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Akinci, Gizem [Verfasser], and Matthias [Akademischer Betreuer] Teschner. "Efficient surface reconstruction for SPH fluids = Effiziente Oberflächenrekonstruktion für SPH Flüssigkeiten." Freiburg : Universität, 2014. http://d-nb.info/1114829315/34.
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JESUS, E. M. "Operadores SPH sobre variedades." Universidade Federal do Espírito Santo, 2017. http://repositorio.ufes.br/handle/10/7408.
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Previous issue date: 2017-02-20Este projeto propõe uma extensão do método SPH (Smoothed Particle Hydrodynamics) [1] para variedade diferenciáveis. Inicialmente desenvolvido no Rn, o método SPH baseia-se no conceito de representação integral que não é estendido de forma natural para variedade. No entanto, este conceito pode ser aplicado ao espaço tangente da variedade. Sendo assim, impondo algumas condições a variedade, o método SPH poderá ser aplicado à pontos projetados no espaço tangente de cada partícula [2]. Esta abordagem resulta numa boa aproximação para os operadores diferenciais sobre a variedade, sendo assim considerada uma generalização consistente do método. Estes operadores generalizados serão utilizados na Decomposição de Helmhotz-Hodge e análise de campos vetoriais [3], simulação de fluidos incompressíveis, resolução de equações clássicas como a equação da onda, equação do calor, dentre outras, sobre variedades. Bibliografia: 1) Liu, Gui-Rong e Liu, M.B. "Smoothed Particle Hydrodynamics: A Meshfree Particle Method". World Scientific, 2003 2) Petronetto, Fabiano, et al. "Mesh-Free Discrete Laplace-Beltrami Operator". Computer Graphics Forum, 2013. 3) Petronetto, Fabiano, et al. "Meshless helmholtz-hodge decomposition". IEEE transactions on visualization and computer graphics, 2010. 4) Mercier, Olivier, et. al. "Surface turbulence for particle-based liquid simulations". ACM Transactions on Graphics (TOG), 2015.
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SILVA, César Leonardo Barbosa da. "Condições de contorno em SPH." Universidade Federal de Pernambuco, 2017. https://repositorio.ufpe.br/handle/123456789/23924.
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CAPES
Nesta dissertação será apresentado o método SPH - Smoothed Particle Hydrodynamics, - em português, Hidrodinâmica da Partícula Suavizada, um método sem malhas baseado em distribuições de partículas. O método foi inicialmente desenvolvido, em 1988, para simulações de sistemas astronômicos, onde as grandezas envolvidas sofrem variações bruscas e e grandes. Seus criadores desejavam um método que fosse fácil de se trabalhar e que, em contrapartida, fornecesse uma precisão coerente. O SPH é muito utilizado em aplicações em sistemas fluidos ou granulares, mas nada impede, e muito tem sido feito, de se aplicar a sistemas sólidos e de alta viscosidade. O SPH, em comparação com, por exemplo, Método do Elemento Finito, apresenta a grande vantagem de não sofrer com as grandes deformaç oes, em virtude de sua natureza particular. Neste trabalho estabeleceremos os fundamentos matemáticos que são a essência método. Serão exibidas algumas de suas aplicações e discutidas as principais condições de contorno utilizadas pelos pesquisadores da área, bem como proposta uma condição funcional que será simulada. Por fim, os resultados serão comparados com alguns outros trabalhos desenvolvidos por outros pesquisadores na área.
The SPH- Smoothed Particle Hydrodynamics-, in portuguese, Hidrodinâmica da Partícula Suavizada, will be presented. It is a meshless method based on particles distributions. The method was initially developed in 1988 for simulations of astronomical systems, where the quantities involved suffer abrupt and large variations. Its creators wanted a method that was easy to work with and, on the counterpart, would give a coherent precision. The SPH is mainly applied to fluid or granular systems but can be applied to solid or high viscous systems. The SPH method in comparison, for example, to Finite Element Method, shows a great advantage once do not have the problem when treating large deformations, in virtue of his particular nature. In this dissertation will be presented the mathematical foundations that are the essence of the method. It will be exhibited some of their applications and some of the major boundary conditions used by the researchers in the subject. It will be also proposed a functional condition to be simulated. Finely, the results will be compared to some other simulations developed by researchers in this area.
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Escartín, Vigo José Antonio. "ISFAA : Implicit SPH for astrophysical apllications." Doctoral thesis, Universitat Politècnica de Catalunya, 2016. http://hdl.handle.net/10803/384002.
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Computational simulation is one of the basic techniques of modern Astrophysics. The long-term time astrophysical processes cannot be treated with explicit approaches because that they are limited, in their maximum time step, by the restriction known as Courant-Friedrichs-Lewy Condition.
In order to use implicit approaches a system of coupled algebraic equations needs to be solved. It is composed by all the equations of each one of the discrete points of the model and the usual solution comes through a Newton-Raphson scheme. The computational cost substantially increases with the number of unknowns of the model. In implicit schemes the properties of the current time step depends on the values of the unknown variables at that time step, so everything has to be calculated simultaneously. The consequence is that all equations should be jointly solved inverting of a huge sparse matrix (it is a squared n*v matrix, being n the number of particles and v the number of independent variables of the system). Due to this restriction, historically the implicit hydrodynamics had been only applied to one-dimensional systems.
It would be very interesting to build an Implicit hydrocode taking advantage of the so called Smoothed Particle Hydrodynamics or SPH. This technique has been being applied successfully in astrophysics and cosmology and fluid physics. SPH integrates the dynamic fluid equations in each point of the Lagragian formalism (named particles because they have an associated mass) calculating speed, position, density and pressure as interpolations from neighbour particles. Unlike Eulerian methods the Lagragian approach does not need from a rectangular grid covering the integration domain. Therefore storage and computing time is not wasted in void regions. Fluids are decomposed in a set of particles where the numerical treatment of the three-dimensional movement derived from pressure and auto-gravity is easier.
The goal of this thesis is to describe the main features and the implementation of a new SPH code which uses implicit approach, called ISFAA (Implicit SPH for Astrophysical Applications). This code enlarges the previous work from "An Implicit Smooth Particle hydrodynamic Code", Knapp C. (2000) and recent developments of the SPH scheme (based on the variation principle), artificial viscosity, gravity and thermal conductivity.
Because of the huge effort which has to be invested to build and validate the new SPH code, it is pretended that in the future its use can be extended to a large number of scenarios. With this end a modular design has been implemented that allows to separate the code general treatment, the particular implementation of the basic evolutionary equations and the physical properties (equation of state, artificial viscosity, etc.). Furthermore, to find the solution of the equations' system, the library of parallel algorithms PARDISO, embodied in the library Intel MKL, has been used. Future improvements in these libraries will have a positive impact on the new code.
To validate the code and check each one of the physical ingredients, a set of basic tests (point-like explosion, The wall heating shock, Rayleigh-Taylor instabilities, Free-Fall collapse, etc) were run and analyzed as well as several tests incorporating gravity (Toy Star, stability of a solar mass star and a White Dwarf).
And finally, we show the evolution of a single quasi-static system. To handle with these scenarios we have built a slightly different implicit scheme, were velocities are not explicitly included in the equations of movement. The main aim of this tests is to demonstrate that an implicit quasi-hydrostatic scheme is able to work with time-steps many orders of magnitude large (10^4) than the characteristic current Courant time.La simulación mediante ordenador es una de las herramientas básicas de la Astrofísica moderna. Los procesos de gran escala temporal son imposibles de tratar con enfoques explícitos ya que estos se encuentran limitados, en su paso de tiempo máximo, por la restricción conocida como condición de Courant-Friedrichs-Lewy. Para utilizar los enfoques implícitos se genera un sistema de ecuaciones algebraicas acopladas, habitualmente resuelto con un esquema de Newton-Raphson y compuesto por todas las ecuaciones de cada uno de los puntos de resolución del modelo. El coste computacional de resolución aumenta sustancialmente con el número de incógnitas que han de determinarse a cada paso de tiempo. Las propiedades del siguiente paso de tiempo dependen de los valores de las variables desconocidas en dicho paso de tiempo y por tanto todas han de ser calculadas simultáneamente. La consecuencia es que todo el sistema de ecuaciones se ha de resolver conjuntamente realizando la inversión de una matriz dispersa enorme (la matriz es cuadrada y tiene un tamaño de n*v, siendo n el numero de partículas y v el número de variables independientes del sistema). Debido a esta restricción, la hidrodinámica implícita históricamente ha sido aplicada a sistemas en una sola dimensión. Para su implementación multidimensional sería interesante utilizar un enfoque lagrangiano como el suavizado de partículas hidrodinámicas denominado "Smooth Particle Hydrodynamics" ó SPH. La técnica se viene aplicando con éxito al campo de la astrofísica, la cosmología y diferentes problemas de la física de fluidos. El SPH integra las ecuaciones de la dinámica de fluidos en cada punto del formalismo lagrangiano (denominado partícula por tener una masa asociada) calculando velocidad, posición, densidad y presión como una interpolación de los valores de las partículas vecinas. Los métodos lagrangianos, a diferencia de los eulerianos, no necesitan de una malla regular que cubra la totalidad del espacio de integración, por tanto, la memoria y el tiempo de cálculo no se desperdician en la resolución de espacios vacíos. Los fluidos se descomponen en un conjunto de partículas donde podemos tratar numéricamente de forma más sencilla el movimiento en tres dimensiones derivado de las fuerzas de presión y auto-gravedad. El objetivo de esta tesis es detallar las principales características y la implementación de un nuevo código SPH, con un enfoque implícito, al que hemos denominado ISFAA (Implicit SPH for Astrophysical Applications). Este código amplia el trabajo previo de Knapp. C., 2000 e incluye el esquema físico más actual del SPH (basado en el principio variacional), viscosidad artificial, gravedad y conductividad térmica. Dado el enorme esfuerzo que supone construir y validar un nuevo código SPH, se pretende que en el futuro su utilidad se extienda al mayor número posible de escenarios. Con este fin se ha optado por un diseño modular que separe el tratamiento general del código de la implementación concreta de ecuaciones evolutivas básicas y de las propiedades del material (ecuación de estado, viscosidad artificial, etc.). Además, para la resolución del sistema de ecuaciones se utiliza la biblioteca de algoritmos paralelos PARDISO, que incorpora la librería Intel MKL y que en el futuro tendrá mejoras que impactarán positivamente en el código. Para comprobar la corrección del código y probar cada uno de los ingredientes físicos, se especifican una serie de test básicos (Explosión puntual, The wall heating shock, inestabilidades de Rayleigh-Taylor, caída libre, etc.) y una serie de test con gravedad (Toy Star, estabilización de una estrella de masa solar y una enana blanca). Por último se muestra la evolución de un sistema cuasiestático, en el que las velocidades no se encuentran explícitamente en el modelo. Este test está orientado a demostrar que el código implícito podría aplicarse con éxito en estas situaciones, consiguiendo simular el sistema en largos intervalos temporales.
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Schindler, Benjamin. "Visualization of vortices in SPH data." Zurich : ETH, Eidgenössische Technische Hochschule Zürich, Department of Computer Science, Computer Graphics Laboratory, 2009. http://e-collection.ethbib.ethz.ch/show?type=dipl&nr=460.
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Chow, Alex. "Incompressible SPH (ISPH) on the GPU." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/incompressible-sph-isph-on-the-gpu(b569f890-78f1-42c2-b9d4-7082b45f45c8).html.
