Métodos multiescala para as equações de Navier-Stokes incompressíveis

• Ano de defesa: 2020
• Autor(a) principal: Baptista, Riedson
• Orientador(a): Catabriga, Lucia
• Banca de defesa: Almeida, Regina Celia Cerqueira de , Devloo, Philippe Remy Bernard, Boeres, Maria Claudia Silva , Valli, Andrea Maria Pedrosa
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Espírito Santo; Doutorado em Ciência da Computação
• Programa de Pós-Graduação: Programa de Pós-Graduação em Informática
• Departamento: Centro Tecnológico
• País: BR
• Palavras-chave em Português: Elementos finitos; Métodos estabilizados multiescala; Equações de Navier-Stokes incompressíveis; Finite element; Multiscale estabilized methods; Incompressible Navier-Stokes equations
• Área do conhecimento CNPq: Ciência da Computação
• Link de acesso: http://repositorio.ufes.br/handle/10/14454

In this work, we present a nonlinear variational multiscale finite element method to solve the incompressible Navier-Stokes equations. The method is based on a decomposition in two levels of the approximation space and the local problem is modified by introducing an artificial diffusion that acts in an adaptive way only on the unresolved discretization scales. It can be considered a self-adaptive method, so that the amount of sub-mesh viscosity is automatically introduced according to the residue of the scales resolved at the element level. To reduce the computational cost typical of two-scale methods, the micro-scale space is defined through polynomial functions that cancel each other out at the border of the elements, known as bubble functions, whose degrees of freedom are eliminated locally in favor of the degrees of freedom that reside on the resolved scales. We compared the numerical and computational performance of the method with the results obtained with the formulation streamline-upwind/Petrov-Galerkin (SUPG) combined with the method pressure stabilizing/Petrov-Galerkin (PSPG) through a set of four two-dimensional reference problems