Vortex Methods for the Simulation of Turbulent Flows: Review

Abstract

Vortex methods are a group of Lagrangian and semi-Lagrangian methods based on the vorticity-streamfunction or vorticity-velocity formulation of the Navier-Stokes equation , and provide an interesting alternative to grid based methods for external flows dominated by unsteady vortical motion. In the present review article, we will assess the advantages and disadvantages of vortex methods for the simulation of incompress-ible turbulent flows, based on the speed and accuracy benchmarks that have been performed recently. Our goal is to objectively and quantitatively evaluate the performance of this non-standard method, by directly comparing it's speed and accuracy against finite difference and pseudo-spectral DNS codes under identical calculation conditions. We also present examples of vortex methods in engineering applications of turbulent flows.