An improved coupling of numerical and physical models for simulating 2D wave propagation is developed in this paper. In the proposed model, an unstructured finite element model （FEM） based Boussinesq equations is applied for the numerical wave simulation, and a 2D piston-type wavemaker is used for the physical wave generation. An innovative scheme combining fourth-order Lagrange interpolation and Runge-Kutta scheme is described for solving the coupling equation. A Transfer function modulation method is presented to minimize the errors induced from the hydrodynamic invalidity of the coupling model and/or the mechanical capability of the wavemaker in area where nonlinearities or dispersion predominate. The overall performance and applicability of the coupling model has been experimentally validated by accounting for both regular and irregular waves and varying bathymetry. Experimental results show that the proposed numerical scheme and transfer function modulation method are efficient for the data transfer from the numerical model to the physical model up to a deterministic level.
In this paper, a numerical model is developed based on the High Order Spectral （HOS） method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
In physical model tests for highly reflective structures, one often encounters a problem of multiple reflections between the reflective structures and the wavemaker. Absorbing wavemakers can cancel the re-reflective waves by adjusting the paddle motion. In this paper, we propose a method to design the controller of the 2-D absorbing wavemaker system in the wave flume. Based on the first-order wavemaker theory, a frequency domain absorption transfer function is derived. Its time realization can be obtained by de- signing an infinite impulse response （IIR） digital filter, which is expected to approximate the absorption transfer function in the least- squares sense. A commonly used approach to determine the parameters of the IIR filter is applying the Taylor expansion to linearize the filter formulation and solving the linear least-squares problem. However, the result is not optimal because the linearization cha- nges the original objective function. To improve the approximation performance, we propose an iterative reweighted least-squares （IRLS） algorithm and demonstrate that with the filters designed by this algorithm, the approximation errors can be reduced. Physical experiments are carried out with the designed controller. The results show that the system performs well for both regular and irregu- lar waves.
