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Fleissner, Florian. "Parallel object oriented simulation with Lagrangian particle methods." Aachen Shaker, 2009. http://d-nb.info/1000976742/04.
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Fleissner, Florian [Verfasser]. "Parallel Object Oriented Simulation with Lagrangian Particle Methods / Florian Fleissner." Aachen : Shaker, 2010. http://d-nb.info/1124364129/34.
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Hosein, Falahaty. "Enhanced fully-Lagrangian particle methods for non-linear interaction between incompressible fluid and structure." Kyoto University, 2018. http://hdl.handle.net/2433/235070.
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Grabel, Michael Z. "A Lagrangian/Eulerian Approach for Capturing Topological Changes in Moving Interface Problems." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563527241172213.
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Rieth, Martin [Verfasser], and Andreas [Akademischer Betreuer] Kempf. "Large eddy and direct numerical simulation of single and multiphase flows relying on lagrangian particle methods / Martin Rieth ; Betreuer: Andreas Kempf." Duisburg, 2018. http://d-nb.info/1153337916/34.
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Pinto, Wesley José Nunes. "Aplicação do método lagrangiano SPH (Smoothed Particle Hydrodynamics ) para a solução do problema das cavidades." Universidade Federal do Espírito Santo, 2013. http://repositorio.ufes.br/handle/10/6144.
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Previous issue date: 2013-08-19Neste estudo foi aplicado do método numérico, sem malhas, baseado em partículas, denominado SPH (Smoothed Particles Hydrodynamics). E um código numérico na linguagem computacional FORTRAN foi utilizado para solucionar as equações de Navier-Stokes. O clássico problema da literatura da dinâmica dos fluidos Computacional, denotado como problema da cavidade quadrada bidimensional (Shear-Driven Cavity Flow) , foi estudado com a intenção de verificar o comportamento do código numérico em relação a resultados específicos já existentes do assunto. O citado problema físico das cavidades abertas é amplamente empregado como benchmark, visando a validação do método numérico utilizado no trabalho desenvolvido na pesquisa. O trabalho de análise e validação do código numérico foi dividido em três seções: a primeira lista as localizações dos centros dos vórtices principais gerados pelo escoamento na aresta superior das cavidades; a segunda plota os perfis das componentes das velocidades centrais das cavidades; e a terceira: lista os desvios absolutos dos perfis das velocidades centrais do presente trabalho, comparados com dados de outros estudos. Constata-se que o método SPH apresentou boa acurácia nas simulações realizadas, obtendo boa concordância entre os resultados das simulações dinâmicas com os dados de referências, validando-se o modelo numérico proposto, tendo melhores resultados para baixos números de Reynolds
In this study, it was applied the numerical method, grid-free, based on particles named SPH (Smoothed Particles Hydrodynamics). Also, a numerical code in the computer language FORTRAN was used to solve the Navier-Stokes Equations. This classic problem of the literature related to Computational Fluid Dynamics indicated as Shear-Driven Cavity Flow was studied to check the behavior of the numerical code regarding specific existing results. Such problem is highly used as Benchmark, aiming the validation of the numerical method used to develop the research. The analysis and validation of the numerical code was divided into three sections: the first one lists the location of the centre of the main vortex generated by the flow of the upper edge of the cavities; the second one plots the profiles of the components of the central speed of the cavities; the third one lists the absolute deviation of the profiles of the central speed of this study compared with other cases data. It is established that the SPH Method presented accuracy in the performed simulations, in a consonance between the results of the dynamic simulations and the reference data, thus the proposed numerical model was validated with better results for low Reynolds numbers
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Góes, Marciana Lima. "Desenvolvimento de um simulador numérico empregando o método Smoothed Particle Hydrodynamics para a resolução de escoamentos incompressíveis. Implementação computacional em paralelo (CUDA)." Universidade do Estado do Rio de Janeiro, 2012. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4029.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorNeste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak).
In this work a numerical simulator was developed based on the mesh-free Smoothed Particle Hydrodynamics (SPH) method to solve incompressible newtonian fluid flows. Unlike most existing versions of this method, the numerical code uses an iterative technique in the pressure field determination. This approach employs a differential state equation for a compressible fluid and the continuity equation to calculate the pressure correction. A parallel version of the numerical code was implemented using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA) from the NVIDIA Corporation. The numerical results were validated and the speed-up evaluated for an one-dimensional Couette flow and two-dimensional Shear Driven Cavity and Dambreak problems.
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Freitas, Mayksoel Medeiros de. "Simulação de escoamentos incompressíveis empregando o método Smoothed Particle Hydrodynamics utilizando algoritmos iterativos na determinação do campo de pressões." Universidade do Estado do Rio de Janeiro, 2013. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=4839.
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Nesse trabalho, foi desenvolvido um simulador numérico (C/C++) para a resolução
de escoamentos de fluidos newtonianos incompressíveis, baseado no método de
partículas Lagrangiano, livre de malhas, Smoothed Particle Hydrodynamics (SPH). Tradicionalmente,
duas estratégias são utilizadas na determinação do campo de pressões
de forma a garantir-se a condição de incompressibilidade do fluido. A primeira delas
é a formulação chamada Weak Compressible Smoothed Particle Hydrodynamics (WCSPH),
onde uma equação de estado para um fluido quase-incompressível é utilizada na determinação
do campo de pressões. A segunda, emprega o Método da Projeção e o campo
de pressões é obtido mediante a resolução de uma equação de Poisson. No estudo aqui
desenvolvido, propõe-se três métodos iterativos, baseados noMétodo da Projeção, para
o cálculo do campo de pressões, Incompressible Smoothed Particle Hydrodynamics (ISPH).
A fim de validar os métodos iterativos e o código computacional, foram simulados dois
problemas unidimensionais: os escoamentos de Couette entre duas placas planas paralelas
infinitas e de Poiseuille em um duto infinito e foram usadas condições de contorno
do tipo periódicas e partículas fantasmas. Um problema bidimensional, o escoamento
no interior de uma cavidade com a parede superior posta em movimento, também foi
considerado. Na resolução deste problema foi utilizado o reposicionamento periódico
de partículas e partículas fantasmas.In this work, we have developed a numerical simulator (C/C++) to solve incompressible Newtonian fluid flows, based on the meshfree Lagrangian Smoothed Particle Hydrodynamics (SPH) Method. Traditionally, two methods have been used to determine the pressure field to ensure the incompressibility of the fluid flow. The first is calledWeak Compressible Smoothed Particle Hydrodynamics (WCSPH) Method, in which an equation of state for a quasi-incompressible fluid is used to determine the pressure field. The second employs the Projection Method and the pressure field is obtained by solving a Poissons equation. In the study developed here, we have proposed three iterative methods based on the Projection Method to calculate the pressure field, Incompressible Smoothed Particle Hydrodynamics (ISPH) Method. In order to validate the iterative methods and the computational code we have simulated two one-dimensional problems: the Couette flow between two infinite parallel flat plates and the Poiseuille flow in a infinite duct, and periodic boundary conditions and ghost particles have been used. A two-dimensional problem, the lid-driven cavity flow, has also been considered. In solving this problem we have used a periodic repositioning technique and ghost particles.
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Cocle, Roger. "Combining the vortex-in-cell and parallel fast multipole methods for efficient domain decomposition simulations : DNS and LES approaches." Université catholique de Louvain, 2007. http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-08172007-165806/.
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This thesis is concerned with the numerical simulation of high Reynolds number, three-dimensional, incompressible flows in open domains. Many problems treated in Computational Fluid Dynamics (CFD) occur in free space: e.g., external aerodynamics past vehicles, bluff bodies or aircraft; shear flows such as shear layers or jets. In observing all these flows, we can remark that they are often unsteady, appear chaotic with the presence of a large range of eddies, and are mainly dominated by convection. For years, it was shown that Lagrangian Vortex Element Methods (VEM) are particularly well appropriate for simulating such flows. In VEM, two approaches are classically used for solving the Poisson equation. The first one is the Biot-Savart approach where the Poisson equation is solved using the Green's function approach. The unbounded domain is thus implicitly taken into account. In that case, Parallel Fast Multipole (PFM) solvers are usually used. The second approach is the Vortex-In-Cell (VIC) method where the Poisson equation is solved on a grid using fast grid solvers. This requires to impose boundary conditions or to assume periodicity. An important difference is that fast grid solvers are much faster than fast multipole solvers. We here combine these two approaches by taking the advantages of each one and, eventually, we obtain an efficient VIC-PFM method to solve incompressible flows in open domain. The major interest of this combination is its computational efficiency: compared to the PFM solver used alone, the VIC-PFM combination is 15 to 20 times faster. The second major advantage is the possibility to run Large Eddy Simulations (LES) at high Reynolds number. Indeed, as a part of the operations are done in an Eulerian way (i.e. on the VIC grid), all the existing subgrid scale (SGS) models used in classical Eulerian codes, including the recent "multiscale" models, can be easily implemented.
