Vortex particles and tree codes: I. flows with arbitrary crossing between solid boundaries and particle redistribution lattice; II. Vortex ring encountering a plane at an angle

The first part of the paper deals with two-dimensional vortex methods. We briefly review the numerical method and describe two points in more detail: the redistribution around an arbitrary body, and a new scheme to diffuse a vortex sheet into particles in a way that is more accurate. These two improvements allow to perform DNS of two-dimensional flows past bodies of arbitrary shape. We test and validate them on the flow past in impulsively started circular cylinder. The second part of the paper is about three-dimensional flows with solid boundaries. We test the viscous method on the interaction between a vortex ring and a plane. We also detail a modified version of the particle strength exchange scheme close to the solid boundary in order to enhance the accuracy of the method. Fast vortex codes are used for both two- and three-dimensional computations. The three-dimensional code is also parallel.