Fast BH/Multipoles Algorithm for Solving Boundary Integral Equation in Vortex Particle Methods of Computational Hydrodynamics

A fast algorithm for solving a boundary integral equation arising in vortex particle methods of computational hydrodynamics is proposed. The algorithm is based on a hybrid fast method combining the Barnes–Hut method and the fast multipole method and is adapted for iterative solution of linear systems for T-schemes with piecewise-constant and piecewise-linear solution representations. Analytical expressions for multipole moments of rectilinear panels and for integrals of local expansion coefficients with constant and linear weight functions are derived, allowing taking into account local influence integration and the vorticity distribution over panels in both nearby and far zones. The proposed algorithm achieves quasi-linear computational complexity without significant accuracy reduction.