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Incompressible free-surface flows involving highly complex and violent phenomena are of great importance to the engineering industry. Applications such as breaking-wave impacts, fluid-structure interaction, and sloshing tanks demand an accurate and noise-free pressure field, and require large-scale simulations involving millions of computation points. This thesis addresses the need with the novel use of a graphics processing unit (GPU) to accelerate the incompressible smoothed particle hydrodynamics (ISPH) method for highly non-linear and violent free-surface flows using millions of particles in three dimensions. Compared to other simulation techniques, ISPH is robust in predicting a highly accurate pressure field, through the solution of a pressure Poisson equation (PPE), whilst capturing the complex behaviour of violent free-surface flows. However, for large-scale engineering applications the solution of extremely large PPE matrix systems on a GPU presents multiple challenges: constructing a PPE matrix every time step on the GPU for moving particles, overcoming the GPU memory limitations, establishing a robust and accurate ISPH solid boundary condition suitable for parallel processing on the GPU, and exploiting fast linear algebra GPU libraries. A new GPU-accelerated ISPH algorithm is presented by converting the highly optimised weakly-compressible SPH (WCSPH) code DualSPHysics and combining it with the open-source ViennaCL linear algebra library for fast solutions of the ISPH PPE. The challenges are addressed with new methodologies: a parallel GPU algorithm for population of the PPE matrix, mixed precision storage and computation, and extension of an existing WCSPH boundary treatment for ISPH. Taking advantage of a GPU-based algebraic multigrid preconditioner for solving the PPE matrix required modification for ISPH's Lagrangian particle system. The new GPU-accelerated ISPH solver, Incompressible-DualSPHysics, is validated through a variety of demanding test cases and shown to achieve speed ups of up to 25.3 times and 8.1 times compared to single and 16-threaded CPU computations respectively. The influence of free-surface fragmentation on the PPE matrix solution time with different preconditioners is also investigated. A profiling study shows the new code to concentrate the GPU's processing power on solving the PPE. Finally, a real-engineering 3-D application of breaking focused-wave impacting a surface-piercing cylindrical column is simulated with ISPH for the first time. Extensions to the numerical model are presented to enhance the accuracy of simulating wave-structure impact. Simulations involving over 5 million particles show agreement with experimental data. The runtimes are similar to volume-of-fluid and particle-in-cell solvers running on 8 and 80 processors respectively. The 3-D model enables post-processing analysis of the wave mechanics around the cylinder. This study provides a substantial step for ISPH. Incompressible-DualSPHysics achieves resolutions previously too impractical for a single device allowing for the simulation of many industrial free-surface hydrodynamic applications.
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Penzhorn, Karl. "Consistency and convergence of SPH approximations." Master's thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/12365.
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Includes bibliographical references (leaves 58-59).Includes abstract.
This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each.
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Joshi, Shrey. "Modélisation de l'érosion de cavitation par SPH." Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAI080/document.
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La thèse est organisée autour du développement d'un modèle numérique d’interaction fluide - structure pour simuler la déformation induite dans un matériau solide lors de l’implosion de bulles de cavitation. Le solveur est développé à partir du code open source SPHYSICS_2D utilisant la méthode des Smoothed Particles Hydrodynamics (SPH). Dans cette thèse, le code 2D a été modifié pour traiter le cas de fluides en conditions 2D-axisymétrique. Le solveur solide SPH a été complètement développé en interne en 2D-axisymétrique avec un nouveau schéma pour résoudre les problèmes apparaissant à proximité de l'axe de symétrie. Une loi de comportement élasto-visco-plastique de type Johnson Cook est implémentée dans le solveur solide afin de prendre en compte l’effet de la vitesse de déformation sur l’écrouissage du matériau.Les applications du solveur FSI traitent le cas d’une bulle unique implosant au voisinage d’une surface solide. Deux cas sont envisagés : celui d’une bulle détachée de la surface solide pour laquelle l’effondrement génère une onde de choc ; et celui d’une bulle au contact de la surface pour lequel un micro-jet de liquide vient impacter la surface solide. Pour une taille de bulle donnée, les résultats montrent que le micro-jet peut produire deux fois solide pour laquelle l’effondrement génère une onde de choc ; et celui d’une bulle au contact de la surface pour lequel un micro-jet de liquide vient impacter la surface solide. Pour une taille de bulle donnée, les résultats montrent que le micro-jet peut produire deux fois plus de déformation plastique que l'onde de choc, réduisant ainsi le temps d'incubation. Par contre, le volume de matière déformée plastiquement dans le cas du micro-jet (cavité attachée) est 800 fois plus petit que celui déformé par l’impact d'une onde de choc (cavité détachée). Par conséquent, la capacité d'érosion d'une cavité détachée est beaucoup plus élevée que celle d'une cavité attachée. Un important résultat de cette étude concerne les cavités détachées où il est montré que la déformation plastique ne se produit pas au centre de l'effondrement mais à un décalage par rapport à l’axe de symétrie. Les résultats montrent également que même si la pression subie par le matériau est la plus élevée au niveau de l’axe de symétrie, la déformation plastique ne sera pas maximale à cet endroit mais dans une zone éloignée du centre. Nous Une étude paramétrique est menée pour quantifier les effets de la distance bulle/paroi, de la pression d’effondrement et du rayon de la bulle. Les résultats montrent que l'énergie totale absorbée et le taux d'érosion devraient être plus élevés pour une cavité détachée que pour une cavité attachée. La densité d'énergie absorbée (d'où le temps d'incubation) et l'énergie totale absorbée (d'où le taux d'érosion) augmentent avec la pression d’effondrement. Le changement du rayon de la bulle tout en gardant les autres paramètres constants n'affecte pas beaucoup l'amplitude de la déformation plastique ni la densité d'énergie absorbée, ce qui suggère que quelle que soit la taille de la bulle de cavitation, le temps d'incubation devrait rester similaire. Cependant, comme le volume de la zone déformée plastiquement varie presque linéairement avec la taille de la bulle, l'énergie totale absorbée ou le taux d'érosion augmente significativement avec la taille de la bulle.Dans le passé, les études similaires n'ont jamais pris en compte la sensibilité à la vitesse de déformation dans le modèle de plasticité. Nos simulations montrent que l'ampleur de la déformation plastique est alors surestimée d'environ 60% pour les cavités détachées présentées dans ce document et d'environ 200% pour les cavités attachées. Nous montrons ainsi que de telles études réductrices fondées sur des modèles de plasticité insensibles à la vitesse de déformation conduisent à une sous-estimation du temps d'incubation et à une surestimation du taux d'érosionThe thesis is focused on development of a Smoothed Particle Hydrodynamics (SPH) Fluid-Structure Interaction (FSI) cavitation solver to understand the phenomenon of material deformation under cavitation load better. This summary presents a brief overview of the methodology used to solve a fluid-structure interaction simulation of a bubble collapse over a deformable solid medium. The fluid solver and the solid solver are validated against Rayleigh-Plesset spherical bubble collapse case and FEM solver respectively. The fluid solver is developed using an open source SPH code SPHYSICS_2D, the code is changed from 2D to 2D axisymmetric. The solid SPH solver is developed in-house in 2D axisymmetric, a novel scheme is derived to solve typical issues near symmetry axis in the solid axisymmetric SPH solver. The solid solver has the capability to solve for non-linear isotropic hardening with strain rate effects (commonly known as Johnson-Cook plasticity model).A case each for a detached and an attached cavity is simulated using the FSI solver, the results show that for the same magnitude of pressure wave initiating the collapse and the same size of the bubble, the micro-jet can produce twice the maximum plastic deformation compared to a shock wave, hence a micro-jet dominated impact would exhibit a smaller incubation time compared to the detached cavity. It is also observed that the volume of material that is plastically deformed in case of a micro-jet is miniscule compared to a shock wave impact (almost 800 times smaller). This would imply that even though the incubation time for material erosion might be lower for a micro jet collapse, the shock wave can plastify a much larger volume of material and so the erosion rate should be higher for a shock wave impact. Hence it could be inferred that the material erosion ability of a shock wave is much higher than a micro-jet.An important and novel finding in the present study is the response of the material for a detached cavity where plastic deformation does not occur at the center of collapse but at an offset from the center. The results show that even though the pressure experienced by the material is the highest at the center, it does not produce the maximum plastic deformation. This is for the first time that such a phenomenon is reported in cavitation studies, we find that the phenomenon is linked to inertial effects where the material does not respond to the load as the rate of loading and unloading is extremely high. The effect is linked to the high loading and unloading rate near the center of the collapse due to the flat geometry of the solid medium. The study clearly demonstrate that maximum pressure does not always correspond to the location of maximum plastic deformation or material erosion.Fluid-Structure Interaction simulations for different stand-off ratios, driving pressure and bubble radius have been computed. Results show that for varying stand-off ratio while keeping the bubble radius and driving pressure constant, the attached cavities (SR<=1) show a higher plastic strain magnitude and a higher absorbed energy density which would suggest a quicker incubation time. However, the volume of plastic defamation zone is much lower in attached cavities thus the total absorbed energy and the erosion rate would be higher for a detached cavity compared to an attached one.The strain rate effects suggest that the magnitude of plastic strain is over predicted while using plasticity models that do not use strain rate sensitivity. The over prediction of the magnitude of plastic strain of around 60% for detached cavities presented in the paper and around 200% for attached cavities presented in the paper is observed. This would lead to an under prediction of incubation time and over prediction of erosion rate while using strain rate insensitive plasticity models
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Viau, Serge. "Transfert radiatif numérique pour un code SPH." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ62106.pdf.
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Cullen, Lee. "SPH and its application to stellar disruption." Thesis, University of Leicester, 2010. http://hdl.handle.net/2381/8577.
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In this thesis we study Smoothed Particle Hydrodynamics (SPH) which is a numerical method for simulating fluid flow used widely in astrophysics. In SPH artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks, particularly in poorly resolved flows. In this study we address this problem by refining the method proposed by Morris & Monaghan (1997). The new scheme uses the rate of change of the velocity divergence, Dt(∇•v), to indicate a shock and focuses on eliminating viscosity away from shocks. The new method works as least as well as any previous technique in the strong-shock regime, but becomes virtually inviscid away from shocks. In particular sound waves or oscillations of self-gravitating gas spheres are hardly damped over many periods. We also look at stability issues for SPH, in particular the well known clumping instability. We perform numerical tests of the stability analysis performed by Morris (1996) and find that there are bands of unstable regions as suggested by Read et al. (2010). We also demonstrate that a cored kernel can greatly reduce the clumping instability. Finally we apply the SPH method to extend the stellar disruption work of Lodato et al. (2009) to orbits with a range of pericentre distances. We find that the light curve produced by this disruption is closer to the predicted L ∝ t−5/3 (Rees, 1988) for encounters that are closer to the black hole than the tidal disruption radius. For encounters that are further from the black hole than the tidal disruption radius, the light curve deviates from this predicted power law. We also look at how elliptical orbits can effect the stability of the star. We find that in elliptical orbits a star can be disturbed further from the black hole than in the parabolic case. We then consider the fate of the S2 star and conclude that when it becomes a red giant and expands, S2 will be tidally disrupted.
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BARBOSA, D. A. "Estudo Numérico do Sloshing Utilizando Método SPH." Universidade Federal do Espírito Santo, 2018. http://repositorio.ufes.br/handle/10/9458.
