This thesis is devoted to mathematical modelling, including numerical simulation, in nonlinear laser physics. We study the concrete problem of finding optimal parameters for soliton lasers which is important for many applications. The basic mathematical tool used in our studies is the theory of nonlinear differential equations and numerical methods of their investigations.

abstract: Numerical simulations are very helpful in understanding the physics of the formation of structure and galaxies. However, it is sometimes difficult to interpret model data with respect to observations, partly due to the difficulties and background noise inherent to observation. The goal, here, is to attempt to bridge this gap between simulation and observation by rendering the model output in image format which is then processed by tools commonly used in observational astronomy. Images are synthesized in various filters by folding the output of cosmological simulations of gasdynamics with star-formation and dark matter with the Bruzual- Charlot stellar population synthesis models. A variation of the Virgo-Gadget numerical simulation code is used with the hybrid gas and stellar formation models of Springel and Hernquist (2003). Outputs taken at various redshifts are stacked to create a synthetic view of the simulated star clusters. Source Extractor (SExtractor) is used to find groupings of stellar populations which are considered as galaxies or galaxy building blocks and photometry used to estimate the rest frame luminosities and distribution functions. With further refinements, this is expected to provide support for missions such as JWST, as well as to probe what additional physics are needed to model the data. The results show good agreement in many respects with observed properties of the galaxy luminosity function (LF) over a wide range of high redshifts. In particular, the slope (alpha) when fitted to the standard Schechter function shows excellent agreement both in value and evolution with redshift, when compared with observation. Discrepancies of other properties with observation are seen to be a result of limitations of the simulation and additional feedback mechanisms which are needed. / Dissertation/Thesis / Ph.D. Physics 2012

学位授与大学：京都大学 ; 取得学位: 博士(工学) ; 学位授与年月日: 2007-09-25 ; 学位の種類: 新制・課程博士 ; 学位記番号: 工博第2845号 ; 請求記号: 新制/工/1419 ; 整理番号: 25530 / Multiphase flows are governed by three-dimensional Navier Stokes equations for each involved phase. Therefore, solution of these equations for given boundary and initial conditions, in principle, would determine the flow field in time and space. Generally, boundaries between involved phases are not known a priory, but are part of the, solution; or in the case of flows in a porous medium, these boundaries have too complicated geometry to be resolved mathematically. This resulted into development of simplified models, where the level of simplifications determines the model applicability. However, in order to represent simulated flows accurately, the model should include as much as possible relevant mechanisms and fluid properties. In this study, a numerical model is developed based on finite volume method, in which the volume averaged governing equations are solved. In contrary to the simplified models. a full momentum equations for each involved phase is considered. Such model is utilized in the study to investigate commonly adopted simplifications, and their effects on the model applicability. Namely, for the flows in porous media, the effects of acceleration terms in momentum equations are investigated; first for the saturated groundwater flow, and then; for the air/water flow during air injection into initially saturated soil. It is revealed that in the case of saturated flow in homogeneous, incompressible, low permeable soils, the pressure adapts the new imposed boundary conditions instantaneously, while the velocities reach the quasi-steady conditions extremely fast. In the case of heterogeneous soil, pressure and velocity field have transient nature, but quickly reach the quasi-steady conditions. Only during this onset of flow, the inertia terms play a role. In the case of air/water flow during air sparging, it is revealed that acceleration becomes important for porous medium with average grain size larger than 2 rum. This implies that simulations of such flow in coarse sands and gravels should include acceleration. It is explicitly shown that phenomena of flow pulsation, manifesting as steady pulsation at the constant air-injection flow rate, can be modeled only by inclusion of acceleration terms in governing equations. Theoretical analysis; conducted by application of one-dimensional stability analysis, revealed that inertial effects promote the instability, while the capillary forces oppose it. Ratio of these forces determines the onset of instability. It is showed that for materials with average grain size smaller than 2 mm, instability can not be expected. In order to apply the model for simulation of contaminant removal during air sparging, the contaminant transport model is supplied. Mechanistic numerical models inherently assume that involved phases are completely mixed, and by now reported models commonly assume the local equilibrium of contaminant between the air and water phase. As reported by many investigators, this leads toward an overestimated contaminant removal. Therefore, in this model a channel air flow pattern is considered, where transfer of contaminant between the water and the air phase is modeled according to two film theory. Diffusive process of contaminant transport toward the air phase is modeled by a first order kinetic process between two water compartments: a immobile compartment in contact with the air phase and mobile compartment which has no contact with the air phase. Application of the developed model to reported two-dimensional experiment, showed a good agreement between simulated and measured transient change of dissolved contaminant in the water. This study also showed that single numerical model, through the minor refinements, can be applied to wide variety of hydraulic engineering problems. By inclusion of gas compressibility, and mass exchange between the gas and the water phase in continuity equations, with adapting the drag term in momentum equations, a bubble phone model is proposed which can be utilized for simulation of lake amelioration by gas (air or pure oxygen) injection. Model is qualitatively and quantitatively validated by comparison with reported experiments from the literature. Hypothetical simulation of pure oxygen injection into 50 in deep lake showed that, due to ambient water entrainment into the gas plume, a significant spreading of dissolved oxygen can not be expected. Therefore, a optional gas injection strategy should be considered. Developed model can be utilized in order to propose an optimal gas injection design. Finally.. the same numerical model is proposed for simulation of flow in complex flow domains, consisting of bulk water and flow in porous medium with free surface boundary. Model is formulated in generalized curvilinear coordinates, in order to provide adequate representation of irregular boundaries. In contrast to earlier proposed boundary conditions at the two domain interface, in this model a continuity of velocities and stresses is assumed; for both regions a single set of governing equations is solved. Model application is illustrated by simulation of embankment overflow and its effect on effective stresses in the porous medium. It is showed that coupled, bulk water and groundwater flow, significantly influence the slope failure potential, here quantified by the Coulomb failure coefficient for non cohesive soils. / Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第13374号 / 工博第2845号 / 新制||工||1419(附属図書館) / 25530 / UT51-2007-Q775 / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 細田 尚, 准教授 牛島 省, 准教授 後藤 仁志 / 学位規則第4条第1項該当

