Integral Equation Method for linear Water Waves

The Boundary Integral Equation Method (BIEM) is applied to transient water wave problems. Only two-dimensional linearized waves are considered. As is general practice, free-surface boundary conditions are applied at the equilibrium surface rather than the actual free surface; thus the problems become fixed-boundary problems rather the free-surface problems. For the cases in which fluid domain is unbounded in the horizontal direction, a radition condition is formulated such that waves pass through the computational boundaries without reflection. The stability limits and frequency distortion of the numerical method are examined and given. Numerical results are compared with analytical solutions or experimental data in three examples. Excellent agreement is observed.