<p>As modeling and simulation becomes a more important part of the modeling process, the demand on a known accuracy of the results of a simulation has grown more important. Sensitivity analysis (SA) is the study of how the variation in the output of a model can be apportioned to different sources of variation. By performing SA on a system, it can be determined which input/inputs influence a certain output the most. The sensitivity measures examined in this thesis are the Effective Influence Matrix, EIM, and the Main Sensitivity Index, MSI.</p><p>To examine the sensitivity measures, two tests have been made. One on a laboratory equipment including a hydraulic servo, and one on the conceptual landing gear model of the Gripen aircraft. The purpose of the landing gear experiment is to examine the influence of different frictions on the unfolding of the landing gear during emergency unfolding. It is also a way to test the sensitivity analysis method on an industrial example and to evaluate the EIM and MSI methods.</p><p>The EIM and MSI have the advantage that no test data is necessary, which means the robustness of a model can be examined early in the modeling process. They are also implementable in the different stages of the modeling and simulation process. With the SA methods in this thesis, documentation can be produced at all stages of the modeling process. To be able to draw correct conclusions, it is essential that the information that is entered into the analysis at the beginning is well chosen, so some knowledge is required of the model developer in order to be able to define reasonable values to use.</p><p>Wishes from the model developers/users include: the method and model quality measure should be easy to understand, easy to use and the results should be easy to understand. The time spent on executing the analysis has also to be well spent, both in the time preparing the analysis and in analyzing the results.</p><p>The sensitivity analysis examined in this thesis display a good compromise between usefulness and computational cost. It does not demand knowledge in programming, nor does it demand any deeper understanding of statistics, making it available to both the model creators, model users and simulation result users.</p>

As modeling and simulation becomes a more important part of the modeling process, the demand on a known accuracy of the results of a simulation has grown more important. Sensitivity analysis (SA) is the study of how the variation in the output of a model can be apportioned to different sources of variation. By performing SA on a system, it can be determined which input/inputs influence a certain output the most. The sensitivity measures examined in this thesis are the Effective Influence Matrix, EIM, and the Main Sensitivity Index, MSI. To examine the sensitivity measures, two tests have been made. One on a laboratory equipment including a hydraulic servo, and one on the conceptual landing gear model of the Gripen aircraft. The purpose of the landing gear experiment is to examine the influence of different frictions on the unfolding of the landing gear during emergency unfolding. It is also a way to test the sensitivity analysis method on an industrial example and to evaluate the EIM and MSI methods. The EIM and MSI have the advantage that no test data is necessary, which means the robustness of a model can be examined early in the modeling process. They are also implementable in the different stages of the modeling and simulation process. With the SA methods in this thesis, documentation can be produced at all stages of the modeling process. To be able to draw correct conclusions, it is essential that the information that is entered into the analysis at the beginning is well chosen, so some knowledge is required of the model developer in order to be able to define reasonable values to use. Wishes from the model developers/users include: the method and model quality measure should be easy to understand, easy to use and the results should be easy to understand. The time spent on executing the analysis has also to be well spent, both in the time preparing the analysis and in analyzing the results. The sensitivity analysis examined in this thesis display a good compromise between usefulness and computational cost. It does not demand knowledge in programming, nor does it demand any deeper understanding of statistics, making it available to both the model creators, model users and simulation result users.

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices. The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed. We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows. / <p>QC 20150303</p>

Le couplage diphasique-turbulence est une propriété clé des écoulements cavitants, qui est un frein important à l’amélioration des modèles de cavitation et de turbulence. Réaliser des simulations directes (DNS) est le moyen proposé ici pour s’affranchir du modèle de turbulence et obtenir des informations nouvelles sur les phénomènes mis en jeu. Ce type de simulation est exigeant sur le plan numérique, et requiert le développement d’un solveur spécifique intégrant les spécificités des modèles de cavitation. Cela inclue notamment des schémas de discrétisation d’ordre élevé, un solveur direct, et une résolution multi-domaines associée à une parrallélisation efficace. Une discrétisation par différences compactes finies s’avère être le meilleur choix. La contrainte de rapidité et de parrallélisation impose un algorithme où les systèmes résoudre n’impliquent des multiplications des variables implicites que par des coefficients invariants au cours du calcul. Un nouvel algorithme réunissant ces critères a été développé durant cette thèse, à partir de la combinaison de la méthode de Concus & Golub et d’une méthode de projection, qui permet de résoudre les équations associées à la modélisation homogène de la cavitation. Une nouvelle approche de vérification de ce nouvel algorithme est également proposée et mise en œuvre sur la base de la méthode des solutions manufacturées (MMS). / Cavitation-turbulence interactions are problematic aspect of cavitating flows which imposes limitations in development of better cavitation and turbulence models. DNS simulations with homogeneous mixture approach are proposed to overcome this and offer more insight into the phenomena. As DNS simulations are highly demanding and a variety of cavitation models exists, a tool devoted specifically to them is needed. Such tools usually demand application of highly accurate discretization schemes, direct solvers and multi domain methods enabling good scaling of the codes. As typical cavitating flow geometries impose limits on suitable discretization methods, compact finite differences offer the most appropriate discretization tool. The need for fast solvers and good code scalability leads to request for an algorithm, capable of stable and accurate cavitating flow simulations where solved systems feature multiplication of implicitly treated variables only by constant coefficients. A novel algorithm with such ability was developed in the scope of this work using Concus and Golub method introduced into projection methods, through which the governing equations for homogeneous mixture modeling of cavitating flows can be resolved. Work also proposes an effective and new approach for verification of the new and existing algorithms on the basis of Method of Manufactured Solutions.

