A two-dimensional axisymmetric implementation of the smoothed particle hydrodynamics (SPH) technique, called for short AxisSPH, has been described in this thesis, along with a number of basic tests and realistic applications. The main goal of this work was to fill a gap on a topic which has been scarcely addressed in the published literature concerning SPH. Although the application of AxisSPH to the simulation of real problems is restricted to those systems which display the appropriate symmetry there are, however, many interesting examples of physical systems which evolve following the axisymmetric premise. These examples belong to a variety of scientific and technological areas such as, for example, astrophysics, laboratory astrophysics or inertial confinement fusion. Additionally AxisSPH can be also useful in convergence studies of the standard 3D-SPH technique because the higher resolution achieved in 2D can be used to benchmark the three-dimensional codes. The main improvements implemented in AxisSPH with respect existing axisymmetric SPH formulations are summarized as follows: 1) We have derived simple analytical expressions for correction factors which largely improves the calculation of density and velocity in the vicinity of the z-axis. These expressions and their derivatives were given as a function of an adimensional parameter and do not increase the computational load of the scheme. 2) We have obtained the appropriate expression of the fluid Euler equations containing the new correction functions and their derivatives. Far enough from the singular axis, the scheme reduces to the standard formulation discussed by Brookshaw (2003). 3) A novel expression for the heat conduction term, which has to be added to the energy equation was devised and checked. This new term improves the description of the heat flux for those particles located at the axis neighborhoods. 4) Until now axisymmetric SPH hydrocodes handle artificial viscosity using a crude approach because it was treated as a simple restriction of the standard 3D Cartesian viscosity to 2D. Here we propose to calculate the viscous pressure as a combination of two terms, the first one is the (standard) Cartesian part and the second is the axis-converging part of the viscosity respectively. As expected this last term is of special relevance to simulate implosions. 5) We have developed an original method to incorporate gravity into AxisSPH. First the direct ring to ring force was found as a function of the Euclidean distance between the 2D particles. In second place the gravitational force on a given particle was obtained by summing the contributions of all N particles. We have also developed a more efficient scheme to obtain the gravitational force calculating the potential of the ring, instead the force because it involves lesser algebraic operations. The scheme has been checked using a large number of tests cases. These tests range from very specific oriented to check a particular algorithm or a piece of physics, to rather complex ones intended to analyze the behavior of the scheme in potential real applications (ICF, jets, astrophysics). At least in one case, the head on collision of a pair of white dwarfs, the result of the simulations carried out using AxisSPH brings new, unpublished, scientific material. / En esta tesis se ha desarrollado un código, que hemos llamado AxisSPH, en dos dimensiones axisimétrico a partir de la técnica conocida como SPH (“smooothed particle hydrodynamics”). AxisSPH ha sido validado después de realizar una serie de tests básicos y algunas simulaciones de situaciones reales. El objetivo principal de este trabajo ha sido llenar, en parte, el vacío existente al respecto en la literatura sobre SPH. Aunque sólo se puede aplicar AxisSPH en problemas reales que presenten la apropiada simetría, existen muchos ejemplos interesantes de sistemas físicos que presentan la simetría axial demandada. Existen ejemplos en campos de aplicación tanto científica como tecnológica, por ejemplo en astrofísica, en el llamado laboratorio de astrofísica o en fusión por confinamiento inercial (ICF). Otra interesante aplicación de AxisSPH puede ser su utilización en estudios de convergencia con otros códigos 3D-SPH debido a su mayor resolución, al tratarse de un código 2D. Las mejoras implementadas en el código AxisSPH en comparación con otros códigos axisimétricos SPH existentes se pueden resumir en los siguientes puntos: 1) Hemos deducido expresiones analíticas simples para unos factores de corrección que mejoran el cálculo de la densidad y la velocidad en las proximidades del eje z. Dichas expresiones y sus derivadas dependen de un parámetro adimensional que no incrementa mucho el peso computacional del esquema propuesto. 2) Hemos obtenido las expresiones adecuadas de las ecuaciones de Euler que contienen estas nuevas funciones correctoras y sus derivadas. Lejos del eje de singularidad estas ecuaciones se transforman en las de la formulación estándar propuesta por Brookshaw (2003). 3) Una expresión novedosa del término de conducción, que debe de añadirse a la ecuación de la energía, se ha propuesto y validado. Este nuevo término mejora la evolución del flujo de calor de las partículas situadas en las proximidades del eje z. 4) Hasta el momento los códigos hidrodinámicos SPH axisimétricos existentes trabajaban con una aproximación poco elaborada de la viscosidad artificial ya que consistían en una restricción a dos dimensiones de la viscosidad estándar 3D. En este trabajo proponemos el cálculo de la presión debida a la viscosidad como combinación de dos términos, el primero reflejo de la parte cartesiana y la segunda da cuenta de la parte relacionada con la convergencia en el eje. Como era de esperar este último término es de relevante importancia en la simulación de implosiones. 5) Hemos desarrollado un método original para incorporar el cálculo de la gravedad en el código AxisSPH. En primer lugar la fuerza directa de anillo a anillo y en segundo lugar la fuerza de la gravedad que sufre una determinada partícula a partir de la contribución del resto de las N partículas existentes. También hemos desarrollado un esquema más eficiente para calcular la gravedad a partir del cálculo del potencial del anillo en lugar del cálculo directo de la fuerza ya que implica un menor número de operaciones algebraicas. El método ha sido verificado con un gran número de test numéricos. Desde los más específicos orientados a comprobar la validez de un algoritmo particular o la capacidad para simular un fenómeno físico en particular, hasta simulaciones bastante más complejas, con la intención de validar la capacidad de simular aplicaciones potencialmente más reales (ICF, jets, astrofísica). Así, en al menos un caso, en la colisión frontal de dos enanas blancas, los resultados de la simulación utilizando AxisSPH pueden aportar material científico publicable.