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Vidal, Seguí Yolanda. "Mesh-Free Methods for Dynamic Problems. Incompressibility and Large Strain." Doctoral thesis, Universitat Politècnica de Catalunya, 2005. http://hdl.handle.net/10803/6709.
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This thesis makes two noteworthy contributions in the are of mesh-free methods: a Pseudo-Divergence-Free (PDF) Element Free Galerkin (EFG) method which alleviates the volumetric locking and a Stabilized Updated Lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way. First of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature.
Secondly, a novel improved formulation of the (EFG) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. In this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard EFG and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard EFG the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly incompressible case and a moderately fine discretization. The improved method has also been used to solve the Stokes equations. In this case the LBB condition is not explicitly satisfied because the pseudo-divergence-free approximation is employed. Reasonable results are obtained in spite of the equal order interpolation for velocity and pressure.
Finally, several techniques have been developed in the past to solve the well known tensile instability in the SPH (Smooth Particle Hydrodynamics) mesh-free method. It has been proved that a Lagrangian formulation removes completely the instability (but zero energy modes exist). In fact, Lagrangian SPH works even better than the Finite Element Method in problems involving distortions. Nevertheless, in problems with very large distortions a Lagrangian formulation will need of frequent updates of the reference configuration. When such updates are incorporated then zero energy modes are more likely to be activated. When few updates are carried out the error is small but when updates are performed frequently the solution is completely spoilt because of the zero energy modes. In this thesis an updated Lagrangian formulation is developed. It allows to carry out updates of the reference configuration without suffering the appearance of spurious modes. To update the Lagrangian formulation an incremental approach is used: an intermediate configuration will be the new reference configuration for the next time steps. It has been observed that this updated formulation suffers from similar numerical fracture to the Eulerian case. A modal analysis has proven that there exist zero energy modes. In the paper the updated Lagrangian method is exposed in detail, a stability analysis is performed and finally a stabilization technique is incorporated to preclude spurious modes.
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Góes, Josecley Fialho. "Resolução numérica de escoamentos compressíveis empregando um método de partículas livre de malhas e o processamento em paralelo (CUDA)." Universidade do Estado do Rio de Janeiro, 2011. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=3082.
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Os métodos numéricos convencionais, baseados em malhas, têm sido amplamente
aplicados na resolução de problemas da Dinâmica dos Fluidos Computacional.
Entretanto, em problemas de escoamento de fluidos que envolvem superfícies livres,
grandes explosões, grandes deformações, descontinuidades, ondas de choque etc., estes
métodos podem apresentar algumas dificuldades práticas quando da resolução destes
problemas. Como uma alternativa viável, existem os métodos de partículas livre de
malhas. Neste trabalho é feita uma introdução ao método Lagrangeano de partículas,
livre de malhas, Smoothed Particle Hydrodynamics (SPH) voltado para a simulação numérica
de escoamentos de fluidos newtonianos compressíveis e quase-incompressíveis.
Dois códigos numéricos foram desenvolvidos, uma versão serial e outra em paralelo,
empregando a linguagem de programação C/C++ e a Compute Unified Device Architecture
(CUDA), que possibilita o processamento em paralelo empregando os núcleos das
Graphics Processing Units (GPUs) das placas de vídeo da NVIDIA Corporation. Os resultados
numéricos foram validados e a eficiência computacional avaliada considerandose
a resolução dos problemas unidimensionais Shock Tube e Blast Wave e bidimensional
da Cavidade (Shear Driven Cavity Problem).The conventional mesh-based numerical methods have been widely applied to solving problems in Computational Fluid Dynamics. However, in problems involving fluid flow free surfaces, large explosions, large deformations, discontinuities, shock waves etc. these methods suffer from some inherent difficulties which limit their applications to solving these problems. Meshfree particle methods have emerged as an alternative to the conventional grid-based methods. This work introduces the Smoothed Particle Hydrodynamics (SPH), a meshfree Lagrangian particle method to solve compressible flows. Two numerical codes have been developed, serial and parallel versions, using the Programming Language C/C++ and Compute Unified Device Architecture (CUDA). CUDA is NVIDIAs parallel computing architecture that enables dramatic increasing in computing performance by harnessing the power of the Graphics Processing Units (GPUs). The numerical results were validated and the speedup evaluated for the Shock Tube and Blast Wave one-dimensional problems and Shear Driven Cavity Problem.
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Jenkinson, William. "Simulation de la mécanique mésoscopique des aliments par méthodes de particules lagrangiennes." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASB047.
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Le rôle des mécanismes mésoscopiques dans le traitement et la conception des aliments est encore mal compris, notamment pour la transformation orale et la perception de la texture. Malgré le développement de la physique de la matière molle, les scientifiques peinent encore à relier les comportements micro-, méso- et macroscopiques par des simulations. Cette thèse se concentre sur les simulations mécaniques, excluant les effets thermiques, chimiques et physico-chimiques, pour explorer le comportement des aliments à l'échelle mésoscopique. Nous avons développé une approche de simulation dans LAMMPS combinant des implémentations de "smoothed-particle hydrodynamics" (SPH) pour les liquides et les solides élastiques. Cette approche a été validée pour des scénarios comme l'écoulement de Couette et la déformation des granules. Les résultats démontrent l'efficacité de l'approche pour capter la dynamique des structures alimentaires et leurs interactions avec des papilles et des cils ; offrant de nouvelles perspectives sur la perception de la texture. L'étude met aussi en évidence l'impact de l'élasticité des granules et de leur fraction volumique sur les propriétés d'écoulement. Ce travail, centré sur la mécanique, reste ouvert à l'intégration future de processus thermiques, chimiques et biologiques dans les modèles alimentaires. Les recherches futures viseront à intégrer plus de physiques et à rendre les outils de simulation plus accessibles aux ingénieurs, pour favoriser les applications pratiques en science des alimentsThe role of mesoscopic mechanics in food processing and design is not well understood, particularly for oral processing and texture perception. Despite the recognized importance of soft matter, the food science community has struggled to bridge the gap between micro-, meso-, and macro-scale behaviours using simulations. This thesis addresses this challenge by focusing on mechanical simulations, excluding thermal, chemical and physicochemical effects, to explore food behaviour at the mesoscopic scale. We have developed a simulation framework within the LAMMPS environment, combining smoothed-particle hydrodynamics (SPH) implementations for liquids and elastic solids. We validated the framework across scenarios such as Couette flow and deformation of granules in a flow. The results show the framework's effectiveness in capturing food structure dynamics and interactions with cilia and papillae and offer new insights into texture perception and hydrodynamics. The study also highlights how granule elasticity and volume fraction impact flow properties and their eventual role in texture perception. This work focuses on mechanics while deliberately remaining flexible enough to integrate mechanical, thermal, chemical, and biological processes in future food science models. Proposed future research includes strategies to integrate more physics and scales and efforts to improve the accessibility of simulation tools for engineers, advancing practical applications in food science
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Tsukamoto, Marcio Michiharu. "Desenvolvimento do método de partículas na representação de corpos flutuantes em ondas altamente não-lineares." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/3/3135/tde-19092006-111325/.
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O método numérico para fluidos incompressíveis desenvolvido no presente estudo é o Moving Particle Semi-Implicit Method (MPS) que enxerga o domínio discretizado em partículas, é baseado em representação lagrangeana e não tem a necessidade de utilização de malhas. O método MPS tem como equações governantes uma forma particular da equação de Navier-Stokes e a equação da continuidade para fluidos incompressíveis e não viscosos. Os métodos de simulação de fluidos mais comumente utilizados são baseados em representação euleriana e utilizam malhas para descrever a geometria do domínio a ser simulado. Devido a essas diferenças, uma das grandes virtudes do método de partículas é a facilidade de investigação de fenômenos altamente não-lineares como o de superfície livre com quebra de ondas, de líquidos no interior de uma embarcação em movimento, de ondas batendo na parte externa do casco de um navio, etc. Em artigos já publicados, resultados de experimentos físicos mostraram boa aderência aos resultados numéricos de simulações realizadas com o método MPS. No presente trabalho, resultados das forças de excitação das simulações com ondas regulares foram comparados com os resultados do programa Wave Analysis MIT (WAMIT) que é um programa consagrado no meio científico. Houve uma boa concordância de resultados entre os dois programas. A otimização do cálculo de vizinhança forneceu uma grande economia de tempo computacional. A maior contribuição deste estudo foi a otimização da função que resolve o sistema linear implementando no código desenvolvido um código paralelizado de uso público existente chamado Portable, Extensible Toolkit for Scientific Computation (PETSc) que proporcionou um bom ganho de desempenho.A numerical method called Moving Particle Semi-implicit (MPS) method was developed in this study to analyze incompressible fluids. It is a particle method using a lagrangean representation without any grid. The governing equations are the Navier-Stokes equation and continuity equation for incompressible and non-viscous flow. Most of the computational fluid dynamics (CFD) methods are based on eulerian representation and use grids to describe the geometry of the simulated domain. These differences make the MPS method easier to analyze highly nonlinear phenomena as free surface with wave breaking, sloshing, slamming, etc. In previously published articles, results of physical experiments had shown good agreement with the numerical results obtained with MPS method. In the present work, results of exciting forces were compared with the results obtained with a validated program called Wave Analysis MIT (WAMIT). It had a good agreement of results between these two programs. The optimization of the neighborhood calculation function got a good economy of computational time. The greatest contribution of this study was the optimization of the linear system solver. It was made implementing in the developed code a parallelized public code called Portable, Extensible Toolkit for Scientific Computation (PETSc) that provided a good performance profit.
