An efficient algorithm for calculating boundary elements in vortex methods

Abstract

A theorem on the conformal mapping of the flow field with a continuous vorticity distribution is proved. An efficient algorithm of the boundary elements computing based on the theorem is applied in simulation of two-dimensional flow around an elliptic cylinder by the meshless method of Viscous Vortex Domains (VVD). The algorithm makes it possible to significantly reduce (orders of magnitude compared to conventional methods) the time spent on calculating boundary elements and multiply the number of calculation points on the body contour, which is necessary for high resolution of the boundary layer at high values of the Reynolds number. The algorithm can also be used to calculate boundary elements on cylindrical surfaces of arbitrary section and in combination with different vortex methods. The flow around an elliptical cylinder is simulated with a high resolution of the boundary layer for Re numbers from 102 to 105.