Accurate higher order automated unstructured triangular meshes for airfoil designs in aerospace applications using parabolic arcs

Abstract This paper presents automatically generated higher order curved triangular meshes around airfoil design using MATLAB code. This work shows a valuable basis for the finite element procedures involved in evaluating aerodynamic performances. Finite element method (FEM) effectively solves all computational fluid dynamics problems around the airfoil and for that region around the airfoil that has been discretized with unstructured curved triangular elements. Meshes have been formed on the basis of subparametric transformation created for the curved triangular element obtained from the nodal relations of parabolic arcs. This scheme can be used to obtain the output data of node coordinates, element connectivity and boundary values for all discretized elements over the airfoil design. A spectacular work done on linear triangular element meshing over a domain by Persson and Gilbert Strang is the basis of present meshing scheme. The proposed meshing scheme presents a refined higher order (HO) curved triangular discretization of few airfoil designs namely NACA0012, NACA0015 and NACA0021 inscribed inside a circle. The approach of the suggested meshing scheme described in this paper can be applied to numerous aerospace applications such as computing pressure gradients, understanding atmospheric nature study, evaluating laminar viscous compressible flow around the airfoil shape, etc. The element and nodal information gained from this discretization is useful for the numerical solutions of FEM and for the aerodynamic portrayal. This paper is aimed at the innovative discretization scheme which can be extended to all kinds of NACA airfoil designs. We have provided the MATLAB code AirfoilHOmesh2d for HO curved meshing around an airfoil with a cubic order triangular element. The mathematical explanation of this along with the description and implementation of it on few airfoil designs is described. The flowchart of the MATLAB code for cubic order meshing over airfoil design has been provided. This implementation supports many applications in an aerodynamic performance that have been elaborated in this paper. Two applications for the analysis of potential flow around airfoil and computation of pressure coefficient ( C p ) on the surface of the airfoil design have been performed. It has been verified and found that the present HO curved meshing technique efficiently gives converging solution.