A higher-order hypersingular Boundary Element Method for the modeling of vortex sheet dynamics

Engineering Analysis with Boundary Elements, 21 (2), 117-129.

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.

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