Regularized inviscid computation of vortex shedding around a moving flat plate

Abstract

The two dimensional flow field around a rigid flat plate in a prescribed motion and its interaction with a free surface are modeled and simulated. The flat plate is represented by a bound vortex sheet whose strength is determined by the body boundary condition and the conservation law of total circulation. The free vortex sheets shed from the edges of the plate is represented by sets of free point vortex blobs determined by the unsteady Kutta condition. When solving for the free vortices` motion, we apply the regularization method in which we modify the vortex equation with a smoothing parameter to avoid the ill-posedness of a vortex sheet. When the distance between two neighboring free vortices exceed a critical value, a new free vortex was inserted in between by quadratic interpolation. To solve for the interaction between vortices and a free surface, we impose the linearized free surface boundary condition with the decomposed velocity potential. Spatial periodicity with a certain computational domain length is assumed for every case, in order to employ the pseudospectral method in solving for the free surface. The evolution of the free surface and the free vortex sheet is calculated via 4th order Runge-Kutta method. The numerical results from each step are shown comparatively with differing numerical parameters.