Geração e otimização de malhas estruturadas sobre domínios bidimensionais arbitrários

Abstract

The aim of this work is to develop an algorithm for optimizing structured meshes generated over generic two dimensional domains, by splitting complex shapes into a collection of quadrilateral sub domains, which are then meshed by a Laplacian elliptic mesh generator, and the mesh smoothness between adjacent areas is imposed later. A parametric formulation for cubic spline interpolation is used both to define the domain and apply the boundary conditions. In order to get square elements, a nodaí repositioning algorithm is used, and two search methods are tested: a genetic algorithm and a gradient based method. The algorithm reallocates the boundary nodes and uses their parametric coordinates as Dirichlet boundary conditions to solve the Laplacian generator system and update the interior nodes coordinates. To get a continuous mesh between adjacent areas, the user gives the same boundary conditions to the nodes located on the common boundaries. If the original geometry of the areas is important to the problem, and must remain unchanged, Dirichlet conditions are applied. Otherwise, the shape of the subdomains is changed so that a smoother mesh is obtained. To ensure this smoothness, Neumann conditions are aplied to the modified boundaries. This method has shown very interesting results when applied to domains that are often found in CFD problems. Because of the large number of design variables, the genetic algorithm had a poor time performance, and could be applied only to simple quadrilateral domains. On the other hand, the gradient based method proved to be fast enough to be applied to problem where remeshing during the iterative process is necessary. The results also show that this method may be adapted to work as a shape optimization algorithm.