Numerical Simulation of Unsteady Capillary-Gravity Waves

Abstract

In this work, plane problems of numerical simulation of wave motion are studied. Potential flows of a perfect incompressible fluid are considered. A numerical algorithm for calculating the shape of a free boundary is proposed. The algorithm is based on the boundary element method with the use of quadrature formulas with no saturation. The algorithm is used for studying the breaking of capillary gravity waves and calculating thin cumulative jets. The stability of the scheme and high accuracy in calculations of sharp cumulative jets are achieved due to special control for the distribution of grid points and a decrease in the grid step in the neighborhood of the forward end of the cumulative jet with an ultimately rapid growth of the curvature.