Regularization fast multipole boundary element method for potential flow problems in 3D vortex method

Abstract

The boundary element method (BEM) is one way for solving the normal flow boundary conditions (potential flow problem) and the pressure distribution in numerical simulation of the three-dimensional vortex method. Because the problem can be reduced from a three-dimensional integral to a two-dimensional integral by BEM, this method is acclaimed in this study. BEM in engineering calculations already has a good application, but with the increasing number of grid problems, the dense matrix generated in the conventional boundary element method (CBEM) is increasing sharply. The fast multipole method (FMM) is introduced to accelerate the computational efficiency and speed of BEM. The three-dimensional vortex method requires solving the velocity and the velocity gradient of potential flow by BEM, and then it will encounter strongly singular integrals. The semi-analytical integral regularization algorithm is applied for solving strongly singular integrals in this paper. The regularization fast multipole boundary element method (FMBEM) is applied to the potential problem of flow over a single sphere, and analyze the results to prove the reliability and efficiency of this method. The calculation parameters which are selected by comparing the influences of them in the single sphere problem are applied to the potential problem of flow over multi-spheres, and the results are analyzed.