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Kim, Ho Jun. "Theoretical and numerical studies of chaotic mixing." Diss., Texas A&M University, 2008. http://hdl.handle.net/1969.1/85940.
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Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties
of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to
carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral
element algorithm for solution of the incompressible Navier-Stokes and species transport
equations is developed. Using Taylor series expansions in time marching, the new algorithm
employs an algebraic factorization scheme on multi-dimensional staggered spectral element
grids, and extends classical conforming Galerkin formulations to nonconforming spectral
elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the
mixing device using spectral element and fourth order Runge-Kutta discretizations in space and
time, respectively. Comparative studies of five different techniques commonly employed to
identify the chaotic strength and mixing efficiency in microfluidic systems are presented to
demonstrate the competitive advantages and shortcomings of each method. These are the stirring
index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the
probability density function of the stretching field, and mixing index inverse, based on the
standard deviation of scalar species distribution. Series of numerical simulations are performed
by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ∝ ln(Pe) scaling is demonstrated for fully
chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the
actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are
identified in a zeta potential patterned straight micro channel, where a continuous flow is
generated by superposition of a steady pressure driven flow and time periodic electroosmotic
flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold
of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in
two-dimensional cavity.
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Veen, Daniel John. "A smoothed particle hydrodynamics study of ship bow slamming in ocean waves." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/1694.
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Smoothed Particle Hydrodynamics (SPH) is a mesh-free Lagrangian computational method suited to modelling fluids with a freely deforming surface. This thesis describes the development, validation and application of a two-dimensional Smoothed Particle Hydrodynamics algorithm to the problem of ship bow slamming in regular ocean waves. Slam events often occur in rough seas and have the potential to cause significant structural and payload damage due to the loads and subsequent whipping experienced by the ship. SPH is well suited to modelling ship bow slamming because the interaction between the bow of the ship and the water surface is of a freely deforming transient nature.The developed SPH algorithm was subjected to an extensive validation using both analytical and experimental data as a basis for comparison. The influence of each numerical correction – necessary for SPH stability – was evaluated using two theoretical problems free from the influence of external forces: the evolution of initially circular and square patches of fluid. Solid boundaries treated by the ghost particle technique were introduced and evaluated by way of the hydrostatic tank and the two-dimensional dam break.Still water impacts of two-dimensional wedges and hull cross-sections were simulated using the SPH algorithm and the results were compared with the experimental data of Aarsnes (1996), Whelan (2004) and Breder (2005). The complexity of the slamming problem was then increased by imposing the relative vertical velocity profile (between the hull and the water surface) measured during the ocean wave basin experiments of Hermundstad and Moan (2005) on a hull cross-section. Reasonable agreement between the simulated and experimental slamming pressures confirmed that the two-dimensional SPH algorithm could be applied to a three-dimensional problem through the use of a relative vertical velocity profile.Finally, the commercial ship motion prediction software SEAWAY and the validated SPH algorithm were combined in a 2D + t method to simulate bow slamming of a slender hull. The relative motion between the bow and the free water surface was extracted from the ship motion data and then imposed on a cross-section of a given hull form. Satisfactory agreement with the peak pressures measured on a model V-form hull in regular waves (Ochi, 1958) demonstrated that the developed two-dimensional SPH code is capable of modelling three-dimensional ship bow slamming.
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Nasar, Abouzied. "Eulerian and Lagrangian smoothed particle hydrodynamics as models for the interaction of fluids and flexible structures in biomedical flows." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/eulerian-and-lagrangian-smoothed-particle-hydrodynamics-as-models-for-the-interaction-of-fluids-and-flexible-structures-in-biomedical-flows(507cd0db-0116-4258-81f2-8d242e8984fa).html.
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Fluid-structure interaction (FSI), occurrent in many areas of engineering and in the natural world, has been the subject of much research using a wide range of modelling strategies. However, problems with high levels of structural deformation are difficult to resolve and this is particularly the case for biomedical flows. A Lagrangian flow model coupled with a robust model for nonlinear structural mechanics seems a natural candidate since large distortion of the computational geometry is expected. Smoothed particle Hydrodynamics (SPH) has been widely applied for nonlinear interface modelling and this approach is investigated here. Biomedical applications often involve thin flexible structures and a consistent approach for modelling the interaction of fluids with such structures is also required. The Lagrangian weakly compressible SPH method is investigated in its recent delta-SPH form utilising inter-particle density fluxes to improve stability. Particle shifting is also used to maintain particle distributions sufficiently close to uniform to enable stable computation. The use of artificial viscosity is avoided since it introduces unphysical dissipation. First, solid boundary conditions are studied using a channel flow test. Results show that when the particle distribution is allowed to evolve naturally instabilities are observed and deviations are noted from the expected order of accuracy. A parallel development in the SPH group at Manchester has considered SPH in Eulerian form (for different applications). The Eulerian form is applied to the channel flow test resulting in improved accuracy and stability due to the maintenance of a uniform particle distribution. A higher-order accurate boundary model is developed and applied for the Eulerian SPH tests and third-order convergence is achieved. The well documented case of flow past a thin plate is then considered. The immersed boundary method (IBM) is now a natural candidate for the solid boundary. Again, it quickly becomes apparent that the Lagrangian SPH form has limitations in terms of numerical noise arising from anisotropic particle distributions. This corrupts the predicted flow structures for moderate Reynolds numbers (O(102)). Eulerian weakly compressible SPH is applied to the problem with the IBM and is found to give accurate and convergent results without any numerical stability problems (given the time step limitation defined by the Courant condition). Modelling highly flexible structures using the discrete element model is investigated where granular structures are represented as bonded particles. A novel vector-based form (the V-Model) is identified as an attractive approach and developed further for application to solid structures. This is shown to give accurate results for quasi-static and dynamic structural deformation tests. The V-model is applied to the decay of structural vibration in a still fluid modelled using Eulerian SPH with no artificial stabilising techniques. Again, results are in good agreement with predictions of other numerical models. A more demanding case representative of pulsatile flow through a deep leg vein valve is also modelled using the same form of Eulerian SPH. The results are free of numerical noise and complex FSI features are captured such as vortex shedding and non-linear structural deflection. Reasonable agreement is achieved with direct in-vivo observations despite the simplified two-dimensional numerical geometry. A robust, accurate and convergent method has thus been developed, at present for laminar two-dimensional low Reynolds number flows but this may be generalised. In summary a novel robust and convergent FSI model has been established based on Eulerian SPH coupled to the V-Model for large structural deformation. While these developments are in two dimensions the method is readily extendible to three-dimensional, laminar and turbulent flows for a wide range of applications in engineering and the natural world.
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Berchet, Adrien. "Modélisation par des méthodes lagrangiennes du transport sédimentaire induit par les mascarets." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2319/document.
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Le travail effectué au cours de cette thèse s'inscrit au sein du projet ANR Mascaret, dont l'objectif est la compréhension du phénomène de mascaret, l'étude de ses conséquences sur l'environnement et sa sensibilité aux modifications de cet environnement. La contribution de cette thèse s'inscrit uniquement dans la partie numérique de ce projet. Seul l'aspect transport sédimentaire causé par le mascaret sera abordé. Le but est de construire un modèle numérique de transport sédimentaire général qui pourra notamment s'appliquer au cas du mascaret. Trois méthodes numériques sont explorées, une première permettant le suivi individuel des grains sédimentaires et deux autres permettant de suivre l'évolution de la concentration en grains au sein de l'écoulement. La première méthode considérera les plus petites échelles et sera appelée méthode tracker et consistera en un suivi individuel des grains sédimentaires. La seconde méthode, dite méthode particulaire, portera sur des échelles plus larges et le transport d'une concentration locale en grains sédimentaires. Enfin, la troisième méthode, que l'on appellera méthode des moments, s'intéressera aux échelles les plus larges en transportant un nuage de particules sédimentaires dans son ensemble grâce à une seule particule numérique caractérisée par les moments de sa distribution en concentration interne. Ceci permettra de caractériser le transport sédimentaire de manière locale qui se produit lors du passage d'un mascaret. Deux mascarets ondulés de nombre de Froude proches seront étudiés. Il sera notamment montré que le nombre de Froude n'est pas un critère permettant de caractériser le transport sédimentaire induit par les mascaretsThe work performed during this thesis is a part of the Mascaret ANR project, which aims to understand the phenomenon of tidal bore, the study of its impact on the environment and its sensitivity to changes in that environment. The contribution of this thesis lies solely in the numerical part of this project. Only the sediment transport caused by the tidal bore is discussed. The goal is to build a generic numerical model of sediment transport which can therefore be applied to the specific case of tidal bores. Three methods are explored, a first for individual tracking of sediment grains and two to model the concentration of grains in the flow. The first method considers the smallest scales and will be called tracking method and consists of individual tracking of sediment grains. The second method, called particle method, focuses on larger scales and the transport of local concentration of sedimentary grains. The third method, which we call moments method, will focus on the largest scales, carrying a cloud of sediment grains as a whole using a single numerical particle characterized by the moments of its internal concentration distribution. This will characterize the local sediment transport process occurring during the passage of a tidal bore. Two undulating bores will be studied whose Froude numbers are close. It will be shown in particular that the Froude number is not a criterion to deduce the intensity of the induced tidal bores sediment transport
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Zhong, Lu. "Compressed Sensing via Partial L1 Minimization." Digital WPI, 2017. https://digitalcommons.wpi.edu/etd-theses/397.
