| dc.description.abstract | Resumo: Os problemas de Dinâmica dos Fluidos Computacional aumentam constantemente em quantidade e complexidade, dada a importância de suas aplicações, tornando-se um desafio que exige aprimoramentos constantes nos métodos que buscam soluções. Neste sentido, esta dissertação aplica técnicas de extrapolação em associação ao método multigrid para obtenção de soluções, com o propósito de reduzir o erro de iteração, o tempo de processamento (tempo de CPU) e melhorar os fatores de convergência. Essa aplicação é feita em um caso de escoamento laminar bidimensional de um fluido incompressível em regime transiente ditado pelas equações de Navier-Stokes, resolvidas iterativamente via método de projeção e o Método de Volumes Finitos. Os métodos de extrapolação utilizados são: Aitken, Empírico, Mitin, Épsilon escalar, Rho escalar, Épsilon topológico e Rho topológico. Para descobrir qual é o mais apropriado para o problema proposto, foram realizadas duas etapas. Primeiramente, os extrapoladores foram aplicados individualmente após a aplicação do método multigrid, para averiguar qual resulta em melhores ganhos em alguns parâmetros, como por exemplo, na redução do erro de iteração. Os extrapoladores que obtiveram melhores resultados foram utilizados na segunda etapa, na qual foram aplicados entre os ciclos do método multigrid. Neste sentido, dentre as técnicas de extrapolação aplicadas, as que apresentaram melhores propriedades de convergência na primeira etapa frente ao multigrid sem extrapolação foram as de Épsilon topológico e Épsilon escalar. Já na segunda etapa, ambas as técnicas mantiveram seu êxito em relação ao multigrid sem extrapolação, entretanto, o extrapolador Épsilon topológico apresentou taxas de convergência mais significativas em relação ao Épsilon escalar. Os outros parâmetros analisados foram: pico de memória de armazenamento, norma adimensionalisada do resíduo com base na estimativa inicial e normas do erro de iteração. Assim é possível afirmar qual técnica de extrapolação é melhor e compará-la com a aplicação do método multigrid sem o uso de extrapoladores. Palavras-chave: aceleração de convergência, Dinâmica dos Fluidos Computacional, Método de Volumes Finitos, método de projeção, Épsilon escalar, Épsilon topológico. | pt_BR |
| dc.description.abstract | Abstract: Computational Fluid Dynamics problems are constantly increasing in quantity and complexity, given the importance of its applications, and this challenge always requires an improvement in methods for finding solutions. In this sense, this dissertation applies solutions of extrapolation techniques in association with the multigrid method, with the purpose of reducing the iteration error, the processing time (CPU time) and to improve the convergence factors. This application is made in a case of two-dimensional laminar flow of a time-dependent incompressible fluid dictated by the Navier-Stokes equations, solved iteratively by the projection method and the Finite Volume Method. The extrapolation methods used are: Aitken, Empiric, Mitin, Scalar epsilon, Scalar rho, Topological epsilon and Topological rho. To find out which one is most appropriate for the proposed problem, they were tested in two steps. First, they are applied individually after the use of the multigrid method, to find out which one presents greater efficiency in some parameters, for example, in the iterative error reduction. The best-performing extrapolation techniques will be used in the second step, where they will be applied between the cycles of the multigrid method. In this sense, among the applied extrapolation techniques, the ones that presented better convergence properties in the first stage against the multigrid without extrapolation were Topological epsilon and Scalar epsilon. In the second stage, both techniques maintained their success in relation to multigrid without extrapolation, however, the topological Epsilon extrapolator presented more significant convergence rates in relation to the scalar Epsilon. The other parameters analyzed were: storage memory peak, dimensionless norm of the residual based on the initial estimate and the error norms of iteration. Thus, it is possible to state which extrapolation technique is best and compare it with the multigrid method without extrapolation methods. Key-words: convergence acceleration, Computational Fluid Dynamics, Finite Volume Method, projection method, scalar Epsilon, topological Epsilon. Computational Fluid Dynamics problems are constantly increasing in quantity and complexity, given the importance of its applications, and this challenge always requires an improvement in methods for finding solutions. In this sense, this dissertation applies solutions of extrapolation techniques in association with the multigrid method, with the purpose of reducing the iteration error, the processing time (CPU time) and to improve the convergence factors. This application is made in a case of two-dimensional laminar flow of a time-dependent incompressible fluid dictated by the Navier-Stokes equations, solved iteratively by the projection method and the Finite Volume Method. The extrapolation methods used are: Aitken, Empiric, Mitin, Scalar epsilon, Scalar rho, Topological epsilon and Topological rho. To find out which one is most appropriate for the proposed problem, they were tested in two steps. First, they are applied individually after the use of the multigrid method, to find out which one presents greater efficiency in some parameters, for example, in the iterative error reduction. The best-performing extrapolation techniques will be used in the second step, where they will be applied between the cycles of the multigrid method. In this sense, among the applied extrapolation techniques, the ones that presented better convergence properties in the first stage against the multigrid without extrapolation were Topological epsilon and Scalar epsilon. In the second stage, both techniques maintained their success in relation to multigrid without extrapolation, however, the topological Epsilon extrapolator presented more significant convergence rates in relation to the scalar Epsilon. The other parameters analyzed were: storage memory peak, dimensionless norm of the residual based on the initial estimate and the error norms of iteration. Thus, it is possible to state which extrapolation technique is best and compare it with the multigrid method without extrapolation methods. Key-words: convergence acceleration, Computational Fluid Dynamics, Finite Volume Method, projection method, scalar Epsilon, topological Epsilon. | pt_BR |
