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.

[Truncated abstract] The hydrodynamics of wave impact on offshore structures is not well understood. Wave impacts often involve large deformations of water free-surface. Therefore, a wave impact problem is usually combined with a free-surface problem. The complexity is expanded when the body exposed to a wave impact is allowed to move. The nonlinear interactions between a moving body and fluid is a complicated process that has been a dilemma in the engineering design of offshore and coastal structures for a long time. This thesis used experimental and numerical means to develop further understanding of the wave impact problems as well as to create a numerical tool suitable for simulation of such problems. The study included the consideration of moving boundaries in order to include the coupled interactions of the body and fluid. The thesis is organized into two experimental and numerical parts. There is a lack of benchmarking experimental data for studying fluid-structure interactions with moving boundaries. In the experimental part of this research, novel experiments were, therefore, designed and performed that were useful for validation of the numerical developments. By considering a dynamical system with only one degree of freedom, the complexity of the experiments performed was minimal. The setup included a plate that was attached to the bottom of a flume via a hinge and tethered by two springs from the top one at each side. The experiments modelled fluid-structure interactions in three subsets. The first subset studied a highly nonlinear decay test, which resembled a harsh wave impact (or slam) incident. The second subset included waves overtopping on the vertically restrained plate. In the third subset, the plate was free to oscillate and was excited by the same waves. The wave overtopping the plate resembled the physics of the green water on fixed and moving structures. An analytical solution based on linear potential theory was provided for comparison with experimental results. ... In simulation of the nonlinear decay test, the SPH results captured the frequency variation in plate oscillations, which indicated that the radiation forces (added mass and damping forces) were calculated satisfactorily. In simulation of the nonlinear waves, the waves progressed in the flume similar to the physical experiments and the total energy of the system was conserved with an error of 0.025% of the total initial energy. The wave-plate interactions were successfully modelled by SPH. The simulations included wave run-up and shipping of water for fixed and oscillating plate cases. The effects of the plate oscillations on the flow regime are also discussed in detail. The combination of experimental and numerical investigation provided further understanding of wave impact problems. The novel design of the experiments extended the study to moving boundaries in small scale. The use of SPH eliminated the difficulties of dealing with free-surface problems so that the focus of study could be placed on the impact forces on fixed and moving bodies.