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Reconstructing sparse signals from undersampled measurements is a challenging problem that arises in many areas of data science, such as signal processing, circuit design, optical engineering and image processing. The most natural way to formulate such problems is by searching for sparse, or parsimonious, solutions in which the underlying phenomena can be represented using just a few parameters. Accordingly, a natural way to phrase such problems revolves around L0 minimization in which the sparsity of the desired solution is controlled by directly counting the number of non-zero parameters. However, due to the nonconvexity and discontinuity of the L0 norm such optimization problems can be quite difficult. One modern tactic to treat such problems is to leverage convex relaxations, such as exchanging the L0 norm for its convex analog, the L1 norm. However, to guarantee accurate reconstructions for L1 minimization, additional conditions must be imposed, such as the restricted isometry property. Accordingly, in this thesis, we propose a novel extension to current approaches revolving around truncated L1 minimization and demonstrate that such approach can, in important cases, provide a better approximation of L0 minimization. Considering that the nonconvexity of the truncated L1 norm makes truncated l1 minimization unreliable in practice, we further generalize our method to partial L1 minimization to combine the convexity of L1 minimization and the robustness of L0 minimization. In addition, we provide a tractable iterative scheme via the augmented Lagrangian method to solve both optimization problems. Our empirical study on synthetic data and image data shows encouraging results of the proposed partial L1 minimization in comparison to L1 minimization.
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Dellinger, Nicolas. "Modélisation de la formation et de l’évolution des particules de suie en approche hybride Euler-Lagrange pour la simulation de foyers aéronautiques." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS074.
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Les suies représentent un enjeu important pour la conception des foyers aéronautiques. Une nouvelle réglementation de leurs émissions doit en effet entrer en vigueur en 2020. Aussi, les suies modifient les transferts radiatifs en leur sein affectant la charge thermique aux parois et la formation des NOx. Prédire précisément et efficacement la formation et l’évolution des particules de suie est cependant une question toujours ouverte en CFD. Ce travail propose de combiner une description eulérienne des précurseurs de suie et une description lagrangienne de l’évolution des particules, celle-ci étant bien adaptée au suivi de l’évolution de leur distribution en taille. La croissance des hydrocarbures aromatiques polycycliques est modélisée par une méthode sectionnelle pour calculer le taux de nucléation de suies et créer les particules suivies dans l’écoulement. Celles-ci sont modélisées par des sphères interagissant avec le gaz et – pour les plus jeunes – entre elles par coalescence selon leur diamètre. La méthode est implantée dans le code CEDRE et associée à une procédure de réduction du nombre de particules pour en contrôler le coût de convergence statistique. Appliquée à des flammes laminaires stationnaires de prémélange C2H4-air, elle est confrontée à des mesures de composition, fraction volumique de suie et diamètre des particules avec succès. La méthode est utilisée, avec l’Approximation de l’État Quasi-Stationnaire appliquée à la chimie du gaz, pour simuler une flamme turbulente pressurisée C2H4-air analogue aux configurations RQL des foyers aéronautiques, et confrontée à des mesures de fraction volumique de suie, vitesse, température et composition avec succèsSoot has become an important issue in the design of aeroengine combustors. New certifications on soot particles are to be applied in 2020 due to growing concern about pollutant emissions in the transportation industry. Soot particles also modify radiative heat transfers in combustion chambers affecting thermal load at walls and NOx formation. Still, efficient and accurate prediction of soot particles formation and evolution is an open field in CFD. This manuscript proposes to combine a Eulerian description of soot precursors and a Lagrangian description of particles evolution, which has the advantage to be well suited to follow the evolution of the particle size distribution. The growth of polycyclic aromatic hydrocarbons is modelled by a sectional method to obtain the soot inception rate and create the particles tracked in the gas flow. The particles are described as spheres interacting with the gas through chemical processes and between each other by coalescence, bounded to young liquid-like particles depending on their diameter. The method is implemented in the CEDRE code and completed by an algorithm for the reduction of the particles population to limit the cost of its statistical convergence. Applied to steady laminar premixed C2H4-air flames, it is confronted with some success to measurements of soot volume fraction, particle diameter and species molar fractions. The method is then applied combined with the Quasi-Steady State Approximation for gas chemistry to a swirled pressurized C2H4-air flame, similar to RQL configurations of aeroengine combustors, and confronted with some success to velocity, temperature, composition and soot volume fraction measurements
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Nguyen, Van Thanh. "Problèmes de transport partiel optimal et d'appariement avec contrainte." Thesis, Limoges, 2017. http://www.theses.fr/2017LIMO0052.
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Cette thèse est consacrée à l'analyse mathématique et numérique pour les problèmes de transport partiel optimal et d'appariement avec contrainte (constrained matching problem). Ces deux problèmes présentent de nouvelles quantités inconnues, appelées parties actives. Pour le transport partiel optimal avec des coûts qui sont donnés par la distance finslerienne, nous présentons des formulations équivalentes caractérisant les parties actives, le potentiel de Kantorovich et le flot optimal. En particulier, l'EDP de condition d'optimalité permet de montrer l'unicité des parties actives. Ensuite, nous étudions en détail des approximations numériques pour lesquelles la convergence de la discrétisation et des simulations numériques sont fournies. Pour les coûts lagrangiens, nous justifions rigoureusement des caractérisations de solution ainsi que des formulations équivalentes. Des exemples numériques sont également donnés. Le reste de la thèse est consacré à l'étude du problème d'appariement optimal avec des contraintes pour le coût de la distance euclidienne. Ce problème a un comportement différent du transport partiel optimal. L'unicité de solution et des formulations équivalentes sont étudiées sous une condition géométrique. La convergence de la discrétisation et des exemples numériques sont aussi établis. Les principaux outils que nous utilisons dans la thèse sont des combinaisons des techniques d'EDP, de la théorie du transport optimal et de la théorie de dualité de Fenchel--Rockafellar. Pour le calcul numérique, nous utilisons des méthodes du lagrangien augmentéThe manuscript deals with the mathematical and numerical analysis of the optimal partial transport and optimal constrained matching problems. These two problems bring out new unknown quantities, called active submeasures. For the optimal partial transport with Finsler distance costs, we introduce equivalent formulations characterizing active submeasures, Kantorovich potential and optimal flow. In particular, the PDE of optimality condition allows to show the uniqueness of active submeasures. We then study in detail numerical approximations for which the convergence of discretization and numerical simulations are provided. For Lagrangian costs, we derive and justify rigorously characterizations of solution as well as equivalent formulations. Numerical examples are also given. The rest of the thesis presents the study of the optimal constrained matching with the Euclidean distance cost. This problem has a different behaviour compared to the partial transport. The uniqueness of solution and equivalent formulations are studied under geometric condition. The convergence of discretization and numerical examples are also indicated. The main tools which we use in the thesis are some combinations of PDE techniques, optimal transport theory and Fenchel--Rockafellar dual theory. For numerical computation, we make use of augmented Lagrangian methods
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Vivion, Léo. "Particules classiques et quantiques en interaction avec leur environnement : analyse de stabilité et problèmes asymptotiques." Thesis, Université Côte d'Azur, 2020. https://tel.archives-ouvertes.fr/tel-03135254.
