This thesis investigates wave loading on bodies in the free surface using smoothed particle hydrodynamics (SPH). This includes wave loading on fixed bodies, waves generated by heaving bodies in still water and the heave response of a body in waves, representing a wave energy device. SPH is a flexible Lagrangian technique for CFD simulations, which in principle applies to steep and breaking waves without special treatment allowing us to simulate highly nonlinear and potentially violent flows encountered in a real sea. However few detailed tests have been undertaken even with small amplitude waves.This research uses the open-source SPH code SPHysics. First two forms of SPH formulation, standard SPH with artificial viscosity and SPH-Arbitrary Lagrange Euler (ALE) with a Riemann solver, are used to simulate progressive waves in a 2-D tank. The SPH-ALE formulation with a symplectic time integration scheme and cubic spline kernel is found to model progressive waves with negligible dissipation whereas with the standard SPH formulation waves decay markedly along the tank. We then consider two well-defined test cases in two dimensions: progressive waves interacting with a fixed cylinder and waves generated by a heaving semi-immersed cylinder. To reduce computer time in a simple manner a variable particle mass distribution is tested with fine resolution near the body and coarse resolution further away, while maintaining a uniform kernel size. A mass ratio of 1:4 proved effective but increasing to 1:16 caused particle clumping and instability. For wave loading on a half-submerged cylinder the agreement with the experimental data of Dixon et al. (1979) for the root mean square force is within 2%. For more submerged cases, the results show some discrepancy, but this was also found with other modelling approaches. For the heaving cylinder, SPH results for the far field wave amplitude and vertical force on the cylinder show good agreement with the data of Yu and Ursell (1961). The variable mass distribution leads to a computer run time speedup of nearly 200% in these cases on a single CPU. The results of the vertical force and wave amplitude are shown to be quite sensitive to the value of the slope limiter in the Riemann solver for the 2-D heaving cylinder problem. A heaving 2-D wedge or 3-D cone whose oscillatory vertical motion is prescribed as the elevation of a focused wave group is a precise test case for numerical free-surface schemes. We consider two forms of repulsive boundary condition (Monaghan & Kos, 1999, and Rogers et al., 2008) and particle boundary force (Kajtar and Monaghan, 2009) for the 2-D wedge case, comparing the result with the experimental data of Drake et al. (2009). The repulsive boundary condition was more effective than the particle boundary force method. Variable particle mass with different kernel sizes was then tested for 2-D problems for mass ratios of 1:4, 1:16 and 1:4:16 with satisfactory results without particle clumping and instability. For the 3-D cone case, SPH reproduces the experimental results very closely for the lower frequency tested where there is no separation from the bottom surface of the body but for the higher frequencies the magnitudes of force minima were underestimated. The mass ratios of 1:8 and 1:8:27 in two and three nested regions are tested for the 3-D cone problem where a computer run time speedup of nearly 500% is achieved on 16 processors for the mass ratio of 1:8.Finally, the floating body of a heaving wave energy device known as the Manchester Bobber is modelled in extreme waves without power take-off. The results for a single float are in approximate agreement with the experiment.

The work of this dissertation will study various aspects of the dynamics of compact objects using numerical simulations.We consider BH dynamics within two modified or alternative theories of gravity. Within a family of Einstein-Maxwell-Dilaton-Axion theories, we find that the GW waveforms from binary black hole (BBH) mergers differ from the standard GW waveform prediction of GR for especially large axion values. For more astrophysically realistic (i.e. smaller) values, the differences become negligible and undetectable. Weestablish the existence of a well-posed initial value problem for a second alternative theory fo gravity (quadratic gravity) and demonstrate in spherical symmetry that a linear instability is effectively removed on consideration of the full nonlinear theory.We describe the key components and development of a code for studying BBH mergers for which the mass ratio of the binaries is not close to one. Such intermediate mass ratio inspirals (IMRIs) are much more difficult to simulate and present greater demands on resolution, distributed computing, accuracy and efficiency. To this end, we present a highly-scalable framework that combines a parallel octree-refined adaptive mesh with a wavelet adaptive multiresolution approach. We give results for IMRIs with mass ratios up to 100:1. We study the ejecta from BNS in Newtonian gravity. Using smoothed particle hydrodynamics we develop and present the highly scalable FleCSPH code to simulate such mergers. As part of the ejecta analysis, we consider these mergers and their aftermath as prime candidates for heavy element creation and calculate r-process nucleosynthesis within the post-merger ejecta. Lastly we consider a non-standard, yet increasingly explored, interaction between a BH and a NS that serves as a toy model for primordial black holes (PBH) and their possible role as dark matter candidates. We present results from a study of such systems in which a small BH forms at the center of a NS. Evolving the spherically symmetric system in full GR, we follow the complete dynamics as the small BH consumes the NS from within. Using numerical simulations, we examine the time scale for the NS to collapse into the PBH and show that essentially nothing remains behind. As a result, and in contradiction to other claims in the literature, we conclude that thisis an unlikely site for ejecta and nucleosynthesis, at least in spherical symmetry.

