Efficiency of Multiscale Hybrid Grid-Particle Vortex Methods

This article presents a study of computational cost for the vortex method, a Lagrangian numerical scheme using particles of fluids for simulation of three-dimensional flows. Its main features are to compute accurately transport effects and to be very robust, that is to say, often without prohibitive stability condition. Special attention is given to hybrid grid-particle vortex methods. They are shown to scale as $\mathcal{O}(n\log n)$, even when used in a multiscale context. Furthermore, a discussion is provided on the best strategies for simulations in complex geometry. Computational cost is shown to have the same efficiency when performing multiscale simulations of three-dimensional flows in complex geometry.