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Au début des années 2000, inspirés par les travaux fondateurs de A.O. Caldeira et A.J. Leggett, L. Bruneau et S. de Bièvre ont introduit un modèle hamiltonien décrivant les échanges d'énergie entre une particule classique et son environnement, ce modèle étant tel que l'environnement agit sur la particule comme une force de friction. D'un côté ce modèle a été étendu au cas de plusieurs particules et, lorsque le nombre de particules considérées est très grand, un modèle cinétique a également été dérivé. Dans la suite ce modèle sera appelé système Vlasov-Onde. De l'autre, comme ce modèle est hamiltonien il est possible de considérer une version quantique de celui-ci. Nous appellerons un tel modèle système Schrödinger-Onde. L'objet de cette thèse est l'étude asymptotique de certaines dynamiques des systèmes Vlasov et Schrödinger-Onde.Dans le cas cinétique il existe des solutions stationnaires telles que la densité de particule dans l'espace des phases soit spatialement homogène. Dans ce cas, par analogie avec le système Vlasov-Poisson, nous nous sommes posé la question de l'existence d'un effet d'amortissement Landau pour de petites perturbations de ces solutions particulières. Nous avons dans un premier temps obtenu un nouveau critère de stabilité linéaire qui nous a ensuite permis de démontrer, en adaptant les travaux de J. Bedrossian, N. Masmoudi, C. Mouhot et C. Villani, un effet d'amortissement Landau non linéaire dans le cas de l'espace entier et du tore. Nous avons en particulier obtenu de nouvelles contraintes (provenant de l'interaction avec l'environnement) sur le taux d'amortissement et nous avons fait le lien entre les équilibres stables du système Vlasov-Onde et ceux du système Vlasov-Poisson, notamment en justifiant qu'un des paramètres du système joue un rôle analogue à la longueur de Jeans dans le cas Vlasov-Poisson attractif. Cette étude théorique est complétée par une étude numérique qui nous a permis de conforter notre compréhension de l'impact des paramètres intervenant dans le système Vlasov-Onde sur la dynamique de ces solutions.Dans le cas du système Schrödinger-Onde nous nous sommes posé la question de la possibilité de mettre en évidence un effet de friction, provenant du milieu et agissant sur la particule quantique. Pour ce faire nous avons dans un premier temps justifié l'existence d'ondes solitaires (ces solutions particulières où la dispersion de l'équation de Schrödinger est parfaitement compensée par un effet attractif) ainsi que la stabilité orbitale des états fondamentaux (une onde solitaire minimisant l'énergie sous une contrainte de masse). Ce résultat de stabilité orbitale nous assure alors qu'une perturbation d'un état fondamental reste en tout temps proche de celui-ci modulo les invariances du système, ici translation et changement de phase. En particulier un état fondamental peut potentiellement se déplacer et nous avons étudié l'existence d'un effet de friction à travers ce possible déplacement. Si dans le cas Schrödinger-Newton l'invariance galiléenne assure l'existence d'états fondamentaux se déplaçant en ligne droite à vitesse constante, le système Schrödinger-Onde ne possède pas cette invariance et l'analogie avec le cas classique suggère que la vitesse de déplacement va nécessairement converger vers zéro. Cette conjecture a été étudiée et confirmée numériquement.Les deux études numériques esquissées précédemment ont nécessité le développement d'une discrétisation temporelle des équations prenant en compte la forme des interactions entre les particules et l'environnement afin de garantir que les échanges d'énergie au niveau discret sont consistants avec ceux au niveau continuAt the beginning of the 2000's, inspired by the prioneering works of A.O. Caldeira and A.J. Leggett, L. Bruneau and S. de Bièvre introduced an Hamiltonian model describing exchanges of energy between a classical particle and its environment in a way that these exchanges lead to a friction effect on the particle. On one hand this model has been extended to the case of several particles and, when the number of particle is large, a kinetic model has also been derived. Hereafter this model will be referred as the Vlasov-Wave system. On the other hand, since this model is Hamiltonian, it is possible to consider its quantum version. We call this new model the Schrödinger-Wave system. The aim of this thesis is to study the asymptotic of particular dynamics of the Vlasov and Schrödinger-Wave systems.In the kinetic case there exists stationary solutions such that the particle density in the phase space is spatially homogeneous. Then, by analogy with the Vlasov-Poisson system we considered the question of the existence of a Landau damping effect for small perturbations of these particular solutions. We obtain a new linear stability criterion which allows us then to obtain, by adapting the works of J. Bedrossian, N. Masmoudi, C. Mouhot and C. Villani, a proof of non linear Landau damping in the free space and torus cases. In particular we exhibit new constraints (due to the interactions with the environment) on damping rates. We also exhibit a link between stable equilibria of the Vlasov-Wave system and those for the Vlasov-Poisson system and we highlight the similarity between a parameter of the system and the Jeans' length in the attractive Vlasov-Poisson case. This study led to a numerical one which allows us to reinforce our comprehension on the role of the system's parameters, more precisely on their role on solutions' dynamic.In the Schrödinger-Wave case we investigated the possibility of highlighting a friction effect on the quantum particle coming from the environment. As a first step we justify the existence of solitary waves (these solutions where the dispersion of the Schrödinger equation is perfectly compensated by an attractive effect) and the orbital stability of ground states (a solitary wave minimizing the energy under a mass constraint). This orbital stability result insures that a small perturbation of a ground state stays, up to the equation's invariances (here translation and change of phase), close to it uniformly in time. Then a ground state might possibly move and we study the existence of a friction effect through this possible displacement. If in the Schrödinger-Newton case the Galilean invariance allows to construct a solution which is a ground states moving on a straight line at constant momentum, the Schrödinger-Wave system is not Galilean invariant and the analogy with the classical case suggested that the momentum of a moving ground state converges to zero. This conjecture has been studied and confirmed numerically. The numerical investigations require the development of a time discretization of the considered equations taking into account the expression of the interactions between particles and the environment in order to insure that the energy exchanges at numerical ground are consistent with those at continuous level
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Bounaim, Aïcha. "Méthodes de décomposition de domaine : application à la résolution de problèmes de contrôle optimal." Phd thesis, Université Joseph Fourier (Grenoble), 1999. http://tel.archives-ouvertes.fr/tel-00004809.
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Ce travail porte sur l'étude des méthodes de décomposition de domaine et leur application pour résoudre des problèmes de contrôle optimal régis par des équations aux dérivées partielles. Le principe de ces méthodes consiste à ramener des problèmes de grande taille sur des géométries complexes en une suite de sous-problèmes de taille plus petite sur des géométries plus simples. En considérant une décomposition sans recouvrement, l'intérêt de ces méthodes pour les problèmes de contrôle optimal réside au niveau de l'intégration de l'équation d'état, puisqu'il est possible de partitionner le problème en une suite de problèmes plus petits, quitte à contraindre les interfaces entre les sous-domaines à obéir à des conditions de raccordement afin de déduire la solution globale à partir des solutions locales. Dans une première partie, nous étudions le cas elliptique. Nous considérons simultanément la minimisation de la fonction coût et des raccordements sur les frontières entre les sous-domaines. Cette combinaison de problèmes de minimisation et de méthodes de décomposition de domaine est traitée par des techniques de Lagrangien augmenté. Nous montrons que, sur le domaine décomposé, le problème initial se réduit à la recherche d'un point-selle. Une étude des méthodes de Lagrangien nous a permis de choisir une variante d'algorithmes existants dans la littérature et de les combiner avec un algorithme de décomposition de domaine. Dans la seconde partie, nous développons l'extension de cette approche aux problèmes de contrôle optimal régis par des systèmes paraboliques en considérant uniquement une décomposition en espace du domaine de calcul. Dans une dernière partie, nous considérons une décomposition de domaine avec recouvrement à chaque pas de la minimisation. D'une part, nous construisons un algorithme parallèle en utilisant la méthode de Schwarz multiplicative en tant que solveur. Ceci permet de déduire naturellement l'état adjoint par transposition des systèmes directs locaux. L'algorithme global défini par la méthode de minimisation de type quasi-Newton et ce solveur de Schwarz constitue une méthode robuste de résolution du problème de contrôle optimal, mais coûteuse. D'autre part, et plus particulièrement, pour des problèmes de grande taille, l'algorithme de type quasi-Newton, combiné avec le solveur de Krylov BiCGSTAB préconditionné par une méthode de Schwarz additive, est plus compétitif dans la mesure oû l'on obtient de bonnes performances parallèles. De nombreux résultats sont présentés pour préciser le comportement des algorithmes d'optimisation quand ils sont utilisés avec des méthodes de Schwarz.
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Pham, Thi Trang Nhung. "Méthodes numériques pour l'équation de Vlasov réduite." Thesis, Strasbourg, 2016. http://www.theses.fr/2016STRAD051/document.