<p>This thesis project addresses the need for an interactive, real-time water animation tech-<br> nique that can showcase visually convincing effects such as splashes and breaking waves while<br> being computationally inexpensive. Our method couples SPH and wave equations in a one-<br> way manner to simulate the behavior of water in real-time, leveraging OpenGL’s Compute<br> Shaders for interactive performance and a novel Uniform Grid implementation. Through a<br> review of related literature on real-time simulation methods of fluids, and water animation,<br> this thesis presents a feasible algorithm, animations to showcase interesting water effects,<br> and a comparison of computational costs between SPH, wave equations, and the coupled<br> approach. The program renders a water body with a planar surface and discrete particles.<br> This project aims to provide a solution that can meet the needs of various water animation<br> use-cases, such as games, and movies, by offering a computationally efficient technique that<br> can animate water to behave plausibly and showcase essential effects in real-time.</p>

This thesis describes efforts to improve the realism of numerical models of giant planet formation and migration in an attempt to better understand these processes. A new approach has been taken to the modelling of accretion, designed to mimic reality by allowing gas to accumulate upon a protoplanetary surface. Implementing this treatment in three-dimensional self-gravity radiation hydrodynamics calculations provides an excellent model for planet growth, allowing an exploration of the factors that affect accretion. Moreover, these calculations have also been extended to investigate the migration of protoplanets through their parent discs as they grow. When focusing on the growth of non-migrating protoplanets, the models are performed using small sections of disc, enabling excellent resolution right down to the core; gas structures and flow can be resolved on scales from ~ 10^4 to 10^11 metres. Using radiative transfer, these models reveal the importance of opacity in determining the accretion rates. For the low mass protoplanets, equivalent in mass to a giant planet core (~ 10 M⊕), the accretion rates were found to increase by up to an order of magnitude for a factor of 100 reduction in the grain opacity of the parent circumstellar disc. However, even these low opacities lead to growth rates that are an order of magnitude slower than those obtained in locally-isothermal conditions. For high mass protoplanets (>~ 100M⊕), the accretion rates show very little dependence upon opacity. Nevertheless, the rates obtained using radiative transfer are still lower than those obtained in locally-isothermal models by a factor of ~2, due to the release of accretion energy as heat. Only high mass protoplanets are found to be capable of developing circumplanetary discs, and this ability is dependent upon the opacity, as are the scaleheights of such discs. However, their radial extents were found to be independent of the opacity and the protoplanet mass, all reaching ≈ RH/3, inline with analytic predictions. Migration is investigated using global models, ensuring a self-consistently evolved disc. Using locally-isothermal calculations, it was found that the capture radius of an accreting sink particle, used to model a protoplanet without a surface, must be small (<< RH) to yield migration timescales consistent with linear theory of Type I migration. In the low mass regime of Type I migration, accreting sinks with such small radii yield timescales consistent with those models in which a protoplanetary surface is used. However, for high mass protoplanets, undergoing Type II migration, the surface treatment leads to faster rates of migration, indicating the importance of a realistic accretion model. Using radiative transfer, with high opacities, leads to a factor of ~ 3 increase in the migration timescale of the lowest mass protoplanets, improving their chances of survival. As suitable gas giant progenitors, their survival is key to understanding the growth of giant planets. An unexpected result of the radiative transfer was a reduction in the migration timescale of high mass planets. This appears to be a result of the less thoroughly evacuated gaps created by planets in non-locally-isothermal discs, which affects the corotation torque.