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Previous issue date: 2018-03-02RESUMO A crescente explotação de petróleo offshore e consequente aumento no número de plataformas FPSO e embarcações para o transporte deste fluido exige atenção cada vez maior aos efeitos produzidos pela oscilação da superfície livre em tanques de transporte e armazenamento de petróleo líquido e gás liquefeito. Nesta Tese, um estudo sobre os impactos nas paredes laterais de contêineres retangulares provocados pelo sloshing é proposto. Para esta tarefa recuperamos três testes experimentais realizados por autores distintos dos quais dois simularam em escala reduzida o comportamento de tanques sob a ação de forças horizontais e um terceiro o movimento de arfagem com o tanque sobre uma plataforma do tipo pêndulo invertido. Os dados quantitativos e qualitativos da pressão hidrodinâmica sobre as bordas foram coletadas a partir de transdutores instalados nas paredes dos recipientes. Estes dados foram aproveitados para validar o modelo proposto que reproduziu com boa qualidade o perfil do escoamento, bem como o carregamento hidrodinâmico em todos os cenários. Nosso modelo foi pautado no método lagrangiano de partículas livres (sem malha) conhecido como SMOOTHED PARTICLE HYDRODYNAMISC SPH, que em sua forma genuína para escoamento de fluidos incompressível faz uso da força oriunda do potencial de Lennard-Jones para manter as partículas no interior do domínio. Contribuições ao método também foram realizadas: como a alteração no sistema de busca de partículas vizinhas; propor uma relação entre o número de partículas virtuais e comprimento de suavização; e apontamento para um número ótimo de partículas de contorno. Porém a contribuição de maior relevância foi à criação de uma nova técnica de tratamento do contorno utilizando a FORÇA DE COULOMB, que se mostrou mais robusta do que a técnica clássica. A modelagem matemática passou pelas equações da conservação da massa e conservação de momento linear. Com isso, simulações com diferentes geometrias foram feitas e após a identificação das causas e efeitos produzidos pelo sloshing, mecanismos de supressão foram instalados no interior dos tanques. Os testes seguiram com defletores de duas alturas distintas e com defletores em forma de seta atuando como aletas. Todos os baffles se mostraram eficientes na redução das tensões normais, contudo aqueles na forma de seta se apresentaram superiores aos baffles verticais padrão, indicando que uma morfologia adequada pode reduzir os danos gerados pelo sloshing.
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Buonomo, Umberto. "Tree-SPH code EvoL: profiling and optimization." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422492.
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This thesis is part of a larger project devoted to modeling galaxies via numerical hydrodynamical simulations, from their formation within their cosmological background throughout their evolutionary history.
The thesis has two primary objectives, strictly linked with one another.
The first one, of astrophysical nature, is to develop a purely theoretical scenario for the formation and evolution of galaxies in the cosmological context.
Given the complexity of the targeted physical systems, it is necessary to rely upon on numerical simulations which in turn require an appropriate numerical code, able to follow the complex physics of galaxies. Therefore, the second objective is the optimization of such code, according to the paradigms of modern computational science. Indeed, given the complexity of the involved physical phenomena the code must be enriched with a number of complex algorithms, which at the same time slow down its performance to such a point that it is difficult to extensively use it to explore the whole scenario in detail, unless sophisticated optimization techniques are applied to drastically reduce the computational time.
In this thesis I have studied the problem of the optimization of numerical codes in serial and parallel architectures and I will present the different strategies I have adopted to make them faster, with particular attention to EvoL, the N-body Tree-SPH code entirely written in the house and widely used by the Padua group. To develop and optimize a code like EvoL, specific skills are needed, ranging from classical astrophysics to computer science. To cope with this, in the thesis I first introduce some general concepts on the functioning of a computer machine, its structure and architecture, the various reasons why a code, although correct from a mathematical and logical point a view, does not in practice work at the maximum level of efficiency and does not exploit the formal computing power to disposal in a optimal form. To this aim, I examine some important aspects of the general behaviour of a code and highlight several strategies that can be followed to optimize it. In particular, I analyze the code response in different situations highlighting the limitations, the routines with the heaviest load, and the importance of the communications between CPUs in parallel environment.
Given these premises, we present EvoL, a lagrangian code based on the classical NB-TSPH formalism, and describe in some detail its structure and physical content. In particular we report on the new physical treatment of the interstellar medium and the companion codes ROBO and MaNN we have recently developed, and how they are implemented in EvoL. Then we describe the various optimizations we have applied to EvoL in order to improve its efficiency. Finally we report on the physical results we have obtained using EvoL, and ancillary codes ROBO and MaNN. In brief, we describe the physical content of the last release of EvoL, and the many hydrodynamical test we have performed to validate it. Second we describe the two studies dedicated to the treatment of the interstellar medium with the state of the art description of its chemistry and thermodynamical properties, and how these results can be implemented in EvoL, thanks to an extensive use of the artificial neural networks. Finally we present a set new models of early type galaxies obtained from cosmological initial conditions at varying the initial mass and density contrast with respect to the cosmological background and their subsequent evolution into well behaved galaxies. Particular attention is paid to the different role played by the density contrast of dark matter in the proto-halo generating the galaxy and the density of the baryonic matter (gas) required to initiate the star formation process. In general, while proto-galaxies of high mass give origin to a single dominant episode of star formation taking place very early on in a galaxy’s history, proto-galaxies of low mass have a more complicated history of star formation, which a series of episodes of variable intensity often interrupted by periods of quiescence.Questa tesi è parte di un più ampio progetto dedicato alla comprensione e alla modellizzazione della formazione ed evoluzione delle galassie da diversi punti di vista: formazione di strutture cosmologiche a tutte le scale e formazione ed evoluzione della singole entità fatte di materia oscura e barionica. La tesi ha due obiettivi fondamentali intimamente legati. Il primo di natura astrofisica è già stato toccato e riguarda lo sviluppo di uno scenario puramente teorico per la formazione ed evoluzione delle galassie in contesto cosmologico. Data la complessità dei sistemi fisici studiati, il lavoro è fortemente basato su simulazioni numeriche che richiedono appropriati codici in grado di seguire la complessa fisica delle galassie. Pertanto, il secondo obiettivo riguarda l’ottimizzazione del codice numerico secondo i paradigmi della moderna scienza computazionale. Infatti, la complessità dei fenomeni fisici considerati, rende il codice più dettagliato da un punto di vista fisico, ma allo stesso tempo, lo rallenta al punto che non può essere direttamente utilizzato in modo sistematico, a meno che non vengano applicate sofisticate tecniche di ottimizzazione per ridurne drasticamente i tempi di calcolo. In questa tesi ho studiato il problema della ottimizzazione di codici numerici in architetture seriali e parallele e le strategie adottate per renderli più veloci, con particolare attenzione al codice EvoL interamente scritto in casa e ampiamente utilizzato il gruppo di Padova. Per sviluppare e ottimizzare un codice come EvoL sono necessarie competenze specifiche che vanno dalla astrofisica classica alla “computer science”. In sintesi, ho esaminato alcuni aspetti importanti del comportamento generale del codice e illustrato le diverse strategie applicate per ottimizzarlo. In particolare ho analizzato la risposta di un codice in situazioni diverse mettendo in evidenza i limiti globali, le routine di calcolo che spendono più tempo, e l’importanza delle comunicazioni MPI. Viene poi presentato il codice evolutivo e il suo contenuto fisico: EvoL è l’ultima versione del codice numerico lagrangiano sviluppato a Padova da C. Chiosi e collaboratori (Carraro et al. 1998; Merlin et al. 2010) basato sui classici algoritmi Tree-code (Barnes and Hut 1986) e SPH (Lucy 1977). Riporto il nuovo trattamento fisico del mezzo interstellare attraverso i codici recentemente sviluppati ROBO e MaNN, e l’implementazione del modello in EvoL. Ancora, vengono descritte le metodologie usate per valutare l’efficienza complessiva di EvoL, e le varie ottimizzazioni applicate; si descrivono anche i risultati ottenuti utilizzando il codice. Prima sono illustrati i diversi miglioramenti fisici che abbiamo incluso in EvoL, e i relativi tests idrodinamici fatti per validare il suo contenuto fisico. Successivamente si descrivono i due studi dedicati al trattamento del mezzo interstellare, della sua chimica, delle sue proprietà termodinamiche. Infine presentiamo una nuova serie di modelli di galassie “early type”, ottenute da condizioni iniziali cosmologiche variando la massa iniziale e il contrasto di densità rispetto al fondo cosmologico, e la loro successiva evoluzione. Particolare attenzione è rivolta al diverso ruolo svolto dal contrasto densità di materia oscura nel proto-alone e la densità della materia barionica (gas) necessaria per avviare il processo di formazione stellare. In generale, mentre le proto-galassie di grande massa danno origine ad un singolo episodio di formazione stellare che avviene precocemente nel corso della storia evolutiva della galassia, le proto-galassie di piccola massa hanno una storia di formazione stellare più complicata, con una serie di episodi di intensità variabile spesso interrotti da periodi di quiescenza.
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Lagergren, Mattias. "GPU accelerated SPH simulation of fluids for VFX." Thesis, Linköping University, Visual Information Technology and Applications (VITA), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-57320.
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Dolag, Klaus. "SPH-Simulationen der Entwicklung von Magnetfeldern in Galaxienhaufen." Diss., lmu, 2000. http://nbn-resolving.de/urn:nbn:de:bvb:19-2773.
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Eriksson, Jonas. "Evaluation of SPH for hydrodynamic modeling,using DualSPHysics." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-339557.
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Computational methods are always being invented, improved and adjusted to newkinds of problems, this is a constant process happening all the time. The studyevaluates a method called Smoothed Particle Hydrodynamics (SPH) for modelingon fluid flows around ship hulls. This has been done mainly using a open sourcecode called DualSPHysics. The SPH method has been applied to complex problemsas well as simple problems for comparison to well known phenomena. It is aearly study of the method and aimed at discovering how to proceed when studyingthe method in the future. The results seem promising especially when computationsare made using Graphics Processing Units (GPU) for calculations. The codeDualSPHysics used in the study shows promise but might be in need of some morefunctions before being practically applicable for simulation of ship hulls.
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Ata, Riadh. "Écoulements à surface libre avec la méthode SPH." Mémoire, École de technologie supérieure, 2002. http://espace.etsmtl.ca/821/1/ATA_Riadh.pdf.
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La méthode SPH (Smoothed Particles Hydrodynamics) est une méthode purement Lagrangienne qui a été utilisée depuis 1977 dans la simulation des problèmes astrophysiques et les chocs à grandes vitesses. Dans le présent travail, une adaptation de cette méthode aux écoulements à surfaces libres est présentée.
Comme première étape, le problème de bris de barrage en mono-dimensionnel est simulé. Cette étape nous a servi à évaluer et se familiariser avec la méthode SPH. Les résultats obtenus ont été validés et comparés avec la solution analytique ainsi qu'avec les résultats déjà publiés dans la littérature.
La deuxième partie de ce mémoire a été consacrée aux cas bidimensionnels. Le problème de bris de barrage dans diverses configurations a été simulé. Les résultats obtenus dépendent directement de chaque cas traité. Pour le cas d'un barrage standard ainsi que le barrage circulaire, les résultats sont très encourageants. En ce qui concerne le cas d'un barrage avec étranglement, le résultat est oscillant.
Ces résultats ont été obtenus avec l'approche standard de la méthode SPH. De plus, une nouvelle forumlation basée sur une combinaison EF-SPH a été introduite et testée. Les résultats obtenus sont meilleurs que celle donnés par la formulation standard. Cette amélioration n'est palpable que dans les premiers instants de la simulation. Durant les derniers instants des simulations, un manque de particules à l'emplacement du barrage, cause une concordance moins bonne des courbes trouvées avec celles fournies par la méthode des volumes finis.
