Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Abstract

In this paper a new angular basis functions (ABFs) formulation which is different from the radial basis functions (RBFs) among the meshless methods is proposed to solve potential flow problems with non-smooth or discontinuous boundaries. The unique property of the ABFs formulation is first investigated in this study. In contrast to the method of fundamental solutions (MFS) using the RBFs, we adopt this ABFs collocation method to deal with the non-smooth or discontinuous boundaries more feasibly and accurately. Both the interior and exterior potential flow problems governed by the 2D Laplace equation are explored by both ABFs and RBFs schemes for comparison purposes. A square cavity, a cusp cavity, a uniform flow past a circular cylinder and the NACA 2418 airfoil are examined to test the merits or demerits of both the ABFs and RBFs formulations. From those four numerical experiments, the complementary ABFs formulation is found to be more effective to simulate domains with non-smooth or discontinuous boundaries such as acute, corner and cusp geometries. Furthermore, the basic aerodynamic problems of airfoils modeling are also discussed in the present study. From these numerical experiments, the angular basis function is found to be favorable of simulating the domains with acute, narrow regions and exterior problems.