Le procédé du rotomoulage réactif est une technologie de fabrication de pièces creuses de taille et géométrie très variés. Une compréhension et une modélisation des phénomènes physiques qui interviennent dans les différentes étapes de la fabrication apportent une contribution importante à la maîtrise de ce procédé. Les travaux abordés dans cette thèse se situent dans le cadre d'un programme plus général visant le contrôle et le pilotage du rotomoulage réactif.Tout d'abord, une caractérisation et modélisation de la cinétique du polyuréthane thermodurcissable en mode dynamique est réalisé suivie par des mesures rhéologiques afin d'établir des lois rhéocinétique ainsi que des lois du comportement viscoélastiques du système réactionnel. Ces lois de comportement sont établies conformément aux conditions réelles de la mise en œuvre du matériau.Ensuite, nous simulons le procédé du rotomoulage en utilisant un code de calcul basé sur la méthode « Smoothed Particle Hydrodynamics » (SPH), développé par notre équipe, en implémentant des nouveaux paramètres physiques: le caractère non-newtonien du mélange réactionnel et les effets de tension superficielle.Le modèle de tension de surface en 2 et 3D développé dans cette thèse permet la détection explicite de l'interface séparant le fluide réactif de l'air. Puis, nous utilisons l'interpolation lagrangienne ou la régression circulaire pour construire la courbe d'interface en 2D et la surface d'interface en 3D sera reconstruite via la régression sphérique. Quant à la modélisation de l'écoulement du fluide non-newtonien, une loi de puissance décrivant l'évolution de la viscosité en fonction du taux de cisaillement a été intégrée dans le solveur pour décrire le caractère non-newtonien du mélange réactionnel durant sa mise en œuvre. Ces paramètres physiques implémentés dans le code ont été validé par une série de cas de tests en 2 et 3D.L'intégration des effets de tension de surface et la prise en compte du caractère non-newtonien du fluide réactif nous ont permis de mieux présenter la mouillabilité de la surface interne du moule et l'étalement des différentes couches du polymères.Mots clés : rotomoulage réactif, polyuréthane thermodurcissable, rhéocinétique, Smoothed Particle Hydrodynamics, tension de surface, fluide non-newtonien, simulation. / Reactive Rotational molding (RRM) is a process for manufacturing hollow plastic products with no weld lines, in virtually any shape, size, color and configuration, using biaxial rotation and high temperature. Understanding and modelling of physical phenomena provide a great contribution for process control that is the purpose of a more general program.Firstly, a characterization and the kinetic modeling of the thermoset polyurethane are performed in anisothermal conditions followed by rheological measurements in order to establish rheokinetik model and the the viscoelastic behavior of the reactive system according with RRM conditions.Afterwards, to simulate the RRM, Smoothed Particles Hydrodynamics (SPH) method is applied which is suited method to simulate the fluid flow with free surface such as occurs at RRM. This solver is developed by our team. Modelling and simulating reactive system flow depend on different parameters; the physical phenomena involved are: surface tension force and non-newtonian fluid behavior.The surface tension method has been successfully applied to simulate RRM using SPH solver taking into account free surface tension force. Surface tension force is given explicitly in the current model. After detecting the boundary particles, the interface is locally fitted by using Lagrangian interpolation polynomial or fitting circle in 2D and by using fitting sphere in 3D, respectively. To study the non-newtonian fluid flow during RRM, a power law describes the evolution of the viscosity versus shear rate was adopted to describe the viscoelastic nature of the reactive fluid during its shaping.The implementation of surface tension and viscoelasticity allows us to present the wettability of internal surface of the mold and the spreading of different polymers layers.Keywords : Reactive rotational molding, thermoset polyurethane, rheokinetik, Smoothed Particle Hydrodynamics, surface tension, non-newtonian fluid, simulation.

