We present simulations of two interacting moving cylinders immersed in a two-dimensional incompressible, viscous flow. Simulations are performed by coupling a wavelet-adapted, remeshed vortex method with the Brinkman penalization and projection approach. This method is validated on benchmark problems and applied to simulations of a master-slave pair of cylinders. The master cylinder's motion is imposed and the slave cylinder is let free to respond to the flow. We study the relative role of viscous and inertia effects in the cylinders interactions and identify related sharp transitions in the response of the slave. The observed differences in the behavior of cylinders with respect to corresponding potential flow simulations are discussed. In addition, it is observed that in certain situations the finite size of the slave cylinders enhances the transport so that the cylinders are advected more effectively than passive tracers placed, respectively, at the same starting position.

International audienceIn this work, a penalization method is discussed in the context of vortex methods for incompressible flowsaround complex geometries. In particular, we illustrate the method in two cases: the flow around a rotatingblade for Reynolds numbers 1000 and 10,000 and the flow past a semi-circular body consisting of a porouslayer surrounding a rigid body at Reynolds numbers 550 and 3000. In the latter example, the results areinterpreted in terms of control strategy

Highlights • A vortex penalization method is proposed to model 3D incompressible flows • Appropriate far field boundary conditions are handled in a FFT-based Poisson solver • The cost is reduced extending a directional remeshing technique to the 3D algorithm • The computational code is validated and applied to flows past a sphere and hemisphere • At Re=1000 the hemisphere maintains its wake symmetry much longer than the sphere 1 ACCEPTED MANUSCRIPT Abstract A vortex method with penalization is proposed in order to simulate threedimensional incompressible bluff body flows. This approach combines the robustness of vortex methods and the flexibility of penalization methods to impose boundary conditions on the obstacle. Far field boundary conditions are handled in a FFT-based Poisson solver. A validation of the proposed numerical method is carried out in the context of flow past a sphere and further simulations are performed in the more challenging case of flow past a hemisphere.Keywords: flow past a sphere, flow past a hemisphere, vortex methods, particle methods, penalization method, semi-Lagrangian methods.

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.