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Beaucoup de méthodes numériques ont été développées pour résoudre l'équation de Vlasov, car obtenir des simulations numériques précises en un temps raisonnable pour cette équation est un véritable défi. Cette équation décrit en effet l'évolution de la fonction de distribution de particules (électrons/ions) qui dépend de 3 variables d'espace, 3 variables de vitesse et du temps. L'idée principale de cette thèse est de réécrire l'équation de Vlasov sous forme d'un système hyperbolique par semi-discrétisation en vitesse. Cette semi-discrétisation est effectuée par méthode d'éléments finis. Le modèle ainsi obtenu est appelé équation de Vlasov réduite. Nous proposons différentes méthodes numériques pour résoudre efficacement ce modèle: méthodes des volumes finis, méthodes semi-Lagrangiennes et méthodes Galerkin discontinusMany numerical methods have been developed in order to selve the Vlasov equation, because computing precise simulations in a reasonable time is a real challenge. This equation describes the time evolution of the distribution function of charged particles (electrons/ions), which depends on 3 variables in space, 3 in velocity and time. The main idea of this thesis is to rewrite the Vlasov equation in the form of a hyperbolic system using a semi-discretization of the velocity. This semi-discretization is achieved using the finite element method. The resulting model is called the reduced Vlasov equation. We propose different numerical methods to salve this new model efficiently: finite volume methods, semi-Lagrangian methods and discontinuous Galerkin methods
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Ould, Salihi Mohamed Lemine. "Couplage de méthodes numériques en simulation directe d'écoulements incompressibles." Phd thesis, Université Joseph Fourier (Grenoble), 1998. http://tel.archives-ouvertes.fr/tel-00004901.
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Ce travail est consacré au développement des méthodes lagrangiennes comme alternatives ou compléments aux méthodes euleriennes conventionnelles pour la simulation d'écoulements incompressibles en présence d'obstacles. On s'intéresse en particulier à des techniques ou des solveurs eulériens et lagrangiens cohabitent dans le même domaine de calcul mais traitent différents termes des équations de Navier-Stokes, ainsi qu'à des techniques de décomposition de domaines ou différents solveurs sont utilisés dans chaques sous-domaines. Lorsque les méthodes euleriennes et lagrangiennes cohabitent dans le même domaine de calcul (méthode V.I.C.), les formules de passage particules-grilles permettent de représenter la vorticité avec la même précision sur une grille fixe et sur la grille lagrangienne. Les méthodes V.I.C. ainsi obtenues combinent stabilité et précision et fournissent une alternative avantageuse aux méthodes différences-finies pour des écoulements confinés. Lorsque le domaine de calcul est décomposé en sous-domaines distincts traités par méthodes lagrangiennes et par méthodes euleriennes, l'interpolation d'ordre élevé permet de réaliser des conditions d'interface consistantes entre les différents sous-domaines. On dispose alors de méthodes de calcul avec décomposition en sous-domaines, de type Euler/Lagrange ou Lagrange/Lagrange, et résolution en formulation (vitesse-tourbillon)/(vitesse-tourbillon) ou (vitesse-pression)/(vitesse-tourbillon). Les différentes méthodes développées ici sont testées sur plusieurs types d'écoulements (cavité entrainée, rebond de dipôles de vorticité, écoulements dans une conduite et sur une marche, écoulements autour d'obstacles) et comparées à des méthodes de différences-finies d'ordre élevé.
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GIANNOPOULOU, Ourania. "Two-dimensional viscous flow studied using vortex particle methods." Doctoral thesis, 2021. http://hdl.handle.net/11573/1531566.
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Vortex particle methods are alternative methods to Eulerian approaches for the solution of the incompressible Navier-Stokes equations in vorticity-velocity variables. They are characterized by the inherent ability to adapt to the flow due to their Lagrangian formulation for the advection and additionally by the decoupling of the pressure from the momentum equation. In this work, we study these methods using the Lagrangian vortex particle method Diffused Vortex Hydrodynamics that uses the operator splitting in time of Chorin. Numerical results are obtained for problems containing solid boundaries in the domain for different test cases. We compare the results with a finite volume solver that discretizes the velocity-pressure formulation of Navier-Stokes and uses artificial compressibility to evolve the solution in time, also introduced by Chorin. The comparison is obtained based on local and global derived quantities. Finally, an application of the method to a physical study is presented regarding the flow past an elliptical cylinder.
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Morley, Christopher Stephen Band. "Pricing CPPI Capital Guarantees: A Lagrangian Framework." Thesis, 2011. http://hdl.handle.net/10012/6277.
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A robust computational framework is presented for the risk-neutral valuation of capital
guarantees written on discretely-reallocated portfolios following the Constant Proportion
Portfolio Insurance (CPPI) strategy. Aiming to address the (arguably more realistic)
cases where analytical results are unavailable, this framework accommodates risky-asset
jumps, volatility surfaces, borrowing restrictions, nonuniform reallocation schedules and
autonomous CPPI floor trajectories. The two-asset state space representation developed
herein facilitates visualising the CPPI strategy, which in turn provides insight into grid
design and interpolation. It is demonstrated that given a deterministic process for the
risk-free rate, the pricing problem can be cast as solving cascading systems of 1D partial
integro-differential equations (PIDEs). This formulation’s stability and monotonicity are
studied. In addition to making more sense financially, the limited borrowing variant of
the CPPI strategy is found to be better suited than the classical (unlimited borrowing)
counterpart for bounded-domain calculations. Consequently, it is demonstrated how the
unlimited borrowing problem can be approximated by imposing an artificial borrowing limit.
For implementation validation, analytical solutions to special cases are derived. Numerical
tests are presented to demonstrate the versatility of this framework.
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Lupieri, Guido. "An investigation of particle dispersion in a tidally driven turbulent flow." Doctoral thesis, 2007. http://hdl.handle.net/10077/2537.
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2005/2006The Gulf of Trieste, subset of our investigation, is a shallow water inlet with a mean depth of 17 m (maximum 25 m) and an area of about 20 km × 25 km. It is located in the north area of the Adriatic Sea. The dynamics of the Gulf is characterized by seasonal variability of temperature and density, and the mixing and dispersion processes are strongly dependent to this context. This variability is due to the combined effects of many factors such as the presence of a strong wind (Bora) whose action is directly related to the water column instability, the input of fresh water from the river Isonzo and the water exchange due to Adriatic sea currents. For all this phenomena an extended quantity of measured data have been collected from more than one hundred years: the interest in the knowledge of these processes is due to the deep impact in the local economy (from fishing to tourism). This allows a correct formulation of the forcing acting in the dispersion problem regarding the Gulf.
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Katta, Ajay. "Particle Trajectories in Wall-Normal and Tangential Rocket Chambers." 2011. http://trace.tennessee.edu/utk_gradthes/989.
Full textAbstract:
The focus of this study is the prediction of trajectories of solid particles injected into either a cylindrically- shaped solid rocket motor (SRM) or a bidirectional vortex chamber (BV). The Lagrangian particle trajectory is assumed to be governed by drag, virtual mass, Magnus, Saffman lift, and gravity forces in a Stokes flow regime. For the conditions in a solid rocket motor, it is determined that either the drag or gravity forces will dominate depending on whether the sidewall injection velocity is high (drag) or low (gravity). Using a one-way coupling paradigm in a solid rocket motor, the effects of particle size, sidewall injection velocity, and particle-to-gas density ratio are examined. The particle size and sidewall injection velocity are found to have a greater impact on particle trajectories than the density ratio. Similarly, for conditions associated with a bidirectional vortex engine, it is determined that the drag force dominates. Using a one-way particle tracking Lagrangian model, the effects of particle size, geometric inlet parameter, particle-to-gas density ratio, and initial particle velocity are examined. All but the initial particle velocity are found to have a significant impact on particle trajectories. The proposed models can assist in reducing slag retention and identifying fuel injection configurations that will ensure proper confinement of combusting droplets to the inner vortex in solid rocket motors and bidirectional vortex engines, respectively.
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Bhatnagar, Akshay. "Direct Numerical Simulations of Fluid Turbulence : (A) Statistical Properties of Tracer And Inertial Particles (B) Cauchy-Lagrange Studies of The Three Dimensional Euler Equation." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/2747.
Full textAbstract:
The studies of particles advected by tubulent flows is an active area of research
across many streams of sciences and engineering, which include astrophysics,
fluid mechanics, statistical physics, nonlinear dynamics, and also chemistry and biology. Advances in experimental techniques and high performance computing have made it possible to investigate the properties these
particles advected by fluid flows at very high Reynolds numbers. The main focus of this thesis is to study the statistics of Lagrangian tracers and heavy inertial particles in hydrodynamic and magnetohydrodynamic (MHD) turbulent
flows by using direct numerical simulations (DNSs). We also study the statistics of particles in model stochastic flows; and we compare our results for such models with those that we obtain from DNSs of hydrodynamic equations. We uncover some of aspects of the statistical properties of particle trajectories that have not been looked at so far. In the last part of the thesis we present some results that we have obtained by solving the three-dimensional
Euler equation by using a new method based on the Cauchy-Lagrange formulation. This thesis is divided into 6 chapters. Chapter 1 contains an introduction
to the background material that is required for this thesis; it also contains an
outline of the problems we study in subsequent Chapters. Chapter 2 contains
our study of “Persistence and first-passage time problems with particles in
three-dimensional, homogeneous, and isotropic turbulence”. Chapter 3 is devoted
to our study of “Universal Statistical Properties of Inertial-particle Trajectories
in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence”.