Submitted by Maria Cristina (library@lncc.br) on 2017-03-14T15:05:16Z No. of bitstreams: 1 tese_lncc_LEANDRO_TAVARES.pdf: 29698763 bytes, checksum: 86bf9653aed054e6fdf52b75fb82a03d (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-03-14T15:06:11Z (GMT) No. of bitstreams: 1 tese_lncc_LEANDRO_TAVARES.pdf: 29698763 bytes, checksum: 86bf9653aed054e6fdf52b75fb82a03d (MD5) / Made available in DSpace on 2017-03-14T15:06:31Z (GMT). No. of bitstreams: 1 tese_lncc_LEANDRO_TAVARES.pdf: 29698763 bytes, checksum: 86bf9653aed054e6fdf52b75fb82a03d (MD5) Previous issue date: 2016-09-19 / The Smoothed Particle Hydrodynamics (SPH) is a Lagrangian and meshless method for discretization of fluid equations. It has been used to fluid simulation in many areas of engineering and applied sciences. This method discretizes the Navier-Stokes equations using a particle system and interpolation theory. In this context, we developed a variational integrator to SPH, using the generalized midpoint rule and fixed point method. Then, we elaborate a implementation of SPH to simulate a quasi-incompressible fluid under influence of disks that rotates with constant angular velocity (N-roll mill setup). The obtained flow patterns are analyzed using Morse and Catastrophe theories. Finally, the two aforementioned works show us the necessity of techniques for comparing fluid simulations. Hence, we developed a framework to generate a visual summary of a computation fluid simulations by adapting techniques of video summary areas. As contribution of this thesis we highlight that the variational integrator has the property of linear momentum conservation being easier to implement than counterpart ones. Also, we emphasize the methodology to analyze the critical points generated by the original implementation of N-roll mill setup using SPH. Besides, the pioneer adaptation of techniques in video summarization, for computation fluid dynamics, allows to capture a detailed picture of important segments of the fluid for both comparison and analysis of the flows. / O método lagrangiano Smoothed Particle Hydrodynamics (SPH) não utiliza malha subjacente para discretização de equações de fluidos e vêm sendo usado para simulações em diversas áreas do conhecimento. Esse método discretiza as equações de Navier-Stokes usando um sistema de partículas e a teoria de interpolação. Neste contexto, desenvolvemos um integrador variacional para o SPH, utilizando a regra do ponto médio generalizada e o método do ponto fixo. Em seguida, elaboramos uma implementação do SPH para simular um fluido quase-incompressível sob a influência de discos que giram com velocidades angulares constantes (\textit{N-roll mill}), denominado nessa tese de problema de N-rolos, e desenvolvemos uma metodologia para analisar os padrões de fluxos gerados. Para esta análise utilizamos a teoria de Morse e a teoria de Catástrofes de René Thom. Finalmente, os dois trabalhos citados nos mostram a necessidade e carência de técnicas para comparação e análise de fluidos. Logo, desenvolvemos um arcabouço para produção de sumários da simulação, adaptando técnicas da área de sumários de vídeo. Como contribuições da tese destacamos que o integrador variacional desenvolvido apresenta facilidade de implementação em relação a esquemas tradicionais e com conservação de momento linear. Destacamos também a metodologia para análise de pontos críticos gerados pela implementação original do problema de N-rolos usando o SPH, bem como a adaptação pioneira de técnicas de sumarização de vídeo para análise de fluidos.

Desde a década de 70, há um crescente interesse em simulações em computador de fenômenos físicos visto sua diversidade de aplicações. Dentre esses fenômenos, podem ser destacados a interação entre corpos rígidos, elásticos, plásticos, quebráveis e também fluidos. Neste trabalho realizamos a simulação de um desses fenômenos, o escoamento de fluidos, por um método conhecido como Smoothed Particles Hydrodynamics, uma abordagem lagrangeana baseada em partículas para resolução das equações que modelam o movimento do fluido. Várias são as vantagens de métodos lagrangeanos usando partículas sobre os que usam malhas, por exemplo, as propriedades do material transladam com as partículas como função do tempo, além da capacidade de lidar com grandes deformações. Dentre as desvantagem, destacamos uma deficiência relacionada ao ganho de energia total do sistema e estabilidade das partículas. Para lidar com isso, utilizamos uma abordagem baseada na lei da conservação da energia: em um sistema isolado a energia total se mantém constante e ela não pode ser criada ou destruida. Dessa forma, alterando o integrador temporal nós restringimos o aumento arbitrário de energia, tornando a simulação mais tolerante às condições iniciais / Since the late 70s, there is a growing interest in physically-based simulations due to its increasing range of application. Among these simulations, we may highlight interaction between rigid, elastic, plastic and breakable bodies and also fluids. In this work, one of these phenomena, fluid flow, is simulated using a technique known as Smoothed Particle Hydrodynamics, a meshless lagrangean method that solves the equations of the flow behavior of fluids. There are several advantages of meshless methods over mesh-based methods, for instance, the material properties are translated along with particles as a function of time and the ability to handle arbitrary deformations. Among the disadvantages, we may highlight a problem related to the gain of energy by the system and stability issues. In order to handle this, we used an approach based on the law of conservation of energy: in an isolated system the total energy remains constant and cannot be created or destroyed. Based on this, we used a technique that bounds the total energy and the simulation becomes less sensitive to initial conditions

