Método semi-lagrangeano das curvas de nível na captura de interfaces móveis em meios porosos

• Autor(a) principal: Gonçalves, Fábio
• Data de Publicação: 2006
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13674
• topic: Porous media; Level set method; Semi-Lagrangian method; Saffman-Taylor instability; Rayleigh-Taylor instability; Escoamento em meios porosos - Métodos de simulação; Equilíbrio - Equações; Métodos iterativos (Matemática); Meios porosos; Método dos conjuntos de nível; Método semi-lagrangeano; Instabilidade de Saffman-Taylor; Instabilidade de Rayleigh-Taylor; Escoamento em meios porosos; Métodos de simulação; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

Briefy, this thesis proposes a method for capturing moving interfaces based on the level set method coupled to a Semi-Lagrangian implementation for problems in porous media. Although this method could, in principle, be applied to any physical problem with moving interfaces, we foccus, in this thesis, on flows inside a consolidated porous media saturated by one or two imiscible and incompressible fluids. Besides, a parallelizable iterative method for solving linear systems defined on a network that can be reduced to the fundamental equilibrium equations, is employed to determine the velocity field associated with the flow in a porous medium. The semi-Lagrangian scheme coupled with the level set method is compared with the well-known implementation with the up-wind scheme. An exhaustive study is performed and reveals the superiority of the proposed scheme in relation to the competing one using the up-wind method. Finally, the level set method with semi-Lagrangian implementation and the iterative method for determining the velocity field are applied to the study of transient problems in porous media which present Saffman-Taylor and Rayleigh-Taylor instabilities. This study involves the application of a linear stability analysis, the introduction of several trigonometric perturbations to the interface and its non-linear evolution.