Chapter 4 deals with “Time irreversibility of Inertial-particle trajectories in
Homogeneous, Isotropic, Fluid Turbulence”. Chapter 5 contains our study
of the “Statistics of charged inertial particles in three-dimensional magnetohydrodynamic (MHD) turbulence”. Chapter 6 is devoted to our study of
“The Cauchy-Lagrange method for the numerical integration of the threedimensional
Euler equation”.
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Bhatnagar, Akshay. "Direct Numerical Simulations of Fluid Turbulence : (A) Statistical Properties of Tracer And Inertial Particles (B) Cauchy-Lagrange Studies of The Three Dimensional Euler Equation." Thesis, 2016. http://hdl.handle.net/2005/2747.
Full textAbstract:
The studies of particles advected by tubulent flows is an active area of research
across many streams of sciences and engineering, which include astrophysics,
fluid mechanics, statistical physics, nonlinear dynamics, and also chemistry and biology. Advances in experimental techniques and high performance computing have made it possible to investigate the properties these
particles advected by fluid flows at very high Reynolds numbers. The main focus of this thesis is to study the statistics of Lagrangian tracers and heavy inertial particles in hydrodynamic and magnetohydrodynamic (MHD) turbulent
flows by using direct numerical simulations (DNSs). We also study the statistics of particles in model stochastic flows; and we compare our results for such models with those that we obtain from DNSs of hydrodynamic equations. We uncover some of aspects of the statistical properties of particle trajectories that have not been looked at so far. In the last part of the thesis we present some results that we have obtained by solving the three-dimensional
Euler equation by using a new method based on the Cauchy-Lagrange formulation. This thesis is divided into 6 chapters. Chapter 1 contains an introduction
to the background material that is required for this thesis; it also contains an
outline of the problems we study in subsequent Chapters. Chapter 2 contains
our study of “Persistence and first-passage time problems with particles in
three-dimensional, homogeneous, and isotropic turbulence”. Chapter 3 is devoted
to our study of “Universal Statistical Properties of Inertial-particle Trajectories
in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence”.
Chapter 4 deals with “Time irreversibility of Inertial-particle trajectories in
Homogeneous, Isotropic, Fluid Turbulence”. Chapter 5 contains our study
of the “Statistics of charged inertial particles in three-dimensional magnetohydrodynamic (MHD) turbulence”. Chapter 6 is devoted to our study of
“The Cauchy-Lagrange method for the numerical integration of the threedimensional
Euler equation”.
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Liu, Rex Kuan-Shuo, and 柳冠碩. "Development of a Coupled Lagrangian-Eulerian Particle and Implicit Forcing Immersed Boundary (IMLE-IFIB) Method to Simulate Three-Dimensional Incompressible Viscous Flow with Complex Geometries." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/zam239.
Full textAbstract:
博士國立臺灣大學
工程科學及海洋工程學研究所
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In this thesis, two major research tasks have been attended with success. In the first part, a new high order incompressible viscous flow solver is developed within the mixed Lagrangian-Eulerian (MLE) framework followed by its improved version called IMLE method. The key contributions of the MLE method are that the total derivative term shown in the incompressible Navier-Stokes (NS) equations is solved under the Lagrangian sense to get rid of problem of convective instability and the spatial derivative terms, such as the pressure gradient term and the velocity diffusion term, are approximated under the Eulerian sense to get a higher accuracy order in comparison with some conventional particle methods. The sixth order accurate combined compact difference (CCD) scheme is adopted to approximate the above mentioned spatial derivative terms on the Eulerian grids. Since particles keep moving within the computational domain, a customized linked list is proposed to manage particles in searching procedure. On the other hand, a linear interpolation is needed to interpolate the approximated spatial derivative terms from Eulerian grids to Lagrangian particles. In order to further improve solution accuracy and computational efficiency, the IMLE method is developed which avoids using linked list to manage particles and linear interpolation to interpolate solutions from the Eulerian grids to Lagrangian particles because a particle reinitialization procedure is adopted in each time step. The second part includes the development of an implicit forcing immersed boundary (IFIB) method which successfully resolves the problem arising in the original continuous IB method that the velocity inside a rigid body does not satisfy the velocity boundary condition. The IFIB method involves iteration to keep refining the numerical solutions of velocity, pressure and forcing terms until convergence is reached. One key difference between the proposed IFIB and the conventional IB methods is that the forcing term is a part of the source term in the pressure Poisson equation (PPE). In this way, both the velocity boundary condition and the continuity equation can be satisfied simultaneously.
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Nguyen, Van thanh. "Problèmes de transport partiel optimal et d'appariement avec contrainte." Thesis, 2017. http://www.theses.fr/2017LIMO0052/document.
Full textAbstract:
Cette thèse est consacrée à l'analyse mathématique et numérique pour les problèmes de transport partiel optimal et d'appariement avec contrainte (constrained matching problem). Ces deux problèmes présentent de nouvelles quantités inconnues, appelées parties actives. Pour le transport partiel optimal avec des coûts qui sont donnés par la distance finslerienne, nous présentons des formulations équivalentes caractérisant les parties actives, le potentiel de Kantorovich et le flot optimal. En particulier, l'EDP de condition d'optimalité permet de montrer l'unicité des parties actives. Ensuite, nous étudions en détail des approximations numériques pour lesquelles la convergence de la discrétisation et des simulations numériques sont fournies. Pour les coûts lagrangiens, nous justifions rigoureusement des caractérisations de solution ainsi que des formulations équivalentes. Des exemples numériques sont également donnés. Le reste de la thèse est consacré à l'étude du problème d'appariement optimal avec des contraintes pour le coût de la distance euclidienne. Ce problème a un comportement différent du transport partiel optimal. L'unicité de solution et des formulations équivalentes sont étudiées sous une condition géométrique. La convergence de la discrétisation et des exemples numériques sont aussi établis. Les principaux outils que nous utilisons dans la thèse sont des combinaisons des techniques d'EDP, de la théorie du transport optimal et de la théorie de dualité de Fenchel--Rockafellar. Pour le calcul numérique, nous utilisons des méthodes du lagrangien augmentéThe manuscript deals with the mathematical and numerical analysis of the optimal partial transport and optimal constrained matching problems. These two problems bring out new unknown quantities, called active submeasures. For the optimal partial transport with Finsler distance costs, we introduce equivalent formulations characterizing active submeasures, Kantorovich potential and optimal flow. In particular, the PDE of optimality condition allows to show the uniqueness of active submeasures. We then study in detail numerical approximations for which the convergence of discretization and numerical simulations are provided. For Lagrangian costs, we derive and justify rigorously characterizations of solution as well as equivalent formulations. Numerical examples are also given. The rest of the thesis presents the study of the optimal constrained matching with the Euclidean distance cost. This problem has a different behaviour compared to the partial transport. The uniqueness of solution and equivalent formulations are studied under geometric condition. The convergence of discretization and numerical examples are also indicated. The main tools which we use in the thesis are some combinations of PDE techniques, optimal transport theory and Fenchel--Rockafellar dual theory. For numerical computation, we make use of augmented Lagrangian methods
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Rioux-Lavoie, Damien. "Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre." Thèse, 2017. http://hdl.handle.net/1866/19377.
Full textAbstract:
L’objectif de ce mémoire est d’introduire une nouvelle méthode smoothed particle hydrodynamics
(SPH) implicite purement lagrangienne, pour la résolution des équations de Navier-
Stokes incompressibles bidimensionnelles en présence d’une surface libre. Notre schéma de
discrétisation est basé sur celui de Kéou Noutcheuwa et Owens [19]. Nous avons traité la
surface libre en combinant la méthode multiple boundary tangent (MBT) de Yildiz et al. [43]
et les conditions aux limites sur les champs auxiliaires de Yang et Prosperetti [42]. Ce faisant,
nous obtenons un schéma de discrétisation d’ordre $\mathcal{O}(\Delta t ^2)$ et $\mathcal{O}(\Delta x ^2)$, selon certaines
contraintes sur la longueur de lissage $h$. Dans un premier temps, nous avons testé notre
schéma avec un écoulement de Poiseuille bidimensionnel à l’aide duquel nous analysons l’erreur
de discrétisation de la méthode SPH. Ensuite, nous avons tenté de simuler un problème
d’extrusion newtonien bidimensionnel. Malheureusement, bien que le comportement de la
surface libre soit satisfaisant, nous avons rencontré des problèmes numériques sur la singularité
à la sortie du moule.The objective of this thesis is to introduce a new implicit purely lagrangian smoothed particle hydrodynamics (SPH) method, for the resolution of the two-dimensional incompressible Navier-Stokes equations in the presence of a free surface. Our discretization scheme is based on that of Kéou Noutcheuwa et Owens [19]. We have treated the free surface by combining Yildiz et al. [43] multiple boundary tangent (MBT) method and boundary conditions on the auxiliary fields of Yang et Prosperetti [42]. In this way, we obtain a discretization scheme of order $\mathcal{O}(\Delta t ^2)$ and $\mathcal{O}(\Delta x ^2)$, according to certain constraints on the smoothing length $h$. First, we tested our scheme with a two-dimensional Poiseuille flow by means of which we analyze the discretization error of the SPH method. Then, we tried to simulate a two-dimensional Newtonian extrusion problem. Unfortunately, although the behavior of the free surface is satisfactory, we have encountered numerical problems on the singularity at the output of the die.
