The development of an all quadrilateral boundary conforming grid generator for high order finite element methods

摘要

A grid generator is developed that produces all quadrilateral meshes. The scheme is automated to work for arbitrary choice of geometry. In addition, a Non-Uniform Rational B-Spline curve fitter is implemented to replicate the curvature of the geometries. The grid elements on the boundaries conform to the curved structure to support high order accuracy for a finite element scheme. Various geometries are used to test the robustness and generality of the meshing algorithm. The initial problems that were encountered are discussed and the solutions explained. The speed of the algorithm is discussed together with the effect of grid and geometry size on runtime. A finite element solver is used to validate the grids. The order of accuracy of the scheme is demonstrated for quadrilateral grids and increased order is compared with a refined grid study.