Nonlinear multiscale viscosity methods and time integration schemes for solving compressible Euler equations

• Ano de defesa: 2018
• Autor(a) principal: Bento, Sérgio Souza
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal do Espírito Santo; BR; Doutorado em Ciência da Computação; Centro Tecnológico; UFES; Programa de Pós-Graduação em Informática
• Palavras-chave em Português: Finite element method; Multiscale formulation; Bubble function; Compressible flow problems; BDF methods; Stiff decay property; Euler equations; Elementos finitos; Métodos estabilizados multiescala; Funções bolha; Métodos BDF; Equações de Euler; Método dos elementos finitos; Rigidez (Geometria); Ciência da Computação; 004
• Link de acesso: http://repositorio.ufes.br/handle/10/10727

In this work we present nonlinear multiscale finite element methods for solving compressible Euler equations. The formulations are based on the strategy of separating scales – the core of the variational multiscale (finite element) methodology. The subgrid scale space is defined using bubble functions that vanish on the boundary of the elements, allowing to use a local Schur complement to define the resolved scale problem. The resulting numerical procedure allows the fine scales to depend on time. The formulations proposed in this work are residual based considering different ways for the artificial viscosity to act on all scales of the discretization. In the first formulation a nonlinear operator is added on all scales whereas in the second different nonlinear operators are included on macro and micro scales. We evaluate the efficiency of the formulations through numerical studies, comparing them with the SUPG combined with the shock-capturing operator YZβ and the CAU methodologies. Another contribution of this work concerns the time integration procedure. Density-based schemes suffer with undesirable effects of low speed flow including low convergence rate and loss of accuracy. Due to this phenomenon, local preconditioning is applied to the set of equations in the continuous case. Another alternative to solve this deficiency consists of using time integration methods with a stiff decay property. For this purpose, we propose a predictor-corrector method based on Backward Differentiation Formulas (BDF) that is not defined in the traditional sense found in the literature, i.e., using a predictor based on extrapolation.