Stephan T. Grilli and Zhimin Hu
Associate Professor Post-doctoral
fellow
Department of Ocean Eng.
University of Rhode Island
Narragansett, RI 02882, USA
Abstract :
A new model is proposed to compute the time evolution of interfaces
between inviscid fluids represented by vortex sheet (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 the 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.