Resumo: Os métodos de fronteira imersa possibilitam a simulação numérica de escoamentos envolvendo contornos complexos e móveis utilizando-se uma malha euleriana fixa para representar o domínio fluido, associada a um conjunto de pontos lagrangianos para descrever interfaces, sem necessidade de remalhagem do domínio de cálculo. No presente trabalho, um método de fronteira imersa baseado no modelo físico virtual foi implementado em um código computacional já existente, com o objetivo de permitir a simulação do escoamento em torno de cilindros de base circular submetidos a oscilações forçadas ou induzidas pelo movimento do fluido. O programa computacional resolve as equações de Navier-Stokes em coordenadas cartesianas através do método de volumes finitos, utilizando uma discretização implícita no tempo. Para testar as novas implementações, foram realizadas simulações para cilindros estacionários e em movimento oscilatório forçado, posicionados em meio infinito ou no interior de um canal. Além disso, foi resolvido um problema de interação fluido-estrutura, constituído por um cilindro móvel e indeformável posicionado dentro de um canal vertical, a jusante de uma obstrução, oscilando linearmente sob a ação de um escoamento pulsátil ascendente, tal como ocorre no funcionamento de alguns tipos de válvula automática. Em várias simulações, observou-se a reentrada de núcleos de vorticidade na saída do domínio de cálculo, interferindo na qualidade dos resultados obtidos. Uma função de amortecimento foi, então, introduzida nesta região, para evitar a ocorrência de instabilidades numéricas. Uma análise da performance global do programa de simulação indica que, embora já produza resultados satisfatórios, a modelagem empregada ainda necessita de aprimoramentos para corrigir algumas imperfeições. Além disso, o código computacional precisa... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Immersed boundary methods allow numerical simulation of flows around complex bodies by using a stationary Eulerian mesh to represent the fluid domain associated to a set of Lagrangian points to describe the interfaces without global remeshing of the domain. In the present work, an immersed boundary method based on virtual physical model has been implemented in a previously available computational code in order to simulate flows around circular cylinders submitted to forced or induced oscillations. The improved computational program deploys Navier-Stokes equations in Cartesian coordinates by using with finite volume method and implicit temporal time discretization. In order to test the new code several simulations have been performed for a confined flow around a fix circular cylinder as well as submitted to forced oscillation. Additionally, a problem of fluid-structure interaction formed by a rigid oscillating circular cylinder positioned in a vertical channel after an abrupt obstruction has been analyzed. The cylinder can freely oscillate in the streamwise direction due to action of an ascendant pulsating flow. This type of flow problem is very similar to those occurring in many types of automatic valves. In some simulations spurious backflow of vorticity nucleus at the computational domain outlet has been observed, interfering in the quality of results. Therefore, a convenient damping function has been introduced in that region to suppress such numerical instabilities. A general performance analysis of the program shows very satisfactory results, however suitable changes in the code should be considered to avoid some remaining instabilities as well as minimize the overall time required for the simulation runs / Orientador: Sérgio Said Mansur / Coorientador: Júlio Militzer / Banca: Emanuel Rocha Woiski / Banca: Marcelo Moreira Ganzarolli / Mestre

