The numerical implementation and stability of first- and second-order absorbing boundary conditions for simulating free surface gravity waves are considered. The free surface waves are solved with a panel method. The stability of the boundary conditions is proved, assuming certain properties of the integral operator. Arguments are given that support these assumptions. The theoretical results are confirmed in the test cases and the boundary conditions give low reflections for plane waves.
Broeze, J., & Romate, J. E. (1992). Absorbing boundary conditions for free surface wave simulations with a panel method. Journal of computational physics, 99(1), 146-158. https://doi.org/10.1016/0021-9991(92)90282-4