Application of a vortex method to free surface flows

Abstract

AbstractVortex methods have found wide applications in various practical problems. The use of vortex methods in free surface flow problems, however, is still very limited. This paper demonstrates a vortex method for practical computation of non‐linear free surface flows produced by moving bodies. The method is a potential flow formulation which uses the exact non‐linear free surface boundary condition at the exact location of the instantaneous free surface. The position of the free surface, on which vortices are distributed, is updated using a Lagrangian scheme following the fluid particles on the free surface. The vortex densities are updated by the non‐linear dynamic boundary condition, derived from the Euler equations, with an iterative Lagrangian numerical scheme.The formulation is tested numerically for a submerged circular cylinder in unsteady translation. The iteration is shown to converge for all cases. The results of the unsteady simulations agree well with classical linearized solutions. The stability of the method is also discussed.