Vortex Particle Methods (VPMs) are meshless Lagrangian methods for computational fluid dynamics (CFD) that are particularly efficient for estimating hydrodynamic loads acting on streamlined airfoils (or their systems), especially for highly unsteady flows and complex fluid-structure interaction (FSI) problems. Their key advantages include low numerical diffusion due to their particle-based nature and computational efficiency. However, at moderate and high Reynolds numbers (~103 and higher), the applicability of two-dimensional VPMs becomes restricted. Reliable simulation results can be obtained only for airfoils with sharp edges. For airfoils with smooth boundaries, the simulation results diverge from experimental data because unresolved three-dimensional turbulent effects govern such flows. To demonstrate this, the flow simulation around an immovable circular cylinder from small to high Reynolds numbers was considered. The numerical results for hydrodynamic loads acting on this cylinder were compared using OpenFOAM and an in-house VPM code, VM2D, which implements the Viscous Vortex Domains (VVD) method. Analysis of the velocity field in a vortex wake behind a circular cylinder showed that the spatial and temporal spectra of turbulence kinetic energy follow a power law with an exponent (–3) instead of the classical (–5/3) predicted by Kolmogorov–Obukhov theory. This result matches theoretical expectations for purely two-dimensional flows, where three-dimensional turbulent effects are not simulated. It confirms that 2D VPMs cannot accurately capture turbulent flow behavior around smooth bodies at high Reynolds numbers. The paper also discusses possible ways to improve two-dimensional vortex methods by adding LES-type turbulence models.
Yu. Izmailova (Fri,) studied this question.