An incompressible Smoothed Particle Hydrodynamics (SPH) method is put forward to simulate non-linear and dispersive solitary wave reflection and transmission characteristics after interacting with a partially immersed curtain-type breakwater. The Naviers¿Stokes equations in Lagrangian form are solved using a two-step split method. The method first integrates the velocity field in time without enforcing incompressibility. Then the resulting deviation of particle density is projected into a divergence-free space to satisfy incompressibility by solving a pressure Poisson equation. Basic SPH formulations are employed for the discretization of relevant gradient and divergence operators in the governing equations. The curtainwall and horizontal bottom are also numerically treated by fixed wall particles and the free surface of wave is tracked by particles with a lower density as compared with inner particles. The proposed SPH model is first verified by the test of a solitary wave with different amplitudes running against a vertical wall without opening underneath. Then it is applied to simulate solitary wave interacting with a partially immersed curtain wall with different immersion depths. The characteristics ofwave reflection, transmission, dissipation and impacting forces on the curtain breakwater are discussed based on computational results

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Yes / This research paper presents an incompressible smoothed particle hydrodynamics (ISPH) technique to investigate a regular wave overtopping on the coastal structure of different types. The SPH method is a mesh-free particle modeling approach that can efficiently treat the large deformation of free surface. The incompressible SPH approach employs a true hydrodynamic formulation to solve the fluid pressure that has less pressure fluctuations. The generation of flow turbulence during the wave breaking and overtopping is modeled by a subparticle scale (SPS) turbulence model. Here the ISPH model is used to investigate the wave overtopping over a coastal structure with and without the porous material. The computations disclosed the features of flow velocity, turbulence, and pressure distributions for different structure types and indicated that the existence of a layer of porous material can effectively reduce the wave impact pressure and overtopping rate. The proposed numerical model is expected to provide a promising practical tool to investigate the complicated wave-structure interactions. / Nazarbayev University Seed Grant, entitled “Environmental assessment of sediment pollution impact on hydropower plants”. S. Shao also acknowledges the Royal Society Research Grant (2008/R2 RG080561)

This work presents a partitioned approach to simulating free-surface flow interaction with hyper-elastic structures in which a smoothed particle hydrodynamics (SPH) solver is coupled with a finite-element (FEM) solver. SPH is a mesh-free, Lagrangian numerical technique frequently employed to study physical phenomena involving large deformations, such as fragmentation or breaking waves. As a mesh-free Lagrangian method, SPH makes an attractive alternative to traditional grid-based methods for modeling free-surface flows and/or problems with rapid deformations where frequent re-meshing and additional free-surface tracking algorithms are non-trivial. This work continues and extends the earlier coupled 2D SPH-FEM approach of Yang et al. [1,2] by linking a double-precision GPU implementation of a 3D weakly compressible SPH formulation [3] with the open source finite element software Code_Aster [4]. Using this approach, the fluid domain is evolved on the GPU, while the CPU updates the structural domain. Finally, the partitioned solutions are coupled using a traditional staggered algorithm. / Ph. D.

L'étude porte sur l'impact de vagues sur une paroi rigide en deux dimensions. Les travaux de modélisation numérique ont été réalisés à partir du code JOSEPHINE, utilisant la méthode Smoothed Particle Hydrodynamics (SPH), développé au sein du laboratoire LOMC. La méthode choisie repose sur une approximation faiblement compressible des équations d'Euler. Dans un premier temps, l'étude d'un cas académique de l'impact d'un jet triangulaire a permis de valider et améliorer le schéma numérique permettant la modélisation d'impacts violents. Les pressions d'impacts ont été étudiées et comparées à d'autres résultats analytiques et numériques. Dans un second temps, l'impact d'une vague solitaire déferlante a été modélisé. Les pressions d'impact ont été déterminées et comparées avec celles issues d'expériences. Après une analyse numérique approfondie des simulations mono-phasiques, un modèle diphasique a été spécifiquement développé pour tenir compte à la fois des phases eau et air. Le modèle SPH diphasique a permis d'améliorer la qualité des résultats, notamment pour le cas « air pocket impact », où une poche d'air est emprisonnée lors de l'impact. Le but final de ce travail est d'étudier la survivabilité des récupérateurs d'énergie marine adossés à des structures côtières lors d'événements météorologiques violents. / The present manuscript focuses on the wave impact on a rigid wall in two dimensions. The numerical computations were performed using a Smoothed Particle Hydrodynamics (SPH) software named JOSEPHINE, developed at the LOMC laboratory. The software is based on a weakly-compressible SPH model, where Euler equation of motion is solved. Firstly, an academic test case, the impact of a triangular jet was used to validate and improve the numerical scheme to model violent impacts.The impact pressures were studied and compared to analytical and other numerical results. Secondly, the impact of a breaking solitary wave was modelled.The impact pressures were determined and compared with those obtained in the experiments. After a depth numerical analysis of mono-phase flow computations, a two-phase model was developed specifically to consider both water and air phases. The two-phase SPH model improved the results quality, especially for the case "air pocket impact", where an air pocket is trapped during the impact. The ultimate goal of this work is to study the survivability of coastal structures equipped with a marine energy recovery device during severe weather events.

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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.

This thesis deals with the optimal control of PDEs. After a brief introduction in the theory of elliptic and parabolic PDEs, we introduce a software that solves systems of PDEs by the finite elements method. In the second chapter we derive optimality conditions in terms of function spaces, i.e. a systems of PDEs coupled by some pointwise relations. Now we present algorithms to solve the optimality systems numerically and present some numerical test cases. A further chapter deals with the so called lack of adjointness, an issue of gradient methods applied on parabolic optimal control problems. However, since optimal control problems lead to large numerical schemes, model reduction becomes popular. We analyze the proper orthogonal decomposition method and apply it to our model problems. Finally, we apply all considered techniques to a real world problem.

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