Modeling of wave run-up by using staggered grid scheme implementation in 1D Boussinesq model

A new numerical method is presented to study free surface waves in coastal areas. The method is based on the phase resolving variational Boussinesq model (VBM) which is solved on a computational staggered grid domain. In this model, the non-hydrostatic pressure term has been incorporated in order to correctly described short wave dynamics. In simulating run-up phenomena, a special treatment, so-called thin layer method, is needed for solving the elliptic equation of the Boussinesq model. As a result, the proposed scheme is capable of simulating various run-up phenomena with great accuracy. Several benchmark tests were conducted, i.e., run-up experiments by Synolakis (Int. J. Numer. Methods Fluids 43(12), 1329–1354 1987) for non-breaking and breaking case, a run-up case proposed by Carrier and Greenspan (J. Fluid Mech. 4(1), 97–109 1958) and a dam-break with shock wave Aureli et al. (J. Hydraul. Res. 38(3), 197–206 2000). Moreover, the ability of the numerical scheme in simulating dispersion and nonlinearity effects were shown via simulation of the broad band waves propagation, i.e., focusing wave and irregular wave. The propagation of regular wave above a submerged trapezoidal bar was shown to confirm Beji-Batjes experiment (Coast. Eng. 19(1–2), 151–162 1993). Moreover, the numerical model is tested for simulating regular wave breaking on a plane beach of Ting and Kirby (Coast. Eng. 24(1–2), 51–80 1995), and for simulating random wave over a barred beach of Boer (1996).