Le succès de la méthode SPH dans sa version standard ainsi que dans sa nouvelle version combinée EF-SPH, dépendent de plusieurs facteurs. Des études supplémentaires sont par conséquent suggérées pour standardiser les paramètres qui interviennent dans ces formulations.
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Takata, Adriano Sueke [UNESP]. "Aspectos teórico-numéricos dos métodos SPH e MPS." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/128166.
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Atualmente, devido ao grande avanço tecnológico o uso dos métodos de partículas vêm ganhando espaço nas simulações de escoamento de fluido. O primeiro método de partículas a ser desenvolvido foi o Smoothed Particle Hydrodynamics (SPH) que se mostrou bastante eficiente para problemas de escoamento compressível, mas ineficiente para escoamento incompressível. Desta forma, surgiu algumas estratégias para resolver problemas de escoamento incompressível como o Incompressible Smoothed Particle Hydrodynamics (ISPH) e o Moving Particle Semi-Implicit (MPS); em ambos os métodos a pressão é atualizada por um equação de Poisson. Portanto para obter uma boa aproximação das equações de Navier-Stokes é necessário antes ter uma boa aproximação da equação de Poisson. Neste trabalho são abordados os métodos de partículas Smoothed Particle Hydrodynamics (SPH) e Moving Particle Semi-Implicit (MPS). A discretização dos operadores diferenciais por esses métodos é feita por meio da aproximação do núcleo e também por partículas. Um estudo comparativo entre discretização foram efetuadas. Afim de saber se os parâmetros utilizados na literatura dos métodos de partículas SPH e MPS dão uma boa solução para equação de Poisson foram realizados vários testes variando os parâmetros com e sem o tratamento de fronteira. Neste trabalho também foi proposta uma estratégia para resolver o problema de oscilação na solução da equação de advecção com descontinuidade nas condições iniciais e os resultados foram bem satisfatório
Currently, due to the technological advances the use of particle methods is gaining ground in the simulations of fluid flow. The first particle method to be developed was the Smoothed Particle Hydrodynamics (SPH) that was very efficient for compressible flow problems, but inefficient for incompressible ones. Thus, there was some strategy to solve incompressible flow problems as the incompressible Smoothed Particle Hydrodynamics (ISPH) and the Moving Particle Semi-Implicit (MPS); in both methods the pressure is updated by a Poisson equation. For an approximation of the Navier-Stokes equations it is first needed a good approximation for the Poisson equation. This paper discusses the following particles methods: Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-Implicit (MPS). The discretization of differential operators by these methods is done through the approximation of the kernel and also by particles. A comparative study of different discretizations were made. In order to know if the parameters used in the literature for the SPH and MPS methods provide a good solution for Poisson equation, have been performed several tests by varying the parameters with and without the borders treatment. This work also proposed a strategy to solve the oscillation problem in advection equation with discontinuity in the initial conditions and the results were very satisfactory
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Takata, Adriano Sueke. "Aspectos teórico-numéricos dos métodos SPH e MPS /." Presidente Prudente, 2015. http://hdl.handle.net/11449/128166.
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Orientador: Messias Meneguette JuniorBanca: Gilcilene Sanchez de Paulo
Banca: Afonso Paiva Neto
Resumo: Atualmente, devido ao grande avanço tecnológico o uso dos métodos de partículas vêm ganhando espaço nas simulações de escoamento de fluido. O primeiro método de partículas a ser desenvolvido foi o Smoothed Particle Hydrodynamics (SPH) que se mostrou bastante eficiente para problemas de escoamento compressível, mas ineficiente para escoamento incompressível. Desta forma, surgiu algumas estratégias para resolver problemas de escoamento incompressível como o Incompressible Smoothed Particle Hydrodynamics (ISPH) e o Moving Particle Semi-Implicit (MPS); em ambos os métodos a pressão é atualizada por um equação de Poisson. Portanto para obter uma boa aproximação das equações de Navier-Stokes é necessário antes ter uma boa aproximação da equação de Poisson. Neste trabalho são abordados os métodos de partículas Smoothed Particle Hydrodynamics (SPH) e Moving Particle Semi-Implicit (MPS). A discretização dos operadores diferenciais por esses métodos é feita por meio da aproximação do núcleo e também por partículas. Um estudo comparativo entre discretização foram efetuadas. Afim de saber se os parâmetros utilizados na literatura dos métodos de partículas SPH e MPS dão uma boa solução para equação de Poisson foram realizados vários testes variando os parâmetros com e sem o tratamento de fronteira. Neste trabalho também foi proposta uma estratégia para resolver o problema de oscilação na solução da equação de advecção com descontinuidade nas condições iniciais e os resultados foram bem satisfatório
Abstract: Currently, due to the technological advances the use of particle methods is gaining ground in the simulations of fluid flow. The first particle method to be developed was the Smoothed Particle Hydrodynamics (SPH) that was very efficient for compressible flow problems, but inefficient for incompressible ones. Thus, there was some strategy to solve incompressible flow problems as the incompressible Smoothed Particle Hydrodynamics (ISPH) and the Moving Particle Semi-Implicit (MPS); in both methods the pressure is updated by a Poisson equation. For an approximation of the Navier-Stokes equations it is first needed a good approximation for the Poisson equation. This paper discusses the following particles methods: Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-Implicit (MPS). The discretization of differential operators by these methods is done through the approximation of the kernel and also by particles. A comparative study of different discretizations were made. In order to know if the parameters used in the literature for the SPH and MPS methods provide a good solution for Poisson equation, have been performed several tests by varying the parameters with and without the borders treatment. This work also proposed a strategy to solve the oscillation problem in advection equation with discontinuity in the initial conditions and the results were very satisfactory
Mestre
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VITANZA, Enrico. "Application of SPH numerical procedures to hydraulic problems." Doctoral thesis, Università degli Studi di Palermo, 2014. http://hdl.handle.net/10447/91267.
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Le, Goff Jean-Marie. "Navier-Stokes modellingof offshore wind turbinesusing the SPH method." Thesis, KTH, Skolan för industriell teknik och management (ITM), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-216161.
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Peer, Andreas [Verfasser], and Matthias [Akademischer Betreuer] Teschner. "Implicit SPH formulations for viscous fluids and elastic solids." Freiburg : Universität, 2019. http://d-nb.info/1188195956/34.
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Krimi, Abdelkader. "Modélisation des écoulements fluide multiphasiques avec une approche SPH." Thesis, Paris, ENSAM, 2018. http://www.theses.fr/2018ENAM0004/document.
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La méthode Smoothed Particle Hydrodynamics (SPH) est une méthode lagrangienne, sans maillage développée initialement pour des simulations de phénomènes astrophysiques. Depuis, elle a connu de nombreuses applications, notamment pour la simulation des écoulements des fluides. Contrairement aux méthodes utilisant un maillage, la méthode SPH peut gérer de manière naturelle et sans traitement spécifique les simulations des écoulements à sur- face libre et multiphasiques avec interface subissant de grandes déformations. Dans cette thèse, une modélisation SPH des écoulements des fluides multiphasiques a été réalisée en tenant compte de différentes complexités (écoulements à surface libre et multiphasiques interfacials) et de natures d'écoulement (si- mulation des fluides, des sols et les deux en interactions). Un modèle SPH faiblement compressible (WCSPH) a été proposé pour simuler les écoulements des fluides multiphasiques avec interface comprenant plus de deux phases de fluide. Ce modèle inclut le développement d’une nouvelle formulation de force de tension de surface en utilisant un opérateur SPH consistant de premier ordre. Une modification de condition généralisée aux parois solides a été apportée pour qu’elle soit appliquée sur les écoulements des fluides multiphasiques avec des rapports de densité et de viscosité élevés. Une nouvelle loi de comportement dépendant de la pression nommée RBMC-αμ ( Regularized Bingham Mohr Coulomb où αμ est un paramètre libre) a également été développée. Cette loi peut simuler les fluides (Newtonien, Binghamien), les sols (cohésif, frictionnel) et les deux en interactions. La loi précédente étant sensible à la pression, une extension du terme diffusif δ-SPH a été faite pour le cas des écoulements des fluides multiphasiques afin de réduire les oscillations de pression à haute fréquence qui sont dues à l’utilisation d’une équation d’état. La validation et l’application des modèles développés dans cette thèse sont montrées à travers plusieurs cas tests de difficulté croissanteSmoothed Particle Hydrodynamics (SPH) is a Lagrangian gridless method developed initially to simulate astrophysical phenomena, and since it has been known for a large number of applications, especially for fluid flow simulations. Contrary to the grid-based method, the SPH method can handle free surface and interfacial fluid flow simulation including large deformations naturally and without the need for any specific treatment. In this thesis a SPH modeling of multiphase fluid flows has been achieved with consideration of different complexities ( free surface and interfacial fluid flows) and natures (simulation of fluids, soil and both in interactions). A consistent weakly compressible SPH model (WCSPH) has been proposed to simulate interfacial multiphase fluid flows with more than two fluid phases. This model includes a new expression of the surface tension force using a first order consistency SPH operator. A modification to the well known generalized wall boundary condition have been brought in order to be applied to multiphase fluid flow with large density and viscosity ratios. A new pressure-based constitutive law named RBMC-αμ (Regularized Bingham Mohr Coulomb with αμ is free parameter) has been developed in this thesis. This model can simulate fluids (Newtonian, Binghamton), soils (cohesive, frictional) and both in interactions. Because the previous model is pressure sensitive, an extension of δ-SPH diffusive term has been proposed for multiphase fluid flows to overcome the hight frequency pressure oscillations due to the determination of pressure from an equation of state. The validation and application of the developed models have been shown in this thesis through several test-cases of increasing difficulty
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Hendra, Aditya. "Accelerating Fluids Simulation Using SPH and Implementation on GPU." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-269807.
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Fluids simulation is usually done with CFD methods which offers high precision but needs days/weeks/months to compute on desktop CPUs which limits the practical use in industrial control systems. In order to reduce the computation time Smoothed Particle Hydrodynamics (SPH) method is used. SPH is commonly used to simulate fluids in computer graphics field, especially in gaming. It offers faster computation at the cost of lesser accuracy. The goal of this work is to determine the feasibility of using SPH method with GPU parallel programming to provide fluids simulation which is fast enough for real-time feedback control simulation. A previous master thesis work about accelerating fluids simulation using SPH method was done by Ann Johansson at ABB. Her work in Matlab using intel i7 - 2.4Ghz needs 7089 seconds to compute a water-jet simulation with 40000 particles and time-step of 0.006 second. Our work utilizes GPU parallel programs implemented in Fluidsv3, an open-source software as the base code. With CUDA C/C++ and Nvidia GTX980, we need 18 seconds to compute a water-jet simulation using 1000000 particles and time-step of 0.0001 second. Currently, our work lacks of validation method to measure the accuracy of the fluids simulation and more work needs to be done about this. However it only takes 80 msec to compute one iteration which opens an opportunity to be used together with any real-time systems, such as a feedback control system, that has a period of 100msec. This mean it could model industry processes that utilize water such as the cooling process in a hot rolling mill. The next question, which is not addressed in this study, would be how to satisfy application dependent needs such as: simulation accuracy, required parameters, simulations duration in real-time, etc.