Zugl.: Freiburg (Breisgau), Univ., Diss., 2009

Due to its adaptable nature in a broad range of problem domains, Smoothed Particle Hydrodynamics (SPH) is a popular numerical technique for computing solutions in astrophysics. This dissertation discusses the SPH technique and assesses its capabilities for reproducing steady-state spherically-symmetric accretion flow. The accretion scenario is of great interest for its applicability in a diverse array of astrophysical phenomena and, under certain assumptions, it also provides an accepted analytical solution against which the numerical method can be validated. After deriving the necessary equations from astrophysical fluid dynamics, giving a detailed review of solving the steady-state spherical accretion problem, and developing the SPH methodology, this work suggests solutions to the issues that must be overcome in order to successfully employ the SPH methodology to reproduce steady-state spherical accretion flow. Several techniques for setting initial data are addressed, resolution requirements are illustrated, inner and outer boundary conditions are discussed, and artificial dissipation parameters and methodologies are explored. / text

Currently, the accurate prediction of the impact of an extreme wave on infrastructure located near shore is difficult to assess. There is a lack of established methods to accurately quantify these impacts. Extreme waves, such as tsunamis generate, through breaking, extremely powerful hydraulic bores that impact and significantly damage coastal structures and buildings located close to the shoreline. The damage induced by such hydraulic bores is often due to structural failure. Examples of devastating coastal disasters are the 2004 Indian Ocean Tsunami, 2005 Hurricane Katrina and most recently, the 2011 Tohoku Japan Tsunami. As a result, more advanced research is needed to estimate the magnitude of forces exerted on structures by such bores. This research presents results of a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method which is used to simulate the impact of extreme hydrodynamic forces on shore protection walls. Typically, fluids are modeled numerically based on a Lagrangian approach, an Eulerian approach or a combination of the two. Many of the common problems that arise from using more traditional techniques can be avoided through the use of SPH-based models. Such challenges include the model computational efficiency in terms of complexity of implementation. The SPH method allows water particles to be individually modeled, each with their own characteristics, which then accurately depicts the behavior and properties of the flow field. An open source code, known as SPHysics, was used to run the simulations presented in this thesis. Several cases analysed consist of hydraulic bores impacting a flat vertical wall as well as a sloping seawall. The analysis includes comparisons of the numerical results with published experimental data. The model is shown to accurately reproduce the formation of solitary waves as well as their propagation and breaking. The impacting bore profiles as well as the resulting pressures are also efficiently simulated using the model.

