internal flow problems and is shown to have better volume conservation and therefore reduced density fluctuations. Also, comments on instabilities arising from particle distributions are made and the role of the smoothing functions in such instabilities is discussed. The challenges in imple-menting the ISPH algorithm in a computer code are discussed and the experience of developing an in-house ISPH code is described. A parametric study on water entry of cylinders of different shapes, angular velocity and density is performed and aspects such as surface profiles, impact pressures and penetration velocities are compared. An analysis on the energy transfer between the solid and the fluid is also performed. Low Froude number water entry of a sphere is studied and the impact pressure is compared with the theoretical estimates. The Incompressible SPH formulation, employing the proposed improvements from the study is then coupled with a compressible SPH formulation to perform two phase flow simulations interacting compressible and incompressible fluids. To gain confidence in its applicability, the simulations are compared against the theoretical predication given by the Rayleigh-Plesset equation for the problem of compressible drop in an incompressible fluid.

Tsunamis are among the most terrifying and complex physical phenomena potentially affecting almost all coastal regions of the Earth. Tsunami waves propagate in the ocean over thousands of kilometres away from their generating source at considerable speeds. Among several other tsunamis that occurred during the past decade, the 2004 Indian Ocean Tsunami and the 2011 Tohoku Tsunami in Japan, considered to be the deadliest and costliest natural disasters in the history of mankind, respectively, have hit wide stretches of densely populated coastal areas. During these major events, severe destruction of inland structures resulted from the action of extreme hydrodynamic forces induced by tsunami flooding. Subsequent field surveys in which researchers from the University of Ottawa participated ultimately revealed that, in contrast to seismic forces, such hydrodynamic forces are not taken into proper consideration when designing buildings for tsunami prone areas. In view of these limitations, a novel interdisciplinary hydraulic-structural engineering research program was initiated at the University of Ottawa, in cooperation with the Canadian Hydraulic Centre of the National Research Council, to help develop guidelines for the sound design of nearshore structures located in such areas. The present study aims to simulate the physical laboratory experiments performed within the aforementioned research program using a single-phase three-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) numerical model. These experiments consist in the violent impact of rapidly advancing tsunami-like hydraulic bores with individual slender structural elements. Such bores are emulated based on the classic dam-break problem. The quantitatively compared measurements include the time-history of the net base horizontal force and of the pressure distribution acting on columns of square and circular cross-sections, as well as flow characteristics such as bore-front velocity and water surface elevation. Good agreement was obtained. Results show that the magnitude and duration of the impulsive force at initial bore impact depend on the degree of entrapped air in the bore-front. The latter was found to increase considerably if the bed of the experimental flume is covered with a thin water layer of even just a few millimetres. In order to avoid large fluctuations in the pressure field and to obtain accurate simulations of the hydrodynamic forces, a Riemann solver-based formulation of the SPH method is utilized. However, this formulation induces excessive numerical diffusion, as sudden and large water surface deformations, such as splashing at initial bore impact, are less accurately reproduced. To investigate this particular issue, the small-scale physical experiment of Kleefsman et al. (2005) is also considered and modeled. Lastly, taking full advantage of the validated numerical model to better understand the underlying flow dynamics, the influence of the experimental test geometry and of the bed condition (i.e. dry vs. wet) is investigated. Numerical results show that when a bore propagates over a wet bed, its front is both deeper and steeper and it also has a lower velocity compared to when it propagates over a dry bed. These differences significantly affect the pressure distributions and resulting hydrodynamic forces acting on impacted structures.

