An absorbing boundary condition for time-domain Numerical Wave Tanks is developed from a previous study related to active physical absorbers for wave basin. The starting point is the same: the optimal (ideal) time domain absorption condition for a moving piston expressed as convolution products of the velocity and the hydrodynamic force on the moving piston. The present extension to fixed boundaries of the numerical fluid domain is based on the approximation of the convolution kernels by exponential series expansions. This is achieved by using the Prony's method which is detailed in appendix. The time-domain absorption condition is then expressed as a set of ordinary differential equations which can be easily and naturally appended to the initial ODEs set of the NWT algorithm. The coefficients of the new ODE for apiston-like' condition are given. To improve the absorption performances, some of these coefficients are continuously varied during the simulation, according to the output of a Kalman filter scanning the instantaneous frequency of the force signal. For this reason the method is saidto be auto-adaptive. This results in very high absorption coefficients in a broad range of wave frequency.
The time-domain simulation of wave generation and propagation in a numerical wave tank (NWT) over long period of time requires a good absorption technique at one (or at both) end of the tank, in order to avoid spurious reflections in the computational domain. The problem also occurs in physical wave tanks, and a lot of researches has been undertaken in the past decade to develop active (or "dynamic") wave absorbers. Among them, an active piston wave absorber was developed and tested numerically in a linear wave tank by Chatty et al. (1998).
