Adytia, D.; Pudjaprasetya, S. R.; Tarwidi, D. Modeling of wave run-up by using staggered grid scheme implementation in 1D Boussinesq model. (English) Zbl 1421.76028 Comput. Geosci. 23, No. 4, 793-811 (2019). Summary: 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 C. E. Synolakis [J. Fluid Mech. 185, 523–545 (1987; Zbl 0633.76021)] for non-breaking and breaking case, a run-up case proposed by G. F. Carrier and H. P. Greenspan [ibid. 4, 97–109 (1958; Zbl 0080.19504)] and a dam-break with shock wave [F. Aureli, P. Mignosa and M. Tomirotti, “Numerical simulation and experimental verification of dam-break flows with shocks”, J. Hydraul. Res. 38, No. 3, 197–206 (2000; doi:10.1080/00221680009498337)]. 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 [S. Beji and J. A. Battjes, “Experimental investigation of wave propagation over a bar”, Coast. Eng. 19, No. 1–2, 151–162 (1993; doi:10.1016/0378-3839(93)90022-Z)]. Moreover, the numerical model is tested for simulating regular wave breaking on a plane beach of F. C. K. Ting and J. T. Kirby [“Observation of undertow and turbulence in a laboratory surf zone”, ibid. 24, No. 1–2, 51–80 (1994; doi:10.1016/0378-3839(94)90026-4)], and for simulating random wave over a barred beach of M. Boers [Simulation of a surf zone with a barred beach. I: Wave heights and wave breaking. in: Communications on hydraulic and geotechnical engineering. Delft, Netherlands: Delft University of Technology. Report No. 1996-05 (1996)]. MSC: 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M12 Finite volume methods applied to problems in fluid mechanics 86A05 Hydrology, hydrography, oceanography Keywords:wave run-up; staggered grid; Boussinesq model; dam-break; shock wave Citations:Zbl 0633.76021; Zbl 0080.19504 PDFBibTeX XMLCite \textit{D. Adytia} et al., Comput. Geosci. 23, No. 4, 793--811 (2019; Zbl 1421.76028) Full Text: DOI References: [1] Adytia, D.: Coastal Zone Simulations with Variations Boussinesq Modelling. 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