L'approche Smoothed Particle Hydrodynamics (SPH) est une méthode de calcul pour simuler des écoulements fluides avec une méthode Lagrangienne de type suivi de particules. A l'inverse des méthodes Euleriennes, ce type d'approche ne nécessite pas de maillage. C'est là l'un des atouts majeurs de l'approche SPH puisqu'elle permet de s'affranchir des méthodes de suivi d'interfaces couramment utilisées dans les approches Euléeriennes (par exemple Volume-of-Fluid, Level-Set ou Front-Tracking). L'approche SPH est donc de plus en plus utilisée dans les domaines de l'hydro-ingénierie et de la géophysique notamment de part le traitement naturel des écoulements à surface libre dans la méthode SPH. Cependant, l'approche SPH n'est utilisée que depuis peu pour simuler des écoulements multiphasiques complexes et de nombreux problèmes restent en suspens, notamment concernant une formulation adéquate ou le micro-mélange aux interfaces. L'un des principaux enjeux de ces travaux de thèse est d'analyser de façon objective les différentes approches de type SPH existantes et d'évaluer leur capacité à simuler des écoulements multiphasiques complexes. Ainsi, la modélisation des phénomènes liés à la tension de surface a été réalisée et validée via l'utilisation de techniques de type Continuum Surface Force. Les phénomènes de convection naturelle ont quant à eux été modélisés grâce à une nouvelle formulation plus générale (non-Boussinesq). Une partie de ces travaux est dédiée à l'étude des problèmes de micro-mélange aux interfaces: les effets indésirables (notamment la fragmentation de l'interface) sont analysés et des solutions sont proposées. Une autre part de travail porte sur la modélisation des mouvements ascendants de bulles dans des liquides, avec l'inclusion des interactions entre bulles. Des simulations SPH ont été réalisées pour différents régimes d'écoulement, chacun d'eux correspondant à un ratio spécifique entre la tension de surface, la viscosité et la flottabilité. Les prédictions numériques de la topographie des bulles, de leur vitesse ainsi que de leur coefficient de trainée ont été validées. Pour ce faire, les résultats numériques ont été comparés non seulement aux données expérimentales de référence mais également à d'autres simulations numériques de bulles ascendantes. Dans ces travaux de thèse, une étude détaillée des concepts liés aux contraintes d'incompressibilité a été réalisée. Dans cet objectif, deux traitements différents ont été comparés: l'approche faiblement compressible (où une équation d'état adéquate est choisie) et l'approche incompressible (où une projection des champs de vitesse sur un espace sans divergence est réalisée de deux facons différentes). La pertinence de ces modèles pour des simulations d'écoulements multiphasiques est également évaluée. Les problèmes associés aux paramètres numériques sont discutés et un choix approprié de ces paramètres est proposé. Pour ce faire, de nombreux calculs de validation en deux et trois dimensions ont été réalisés. Enfin, une extension est proposée pour simuler les phénomènes liés à l'ébullition via une approche SPH. Ce sujet étant encore en friche, de nouvelles idées et schémas sont proposés pour le changement de phase liquide-vapeur dans l'approche SPH / Smoothed Particle Hydrodynamics (SPH) is a fully Lagrangian, particle based approach for fluid-flow simulations. One of its advantages over Eulerian techniques is no need of a numerical grid. Therefore, there is no necessity to handle the interface shape as it is done in Volume-of-Fluid, Lavel-Set or Front-Tracking methods. Thus, the SPH approach is increasingly used for hydro-engineering and geophysical applications involving free-surface flows where the natural treatment of evolving interfaces makes it an attractive method. However, for real-life multi-phase simulations this method has only started to be considered and many problems like a proper formulation or a spurious fragmentation of the interface remain to be solved. One of the aims of this work is to critically analyse the existing SPH variants and assess their suitability for complex multi-phase problems. For modelling the surface-tension phenomena the Continuum Surface Force (CSF) methods are validated and used. The natural convection phenomena are modeled using a new, more general formulation, beyond the Boussinesq approximation. A substantial part of the work is devoted to the problem of a spurious fragmentation of the interface (the micro-mixing of SPH particles). Its negative effects and possible remedies are extensively discussed and a new variant is proposed. Contrary to general opinion, it is proven that the micro-mixing is not only the problem of flows with neglegible surface tension. A significant part of this work is devoted to the modelling of bubbles rising through liquids, including bubble-bubble interactions. The SPH simulations were performed for several flow regimes corresponding to different relative importance of surface tension, viscosity and buoyancy effects. The predicted topological changes, bubble terminal velocity and drag coefficients were validated with respect to reference experimental data and compared to other numerical methods. In the work, fundamental concepts of assuring the incompressibility constraint in SPH are also recalled. An important part of work is a thorough comparison of two different incompressibility treatments: the weakly compressible approach, where a suitably chosen equation of state is used, and truly incompressible method (in two basic variants), where the velocity field is projected onto a divergence-free space. Their usefulness for multi-phase modelling is discussed. Problems associated with the numerical setup are investigated, and an optimal choice of the computational parameters is proposed and verified. For these purposes the study is supported by many two- and three-dimensional validation cases. In addition, the present work opens new perspectives to future simulations of boiling phenomena using the SPH method. First ideas and sketches for the implementation of the liquid-vapour phase change are presented