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Fourtakas, Georgios. "Modelling multi-phase flows in nuclear decommissioning using SPH." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/modelling-multiphase-flows-in-nuclear-decommissioning-using-sph(f5ed0b5b-ea62-431a-bb6e-a18635d396bc).html.
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This thesis presents a two-phase liquid-solid numerical model using Smoothed Particle Hydrodynamics (SPH). The scheme is developed for multi-phase flows in industrial tanks containing sediment used in the nuclear industry for decommissioning. These two-phase liquid-sediments flows feature a changing interfacial profile, large deformations and fragmentation of the interface with internal jets generating resuspension of the solid phase. SPH is a meshless Lagrangian discretization scheme whose major advantage is the absence of a mesh making the method ideal for interfacial and highly non-linear flows with fragmentation and resuspension. Emphasis has been given to the yield profile and rheological characteristics of the sediment solid phase using a yielding, shear and suspension layer which is needed to predict accurately the erosion phenomena. The numerical SPH scheme is based on the explicit treatment of both phases using Newtonian and non-Newtonian Bingham-type constitutive models. This is supplemented by a yield criterion to predict the onset of yielding of the sediment surface and a suspension model at low volumetric concentrations of sediment solid. The multi-phase model has been compared with experimental and 2-D reference numerical models for scour following a dry-bed dam break yielding satisfactory results and improvements over well-known SPH multi-phase models. A 3-D case using more than 4 million particles, that is to the author’s best knowledge one of the largest liquid-sediment SPH simulations, is presented for the first time. The numerical model is accelerated with the use of Graphic Processing Units (GPUs), with massively parallel capabilities. With the adoption of a multi-phase model the computational requirements increase due to extra arithmetic operations required to resolve both phases and the additional memory requirements for storing a second phase in the device memory. The open source weakly compressible SPH solver DualSPHysics was chosen as the platform for both CPU and GPU implementations. The implementation and optimisation of the multi-phase GPU code achieved a speed up of over 50 compared to a single thread serial code. Prior to this thesis, large resolution liquid-solid simulations were prohibitive and 3-D simulations with millions of particles were unfeasible unless variable particle resolution was employed. Finally, the thesis addresses the challenging problem of enforcing wall boundary conditions in SPH with a novel extension of an existing Modified Virtual Boundary Particle (MVBP) technique. In contrast to the MVBP method, the extended MVBP (eMVBP) boundary condition guarantees that arbitrarily complex domains can be readily discretized ensuring approximate zeroth and first order consistency for all particles whose smoothing kernel support overlaps the boundary. The 2-D eMVBP method has also been extended to 3-D using boundary surfaces discretized into sets of triangular planes to represent the solid wall. Boundary particles are then obtained by translating a full uniform stencil according to the fluid particle position and applying an efficient ray casting algorithm to select particles inside the fluid domain. No special treatment for corners and low computational cost make the method ideal for GPU parallelization. The models are validated for a number of 2-D and 3-D cases, where significantly improved behaviour is obtained in comparison with the conventional boundary techniques. Finally the capability of the numerical scheme to simulate a dam break simulation is also shown in 2-D and 3-D.
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Xenakis, Antonios. "Modelling multi-phase non-Newtonian flows using incompressible SPH." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/modelling-multiphase-nonnewtonian-flows-using-incompressible-sph(e7157868-b2df-4b78-be10-b980eeef31d8).html.
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Non-Newtonian fluids are of great scientific interest due to their range of physical properties, which arise from the characteristic shear stress-shear rate relation for each fluid. The applications of non-Newtonian fluids are widespread and occur in many industrial (e.g. lubricants, suspensions, paints, etc.) and environmental (e.g. mud, ice, blood, etc.) problems, often involving multiple fluids. In this study, the novel technique of Incompressible Smoothed Particle Hydrodynamics (ISPH) with shifting (Lind et al., J. Comput. Phys., 231(4):1499-1523, 2012), is extended beyond the state-of-the-art to model non-Newtonian and multi-phase flows. The method is used to investigate important problems of both environmental and industrial interest. The proposed methodology is based on a recent ISPH algorithm with shifting with the introduction of an appropriate stress formulation. The new method is validated both for Newtonian and non-Newtonian fluids, in closed-channel and free-surface flows. Applications in complex moulding flows are conducted and compared to previously published results. Validation includes comparison with other computational techniques such as weakly compressible SPH (WCSPH) and the Control Volume Finite Element method. Importantly, the proposed method offers improved pressure results over state-of-the-art WCSPH methods, while retaining accurate prediction of the flow patterns. Having validated the single-phase non-Newtonian ISPH algorithm, this develops a new extension to multi-phase flows. The method is applied to both Newtonian/Newtonian and Newtonian/non-Newtonian problems. Validations against a novel semi-analytical solution of a two-phase Poiseuille Newtonian/non-Newtonian flow, the Rayleigh-Taylor instability, and a submarine landslide are considered. It is shown that the proposed method can offer improvements in the description of interfaces and in the prediction of the flow fields of demanding multi-phase flows with both environmental and industrial application. Finally, the Lituya Bay landslide and tsunami is examined. The problem is approached initially on the real length-scales and compared with state-of-the-art computational techniques. Moreover, a detailed investigation is carried out aiming at the full reproduction of the experimental findings. With the introduction of a k-ε turbulence model, a simple saturation model and correct experimental initial conditions, significant improvements over the state-of-the-art are shown, managing an accurate representation of both the landslide as well as the wave run-up. The computational method proposed in this thesis is an entirely novel ISPH algorithm capable of modelling highly deforming non-Newtonian and multi-phase flows, and in many cases shows improved accuracy and experimental agreement compared with the current state-of-the-art WCSPH and ISPH methodologies. The variety of problems examined in this work show that the proposed method is robust and can be applied to a wide range of applications with potentially high societal and economical impact.
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Green, Mashy David. "Sloshing simulations with the smoothed particle hydrodynamics (SPH) method." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/45367.
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The main aims of this work are to identify, verify, and validate a smoothed particle hydrodynamics (SPH) method for simulating long duration transient and steady- state fluid sloshing in complex geometries. The validation will be carried out by comparing the SPH simulations against experimental data provided by ESA/ESTEC for transient and steady-state sloshing in a rectangular tank with a low filling ratio and of transient sloshing in a pill-shaped tank that exhibits transition from swaying to swirling waves. The experimental tests proved to be extremely challenging due to the low fill ratio of the rectangular tank and the long duration of both experiments. The main challenge is to devise a SPH scheme that balances spatial and temporal accuracy with an efficient computer implementation to produce accurate simulations at a reasonable computing cost. The investigation highlighted three issues of critical importance: the treatment of solid boundaries in order to limit the introduction numerical errors into the system; the application of a correct numerical dissipation scheme to reduce existing numerical errors; and the need for a massively parallel implementation. Careful examination of the most suitable techniques led to the adoption a cor- rected δ-SPH scheme that provides numerical dissipation to reduce spurious pressure oscillations, and a fixed ghost particle boundary condition to accurately impose wall boundary conditions. The proposed SPH methods were coded in the open source parallel code DualSPHysics. The implementation showed significant improvements in energy conservation and solution accuracy when compared to state-of-the-art SPH methods, and accurately reproduced known analytical solutions to linear sloshing. The validation against the ESA/ESTEC experimental data showed excellent agreement between the SPH simulations and experiments, accurately reproducing the time history of wave heights and sloshing forces as well as capturing the full free-surface shapes. Only the careful selection of appropriate boundary conditions, artificial dissipation and a massively parallel GPU architecture allowed to accurately simulate these experiments.
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Band, Stefan [Verfasser], and Matthias [Akademischer Betreuer] Teschner. "Boundary handling and neighbor search in iterative incompressible SPH." Freiburg : Universität, 2020. http://d-nb.info/1214592759/34.
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Taylor, Paul A. "Understanding long-duration gamma-ray bursts : modelling collapsars with SPH." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497107.
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NAKAMURA, FABIO ISSAO. "FLUID INTERACTIVE ANIMATION BASED ON PARTICLE SYSTEM USING SPH METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10087@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORNeste trabalho foi feito um estudo investigativo sobre animação de fluidos utilizando sistemas de partículas. Baseado nas propostas apresentadas por Muller et al., esta dissertação objetiva investigar e compreender o uso do método Lagrangeano baseado em partículas, conhecido como Smoothed Particle Hydrodynamics (SPH), para simulação de fluidos. A validação do método foi feita através da implementação de uma biblioteca capaz de animar fluidos a taxas interativas. Para testar a eficácia e eficiência do método, a biblioteca desenvolvida permite a instanciação de diferentes configurações, incluindo o tratamento de colisões do fluido com obstáculos, o tratamento da interação entre dois fluidos distintos e o tratamento de forças externas exercidas pelo usuário via um mecanismo de interação.
This work investigates the use of particle-based system for fluid animation. Based on proposals presented by Müller et al., the goal of this dissertation is to investigate and fully understand the use of a Lagrangian method known as Smoothed Particle Hydrodynamics (SPH) for fluid simulations. A library has been implemented in order to validate the method for fluid animation at interactive rate. To demonstrate the method effectiveness and efficiency, the resulting library allows the instantiation of different configurations, including the treatment of fluid-obstacle collisions, interaction between two distinct fluids, and fluid-user interaction.
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CARMO, FABIANO PETRONETTO DO. "POISSON EQUATION AND THE HELMHOLTZ-HODGE DECOMPOSITION WITH SPH OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=12140@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORFUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
A equação diferencial parcial de Poisson é de fundamental importância em várias áreas de pesquisa, dentre elas: matemática, física e engenharia. Para resolvê-la numericamente utilizam-se vários métodos, tais como os já tradicionais métodos das diferenças finitas e dos elementos finitos. Este trabalho propõe um método para resolver a equação de Poisson, utilizando uma abordagem de sistema de partículas conhecido como SPH, do inglês Smoothed Particles Hydrodynamics. O método proposto para a solução da equação de Poisson e os operadores diferenciais discretos definidos no método SPH, chamados de operadores SPH, são utilizados neste trabalho em duas aplicações: na decomposição de campos vetoriais; e na simulação numérica de escoamentos de fluidos monofásicos e bifásicos utilizando a equação de Navier-Stokes.
Poisson`s equation is of fundamental importance in many research areas in engineering and the mathematical and physical sciences. Its numerical solution uses several approaches among them finite differences and finite elements. In this work we propose a method to solve Poisson`s equation using the particle method known as SPH (Smoothed Particle Hydrodynamics). The proposed method together with an accurate analysis of the discrete differential operators defined by SPH are applied in two related situations: the Hodge-Helmholtz vector field decomposition and the numerical simulation of the Navier-Stokes equations.
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Cartwright, Annabel. "SPH simulation of the formation and evolution of protoplanetary disks." Thesis, Cardiff University, 2006. http://orca.cf.ac.uk/56122/.
