Implementation of fast algorithms for 2D flow simulation using vortex particle methods

Vortex particle methods of computational hydrodynamics are widely employed by engineers to solve the problems of flow simulation and estimation of unsteady hydrodynamic loads acting on bodies. The main advantage of such methods is a relatively low computational cost, but their applicability is limited to subsonic incompressible single-phase non-heat-conducting flows. If high-order discretization is required, the usage of direct algorithms leads to a significant increase in computational complexity and memory demand. To overcome this limitation, approximate fast algorithms of quasilinear computational complexity were developed and implemented for the most time-consuming operations, such as the computation of convective velocities and the solution of the boundary integral equation. The general principles of fast algorithms were described. Their modifications for the problems mentioned above were discussed, and their efficiency was evaluated. The results obtained show that the application of fast algorithms enables a computational speedup of up to several hundred times for around a million vortex particles.