In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge instead of in the expected downstream direction, as observed in the non-rotating case. The second problem considered in this thesis is the separation of western boundary currents from a curved coastline. This problem is also governed by the barotropic vorticity equation, and it is solved on an idealized model domain suitable for investigating the effects that boundary curvature has on the tendency of a boundary current to separate. The numerical method employed is a two-dimensional Chebyshev spectral collocation method and yields high order accuracy that helps to better resolve the boundary-layer dynamics in comparison to low-order methods. Results are given for a selection of boundary curvatures, non-dimensional β-parameters (β^), Reynolds numbers (Re), and Munk Numbers (Mu). In general, it is found than an increase in β^ will act to suppress boundary-layer separation. However, a sufficiently sharp obstacle can overcome the β-effect and force the boundary current to separate regardless of the value of β^. It is also found that in the inertial limit (small Mu, large Re) the flow region to the east of the primary boundary current is dominated by strong wave interactions and large eddies which form as a result of shear instabilities. In an interesting case of the inertial limit, strong waves were found to interact with the separation region, causing it to expand and propagate to the east as a large eddy. This idealized the mechanism by which western boundary currents such as the Gulf Stream generate eddies in the world's oceans.

In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge instead of in the expected downstream direction, as observed in the non-rotating case. The second problem considered in this thesis is the separation of western boundary currents from a curved coastline. This problem is also governed by the barotropic vorticity equation, and it is solved on an idealized model domain suitable for investigating the effects that boundary curvature has on the tendency of a boundary current to separate. The numerical method employed is a two-dimensional Chebyshev spectral collocation method and yields high order accuracy that helps to better resolve the boundary-layer dynamics in comparison to low-order methods. Results are given for a selection of boundary curvatures, non-dimensional β-parameters (β^), Reynolds numbers (Re), and Munk Numbers (Mu). In general, it is found than an increase in β^ will act to suppress boundary-layer separation. However, a sufficiently sharp obstacle can overcome the β-effect and force the boundary current to separate regardless of the value of β^. It is also found that in the inertial limit (small Mu, large Re) the flow region to the east of the primary boundary current is dominated by strong wave interactions and large eddies which form as a result of shear instabilities. In an interesting case of the inertial limit, strong waves were found to interact with the separation region, causing it to expand and propagate to the east as a large eddy. This idealized the mechanism by which western boundary currents such as the Gulf Stream generate eddies in the world's oceans.