Thesis (MEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: The Touw River estuary and Wilderness coastal lakes is a sensitive system from a flooding and ecological viewpoint and, therefore, careful consideration is placed on the hydrodynamics and salinity levels within the system. The estuary consists of a “temporary open/closed” estuary, where during closed mouth conditions, the sand bar at the estuary mouth is artificially managed in an attempt to reduce flood water levels in the system. The reason behind this management strategy is the construction of residential property along the flood plains of the estuary and coastal lakes, which in the past, had been exposed to regular cycles of inundation during flood events. In an attempt to reduce flood water levels in all water bodies and hence reduce the risk of inundation, a management policy was formulated. The past and present management plan is to maintain the sand bar at Touw estuary mouth, during closed mouth conditions, at an elevation of between +2.1m to +2.4m MSL, based on proposals made by the CSIR in 1981. Recent flood events, after the implementation of the management policy, still occasionally result in significant inundation of residential property, which has raised concern for some interested parties over the effectiveness of the management strategy. Furthermore, a growing concern was also evident over the long term wellbeing of the system from an ecological viewpoint. Historical data shows significant changes in salinity levels since the implementation of the management strategy which could impose negative long term effects on the system. In this study, numerical models were consequently constructed and applied in order to analyse the effectiveness of the current management policy and recalculate flood water levels under a number of proposed scenarios. Long term salinity changes were also analysed in an attempt to better understand salinity propagation throughout the system, using extreme hypothetical cases. Through the analysis of the simulation results, it was concluded that flood water levels in the Touw estuary were almost completely dependent on the size of the Touw River flood and the initial height of the sand bar at the estuary mouth. Whereas, water levels in the coastal lakes are almost entirely dependent on the quantity of runoff into the lakes and their initial water levels. The current management plan, involving only artificial manipulation of the sand bar at the estuary mouth, therefore has a fairly insignificant effect on flood water levels achieved in the coastal lakes. Furthermore, it was concluded that the construction of the preparatory channel is a vitally important aspect of the current management plan and that skimming of the sand bar alone is ineffective to completely mitigate the risk of residential inundation along the banks of the Touw River. The salinity modelling study provided a first indication of the salinity characteristics within the system. It was found that the penetration of seawater into the system was less prominent as the water bodies became further removed from the ocean and that a direct relationship was evident between the volume of direct freshwater inflow to a water body and the degree of salinity variation in that specific water body. In water bodies with high volumes of direct freshwater inflow such as the Touw estuary, a large degree of salinity variation is evident. However, in water bodies with no freshwater inflow, such as Rondevlei, salinity levels remain more stable and are less likely to fluctuate. / AFRIKAANSE OPSOMMING: Uit ‘n vloed- en ekologiese oogpunt is die Touwsriviermonding en Wilderniskusmere ‘n uiters sensitiewe stelsel en daar is dus deeglike oorweging gegee aan die hidrodinamika en soutvlakke in die stelsel. Die monding bestaan uit 'n "tydelike oop / geslote" monding, en tydens geslote mondtoestande word die sandbank by die riviermond kunsmatig beheer in 'n poging om vloedwatervlakke binne die stelsel te verminder. Die rede vir hierdie strategie is omdat baie residensiële eiendomme langs die vloedvlaktes van die monding en kusmere gebou is, wat in die verlede aan 'n gereelde siklus van oorstromings blootgestel is tydens vloede. In 'n poging om vloedwatervlakke in al die watermassas te verminder, en sodoende die risiko van oorstroming te verminder, is 'n bestuursbeleid geformuleer. In beide die vorige en die huidige bestuursplanne is die sandbank in die Touwsriviermond tydens geslote mondtoestande in stand gehou op 'n hoogte van tussen 2,1 m en 2,4 m MSL, gebaseer op die voorstelle wat deur die WNNR in 1981 gemaak is. Onlangse vloede wat plaasgevind het na die implementering van die beleid, het steeds van tyd tot tyd gelei tot noemenswaardige oorstromings van residensiële eiendomme, en kommer is uitgespreek deur 'n paar belanghebbende partye oor die doeltreffendheid van die strategie vir die bestuur. Daar is verder kommer uitgespreek oor die langtermyn welstand van die stelsel uit 'n ekologiese oogpunt. Historiese data toon 'n beduidende verandering in soutvlakke sedert die implementering van die bestuurstrategie met ‘n negatiewe langtermyn uitwerking op die stelsel. In hierdie studie is daar derhalwe numeriese modelle opgestel en toegepas ten einde die doeltreffendheid van die huidige bestuur van die beleid te bepaal, asook om die vloedvlakke te herbereken en te analiseer na aanleiding van 'n aantal voorgestelde scenario's. Langtermyn soutgehalte veranderinge is ook ontleed in 'n poging om die soutgehalte verspreiding deur die hele stelsel beter te verstaan, deur gebruik te maak van uiterste hipotetiese gevalle. Deur die ontleding van die simulasie resultate, is daar tot die gevolgtrekking gekom dat vloedwatervlakke in die Touwsrivier-monding byna heeltemal afhanklik was van die grootte van die Touwsrivier vloed en die aanvanklike hoogte van die sandbank by die riviermond. Watervlakke in die kusmere is egter byna heeltemal afhanklik van die hoeveelheid afloop na die mere en die aanvanklike watervlakke. Die huidige bestuursplan, wat slegs ‘n kunsmatige manipulasie van die sandbank by die riviermond behels, het dus 'n redelik onbeduidend invloed op die vloedwatervlakke wat in die kusmere bereik is. Daar is verder tot die gevolgtrekking gekom dat die konstruksie van die voorbereidende kanaal 'n uiters belangrike aspek van die huidige bestuursplan is, en dat die afskraping van die sandbank alleen oneffektief sou wees om die risiko van residensiële oorstroming langs die oewer van die Touwsrivier uit te skakel. Die soutgehalte modelleringstudie verskaf 'n eerste aanduiding van die soutgehalte eienskappe binne die stelsel. Daar is gevind dat die penetrasie van seewater in die stelsel minder prominent was as in die watermassas verder van die see af, en dat daar 'n duidelike direkte verband is tussen die volume van die varswater wat direk invloei na 'n watermassa en die mate van soutgehalte variasie in daardie spesifieke watermassa. In watermassas waar hoë volumes varswater direk invloei soos die Touwsrivier-monding, is 'n groot mate van soutgehalte variasie sigbaar. In die watermassas waar geen varswater invloei nie, soos die Rondevlei, bly soutvlakke meer stabiel en is minder geneig om te wissel.