Nos últimos anos, o estudo de métodos de animação de escoamento de fluidos tem sido uma área de intensa pesquisa em Computação Gráfica. O principal objetivo desse projeto é desenvolver novas técnicas em GPGPU baseadas na arquitetura CUDA para simular o escoamento de fluidos não-newtonianos, tais como fluidos viscoplásticos e viscoelásticos. Ao invés dos tradicionais métodos com malha diferenças finitas e elementos finitos, essas técnicas são baseadas em uma discretização lagrangeana das equações de governo desses fluidos através do método sem malha conhecido como SPH (Smoothed Particle Hydrodynamics) / I n recent years, the study of methods of animating fluid flow has been an area of intense research in Computer Graphics. The main objective of this project is to develop new techniques based on the CUDA GPGPU architecture to simulate the flow of non-Newtonian fluids, such as viscoelastic and viscoplastic fluids. Instead of traditional methods with mesh - finite differences and finite elements, these techniques are based on a Lagrangian discretization of the governing equations of these fluids through the mesh free method known as SPH (Smoothed Particle Hydrodynamics)

Ionising radiation is present in a variety of astrophysical problems, and it is particularly important for shaping the process of star formation in molecular clouds, containing hot, high-mass stars. In order to account for the effects of ionising radiation within numerical models of star formation, we need to combine a hydrodynamics method with a radiative transfer method and obtain a radiation hydrodynamics scheme (RHD). In this thesis I achieve live radiation hydrodynamics by coupling the Smoothed Particle Hydrodynamics (SPH) code Phantom with the Monte Carlo Radiative Transfer (MCRT) code CMacIonize. Since SPH is particle-based and MCRT is grid-based, I construct an unstructured, Voronoi grid in order to establish a link between the two codes. In areas with large density gradients, a Voronoi grid based purely on the SPH particle positions achieves insufficient resolution, and therefore I propose a novel algorithm for inserting a small number of additional grid cells to improve the local resolution. Furthermore, the MCRT calculations require the knowledge of an average density for each Voronoi cell. To address this, I develop an analytic density mapping from SPH to a Voronoi grid, by deriving an expression for the integrals of a series of kernel functions over the volume of a random polyhedron. Finally, I demonstrate the validity of the live RHD through the benchmark test of D-type expansion of an H II region, where good agreement is shown with the existing literature. The RHD implementation is then used to perform a proof-of-concept simulation of a collapsing cloud, which produces high-mass stars and is subsequently partially ionised by them. The presented code is a valuable tool for future star formation studies, and it can be used for modelling a broad range of additional astronomical problems involving ionising radiation and hydrodynamics.

Smoothed Particle Hydrodynamics (SPH) is analysed as the weighted residual method. In particular the analysis focuses on the collocation aspect of the method. Using Monte Carlo experiments we demonstrate that SPH is highly sensitive to node disorder, especially in its symmetrised energy and momentum conserving form. This aspect of the method is related to low [Beta] MHD instabilities observed by other authors. A remedy in the form of the Weighted Differences Method is suggested, which addresses this problem to some extent, but at a cost of losing automatic conservation of energy and momentum. ¶ The Weighted Differences Method is used to simulate propagation of Alfven and magnetosonic wave fronts in [Beta] = 0 plasma, and the results are compared with data obtained with the NCSA Zeus3D code with the Method of Characteristics (MOC) module. ¶ SPH is then applied to two interesting astrophysical situations: accretion on to a white dwarf in a compact binary system, which results in a formation of an accretion disk, and gravitational collapse of a magnetised vortex. Both models are 3 dimensional. ¶ The accretion disk which forms in the binary star model is characterised by turbulent flow: the Karman vortex street is observed behind the stream-disk interaction region. The shock that forms at the point of stream-disk interaction is controlled by the means of particle merges, whereas Monaghan-Lattanzio artificial viscosity is used to simulate Smagorinsky closure. ¶ The evolution of the collapsing magnetised vortex ends up in the formation of an expanding ring in the symmetry plane of the system. We observe the presence of spiralling inward motion towards the centre of attraction. That final state compares favourably with the observed qualitative and quantitative characteristics of the circumnuclear disk in the Galactic Centre. That simulation has also been verified with the NCSA Zeus3D run. ¶ In conclusions we contrast the result of our Monte Carlo experiments with the results delivered by our production runs. We also compare SPH and Weighted Differences against the new generation of conservative finite differences methods, such as the Godunov method and the Piecewise Parabolic Method. We conclude that although SPH cannot match the accuracy and performance of those methods, it appears to have some advantage in simulation of rotating flows, which are of special interest to astrophysics.