Coupling of Two Absorbing Boundary Conditions for 2D Time-Domain Simulations of Free Surface Gravity Waves

Abstract

The numerical simulation of nonlinear gravity waves propagating at the surface of a perfect fluid is now usually solved by totally nonlinear time-domain numerical models in two dimensions, and this approach is being extended to three dimensions. The original initial boundary value problem is posed in an unbounded region, extending horizontally up to infinity to model the sea. Its numerical solution requires truncating the domain at a finite distance. Unfortunately, no exact nonreflecting boundary condition on the truncating surface exists in this time-domain formulation. The proposed strategy is based on the coupling of two previously known methods in order to benefit from their different, and complementary, bandwidth: the numerical “beach,” very efficient in the high frequency range; and a piston-like Neumann condition, asymptotically ideal for low frequencies. The coupling method gives excellent results in the whole range of frequencies of interest and is as easy to implement in nonlinear as in linear versions. One of its major advantages is that it does not require any spectral knowledge of the incident waves.