This thesis investigates tsunami impact on shore-based, low-rise structures in coastal areas. The aims are to investigate tsunami wave inundation in built-up coastal areas with reference to structural response to wave inundation, to assess the performance of current design codes in comparison with validated state-of-the-art numerical models and to improve structural design of residential buildings in tsunami risk areas. Tsunami events over the past few decades have shown that a significant proportion of fatalities can be attributed to the collapse of building infrastructure due to various actions of the incident waves. Although major tsunami events have demonstrated the potential catastrophic effects on built infrastructure, current building codes have no detailed or consistent guidance on designing structures in tsunami-prone regions. Furthermore, considerable differences in existing empirical formulae highlight that new research is necessary to appropriately address the particularities of the tsunami-induced forces and structure response into the design standards. In this thesis, numerical modelling methods are used to simulate hydrodynamic impact on shore-based coastal structures. The hydrodynamic simulations were conducted using a novel meshless numerical method, smoothed particle hydrodynamics (SPH), which is coupled with the finite element (FE) method to model structural behaviour. The SPH method was validated with experimental data for bore impact on an obstacle using a convergence study to identify the optimum particle size to capture the hydrodynamics. The FE model was validated against experimental data for plates under transient blast loads which have similar load characteristics with impulsive tsunami-induced bore impacts. One of the contributions of the thesis is the use of a new coupling method of the SPH-based software DualSPHysics and FE-based software ABAQUS. Using SPH particle spacing of the same size as the FE mesh size, enables the SPH output pressure to be directly applied as an input to the structural response model. Using this approach the effects of arrangement and orientation of single and multiple low rise structures are explored. Test cases were performed in 2-D and 3-D involving a discrete structure and multiple structures. The 3-D SPH simulations with single and multiple structures used an idealised coastal structure in the form of a cube with different on-plan orientations (0°, 30°, 45° and 60°) relative to the oncoming bore direction. The single structure cases were intended to study the improvement of the resilience of coastal structures by reducing the acting pressures on the vertical surfaces by changing the structure’s orientation. It was found the pressure exerted on the vertical surface of structure can be reduced by up to 50% with the 60° orientation case. The multiple structure models were conducted to examine shielding and flow focusing phenomena in tsunami events. The results reveal that the distance between two adjacent front structures can greatly influence the pressure exerted on the rear structure. This thesis also demonstrates the capability of SPH numerical method in simulating standard coastal engineering problems such as storm waves impact on a recurve wall in 2-D. The idealised structures were represented as standard timber construction and the finite element modelling was used to determine the corresponding stress distributions under tsunami impact. Following the comparison of the method used in this thesis with commonly used design equations based on the quasi-static approach, large differences in stress prediction were observed. In some cases the loads according to the design equations predicted maximum stresses almost one order of magnitude lower. This large discrepancy clearly shows the potential for non-conservative design by quasi-static approaches. The new model for the simulation of tsunami impact on discrete and multiple structures shows that the resilience of a coastal structure can be improved by changing the orientation and arrangement. The characteristics of tsunami waves during propagation and bore impact pressures on structures can be assessed in great detail with the combined SPH and FE modelling strategy. The techniques outlined in this thesis will enable engineers to gain a better insight into tsunami wave-structure interaction with a view towards resilience optimisation of structures vulnerable to tsunami impact events.

Context. Simulating realistic fluid behavior in incompressible fluids for computer graphics has been pioneered with the implicit incompressible smoothed particle hydrodynamics (IISPH) solver. The algorithm converges faster than other incompressible SPH-solvers, but real-time performance (in the perspective of video games, 30 frames per second) is still an issue when the particle count increases. Objectives. This thesis aims at improving the performance of the IISPH-solver by proposing a parallel solution that runs on the GPU using CUDA. The solution should not compromise the physical accuracy of the original solution. Investigated aspects are execution time, memory usage and physical accuracy. Methods. The proposed implementation uses a fine-grained approach where each particle is calculated on a separate thread. It is compared to a sequential and a parallel OpenMP implementation running on the CPU. Results and Conclusions. It is shown that the parallel CUDA solution allow for real-time performance for approximately 19 times the amount of particles than that of the sequential implementation. For approximately 175 000 particles the simulation runs at the constraint of real-time performance, more particles are still considered interactive. The visual result of the proposed implementation deviated slightly from the ones on the CPU.