Esta dissertação de mestrado propõe o estudo e a implementação de um método de deformação usando modelos tridimensionais sem o uso de malhas baseado na técnica Smoothed Particles Hydrodynamics (SPH), que consiste num sistema de resolução de equações diferenciais para aplicação de conceitos físicos para simular deformação de tecidos moles. A opção pelo método sem malha para processo de deformação é apresentado nesta dissertação como alternativa a um dos métodos mais comuns em simulação de deformação de tecidos, o método massa-mola, explorando questões referentes ao uso de recursos computacionais. Para chegada a definição do método foram analisados os temas envolvendo métodos de deformação, modelos baseados em pontos e o SPH como plataformas para alcançar o desenvolvimento do método proposto pela dissertação. Como forma de comprovar as propriedades do método desenvolvido foi realizada a implementação e testes levando em consideração os modelos de deformação e a interação em tempo real num ambiente de simulação que contempla a deformação de uma mama, levando em conta a comparação com o método massa-mola, o uso de recursos do próprio método em função do aumento de detalhe e do uso de objeto com múltiplas propriedades / This master thesis proposes a study and implementation of deformation method using tridimensional models without edge composed meshes based on Smoothed Particles Hydrodynamics (SPH) technique, that consists on diferential equation solving system to reproduce physical concepts to simulate soft tissue deformation. The option for a meshless method to deformation process is shown in this thesis as an alternative to a very common method in tissue deform simulation, the mass-spring method, reviewing a comparison based on computational resources. To achieve a method definition were analyzed fields of study involving deformation methods, point-based models and SPH as platforms to build and deploy the proposed method for this thesis. To show the characteristics for this developed deformation method was realized the implementation and tests based on deformation models and real time interaction on a simulation environment that includes a breast deformation, taking in account the comparison to mass-spring, number of points of the cloud model and multiple properties

Esta dissertação de mestrado propõe o estudo e a implementação de um método de deformação usando modelos tridimensionais sem o uso de malhas baseado na técnica Smoothed Particles Hydrodynamics (SPH), que consiste num sistema de resolução de equações diferenciais para aplicação de conceitos físicos para simular deformação de tecidos moles. A opção pelo método sem malha para processo de deformação é apresentado nesta dissertação como alternativa a um dos métodos mais comuns em simulação de deformação de tecidos, o método massa-mola, explorando questões referentes ao uso de recursos computacionais. Para chegada a definição do método foram analisados os temas envolvendo métodos de deformação, modelos baseados em pontos e o SPH como plataformas para alcançar o desenvolvimento do método proposto pela dissertação. Como forma de comprovar as propriedades do método desenvolvido foi realizada a implementação e testes levando em consideração os modelos de deformação e a interação em tempo real num ambiente de simulação que contempla a deformação de uma mama, levando em conta a comparação com o método massa-mola, o uso de recursos do próprio método em função do aumento de detalhe e do uso de objeto com múltiplas propriedades / This master thesis proposes a study and implementation of deformation method using tridimensional models without edge composed meshes based on Smoothed Particles Hydrodynamics (SPH) technique, that consists on diferential equation solving system to reproduce physical concepts to simulate soft tissue deformation. The option for a meshless method to deformation process is shown in this thesis as an alternative to a very common method in tissue deform simulation, the mass-spring method, reviewing a comparison based on computational resources. To achieve a method definition were analyzed fields of study involving deformation methods, point-based models and SPH as platforms to build and deploy the proposed method for this thesis. To show the characteristics for this developed deformation method was realized the implementation and tests based on deformation models and real time interaction on a simulation environment that includes a breast deformation, taking in account the comparison to mass-spring, number of points of the cloud model and multiple properties

No / Two numerical particle models, the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods, coupled with a sub-particle scale (SPS) turbulence model, are presented to simulate free surface flows. Both SPH and MPS methods have the advantages in that the governing Navier¿Stokes equations are solved by Lagrangian approach and no grid is needed in the computation. Thus the free surface can be easily and accurately tracked by particles without numerical diffusion. In this paper different particle interaction models for SPH and MPS methods are summarized and compared. The robustness of two models is validated through experimental data of a dam-break flow. In addition, a series of numerical runs are carried out to investigate the order of convergence of the models with regard to the time step and particle spacing. Finally the efficiency of the incorporated SPS model is further demonstrated by the computed turbulence patterns from a breaking wave. It is shown that both SPH and MPS models provide a useful tool for simulating free surface flows

<p>Simulating fluid behavior has proven to be a demanding challenge which requires complex computational models and highly efficient data structures. Smoothed Particle Hydrodynamics (SPH) is a particle based computational model used to simulate fluid behavior that has been found capable of producing convincing results. However, the SPH algorithm is computational heavy which makes it cumbersome to work with.</p><p>This master thesis describes how the SPH algorithm can be accelerated by utilizing the GPU’s computational resources. It describes a model for how to distribute the work load on the GPU and presents a suitable data structure. In addition, it proposes a method to represent and handle moving objects in the fluids surroundings. Finally, the performance gain due to the GPU is evaluated by comparing processing times with an identical implementation running solely on the CPU.</p>