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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

[en] A NUMERICAL METHOD FOR SOLVING FLOWS USING COVARIANT COMPONENTS IN NON-ORTHOGONAL COORDINATES / [pt] UM MÉTODO NUMÉRICO PARA SOLUÇÃO DE ESCOAMENTOS UTILIZANDO COMPONENTES CONTRAVARIANTES EM COORDENADAS NÃO ORTOGONAIS

LUIS FERNANDO GONCALVES PIRES 03 November 2011 (has links)
[pt] O trabalho desenvolveu uma metodologia de solução numérica de escoamentos em geometrias complexas, numa formulação incompressível e bi-dimensional. As equações de conservação são discretizas com o emprego da técnica de volumes finitos em coordenadas não ortogonais. Esta técnica mapeia o espaço real num espaço transformado, no qual as fronteiras do domínio de cálculo coincidem com as fronteiras do domínio físico. Os componentes contravariantes da velocidade foram empregados como variáveis dependentes nas equações de conservação de quantidade de movimento. Estas equações foram obtidas em coordenadas não ortogonais pela manipulação algébrica das equações discretizadas para os componentes cartesianos. Este procedimento, que emprega um sistema de coordenadas auxiliar fixo localmente, evita o surgimento dos diversos termos oriundos da curvutura e da não ortogonalidade da malha, que seriam obtidos caso fosse empregada a análise tensorial para a derivação destas equações. O ocoplamento pressão-velocidade é feito utilizando SIMPLEC. O conjunto de equações algébricas resultante é resolvido por um esquema de solução segregado, no qual é empregado um esquema de solução linha-a-a linha(TDMA), com um processo de correção por blocos para acelerar a convergência. A metodologia desenvolvida foi utilizada para solução de diversos problemas visando analisar o seu desempenho. Foram estudados os seguintes casos-escoamento laminar entre dois cilindros, convecção natural entre dois cilidros excêntricos, escoamento induzido numa cavidade trapezoidal pelo movimento de suas bases, escoamento laminar num canal, escoamento axi-simétrico num duto com estrangulamento.Tendo em vista os bons resultados obtidos para testes, pode-se concluir que as opções realizadas para a confeção do esquema desenvolvido foram corretas, pois geraram um algoritimo efeciente e versátil. / [en] A solution method for bi-dimensional incompressibible fluid flow problems in complex geometrics is developed in this work. The method solves the conservation equations in nonorthogonal coordinate system using the finite volumes technique. The contravariant velocities are kept as dependent variables in the momentum equations. These equations are obtained by an algebric manipulation of the discretization equations written in locally fixed coordinate system. This producedure avoids the treatment of the extra terms if the discretization equations for the curvilinear velocities are obtained in the conventional manner. The coupling of pressure and velocities are performed by the SIMPLEC algorithm. The set of algebric equations are solved using an iterative method in conjunction with coefficient update for linerization. In the computer implementation of the proposed scheme a line-by-line algorithm (TDMA) has been employed with a block corretion procedure to enhance the convergence. The method is tested by solving a variety of problems. The problems include-flow between two concentric rotating cylinders, natural convection in an eccentric annuli, driven flow in a trapezoidal cavity with moving lids, laminar flow in a channel, exismetric flow in duct with reduced cross section and laminar and turbulent flow through a tube with an axisimetric constriction. The objetive of these tests is to establish the validity of the proposed scheme and demonstrate its applicability to a wide variety of problems.
2

THE EQUIVALENCE PROBLEM FOR ORTHOGONALLY SEPARABLE WEBS ON SPACES OF CONSTANT CURVATURE

Cochran, Caroline 09 June 2011 (has links)
This thesis is devoted to creating a systematic way of determining all inequivalent orthogonal coordinate systems which separate the Hamilton-Jacobi equation for a given natural Hamiltonian defined on three-dimensional spaces of constant, non-zero curvature. To achieve this, we represent the problem with Killing tensors and employ the recently developed invariant theory of Killing tensors. Killing tensors on the model spaces of spherical and hyperbolic space enjoy a remarkably simple form; even more striking is the fact that their parameter tensors admit the same symmetries as the Riemann curvature tensor, and thus can be considered algebraic curvature tensors. Using this property to obtain invariants and covariants of Killing tensors, together with the web symmetries of the associated orthogonal coordinate webs, we establish an equivalence criterion for each space. In the case of three-dimensional spherical space, we demonstrate the surprising result that these webs can be distinguished purely by the symmetries of the web. In the case of three-dimensional hyperbolic space, we use a combination of web symmetries, invariants and covariants to achieve an equivalence criterion. To completely solve the equivalence problem in each case, we develop a method for determining the moving frame map for an arbitrary Killing tensor of the space. This is achieved by defining an algebraic Ricci tensor. Solutions to equivalence problems of Killing tensors are particularly useful in the areas of multiseparability and superintegrability. This is evidenced by our analysis of symmetric potentials defined on three-dimensional spherical and hyperbolic space. Using the most general Killing tensor of a symmetry subspace, we derive the most general potential “compatible” with this Killing tensor. As a further example, we introduce the notion of a joint invariant in the vector space of Killing tensors and use them to characterize a well-known superintegrable potential in the plane. xiii

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