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Jaruga, Anna. "Chemical aspects of cloud - aerosol interactions." Doctoral thesis, 2017. https://depotuw.ceon.pl/handle/item/2038.
Full textAbstract:
In the atmosphere cloud droplets form and grow on aerosol particles - tiny solid or liquid particles suspended in the air. When trapped inside water drops aerosol particles are affected by the processes happening in clouds such as collisions between water drops or aqueous phase chemical reactions inside water drops. It can be said that clouds and aerosol particles coexist, continuously changing each others properties. This dissertation studies the interactions between aerosol particles and water drops in warm (i.e. ice free) boundary layer clouds. The main focus is on the collisions between water drops and the aqueous phase oxidation of sulfur to sulfate occurring inside cloud droplets and the impact of those processes on the size distribution of aerosol particles.The study is carried out using numerical simulations employing a Lagrangian representation of cloud microphysics and aqueous phase chemical reactions. The Lagrangian methods, also called particle tracking or particle based, allow to represent cloud microphysical and chemical processes as if from a point of view of an aerosol particle or a water drop. They are computationally expensive but allow to resolve numerically the changes to both aerosol particle and water drop size distribution.This study uses the Lagrangian microphysics scheme developed at the Faculty of Physics at the University of Warsaw. For the purpose of this study the Lagrangian scheme was extended to cover also the aqueous phase processes in cloud droplets. The list of chemical processes includes the dissolving of trace gases into water drops their dissociation and the oxidation reaction of sulfur to sulfate by ozone and hydrogen peroxide.Six trace gases are included in the scheme: sulfur dioxide, ozone, hydrogen peroxide, carbon dioxide, ammonia and nitric acid. The scientific software created during this study is available for further use as a part of an open source library of schemes. Parts of this dissertation may serve as the first documentation of the design, performance and the user interface of the created Lagrangian microphysics and aqueous phase chemistry scheme.The dissertation contains a short theoretical introduction to the microphysical and chemical processes occurring in warm clouds. It presents the details of the Lagrangian representation of microphysics in a numerical scheme.The new module of the Lagrangian scheme responsible for aqueous phase chemical reactions is described and tested in an adiabatic parcel model framework. Next, the created Lagrangian microphysics and aqueous phase chemistry scheme is used in a 2-dimensional kinematic setup representing a vertical slice through a boundary layer topped with a stratocumulus deck. The discussion focuses on the impact of collisions between water drops and the in-cloud oxidation of sulfur to sulfate on the size distribution on aerosol particles. The sensitivity of the obtained results to different microphysical and chemical conditions is also investigated.Kropelki chmurowe tworzą się na cząstkach aerozolu czyli drobinach zanieczyszczeń w fazie stałej lub ciekłej zawieszonych w powietrzu. Cząstki aerozolu znajdujące się w kropelkach chmurowych są poddane działaniom procesów chmurowych takich jak zderzenia między kropelkami wody lub reakcje chemiczne zachodzące w kropelkach wody. Chmury i cząstki aerozolu wzajemnie ze sobą oddziałują i wzajemnie wpływają na swoje własności. Przedstawiona rozprawa doktorska bada interakcje pomiędzy drobinami aerozolu atmosferycznego i kropelkami wody w płytkich chmurach warstwy granicznej (t.j. w chmurach bez lodu). Przedstawione wyniki skupiają się na zderzeniach miedzy kropelkami wody i reakcji utlenienia dwutlenku siarki do kwasu siarkowego VI zachodzącej w kropelkach chmurowych oraz ich wpływie na widmo rozmiarów drobin aerozolu.Badania przedstawione w rozprawie doktorskiej są prowadzone przy użyciu symulacji numerycznych wykorzystujących lagranżowski sposób opisu mikrofizyki chmur i reakcji chemicznych w kropelkach chmurowych. Metody te są kosztowne numerycznie, ale pozwalają na dokładną reprezentację w modelu numerycznym ewolucji widma rozmiarów zarówno kropel wody jak i cząstek aerozolu.W trakcie przeprowadzonych badań użyty został lagranżowski schemat mikrofizyczny tworzony na Wydziale Fizyki Uniwersytetu Warszawskiego. Na potrzeby przeprowadzonych badań schemat ten został rozszerzony o opis procesów chemicznych zachodzących w kropelkach chmurowych. Do schematu dodany został opis rozpuszczania gazów śladowych w kropelkach chmurowych, dysocjacji rozpuszczonych związków na jony i reakcji utlenienia rozpuszczonego dwutlenku siarki do kwasu siarkowego przez ozon i nadtlenek wodoru. Do schematu zostało dodanych sześć gazów śladowych: dwutlenek siarki, ozon, nadtlenek wodoru, dwutlenek węgla, amoniak i kwas azotowy. Stworzone oprogramowanie jest dostępne jako część otwartej biblioteki schematów numerycznych. Część przedstawionej rozprawy doktorskiej może służyć jako opis struktury i sposobu działania stworzonego oprogramowania oraz dokumentacja interfejsu użytkownika.Rozprawa doktorska zawiera krótki wstęp przedstawiający teoretyczne podstawy opisu procesów mikrofizycznych i chemicznych zachodzących w płytkich chmurach warstwy granicznej. Następnie zaprezentowany jest opis zasady działania mikrofizycznego schematu lagranżowskiego. W rozprawie opisany jest również nowy moduł odpowiedzialny za reakcje chemiczne zachodzące w kropelkach chmurowych. Poprawność stworzonego opisu reakcji chemicznych w kropelkach jest przetestowana przy użyciu adiabatycznego modelu cząstki. W ostatniej części rozprawy lagranżowski opis mikrofizyki i reakcji chemicznych w chmurach jest zastosowany w 2-wymiarowym modelu reprezentującym przekrój przez warstwę graniczną przykrytą chmurą stratocumulus. Dyskusja wyników skupia się na przedstawieniu wpływu zderzeń między kropelkami oraz reakcji chemicznych zachodzących w kropelkach chmurowych na widmo rozmiarów drobin aerozolu. Dyskutowane są również symulacje testujące czułość otrzymanych wyników na początkowe warunki mikrofizyczne i chemiczne panujące w modelu.
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Mullan, Sean. "Tidal sedimentology and geomorphology in the central Salish Sea straits, British Columbia and Washington State." Thesis, 2017. https://dspace.library.uvic.ca//handle/1828/8943.
Full textAbstract:
Intra-archipelago waterways, including tidal strait networks, present a complex set of barriers to, and conduits for sediment transport between marine basins. Tidal straits may also be the least well understood tide-dominated sedimentary environment. To address these issues, currents, sediment transport pathways, and seabed sedimentology & geomorphology were studied in the central Salish Sea (Gulf and San Juan Islands region) of British Columbia, Canada and Washington State, USA. A variety of data types were integrated: 3D & 2D tidal models, multibeam bathymetry & backscatter, seabed video, grab samples, cores and seismic reflection. This dissertation included the first regional sediment transport modelling study of the central Salish Sea. Lagrangian particle dispersal simulations were driven by 2D tidal hydrodynamics (~59-days). It was found that flood-tide dominance through narrow intra-archipelago connecting straits resulted in the transfer of sediment into the inland Strait of Georgia, an apparent sediment sink. The formative/maintenance processes at a variety of seabed landforms, including a banner bank with giant dunes, were explained with modelled tides and sediment transport. Deglacial history and modern lateral sedimentological and morphological transitions were also considered. Based on this modern environment, adjustments to the tidal strait facies model were identified. In addition, erosion and deposition patterns across the banner bank (dune complex) were monitored with 8-repeat multibeam sonar surveys (~10 years). With these data, spatially variable bathymetric change detection techniques were explored: A) a cell-by-cell probabilistic depth uncertainty-based threshold (t-test); and B) coherent clusters of change pixels identified with the local Moran's Ii spatial autocorrelation statistic. Uncertainty about volumetric change is a considerable challenge in seabed change research, compared to terrestrial studies. Consideration of volumetric change confidence intervals tempers interpretations and communicates metadata. Techniques A & B may both be used to restrict volumetric change calculations in area, to exclude low relative bathymetric change signal areas.Graduate
2018-12-07