The expansion ratio (defined as the ratio of the expanded thickness to the original thickness) of intumescent coatings is the most important quantity that determines their fire protection performance. This thesis explores two possible methods of predicting intumescent coating expansion: an analytical method, and a detailed numerical simulation method using Smoothed Particle Hydrodynamics (SPH).The analytical method is based on a cell-model and predicts bubble growth due to pressure increase in viscous liquid with constant viscosity. It has been extended to non-uniform temperature field and temperature-dependent viscosity of intumescent melt. Accuracy of this extended analytical method is assessed by comparison against the cone calorimeter and furnace fire tests on intumescent coating protected steel plates with different intumescent coating thicknesses, steel plate thicknesses, and heating conditions. The extended analytical method is then used to investigate how intumescent coating expansion and intumescent coating effective thermal conductivity are affected by changing the coating thickness, the steel thickness and the fire condition (including smouldering fire). The main conclusion is that the expansion ratio decreases as the rate of heating increases. Therefore, the intumescent coating properties obtained from the Standard fire exposure may be safely used for slower realistic fires, but would produce unsafe results for faster fires. The second method explores the potential of a meshless numerical simulation: Smoothed Particle Hydrodynamics (SPH). SPH modelling of intumescent coating expansion has been implemented using the SPHysics FORTRAN open-source code as a platform. To check the validity of this modelling method, the modelling results are compared against theoretical solutions for surface tension (Young-Laplace theorem), and available numerical and analytical solutions for bubble expansion. A new algorithm for representing the mass transfer of gas into the bubble using SPH particle insertion and particle shifting scheme is presented to simulate the bubble expansion process. Close agreement with an analytical solution for the initial bubble expansion rate computed by SPH is obtained. Whilst this research has demonstrated the potential of using SPH to numerically simulate intumescent coating expansion, it has also revealed significant challenges that should be overcome to make SPH a feasible method to simulate intumescent coating expansion. The main challenges include:• Simulating gas-polymer flows when expansion is occurring where there are vastly different properties of these two fluids with a density ratio of about 1000. This high density ratio may easily cause numerical pressure noise, especially at the liquid-gas interface.• Extremely high computational cost necessary to achieve sufficient accuracy by using a large number of particles (higher resolution), especially for the multi-phase SPH program, and very small time step for the lighter fluid (air). • The behaviour of intumescent coatings involves expansion ratios on the order of 10-100 with thousands of bubbles which grow, merge and burst. Based on the results of this exploratory research, future improvements are outlined to further develop the SPH simulation method.

[pt] Estruturas submarinas utilizadas nos sistemas de produção de óleo e gás offshore são normalmente projetadas para permanecerem no leito marinho por décadas. Para a grande maioria dessas estruturas a instalação é uma etapa crítica que pode requerer recursos dispendiosos e significativos esforços de engenharia. A descida de estruturas submarinas em regiões de ondas marinhas é uma operação complexa, uma vez que envolve acelerações desses corpos induzidas pelos movimentos das embarcações que, associados com os deslocamentos da superfície do mar, podem levar a significativas cargas de impacto nessas estruturas durante a entrada na água. O estágio inicial do impacto durante a entrada na água tem sido tema de muita pesquisa no último século, desde os trabalhos pioneiros de von Kármán e Wagner sobre a hidrodinâmica do pouso de hidroaviões. O cenário do impacto da proa de navios na superfície do mar também tem sido objeto de estudo, uma vez que pode levar a danos localizados ou mesmo catastróficos ao casco. Diferentes métodos numéricos têm sido aplicados para análise desse problema. A principal contribuição desse trabalho é a utilização do método numérico Smoothed Particle Hydrodynamics (SPH) para estimar as cargas de slamming em corpos rígidos durante a entrada na água considerando superfícies em repouso e sob o efeito de ondas. Inicialmente é introduzida a fundamentação teórica básica sobre o impacto hidrodinâmico, seguida da descrição do método SPH. Aplicações do SPH para simular a entrada na água de corpos rígidos são apresentadas considerando casos em queda livre e com velocidade constante e os resultados são comparados com experimentos e simulações numéricas obtidos na literatura. A presença de ondas regulares durante a entrada na água com velocidade constante também é considerada. Os resultados numéricos obtidos neste trabalho demonstram a viabilidade da abordagem proposta para estimar as cargas de slamming em estruturas submarinas durante a entrada na água. / [en] Subsea structures employed on offshore oil and gas production systems are commonly designed to be laid on seafloor for decades. For most of these structures the installation is a critical stage and may require costly resources and significant engineering effort. Lowering subsea structures through the wave zone is a complex operation as it involves accelerations of these bodies induced by the vessel motion which, associated to the sea surface displacements, may lead to significant impact loads on these structures during water entry. The initial stage of impact during water entry has been a subject of many researches over the past century since the pioneering work of von Kármán and Wagner on the hydrodynamics of an alighting sea plane. The scenario of impact of the forebody of a ship on the sea surface has also been subject of studies, as it may cause localized and eventually catastrophic damage to the hull. Different numerical methods have been applied to the analysis of this problem. The main contribution of this work is the use of the Smoothed Particle Hydrodynamics (SPH) method to estimate slamming loads on rigid bodies during water entry considering both calm and wavy surfaces. A basic theoretical background on hydrodynamic impact load is firstly introduced, followed by the description of the SPH method. Applications of SPH to simulate water entry of rigid bodies considering both free fall and constant velocity cases are presented and results are compared with experiments and numerical simulations from the literature. The presence of regular waves during constant velocity water entry is also considered. The numerical results obtained here demonstrate the effectiveness of the proposed approach to estimate slamming loads on subsea structures during water entry.

