Análise dos erros na estimação de gradientes em malhas de Voronoi

• Autor(a) principal: Santos, Jailson França dos
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13767
• topic: Finite Volumes; Gradient estimation; Voronoi diagrams; Analyses errors; Método dos volumes finitos; Estimativas de gradientes; Diagrama de Voronoi; Análise de erros (Matemática); Geração numérica das malhas (Análise numérica); CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

This work presents a theoretical and numerical study on the errors that occur in the calculation of gradients on unstructured meshes Voronoi type, these meshes, also formed by Delaunay triangulation. The meshes adopted in the work were cartesian and triangular meshes, the latter is formed by dividing a square in two or four equal triangles. For this analysis, we adopt the choice of three different methodologies for the calculation of gradients: Green Gauss method, weighted least-squares method and mean value of the projected gradients method. The text is based on two main approaches: to show that the equations of errors given by the gradients may be similar, but with opposite signs, for calculation point in opposite volumes. And show that the order of the error of the analytical equations can be improved in uniform mesh when compared to not uniform, the one-dimensional case, and when viewed from the opposite face of such volumes for the two-dimensional case.