Numerical simulations using conserved wave absorption applied to Navier–Stokes equation model

• A new absorption method-the conserved absorption method, which better adapts to the varying wave field, is proposed.
• The conserved absorption method is applicable to various waves, including unusual waves such as rogue waves.
• The main idea of the conserved method may be further used to other wave absorption methods.

A relaxation method was adopted by Mayer et al. (1998) to absorb waves under a time-dependent 2-D Euler model with full nonlinear free surface boundary conditions. In this paper, we propose a conserved wave absorption method based on the relaxation method. Instead of deciding the absorption coefficient empirically, the conserved absorption method dynamically determines the absorption coefficient by solving the mass conservation equation derived in this article. In order to validate the conserved absorption method, a 2-D numerical wave flume is established and a series of numerical tests are conducted. The numerical wave tank solves the Navier–Stokes equations and constructs free surface with a VOF (volume of fluid) scheme. In the first test, the conserved absorption is validated at the end of the channel by generating regular waves, 2-order and 5-order Stokes waves and solitary waves of various amplitudes and frequencies. In the second test, the conserved absorption is tested with reflected waves, by generating standing waves in a tank with a sponge layer adjacent to the wave-generating boundary and a vertical wall at the opposite end. The third test validates the conserved absorption with both incident waves and reflected waves, i.e., the sponge layers are at both ends of the tank. The fourth test investigates the conserved absorption with large-amplitude waves under a realistic sea scale. In these tests, measurements of real sea states (Mori et al., 2002) as well as theoretical and experimental results (Luth et al., 1994) are employed to make comparison against the simulated results. It is found that the conserved wave absorption is applicable to various waves, at both the head and the end of the wave channel. In addition, it can give acceptable results with a short absorption length.