[pt] A periferia urbana sul da Cidade do México apresenta atualmente um padrão de crescimento conhecido como cidade difusa, em que a dispersão urbana e mistura de atividades urbanas e rurais põem em interdito a dualidade campo-cidade com a que havia sido tratado tradicionalmente o limite no marco de planejamento territorial; e merece o reconhecimento de seu possível rol na promoção do desenvolvimento sustentável deste centro povoado, à luz de uma consolidação urbana futura e de sua vizinhança com sistemas naturais frágeis. Trata-se, pois, de um espaço que deveria ser planejado partindo do reconhecimento destas novas dinâmicas e em que a metodologia de desenvolvimento e design regenerativos, criada à luz do paradigma da sustentabilidade ecológica, poderia ser útil para definir delineamentos que orientassem o ordenamento sustentável deste território. Esta metodologia reconhece o lugar de intervenção e seu caráter único (essência), como as bases fundamentais do processo de definição de estratégias que permitiriam fomentar seu desenvolvimento regenerativo a partir de projetos arquitetônicos ou urbanos. Não obstante, apesar da metodologia propor um marco de trabalho que compreenda o lugar a partir do reconhecimento dos padrões presentes, não fica claro como, em função dos mesmos, se pode determinar os que são centrais e definem, por sua vez, seu caráter único. Ante este vazio metodológico para definir a essência de um lugar a partir do entendimento de seus padrões, e considerando-se que, de acordo com a teoria de sistemas complexos, a compreensão das relações entre os elementos de um sistema permite entender sua estrutura e determinar por sua vez, aqueles que seriam centrais para a organização das dinâmicas presentes, se identificou a metodologia Matriz de Influência como uma possível ferramenta para compreender as relações dos elementos de um sistema a partir da detecção dos níveis de influência dos mesmos. Em função do anterior, se colocou como objetivo desenhar uma ferramenta metodológica que permita detectar os padrões da periferia urbana da Cidade do México que poderiam definir a essência do lugar situado em este território e promover seu desenvolvimento regenerativo; para o qual foi criada uma versão da Matriz de Influência adaptada ao estudo dos padrões e foi expandida a análise objetiva e subjetiva da metodologia de Desenvolvimento e Design Regenerativos. Finalmente, a ferramenta proposta foi testada no Santa María Tepepan, Xochimilco, com o objetivo de determinar sua essência. / [en] Mexico City s south urban periphery is now characterized by a growth pattern known as dispersed city, where urban dispersion and mixing of urban and rural activities, calls into question the rural-urban duality with which the territorial planning had traditionally treated this fringe. It also merits recognition for its possible role in promoting the sustainable development of this city, especially considering its future urban consolidation and its proximity to fragile natural systems. Thus, it is a space that should be planned keeping these new dynamics in mind, and where the regenerative development and design methodology, created under the paradigm of ecological sustainability, could be useful to define guidelines that orient the sustainable development of this area. This methodology recognizes the place itself and its unique character (essence), as the fundamental bases of the project, hence useful in defining the strategies for its regenerative development through architectural or urban projects. Even though the methodology proposes a framework for understanding the place of implementation recognizing its present patterns, it is not clear how to determine the core patterns that define the place’s unique character. To address this methodological void and define the essence of a place on the bases of an understanding of its patterns, and considering that, according to the theory of complex systems, the compression of relations amongst the elements of a system permits us to understand and determine those which are central to the present organizational dynamics; it has been identified the methodology called Influence Matrix which permits leads to the understanding of the relationallity of the elements of a system by detecting their own level of influence. Hence, the proposed objective was to design a methodological tool to detect the patterns of the southern urban periphery of Mexico City that could define the essence of a place located within this territory, and therefore promote its regenerative development. This methodological tool was based on a version of the Matrix of Influence, adapted to the analysis of patterns and on an expanded objective and subjective analysis from the Regenerative Development and Design methodology. Finally, the proposed tool was tested in the town of Santa María Tepepan, Xochimilco, to determine its essence. / [es] La periferia urbana Sur de la Ciudad de México presenta actualmente un patrón de crecimiento conocido como ciudad difusa, en donde la dispersión urbana y mezcla de actividades urbanas y rurales, pone en entredicho la dualidad campo-ciudad con la que había sido tratado tradicionalmente este borde en el marco de la planeación territorial; y amerita el reconocimiento de su posible rol en la promoción del desarrollo sustentable de este centro poblado, a la luz de una consolidación urbana futura y de su cercanía con sistemas naturales frágiles. Se trata pues de un espacio que debería planearse partiendo del reconocimiento de estas nuevas dinámicas y en donde la metodología de Desarrollo y Diseño Regenerativos, creada a la luz del paradigma de la sustentabilidad ecológica, podría ser útil para definir lineamientos que orienten el ordenamiento sustentable de este territorio. Esta metodología reconoce el lugar de intervención y su carácter único (esencia), como las bases fundamentales del proceso de definición de estrategias que permitirían fomentar su desarrollo regenerativo a partir de proyectos arquitectónicos o urbanos. No obstante, si bien es cierto que la metodología propone un marco de trabajo para comprender el lugar a partir del reconocimiento de los patrones presentes, no queda claro cómo en función de los mismos se pueden determinar los que son centrales y definen a su vez su carácter único. Ante este vacío metodológico para definir la esencia de un lugar a partir del entendimiento de sus patrones, y considerando que de acuerdo a la teoría de los sistemas complejos, la comprensión de las relaciones entre los elementos de un sistema permite entender su estructura y determinar a su vez los que son centrales para la organización de las dinámicas presentes; se identificó la metodología Matriz de Influencia, como una posible herramienta que permitiría justamente comprender las relaciones de los elementos de un sistema a partir de la detección de los niveles de influencia de los mismos. En función de lo anterior, se planteó como objetivo diseñar una herramienta metodológica que permita detectar los patrones de la periferia urbana Sur de la Ciudad de México que podrían definir la esencia de un lugar emplazado en este territorio y promover su desarrollo regenerativo; para lo cual se hizo una versión de la Matriz de Influencia adaptada al estudio de patrones y se amplió el análisis objetivo y subjetivo manejado en el marco de la metodología de Desarrollo y Diseño Regenerativos. Finalmente, la herramienta propuesta fue probada en el pueblo de Santa María Tepepan, Xochimilco, con miras a determinar su esencia.