A Review of Vortex Methods and Their Applications: From Creation to Recent Advances

Abstract

This review paper presents an overview of Vortex Methods for flow simulation and their different sub-approaches, from their creation to the present. Particle methods distinguish themselves by their intuitive and natural description of the fluid flow as well as their low numerical dissipation and their stability. Vortex methods belong to Lagrangian approaches and allow us to solve the incompressible Navier-Stokes equations in their velocity-vorticity formulation. In the last three decades, the wide range of research works performed on these methods allowed us to highlight their robustness and accuracy while providing efficient computational algorithms and a solid mathematical framework. On the other hand, many efforts have been devoted to overcoming their main intrinsic difficulties, mostly relying on the treatment of the boundary conditions and the distortion of particle distribution. The present review aims to describe the Vortex methods by following their chronological evolution and provides for each step of their development the mathematical framework, the strengths and limits as well as references to applications and numerical simulations. The paper ends with a presentation of some challenging and very recent works based on Vortex methods and successfully applied to problems such as hydrodynamics, turbulent wake dynamics, sediment or porous flows.

Tracking the vortex motion by using Brownian fluid particles

“…which coincides with (3) if K is the Biot-Savart kernel G. The dynamics of (X n , A n ) are still defined by ( 7) and ( 8). Together with (5) we deduce that…”

“…Among them, various vortex methods which are based on the vorticity transport equation have become an attractive approach for simulating fluid flows in particular turbulent flows. One may find a comprehensive account in the monographs Cottet and Koumoutsakos 1 , Majda and Bertozzi 2 , Saffman 3 , Ting and Knio 4 , and the recent review Mimeau and Mortazavi 5 .…”

Experimental Investigation of the Near-Surface Flow Dynamics in Downburst-like Impinging Jets Immersed in ABL-like Winds

“…A decisive support in this sense will also come from ongoing numerical simulations modeling the experimental downburst scenario at the WindEEE Dome that was discussed in the current study. As described in Section 1, numerical studies on the DB-ABL interaction have already been performed in recent years (e.g., [31]) and give important insights into vortical structure dynamics, also taking advantage of the Lagrangian vortex method [47,48]. The meshless approach by means of Large Eddy Simulation (LES), for instance, appears very promising in reconstructing the spatial evolution of such a complex flow interaction, where the experimental grid of measurement locations assessed in this study still seems coarse for this purpose.…”

Effect of Wax Composition and Shear Force on Wax Aggregation Behavior in Crude Oil: A Molecular Dynamics Simulation Study

“…The SLLOD equation is used to apply Couette flow to the simulated system to obtain the viscosity. Shear boundary conditions are applied to the system, which is expected to drive the system to the steady state [ 34 , 35 ]. The temperature was maintained with the Nose–Hover thermostat.…”