Fast Multipole Discrete Vortex Method Applied to Unsteady Flow Simulations

Tulio Rodarte Ricciardi¹; William Roberto Wolf¹; Alex Mendonça Bimbato²

¹ Universidade Estadual de Campinas; ² Universidade Estadual Paulista

doi:10.20906/CPS/COB-2015-0154

Resumo

The discrete vortex method (DVM) is based on a Lagrangian description of the vorticity transport equation. However, the solution of the fluid velocity field requires the evaluation of the contributions from the incident flow, the perturbation due to the body and the particle interactions. The latter contribution is computationally expensive since the Biot-Savart law is used to compute the induced velocity by all discrete vortices in the cloud. The fast multipole method is an attractive algorithm used to accelerate the expensive interactions of the discrete vortices. It reduces the computational cost of the Biot-Savart law from O(N2) to O(N), where N is the number of discrete vortices in the cloud for a particular time step. In the present work, the computation cost of the a simulation of the flow past a impulsively started cylinder is presented, and also the results from this analysis.

Palavras-chave: Discrete Vortex Method; Fast Multipole Method; Fluid Mechanics