Tikhonov regularisation in discrete vortex methods

In this study we propose the Tikhonov regularisation technique as a useful tool in discrete (blob) vortex methods (DVM). The effectiveness of Tikhonov technique is illustrated for the case of a specific blob vortex method, although the idea may be applicable to a wide class of vortex methods. The flow under consideration, modelled with blob vortices, is inviscid and two-dimensional. Flows past two geometries are considered. The first is a vertical flat plate for which the solution becomes unstable if no regularisation is used. The second is the case of a flow past a circular cylinder where it is demonstrated that the noise in the solution reduces when regularisation is applied.