Applications of boundary integral equation methods for two‐dimensional non‐linear water wave problems

Abstract

Abstract On the basis of the integral equation approach, numerical algorithms for solving non‐linear water wave problem are presented. The free surface flow is assumed to be irrotational. Two different Green functions are used in the integral equations. The non‐linear free‐surface boundary conditions are treated by a time‐stepping Lagrangian technique. Several numerical examples are given, including permanent periodic waves, overturning progressive waves, breaking standing waves and sloshing problems.