A higher-order hypersingular boundary element method for the modeling of vortex sheet dynamics

Abstract

A new model is proposed to compute the time evolution of interfaces between inviscid fluids represented by vortex sheets (VS), under the controlling effects of gravity, density difference, and interfacial tension. In this model, a higher-order boundary element method (BEM) is used to compute flow velocities on the VSs, based on Biot-Savart integral equations, and an explicit Taylor expansion scheme is used for time updating. An accurate numerical method is proposed to calculate hypersingular integrals occurring in the BEM. Applications are presented for the steady flow around a circular cylinder, for the propagation of a nonlinear surface wave over constant depth, and for a periodic Kelvin- Helmholtz instability. The effects of model parameters on the accuracy of the solution are discussed.