Piston-driven numerical wave tank based on WENO solver of well-balanced shallow water equations

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model

Physical Modeling of Extreme Waves Propagating from the Open Sea to the Coastal Zone

International audienceThe evolution of solitary wave along the flume is investigated. Experiments were conducted in a smooth, rectangular sloping flume. Solitary waves are generated using a piston-type wave maker. These type of waves are generated by impulsive mechanism, close to the generation zone, their profile contains both elevation and depression components. These depressions are attached to the main solitary wave along the flume during the propagation. The main hydraulic parameters investigated are: energy damping along the flat bottom, wave height evolution on the slope (shoaling), breaking process and runup heights. It was found that experimental results are almost in good agreement with earlier studies. An empirical formula for runup heights determination is suggested. A good way for tracking the evolution of a solitary wave on flat and sloping bottom is presented thanks to spatiotemporal diagram. It is noted that for better accuracy, especially when investigating breaking, it is better to use camera