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

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

[Truncated abstract] Mine lakes are a water body created after an open-cut mine ceases operating. The lakes develop in the former mine-pit due to the combination of groundwater inflow, surface run-off and, in some cases, due to rapid filling from river diversion. While potentially valuable water resources, these lakes often have poor water quality and managing the water body is an important part of the overall process of mine site rehabilitation. As mine lakes form in man-made pits, they have a bathymetry that is typically quite distinct from natural lakes and this can, in turn, strongly influence the hydrodynamics and hence the water quality of the water body. Despite the potential importance of these water bodies, there have been very few studies on the hydrodynamics of mine lakes. This study describes a field investigation of the hydrodynamics of a former coal mine lake, Lake Kepwari, in south-western Western Australia. In particular, this study examines the hydrodynamic processes in both the surface mixing layers and the internal mixing in the density stratified lake. Wind sheltering in the surface mixing layer occurs due to the presence of the steep walls and lake embankments. A week long field experiment was conducted in December 2003 using a combination of moored thermistor chains with meteorological stations and the deployment of rapid vertical profiling turbulent microstructure instruments and CTD drops from two boats operating on the lake. ... Simulations indicated that inclusion of a site specific sheltering effect, based on the results of the field campaign, significantly improved the models‘ performance in capturing the surface mixed layer deepening associated with episodic strong wind events that occur on the lake. Considerable internal mixing was indicated by the high dissipation rates observed, particularly near the boundaries. Large basin-wide diffusivities were also calculated from the heat budget method over long periods, showed a consistency with time, and were slightly higher in summer than during the Autumn Winter period. Although light, there are persistent winds over the lake and yet little basin-scale internal wave activity or seiching. It is hypothesized that any seiching motion was rapidly damped by strong mixing over the hydraulically rough bathymetry bathymetry created by the remnant benches from the open cut mining operation itself. This boundary mixing, in turn, drives secondary relaxation currents that transport mixed fluid from the boundaries to the interior, resulting in high effective basin-wide diffusivities. A simple boundary mixing model is proposed to describe this process.

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.

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

Modeling the free surface flows is important in order to estimate the total drag of the sea Vessels. It is also necessary to study the effects of various maritime maneuvers. In this work, different ways of approximating an unstructured free surface grid with a B-spline surface are investigated. The Least squares and Galerkin approaches are studied in this regard. B-spline nite element method (BSPFEM) is studied for the solution of the steady-state kinematic free surface equation. The volume grid has to be moved in order to match the free boundary when the surface-tracking approach is adopted for the solution of free surface problem. Inherent smoothness of the B-spline representation of the free surface aids this process. B-spline representation of the free surface aids in building viscous volume grids hose boundaries closely match the steady state free surface. The B-spline approximation algorithm and BSPFEM solution of free surface equation have been tested with hypothetical algebraic testcases and real cases such as Gbody, Wigley hull and David Taylor Model Basin(DTMB) 5415 hull series.

Thesis: M.S., Massachusetts Institute of Technology, Department of Civil Engineering, 1981 / Includes bibliographical references. / by Sacha Sethaputra. / M.S. / M.S. Massachusetts Institute of Technology, Department of Civil Engineering