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 2-D vortex methods. We briefly review the numerical method and we extensively describe two points in more details: the redistribution around an arbitrary body and a new scheme to diffuse a vortex sheet onto particles in a way that is most accurate. These two improvements allow to perform DNS of 2-D flows past bodies of arbitrary shape. We test and validate them on the flow past an impulsively started circular cylinder. The second part of the paper is about 3-D 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 (PSE) scheme close to the solid boundary so as to enhance the accuracy of the method. Fast vortex codes are used for both 2-D and 3-D computations. The 3-D code is also parallel