Métodos de elementos finitos estabilizados para escoamentos de Darcy e de Stokes-Darcy acoplados

• Autor(a) principal: Correa, Maicon Ribeiro
• Data de Publicação: 2006
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/47
• topic: Escoamento de Darcy; Escoamento de Stokes-Darcy; Meios porosos heterogêneos; Numerical analysis; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

In this thesis we propose new stabilized finite element methods for Darcy flow and for the coupled Stokes-Darcy flow. We review the Galerkin method applied to the classical variational formulations of the Darcy's system, and comment on some stabilization techniques proposed in the literature. Through the consistent combination of least square residuals of the Darcy's law, the mass balance equation and the curl of Darcy's law, we develop new finite element formulations to porous media flow, that have higher stability than the usual stabilizations. We present a methodology to incorporate restrictions that allows the application of these formulations to flow in heterogeneous porous media with an interface of discontinuity of the hydraulic conductivity tensor. By combining the new stabilized formulations for Darcy flow with Petrov-Galerkin formulations to Stokes flow, we develop stabilized methods for the coupled Stokes-Darcy flow that employ Lagrangian finite element spaces in both domains, continuous for the velocity and continuous or discontinuous for the pressure. Equal-order interpolations can be adopted for both velocity and pressure spaces.