This thesis investigates turbulent wall-bounded flows using the Smoothed Particle Hydrodynamics (SPH) method. The first part focuses on the SPH method itself in the context of the Navier-Stokes equations with a special emphasis on wall boundary conditions. After discussing classical wall boundary conditions a detailed introduction to unified semi-analytical wall boundary conditions is given where the key parameter is a renormalization factor that accounts for the truncated kernel support in wall-bounded flows. In the following chapter it is shown that these boundary conditions fulfill energy conservation only approximately. This leads to numerical noise which, interpreted as form of Brownian motion, is treated using an additional volume diffusion term in the continuity equation where it is shown to be equivalent to an approximate Riemann solver. Two extensions to the boundary conditions are presented dealing with variable driving forces and a generalization to Robin type and arbitrary-order interpolation. Two modifications for freesurface flows are then presented, one for the volume diffusion term and the other for the algorithm that imposes Robin boundary conditions. The variable driving force is validated using a Poiseuille flow and the results indicate an error which is five orders of magnitude smaller than with the previous formulation. Discretising the wave equation with Robin boundary conditions proves that these are correctly imposed and that increasing the order of the interpolation decreases the error. The two modifications for flows under the influence of external forces significantly reduce the error at the free-surface. Finally, a dam break over a wedge demonstrates the capabilities of all the proposed modifications. With the aim of simulating turbulent flows in channels, the thesis moves on to extending the unified semi-analytical wall-boundary conditions to three dimensions. The thesis first presents the consistent computation of the vertex particle mass. Then, the computation of the kernel renormalization factor is considered, which in 3-D consists of solving an integral over a two dimensional manifold where the smoothing kernel intersects the boundary. Using a domain decomposition algorithm special integration areas are obtained for which this integral can be solved for the 5 th -order Wendland kernel. This algorithm is successfully applied to several validation cases including a dam break with an obstacle which show a significant improvement compared to other approximative methods and boundary conditions. The second part of this thesis investigates turbulent flows, in particular turbulent channel flow. This test case is introduced in detail showing both the physical properties as well as established numerical methods such as direct numerical simulation (DNS) and large eddy simulation (LES). In the penultimate chapter several SPH simulations of the turbulent channel flow are shown. The first section deals with a quasi DNS of the minimal-flow unit, a channel flow with a minimal domain size to sustain turbulent flow structures. The Eulerian statistics are compared to literature and show good agreement except for some wall-normal quantities. Furthermore, preliminary Lagrangian statistics are shown and compared to results obtained from a mesh-based DNS. The final simulation shows a LES of a full-sized channel at Reynolds number Re τ = 1000. The Eulerian statistics are compared to literature and the discrepancies found are explained using simulations of the Taylor-Green vortex, indicating that the momentum is not transferred appropriately due to an unresolved velocity-pressure-gradient tensor.

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.