Mesh anisotropy influence in a Poisson solver solution

• Grant number: 12/16217-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2012
• End date: September 30, 2013
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Leandro Franco de Souza
• Grantee: Patricia Boer
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The research project aims to the study the anisotropy phenomena influence - resulting from the use of stretched meshes - on the solution of two-dimensional elliptic problems. Anisotropy is a common problem and efficient solutions to this kind of problem are connected to the discretization and the appropriate choice of the numerical method. It is adopted a finite differences method. Thus, it is necessary the study of the derivation of classical and compact schemes in structured uniform and non uniform meshes. Aiming a better agreement among the research's group studies, a multigrid method will be adopted. The investigation of the properties of the multigrid methods is critical to their understanding. Moreover, there is a significant amount of performance factors related to the chosen method that can be investigated: the structure of the multigrid method, smoothing methods, relaxation factors, number of iterations at each level, restriction and prolongation operators, among others. The code verification is carried out by use of a manufactured solutions. The results will contribute on the identifying parameters to accelerate convergence and / or runtime problems under investigation. (AU)