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The formation and evolution of protoplanetary disks is simulated by computer modelling, using the Smoothed Particle Hydrodynamics (SPH) method. The suitability of SPH for modelling disks is investigated, and problems are identified with the SPH implementation of Artificial Viscosity in disks with Keplerian velocity profiles. Analytical and experimental results reveal that the resultant viscous force for a simulated Keplerian disk is in the opposite direction to that produced by linear shear. Applying Artificial Viscosity only to approaching particles results in a radial force four times larger than the force in the direction of the orbit. The viscous force can change direction if temperature, and therefore sound speed, decreases. Techniques for activating Artificial Viscosity only when convergence is detected are found to fail in differentially rotating disks. Both the Balsara Switch and Time Dependent Artificial Viscosity use the SPH estimate of V v sph, which has a low freqency time varying component which is independent of h, and so cannot be removed by increasing the number of SPH particles. An alternative method, based on pattern recognition, is shown to reduce the viscous spread of a differentially rotating ring by an order of magnitude. We also identify problems associated with the gravitational field of disks. The use of an annulus to represent a portion of a much larger, continuous disk, may yield unrepresentative results. The edge effects can cause preferential accretion zones, where the Toomre Q parameter is not the same as it would be for the same region of an extended disk. SPH simulations of Protoplanetary disks produce condensations which do not persist long enough to collapse. The high tidal shearing forces in a Keplerian accretion disk disrupt the condensations before they accumulate enough mass to collapse. Including a more realistic treatment of the thermal physics, and reducing the effective shear viscosity, makes the situation worse.
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Almeida, Ana Carolina de. "Expressão de SIRP'alfa' e SPH-1 na anemia hemolitica autoimune." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/308297.
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Orientadores: Antonio Condino Neto, Sara Teresinha Olalla SaadTese (doutorado)- Universidade Estadual de Campinas, Faculdade de Ciencias Medicas
Made available in DSpace on 2018-08-13T18:06:47Z (GMT). No. of bitstreams: 1 Almeida_AnaCarolinade_D.pdf: 1227023 bytes, checksum: 25438a379e180eeb0d1972b464b909b0 (MD5) Previous issue date: 2009
Resumo: SIRP 'alfa'(Signal Regulatory Protein 'alfa') é um receptor que medeia funções inibidoras em fagócitos. Sua ativação e conseqüente fosforilação dos ITIMs ocorre pela ligação ao CD47 presente na membrana dos eritrócitos, e permite o recrutamento e a ativação de SHP-1, a qual desfosforila substratos específicos envolvidos na mediação de diversos efeitos fisiológicos. O objetivo deste trabalho foi avaliar o papel da dexametasona (dexa) e de IFN?/TNFa sobre a expressão de SIRPa e SHP-1; a consequência desta regulação sobre a eritrofagocitose; e o nível de expressão gênica de SIRPa e SHP-1 em monócitos de pacientes com anemia hemolítica autoimune (AHAI) antes e depois de corticoterapia. Monócitos de doadores sadios e células mielomonocíticas U937 foram cultivados por 48 horas com dexa (1µM) ou IFN? (100U/ml) e TNFa (1000U/ml), por 6 horas com Hemina® (30uM), ou por 72 horas com prednisolona (0,15 e 1mg/l). Monócitos foram isolados de pacientes com AHAI antes e depois da corticoterapia. A expressão gênica de SIRPa e SHP-1 foi determinada por PCR em Tempo Real, a expressão protéica de SIRPa e SHP-1 foi determinada por Western Blotting, e a capacidade de eritrofagocitose foi determinada por microscopia. IFN? e TNFa, in vitro, promoveram o aumento da expressão gênica e protéica de SIRPa e a expressão gênica de SHP-1, em paralelo com a redução da capacidade de eritrofagocitose em monócitos normais. Em contrapartida, embora tenha aumentado a expressão gênica de SIRPa e SHP-1, dexa in vitro não alterou a expressão destas proteínas, assim como não alterou a capacidade de eritrofagocitose de monócitos normais. A expressão gênica de SIRPa e SHP-1 foi maior em monócitos de pacientes com AHAI em comparação a doadores sadios. Após corticoterapia, a expressão gênica de SIRPa e SHP-1 em monócitos de pacientes com AHAI se mostrou similar a doadores sadios. Pacientes com AHAI estudados antes da corticoterapia apresentaram baixos níveis de hemoglobina e após corticoterapia esse índice de mostrou normal. A expressão gênica de SIRPa foi aumentada pela cultura de monócitos com hemina, mas a expressão de proteína permaneceu a mesma. Nossos resultados confirmam o papel fundamental da SIRPa na regulação da eritrofagocitose e sugere que a expressão de mRNA de SIRPa em monócitos de pacientes com AHAI antes de corticoterapia é aumentada pela liberação de heme, e que a redução da expressão gênica de SIRPa após corticoterapia se deve a um efeito indireto desta droga pela redução da eritrofagocitose e diminuição da disponibilidade de heme.
Abstract: SIRPa (Signal Regulatory Protein a) is an inhibitory receptor in phagocytes. Its activation and consequent phosphorylation of ITIMs occurs by the binding to CD47 on erythrocyte membrane, what allows SHP-1 recruitment, which dephosphorylates specific substrates involved in the mediation of several physiologic effects. The aim of this work was to determine the role of dexamethasone and IFN?/TNFa upon SIRPa and SHP-1 expression, and the consequence of this regulation over erythrophagocytosis; and to evaluate the regulation of SIRPa and SHP-1 in peripheral blood monocytes (PBM) of autoimmune hemolytic anemia (AIHA) patients before and after glucocorticoid (GC) therapy. PBM from healthy donors and U937 myelomonocytic cells were cultured for 48 hours with dexamethasone (1µM) or IFN? (100U/ml) and TNFa (1000U/ml), for 6 hours with Hemin (30uM), or for 72 hours with prednisolone (0.15 and 1mg/l). PBM were isolated from AIHA patients under GC therapy or not. SIRPa and SHP-1 gene expression was determined by Real Time PCR, SIRPa and SHP-1 protein level was determined by Western Blotting, and erythrophagocytosis was determined by microscopy. IFN? and TNFa increased SIRPa gene and protein expression and SHP-1 gene expression, in parallel with a decrease in erythrophagocytosis ability in PBM. On the other hand, although SIRPa and SHP-1 gene expression was significantly increased, dexamethasone did not alter SIRPa and SHP-1 protein expression, and did not alter erythrophagocytosis ability in monocytes. SIRPa and SHP-1 expression was significantly higher in PBM from AIHA patients compared to normal. After GC therapy, SIRPa and SHP-1 expression was similar in PBM of AIHA patients compared to healthy donors. AIHA patients studied before glucocorticoid therapy showed low hemoglobin and after glucocorticoid therapy the level of hemoglobin was normal. SIRPa gene expression was increased by culture with hemin, but protein expression remained the same. Our results confirm the key role of SIRPa in erythrophagocytosis regulation and suggest that SIRPa mRNA expression in AIHA patients before glucocorticoid therapy is increased by heme release, and the decrease of SIRPa gene expression after glucocorticoid therapy is due to an indirect effect of this drug by the reduction of erythophagocytosis and free heme availability.
Doutorado
Doutor em Farmacologia
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Queiroz, Tiago Etiene. "Animação computacional de escoamento de fluidos utilizando o método SPH." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-10112008-110933/.
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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 iniciaisSince 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
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LACOME, JEAN-LUC. "Analyse de la methode particulaire sph applications a la detonique." Toulouse, INSA, 1998. http://www.theses.fr/1998ISAT0006.
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On propose une analyse de la methode particulaire sph (smoothed particle hydrodynamics). L'absence de grille consuit a quelques caracteristiques seduisantes de la methode comme la capacite de traiter les grandes deformations dans un environnement lagrangien pur. On presente tout d'abord des resultats de consistance pour les differentes approximations scatter et gather. On propose ensuite un nouveau modele d'approximation particulaire conservatif. Les applications aux equations d'euler et de la mecanique des milieux continus sont enfin presentees. Certains problemes de mecaniques des milieux continus presentant de fortes anisotropies, on developpe une longueur de lissage tensorielle. Des tests numeriques viennent achever l'analyse theorique de la methode.
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Fonty, Thomas. "Modélisation de l’entraînement d’air dans l'eau avec la méthode SPH." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC1013.
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Les écoulements au sein d'ouvrages hydrauliques – déversement au-dessus d'un barrage, déferlement d'une vague sur une digue, etc. – sont le siège de forts mélanges d'eau et d'air qui se traduisent visuellement par la formation d'eaux blanches à la dynamique complexe. Représenter fidèlement le phénomène d'entraînement/capture des bulles d'air dans l'eau revêt donc un aspect stratégique important pour le dimensionnement de ces ouvrages. La modélisation tant physique que numérique de tels cas s'avère délicate à cause du fort rapport de densité entre les phases et de la nature multi-échelle de ces écoulements impliquant des effets de turbulence et de tension de surface. La méthode numérique SPH (Smoothed Particle Hydrodynamics), approche totalement lagrangienne qui représente l'écoulement comme un ensemble de particules en mouvement sans recours à un maillage, est particulièrement adaptée à la simulation de tels écoulements fortement déformés. Néanmoins, les limites actuelles de puissance de calcul empêchent encore de simuler finement des cas d'application industriels à large emprise en hydraulique. On se propose donc dans cette thèse de modéliser ces écoulements de manière macroscopique via un modèle de mélange qui consiste à voir chaque particule SPH comme un volume de mélange d'eau et d'air en mouvement. On détaille d'abord la dérivation des équations continues de ce modèle de mélange, puis on présente un état de l'art des simulations multiphasiques SPH. A partir du modèle continu et des outils actuels de discrétisation, un modèle de mélange diphasique SPH est ensuite mis en place en vue de son implémentation sur GPU (Graphics Processing Unit). Un accent tout particulier est mis sur les éléments originaux de discrétisation développés, notamment la dérivation d'un schéma aux bonnes propriétés numériques pour le suivi de l'évolution des volumes par phase et l'écriture d'un formalisme de frontières ouvertes pour un mélange. La turbulence, centrale dans le phénomène d'entraînement d’air, est modélisée via un modèle k-ϵ incluant un terme de flottabilité. Ce modèle de mélange est validé sur des cas académiques bidimensionnels de complexité croissante tels que la séparation d'un mélange eau-huile, un écoulement de Poiseuille diphasique, l'instabilité de Rayleigh–Taylor et un lâché de sédiments, illustrant sa polyvalence. La phénoménologie de l'entraînement d'air est ensuite décrite, et le modèle appliqué à des structures communément rencontrées en hydraulique, comme des jets plongeants et des coursiers en marches d'escalier, en introduisant une fermeture spécifique de la vitesse relative entre les phases. Enfin, on présente des premiers cas d'application industriels aux géométries et dynamiques complexesFlows over hydraulic works – a nappe falling over a spillway, a wave breaking on a dike, etc. – undergo strong mixtures of air and water that lead to the appearance of white waters with complex dynamics. Faithfully capture the phenomenon of air bubbles entrainment/entrapment in the flowing water is therefore pivotal for the design of those works. Both experimental and numerical modeling prove to be complex due to high density ratio between phases and the multiscale nature of those flows involving turbulence and surface tension effects. The SPH (Smoothed Particle Hydrodynamics) method, a fully Lagrangian approach that models the flow as a set of moving particles without any mesh, is particularly well-suited to simulate such highly-distorted flows. Nevertheless, the current computational limits still prevent one from finely simulating industrial application cases with large domains in hydraulics. In this work, we aim at simulating macroscopically those flows with a mixture model in which each SPH particle stands for a moving volume of air and water. The derivation of the continuous equations of this mixture model is first detailed, then a state of the art of multiphase simulations in SPH is presented. Equipped with this continuous model and the existing discretization tools, a two-phase SPH mixture model is then derived and implemented on GPU (Graphics Processing Unit). A focus is made on original elements developed in the discretization, especially the derivation of a scheme with good numerical properties to follow the phase volume variations and the writing of an open boundary framework for mixtures. Turbulence, prominent for the air entrainment phenomenon, is modeled with a k-ϵ model including a buoyancy term. This model is validated against bidimensional academic test cases of increasing complexity, namely an oil-water separation, a two-phase Poiseuille flow, the Rayleigh-Taylor instability and a sand dumping case, proving its versatility. The air entrainment phenomenology is then described and the model is applied to common structures in hydraulics such as plunging jets and stepped spillways by introducing a specific closure for the relative velocity between phases. Finally, first industrial application cases with complex geometries and dynamics are presented
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Jachym, Pavel. "Gas stripping in galaxy clusters : a new SPH simulation approach." Paris 6, 2006. http://www.theses.fr/2006PA066369.
