A HIGHER-ORDER HYPERSINGULAR BOUNDARY-ELEMENT METHOD FOR THE MODELINGOF VORTEX SHEET DYNAMICS

A new model is proposed to compute the time evolution of interfaces be tween inviscid fluids represented by vortex sheets (VS), under the con trolling effects of gravity, density difference, and interfacial tensi on. In this model, a higher-order boundary element method (BEM) is use d to compute flow velocities on the VSs, based on Biot-Savart integral equations, and an explicit Taylor expansion scheme is used for time u pdating. An accurate numerical method is proposed to calculate hypersi ngular integrals occurring in the BEM. Applications are presented for the steady flow around a circular cylinder, for the propagation of a n onlinear surface wave over constant depth, and for a periodic Kelvin-H elmholtz instability. The effects of model parameters on the accuracy of the solution are discussed. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.