[pt] Neste trabalho, a propagação de sólitons em fibras óticas é analisada através de simulação numérica da equação não linear de Schrödinger, a qual descreve a propagação de pulsos óticos em fibras monomodo do tipo degrau. Uma vez que soluções analíticas para esta equação só podem ser obtidas em alguns casos específicos, implementaram-se dois métodos numéricos, possibilitando a análise da evolução de diferentes formas de pulsos incidentes ao longo de fibras com propriedades diversas de atenuação, dispersão e não linearidades. O método da propagação de Raios, cujo desempenho mostrou-se superior ao do método da série de Fourier, foi o escolhido para a obtenção dos resultados aqui apresentados. Várias características do sóliton fundamental, dos sólitons de ordens superiores, dos sólitons escuros e do fenômeno da interação entre pulsos adjacentes são apresentadas e discutidas, levando-se em consideração as possíveis implicações no desempenho de sistemas óticos. Contrabalançando os efeitos da dispersão da fibra com os efeitos não lineares da automodulações de fase, o que permite sua propagação sem alteração de forma, os sólitons encontram potencial aplicação na transmissão de altas taxas a longas distâncias. / [en] In this work, soliton propagation in optical fibres is analysed by means of numerical simulation of the nonlinear Schrödinger equation, which governs optical pulse propagation in step-index monomode fibres. Since analytic solutions to this equation are admitted only for some specific cases, two numerical methods have been implemented in order to study the evolution of different kinds of input pulses, under the effects of attenuation, dispersion and nonlinearities. Showing a better performance than the Fourier Series Method in a comparative test, the Beam Propagation Method has been chosen to obtain the results here presented. Many characteristics of the fundamental, higher order and dark solitons, as well as interaction phenomena between adjacent pulses, are investigated, taking into account possible implications on optical systems performance. By properly counteracting the effects of fibre dispersion and nonlinearities, solitons can propagate without changing its shape, finding potential application in high bit-rate long distance optical communication systems.

Laser welding of metals and alloys is extensively used in industry due to its advantages of controlled heating, narrow weld bead, low heat affected zone (HAZ) and its ability to weld a wide range of metals and dissimilar metals. Laser welding of dissimilar metals such as carbon steels and stainless steel is still a challenging task, particularly due to the formation of brittle phases in the weld, martensitic formation in the HAZ and solidification cracking in the fusion zone. These issues can significantly deteriorate the strength of the welded joint. The aim of this work is to investigate the fundamental phenomena that occur inside the dissimilar weld zone and their effect on weld quality. In order to establish the key process variables, an initial study concentrated on the effect of different laser process parameters on dissimilar weld quality. In the second part of the work, a comprehensive study was performed to understand and subsequently control the alloying composition in laser dissimilar welding of austenitic stainless steel and low carbon steel. A dissimilar weld that is predominantly austenitic and homogeneous was obtained by controlling the melt pool dynamics through specific point energy and beam alignment. The significance of dilution and alloying elements on joint strength was established. A coupled CFD and FEM numerical model was developed to assist in understanding the melt pool dynamics and transportation processes of alloying elements. The model has been validated by a series of laser welding experiments using various levels of specific point energy. The laser welding characteristics in terms of geometric dimensions, surface morphology, alloying concentration, and dilution, were compared, and it is concluded that the specific point energy and laser beam position are the key parameters that can be controlled to obtain a weld bead with characteristics most suitable for industrial applications. In the third part of the work, a comparative study was performed to understand the significance of cooling rate, and alloying composition on the microstructure and phase structure of the dissimilar weld zone. Results show that the HAZ within the high carbon steel has significantly higher hardness than the weld area, which severely undermines the weld quality. A new heat treatment strategy was proposed based on the results of the numerical simulation, and it is shown to control the brittle phase formation in HAZ of high carbon steel. A series of experiments was performed to verify the developed thermo-metallurgical FEA model and a good qualitative agreement of the predicted martensitic phase distribution is shown to exist. Although this work is presented in the context of dissimilar laser welding of mild steel to stainless steel, the concept is applicable to any dissimilar fusion welding process.