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Lelli, Lorenzo. "Un approccio numerico per problemi di fluidodinamica: il metodo SPH." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2595/.
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Pereira, Clicia Giovane Alves. "Estudo matemático do método SPH para modelo Wet-Dam-Break /." Presidente Prudente, 2019. http://hdl.handle.net/11449/181857.
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Orientador: Carlos Alberto Dutra Fraga FilhoBanca: Messias Meneguette Júnior
Banca: Vanessa Avansini Botta Pirani
Banca: Andriana Susana Lopes de Oliveira Campanharo
Resumo: Neste trabalho, apresenta-se o método Lagrangiano de partículas livre de malhas, Smoothed Particle Hydrodynamics (SPH). Neste método, o domínio do problema é discretizado empregando partículas que possuem propriedades físicas calculadas a partir das propriedades das partículas vizinhas, por meio de uma interpolação, utilizando uma função de suavização. O método foi aplicado para discretizar e adaptar para SPH um modelo de ruptura de barragem sobre um leito úmido conhecido como Dam-Break in Wet-Bed. Tal modelo, considerado ideal, é empregado nos testes de desempenho, precisão e confiabilidade de modelos matemáticos para validação de métodos numéricos aplicados a problemas de vertedouros em barragens hidrelétricas e ondas em praias.
Abstract: In this work, we present the Lagrangian mesh-free method of particles, Smoothed Particle Hydrodynamics (SPH). In this method, the problem domain is discretized using particles having physical properties calculated from neighboring particles by means of interpolation using a smoothing function. The method was applied to discretize and to adapt the SPH for a model of dam rupture on a wet-bed known as Wet-Dam-Break. This model, considered as ideal, is used in tests of performance, accuracy and reliability of mathematical models for validation of numerical methods applied to spillways problems in hydroelectric dams and waves at beaches.
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Ghaïtanellis, Alex. "Modélisation du charriage sédimentaire par une approche granulaire avec SPH." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1087/document.
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Cette thèse a pour objet le développement d’un modèle de transport sédimentaire avec la méthode SPH (Smoothed Particle Hydrodynamics). Si les modèles couramment proposés dans la littérature reposent sur un solveur hydrodynamique couplé à des lois semi-empiriques qui modélisent le transport sédimentaire, une approche différente est proposée ici. Dans le modèle proposé dans ce travail, la dynamique du sédiment est également résolue. Celui-ci est assimilé à un milieu continu dont la loi de comportement rend compte de la nature granulaire.Pour ce faire, le modèle élastique-viscoplastique d’Ulrich (2013) a été implémenté dans un code SPH préexistant programmé en langage Cuda, et amélioré du point de vue physico-numérique. Le comportement mécanique du sédiment dépend donc d’une contrainte de rupture déterminée conformément au critère de Drucker-Prager. Dans les zones du matériau où la rupture n’a pas eu lieu, les contraintes de cisaillement sont calculées selon la loi de Hooke généralisée. Dans les zones où la contrainte de rupture a été dépassée, le matériau est assimilé à un fluide rhéofluidifiant. Numériquement, la transition entre les deux états est opérée à l’aide d’une fonction de raccord qui dépend notamment du l’amplitude du taux de déformation et des propriétés granulaires du sédiment.L’eau et le sédiment sont modélisées comme deux phases immiscibles, dans le cadre d’une formulation SPH multi-phase. Pour ce faire, le modèle de Hu et Adams (2006) a été adapté aux modèles de conditions limites semi-analytiques (Ferrand, 2013). Enfin, un schéma d’intégration implicite des forces visqueuses a été développé dans ce contexte, afin d’améliorer les performances du solveur lors de modélisation d’écoulement à bas Reynolds.Plusieurs cas tests sont proposés pour valider le modèle multiphasique, le schéma implicite et le modèle élastique-viscoplastique. De manière générale, les résultats sont en bon accord avec les données expérimentales et analytiques. Le modèle permet de représenter des écoulements multi-fluide avec une bonne précision, même en présence de grand rapport de densité entre les phases. Il en va de même pour les écoulements de fluide non-newtonien et les écoulements à bas Reynolds, pour lesquels le schéma implicite conduit à des résultats très satisfaisants. Enfin, le modèle élastique-viscoplastique a été appliqué à divers cas d’écoulements granulaires, dans le cas d’un matériau sec et saturé, ainsi qu’à des cas d’érosion et d’affouillement. Là encore, les résultats sont globalement en bon accord avec l’expérienceThis thesis presents the development and application of a Smoothed Particle Hydrodynamics (SPH) model to bed-load transport. While state of the art simulation methods commonly rely on a fluid dynamics solver coupled to semi-empirical relationships to model the sediment transport, a completely different approach is investigated in this work. The sediment is treated as a continuum whose behaviour law takes account for its granular nature. citepos{ulrich2013smoothed} elastic-viscoplastic model is thus implemented in an in-house code based on the Cuda language, and improved on physical and numerical aspects. The sediment behaviour depends on a yield stress determined according to Drucker-Prager's criterion. In unyielded regions, the shear stresses are calculated in line with the linear elastic theory. In yielded regions, a shear thinning rheological law is used and the transitions between solid and liquid states are ensured by a blending function driven by the strain rate magnitude and sediment granular properties. Water and sediment are modelled as two immiscible phases in the frame of a multi-phase SPH model with semi-analytical wall boundary conditions cite{ferrand2013unified}. An implicit viscous forces integration scheme is also developed to improve the code performance as for low-Reynolds flows.The multi-phase model, as well as the implicit viscous forces integration scheme, were validated on analytical test cases and good agreement was obtained. The multi-phase formulation has also proven its capability to handle flows involving high density ratio, while the implicit viscous forces integration scheme was successfully applied to the simulation of a non-Newtonian flow. The elastic-viscoplastic model was tested on dry and submerged granular flow problems. The model was able to correctly capture the liquid and solid states of the granular material, as well as the failure and the regime transitions. It was also applied to bed-load transport problems for which a good agreement with the experiment was generally found
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Grobotek, Daniel [Verfasser]. "Lacktrocknungssimulation mit Kalibrationsmethoden : Modifikation von Düsensichtfaktoren mittels SPH-Methode / Daniel Grobotek." Aachen : Shaker, 2015. http://d-nb.info/1069046817/34.
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Sjah, Jessica. "Couplage SPH-DEM pour l'étude de l'érosion dans les ouvrages hydrauliques." Phd thesis, Ecole Centrale de Lyon, 2013. http://tel.archives-ouvertes.fr/tel-01000447.
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L'érosion est un phénomène d'arrachage et de transport de particules solides par des efforts hydrauliques au sein des ouvrages hydrauliques. Cette pathologie très représentée dans les ouvrages en terre peut conduire à la rupture, aussi, la comprendre et la maîtriser constituent des enjeux sociétaux et industriels très forts. L'érodabilité des matériaux se caractérise au travers notamment d'un essai dit d'érosion de conduit et sa modélisation numérique constitue le pivot de ce travail de thèse. Le phénomène d'érosion est un problème couplé entre le fluide et le solide et nous utiliserons deux codes construits sur des approches particulaires pour aborder le problème : ASPHODEL (ANDRITZLMFA) pour la partie fluide (méthode SPH-ALE Smoothed Particle Hydrodynamics - Arbitrary Lagrangian Eulerian) et YADE (L3S-R) pour la fraction solide (méthode DEM Discrete Element Method). Alors que YADE a été largement utilisé pour modéliser des problèmes géotechniques, ASPHODEL n'a pas encore été évalué dans un tel contexte. Ce travail constituera alors une étude de faisabilité pour l'utilisation d'ASPHODEL dans un contexte du génie civil et donnera les conditions pour espérer obtenir des résultats quantitatifs pour les phénomènes étudiés. Dans un deuxième temps, le couplage entre les deux codes sera construit dans le but d'étudier les phénomènes d'arrachage de particules le long de conduits formés à travers des matériaux granulaires cohérents. La validation du code ASPHODEL à l'échelle de la particule a été effectuée par l'étude de l'écoulement visqueux autour d'un objet 2D (cylindre) fixe et isolé de section circulaire mais aussi carrée ou triangulaire. Les forces de trainée, de portance, le coefficient de pression autour du cylindre et le nombre de Strouhal sont comparés à des résultats issus de la littérature pour différents Reynolds en régime laminaire. La validation du code ASPHODEL à l'échelle de l'échantillon a consisté à étudier un écoulement fluide entre des parois lisses ainsi que des parois constituées de particules solides fixes créant une rugosité. Le coefficient de frottement a été systématiquement calculé et comparé aux résultats issus de la littérature et le torseur fluide sur chaque particule solide des parois a été aussi évalué. Enfin, le couplage partitionné entre les deux codes fluide et solide a été construit et validé qualitativement pour le problème de la sédimentation sous gravité d'un grain solide rigide dans un fluide visqueux.
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MOMM, GUSTAVO GARCIA. "ASSESSMENT OF SLAMMING LOADS ON SUBSEA STRUCTURES USING THE SPH METHOD." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2016. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=29340@1.
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PETRÓLEO BRASILEIRO S. A.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.
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.
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Andrade, Luiz Fernando de Souza. "Animação de jatos oscilantes em fluidos viscosos usando SPH em GPU." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-08082014-113954/.
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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)
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Gui, Qinqin. "Improved incompressible SPH method for predicting wave impacts on coastal structures." Thesis, University of Dundee, 2014. https://discovery.dundee.ac.uk/en/studentTheses/efa775e0-fd40-4b96-b0d4-98ff9957e819.
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Smoothed Particle Hydrodynamics (SPH) is a simple and attractive meshless Lagrangian particle method for simulating free surface flows and has been widely applied in predicting wave impacts on coastal structures. However, despite the superior theoretical basis the performance of the existing Incompressible SPH models based on either a density invariant or a velocity divergence-free formulation is often not better than the recently improved Weakly Compressible SPH models. This could be largely caused by the particular formulations of the Pressure Poisson Equation (PPE) source term in the existing ISPH models and a better formulation of this source term can be expected to significantly improve the accuracy of the ISPH models This thesis presents an improved incompressible smoothed particle hydrodynamics (ISPH) method for wave impact applications by combining the density invariant and velocity divergence free formulations in a weighted average manner to form a general source term. The model is then applied to two problems: (1) dam-breaking wave impact on a vertical wall and (2) solitary wave run-up and impact on a coastal structure. The computational results have indicated that the new source term treatment can predict the wave impact pressure and force more accurately compared with using either density invariant or a velocity divergence-free formulation alone. It was further found that depending on the application case, the influence of the density invariant and velocity divergence-free parts could be quite different. A simple parameterisation that relates the weighting coefficient a in the mixed pressure source term to the ratio of the characteristic height to length scales of the flow system is proposed and evaluated. In order to gain further insight into the effects of the source term formulations on the impact pressure prediction, three more benchmark fluid impact problems including two dam break flows and one solitary wave impact are investigated using the three different ISPH numerical schemes, respectively. The computational results are validated against either the experimental data or numerical data based on the WCSPH. The in-depth numerical analysis has revealed that the pure density-invariant formulation can lead to relatively large divergence errors while the velocity divergence-free formulation may cause relatively large density errors. As compared with these two approaches the mixed source term formulation performs much better having the minimum total errors in all test cases. Finally, the SPH model was applied to study the wave interaction with porous structure to investigate the flow motion in and around the porous structure. In order to describe correctly the flow through the interface between the porous region and pure fluid region within the SPH framework a heuristic and boundary treatment method was proposed. The SPH model was validated against the theoretical data of wave propagating over a porous bed and further investigated by comparing the predicted wave surface profile and velocity results with the experiment data for a typical case of flow motion inside of a submerged the porous structure. A good agreement is obtained between the numerical results and experiment data. All these demonstrate that the improved ISPH model developed in this work is capable of modelling the wave interaction with porous structure.
