Two-dimensional non-uniform mesh generation for finite element models using MATLAB

Abstract

This paper demonstrates non-uniform mesh generation scheme for two-dimensional domains. For many models in fluid dynamics like turbulent flow, channel flow there is large gradient in the small narrow portion, for example near the wall region. To solve this kind of problems the non-uniform meshing scheme near the wall region helps to capture the fine details of the region. Meshing is carried through MATLAB codes which generate triangular meshes for two dimensional domains. The MATLAB code is based on distmesh2d developed for linear straight sided triangular element by Persson and Gilbert Strang (2004). The proposed meshing scheme is based on nodal relation and subparametric point transformations extracted from parabolic arcs developed by Rathod.et.al (2008). In this work a higher order triangular meshing upto quartic order for two domains the holey pie slice and a circle inscribed in a square has been demonstrated. These in turn finds its application in flow problems, thermodynamics and aerospace engineering. Present meshing scheme provides an improved high quality meshes for these domains and produce accurate results of the nodal position, boundary nodes and element connectivity for the discretized domain. The obtained output is advantageous in executing finite element procedure with less computational efforts.