Author(s)

ALEXANDRA KOLGANOVA, ILIA K. MARCHEVSKY

Abstract

In the case of low subsonic velocities, when the compressibility of the medium can be neglected, vortex methods can be efficiently applied to simulate flows and estimate hydrodynamic loads acting on airfoils. The primary variable in vortex method is vorticity field, while the velocity and pressure fields can be reconstructed; there is also the possibility of computation of integral force and momenta acting on the airfoil, as well as viscous friction forces. The use of vortex methods requires multiple (at each time step) solution of the boundary integral equation (BIE) that describes the generation of vorticity on the airfoil surface, solution of several problems of N-body type and some other operations. Direct algorithms for these sub-problems have quadratic computational complexity with respect to number of particles, that significantly bounds the applicability of vortex methods for solving problems that require detailed discretisation. This paper presents description of fast algorithms based both on well-known approaches and some original modifications. The basic algorithm is hybrid algorithm for simulation of interaction of vortex particle in the flow domain; its generalisation is suggested for efficient solving of the BIE arising in vortex methods. The quasi-linear computational complexity of all suggested algorithms is achieved; their implementation is developed for multi-core CPUs.

Keywords

vortex methods, fast algorithm, boundary integral equations, n-body problem