Boundary integral equation methods applied to overturning waves.

摘要

Weakly singular and singular integral equation methods are presented to model overturning waves numerically. After testing each method against the exact solutions in some simple cases, a direct comparison of two integral equation methods is made on progressive waves of permanent form. The accurate results of steady progressive waves are obtained by using velocity potential represented by a Stokes expansion. Singular integral equation methods are found to be accurate and efficient for modelling unsteady steep waves. After introducing an efficient time-marching method, overturning waves on infinite and finite depth are obtained by a cubic element of the singular integral equation.;Various ways to stabilize the discretized boundary integral equation are presented.