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Yang, Qing. "SPH Simulation of Fluid-Structure Interaction Problems with Application to Hovercraft." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/26785.
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A Computational Fluid Dynamics (CFD) tool is developed in this thesis to solve complex fluid-structure interaction (FSI) problems. The fluid domain is based on Smoothed Particle Hydro-dynamics (SPH) and the structural domain employs large-deformation Finite Element Method (FEM). Validation tests of SPH and FEM are first performed individually. A loosely-coupled SPH-FEM model is then proposed for solving FSI problems. Validation results of two benchmark FSI problems are illustrated (Antoci et al., 2007; Souto-Iglesias et al., 2008). The first test case is flow in a sloshing tank interacting with an elastic body and the second one is dam-break flow through an elastic gate. The results obtained with the SPH-FEM model show good agreement with published results and suggest that the SPH-FEM model is a viable and effective numerical tool for FSI problems.
This research is then applied to simulate a two-dimensional free-stream flow interacting with a deformable, pressurized surface, such as an ACV/SES bow seal. The dynamics of deformable surfaces such as the skirt/seal systems of the ACV/SES utilize the large-deformation FEM model. The fluid part including the air inside the chamber and water are simulated by SPH. A validation case is performed to investigate the application of SPH-FEM model in ACV/SES via comparison with experimental data (Zalek and Doctors, 2010). The thesis provides the theory of the SPH and FEM models incorporated and the derivation of the loosely-coupled SPH-FEM model. The validation results have suggested that this SPH-FEM model can be readily applied to skirt/seal dynamics of ACV/SES interacting with free-surface flow.Ph. D.
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Gissler, Christoph [Verfasser], and Matthias [Akademischer Betreuer] Teschner. "Beyond fluids: SPH simulation of rigid bodies, snow and air interactions." Freiburg : Universität, 2021. http://d-nb.info/1238016057/34.
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Leroy, Agnes. "Un nouveau modèle SPH incompressible : vers l’application à des cas industriels." Thesis, Paris Est, 2014. http://www.theses.fr/2014PEST1065/document.
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Cette thèse a pour objet le développement d'un modèle numérique de simulation des fluides fondé sur la méthode Smoothed Particle Hydrodynamics (SPH). SPH est une méthode de simulation numérique sans maillage présentant un certain nombre d'avantages par rapport aux méthodes Eulériennes. Elle permet notamment de modéliser des écoulements à surface libre ou interfaces fortement déformées. Ce travail s'adresse principalement à quatre problématiques liées aux fondements de la méthode SPH : l'imposition des conditions aux limites, la prédiction précise des champs de pression, l'implémentation d'un modèle thermique et la réduction des temps de calcul. L'objectif est de modéliser des écoulements industriels complexes par la méthode SPH, en complément de ce qui peut se faire avec des méthodes à maillage. Typiquement, les problèmes visés sont des écoulements 3-D à surface libre ou confinés, pouvant interagir avec des structures mobiles et/ou transporter des scalaires, notamment des scalaires actifs (e.g. température). Dans ce but, on propose ici un modèle SPH incompressible (ISPH) basé sur une représentation semi-analytique des conditions aux limites. La technique des conditions aux limites semi-analytiques permet d'imposer des conditions sur la pression de manière précise et physique, contrairement à ce qui se fait avec des conditions aux limites classiques en SPH. Un modèle k-epsilon a été incorporé à ce nouveau modèle ISPH, à partir des travaux de Ferrand et al. (2013). Un modèle de flottabilité a également été ajouté, reposant sur l'approximation de Boussinesq. Les interactions entre flottabilité et turbulence sont prises en compte. Enfin, une formulation pour les frontières ouvertes dans le nouveau modèle est établie. La validation du modèle en 2-D a été réalisée sur un ensemble de cas-tests permettant d'estimer les capacités de prédiction du nouveau modèle en ce qui concerne les écoulements isothermes et non-isothermes, laminaires ou turbulents. Des cas confinés sont présentés, ainsi que des écoulements à surface libre (l'un d'eux incluant un corps solide mobile dans l'écoulement). La formulation pour les frontières ouvertes a été testée sur un canal de Poiseuille plan laminaire et sur deux cas de propagation d'une onde solitaire. Des comparaisons sont présentées avec des méthodes à maillage, ainsi qu'avec un modèle SPH quasi-incompressible (WCSPH) avec le même type de conditions aux limites. Les résultats montrent que le modèle permet de représenter des écoulements dans des domaines à géométrie complexe, tout en améliorant la prédiction des champs de pression par rapport à la méthode WCSPH. L'extension du modèle en trois dimensions a été réalisée dans un code massivement parallèle fonctionnant sur carte graphique (GPU). Deux cas de validation en 3-D sont proposés, ainsi que des résultats sur un cas simple d'application en 3-DIn this work a numerical model for fluid flow simulation was developed, based on the Smoothed Particle Hydrodynamics (SPH) method. SPH is a meshless Lagrangian Computational Fluid Dynamics (CFD) method that offers some advantages compared to mesh-based Eulerian methods. In particular, it is able to model flows presenting highly distorted free-surfaces or interfaces. This work tackles four issues concerning the SPH method : the imposition of boundary conditions, the accuracy of the pressure prediction, the modelling of buoyancy effects and the reduction of computational time. The aim is to model complex industrial flows with the SPH method, as a complement of what can be done with mesh-based methods. Typically, the targetted problems are 3-D free-surface or confined flows that may interact with moving solids and/or transport scalars, in particular active scalars (e.g. the temperature). To achieve this goal, a new incompressible SPH (ISPH) model is proposed, based on semi-analytical boundary conditions. This technique for the representation of boundary conditions in SPH makes it possible to accurately prescribe consistent pressure boundary conditions, contrary to what is done with classical boundary conditions in SPH. A k-epsilon turbulence closure is included in the new ISPH model. A buoyancy model was also added, based on the Boussinesq approximation. The interactions between buoyancy and turbulence are modelled. Finally, a formulation for open boundary conditions is proposed in this framework. The 2-D validation was performed on a set of test-cases that made it possible to assess the prediction capabilities of the new model regarding isothermal and non-isothermal flows, in laminar or turbulent regime. Confined cases are presented, as well as free-surface flows (one of them including a moving body in the flow). The open boundary formulation was tested on a laminar plane Poiseuille flow and on two cases of propagation of a solitary wave. Comparisons with mesh-based methods are provided with, as well as comparisons with a weakly-compressible SPH (WCSPH) model using the same kind of boundary conditions. The results show that the model is able to represent flows in complex boundary geometries, while improving the pressure prediction compared to the WCSPH method. The extension of the model to 3-D was done in a massively parallel code running on a Graphic Processing Unit (GPU). Two validation cases in 3-D are presented, as well as preliminary results on a simple 3-D application case
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Messahel, Ramzi. "ALE and SPH formulations for Fluid Structure Interaction : shock waves impact." Thesis, Lille 1, 2016. http://www.theses.fr/2016LIL10022/document.
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Ce travail de thèse porte sur l’étude numérique de la propagation d’ondes de choc dans les écoulements compressibles multiphasiques et en interaction (fluide-structure). Deux approches sont étudiées pour la résolution numérique de la partie fluide : L’approche ALE (Arbitrary Lagrangian Eulerian) et l’approche lagrangienne SPH (Smoothed Particle Hydrodynamics) ; la partie structure, quant à elle, est résolue par une approche classique EF (Éléments finis). L’étude des méthodes ALE et SPH constituent les deux principaux axes de recherche. La problématique des coups de bélier dans l’ingénierie nucléaire est abordée dans cette thèse. Lors d’un coup de bélier, les nombreuses réflexions d’ondes de choc dans les tuyauteries nucléaires peuvent faire baisser la pression de l’eau en dessous de sa pression de saturation et générer localement de la cavitation. Le modèle HEM (Homogeneous Equilibrium Model) de changement de phase proposé par Saurel et al. (1999) à trois équations est étudié et appliqué aux coups de bélier. Les résultats obtenus sont comparés aux données expérimentales. Malgré l’utilisation des techniques de renormalisation en SPH, des instabilités (oscillations numériques) se développent à l’interface entre les particules de matériaux différents. Ces instabilités restreignent l’utilisation des schémas SPH classiques pour des problèmes à faible ratio de densité. Afin de résoudre les problèmes de choc, le schéma proposé par Hu et Adams (2006) est adapté au régime fortement compressible en considérant le couplage entre la densité et la longueur de lissage. Les différents schémas SPH sont comparés entre eux pour les problèmes de chocs multiphasiques en 1-D et 2-D. Les résultats SPH sont validés avec la solution exacte pour les problèmes 1-D et la solution ALE pour les problèmes 2-DThis thesis focuses on the numerical study of the propagation of shock waves in compressible multiphase flows and fluid structure interaction. Two approaches are being studied for the numerical solution of the fluid part: the ALE approach (Arbitrary Lagrangian Eulerian) and the Lagrangian SPH (Smoothed Particle Hydrodynamics) approach; while the structure part is solved by a conventional FE (Finite Element). The numerical investigation of the ALE and SPH methods are the two main areas of research.Water Hammers phenomena occuring in nuclear industries are investigated in this thesis. During a Water Hammer, the shock waves reflections in nuclear piping may drop locally the water pressure below its saturation pressure and generate cavitation. The three equations HEM (Homogeneous Equilibrium Model) phase change model proposed by Saurel et al. (1999) is studied and applied to solve water hammers. The obtained results are compared with experimental data. Despite the use of renormalization techniques in SPH, instabilities (numerical oscillations) are developed at the interface between particles from different materials. These instabilities restrict the use of traditional SPH schemes to problems with low density ratio. In order to solve the shock problems in the compressible regime, the scheme originally proposed by Hu and Adams (2006) is adapted to fully compressible regime (FC-SPH) by considering the coupling between the density and the smoothing length. The different SPH schemes are compared for 1-D and 2-D multiphase shock problems. Validation is performed in comparison with exact solutions for 1-D problems and ALE solution for 2-D problems
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Orthmann, Jens [Verfasser]. "Efficient SPH-based simulation and rendering of fluid transport dynamics / Jens Orthmann." Siegen : Universitätsbibliothek der Universität Siegen, 2015. http://d-nb.info/1068362847/34.
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Muir, Stuart. "A relativisitic, 3-dimensional smoothed particle hydrodynamics (SPH) algorithm and its applications." Monash University, School of Mathematical Sciences, 2003. http://arrow.monash.edu.au/hdl/1959.1/9513.
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