Controlled cooling is an important part of steel production industry that affects the properties of the outcome steel. Many of the researches done in controlled cooling are experimental. Due to progress in the numerical techniques and high cost of experimental works in this field the numerical work seems more feasible. Heat transfer analysis is the necessary element of successful controlled cooling and ultimately achievement of novel properties in steel. Heat transfer on the surface of the plate normally contains different regimes such as film boiling, nucleate boiling, transition boiling and radiation heat transfer. This makes the analysis more complicated. In order to perform the heat transfer analysis often empirical correlations are being used. In these correlations the velocity and pressure within the fluid domain is involved. Therefore in order to obtain a better understanding of heat transfer process, study of hydrodynamics of the fluid becomes necessary. Circular jet due to its high efficiency has been used vastly in the industry. Although some experimental studies of round jet arrays have been done, yet the characteristics of a single jet with industrial geometric and flow parameters on the surface of a flat plate is not fully understood. Study of hydrodynamics of the jet impingement is the first step to achieve better understanding of heat transfer process. Finite element method as a popular numerical method has been used vastly to simulate different domains. Traditional approaches of finite element method, Lagrangian and Eulerian, each has its own benefits and drawbacks. Lagrangian approach has been used widely in solid domains and Eulerian approach has been widely used in fluid fields. Jet impingement problem, due to its unknown free surface and the change in the boundary, falls in the category of special problems and none of the traditional approaches is suitable for this application. The Arbitrary Lagrangian Eulerian (ALE) formulation has emerged as a technique that can alleviate many of the shortcomings of the traditional Lagrangian and Eulerian formulations in handling these types of problems. Using the ALE formulation the computational grid need not adhere to the material (Lagrangian) nor be fixed in space (Eulerian) but can be moved arbitrarily. Two distinct techniques are being used to implement the ALE formulation, namely the operator split approach and the fully coupled approach. This thesis presents a fully coupled ALE formulation for the simulation of flow field. ALE form of Navier-Stokes equations are derived from the basic principles of continuum mechanics and conservation laws in the fluid. These formulations are then converted in to ALE finite element equations for the fluid flow. The axi-symmetric form of these equations are then derived in order to be used for jet impingement application. In the ALE Formulation as the mesh or the computational grid can move independent of the material and space, an additional set of unknowns representing mesh movement appears in the equations. Prescribing a mesh motion scheme in order to define these unknowns is problem-dependent and has not been yet generalized for all applications. After investigating different methods, the Winslow method is chosen for jet impingement application. This method is based on adding a specific set of partial differential Equations(Laplace equations) to the existing equations in order to obtain enough equations for the unknowns. Then these set of PDEs are converted to finite element equations and derived in axi-symmetric form to be used in jet impingement application. These equations together with the field equations are then applied to jet impingement problem. Due to the number of equations and nonlinearity of the field equations the solution of the problem faces some challenges in terms of convergence characteristics and modeling strategies. Some suggestions are made to deal with these challenges and convergence problems. Finally the numerical treatment and results of analyzing hydrodynamics of the Jet Impingement is presented. The work in this thesis is confined to the numerical simulation of the jet impingement and the specifications of an industrial test setup only have been used in order to obtain the parameters of the numerical model. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

A novel approach to modelling highly compressible and reactive flows is formulated to provide high resolution closure of turbulent-scale reaction rates in the presence of very rapid transients in pressure and energy. For such flows, treatment of turbulent-micro scales are generally unattainable through traditional modelling techniques. To address this, the modelling strategy developed here is based on the Linear Eddy Model for Large Eddy Simulation (LEM-LES); a technique which has only previously been applied to weakly compressible flows. In the current formulation of the Compressible LEM-LES (CLEM-LES), special treatment of the energy balance on the model subgrid is accounted for in order for the model reaction rates to respond accordingly to strong shocks and rapid expansions, both of which may be present in reactive and supersonic flow fields. In the current study, the model implemented is verified and validated for various 1D and 2D flow configurations in a compressible Adaptive Mesh Refinement (AMR) framework. In 1D test cases, laminar and turbulent flame speeds and structure have been reproduced. Also, detonation speeds and initiation events are also captured with the model. For 2D model validation, unsteady and turbulent detonation propagation and initiation events, in a narrow channel, are simulated. Both test cases involve premixed methane-oxygen mixture at low pressures. The model is found to capture well the two-dimensional detonation cellular structure, behaviour, and initiation events that are observed in corresponding shock tube experiments. Furthermore, the effect of turbulent mixing rates is investigated though a single tuning constant. It was found that by increasing the intensity of turbulent fluctuations present, detonations exhibit larger and more irregular cell structures. Furthermore, the intensity of turbulent fluctuations is found to also have an effect on initiation events.

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