Two-Layer Non-Hydrostatic Scheme for Simulations of Wave Runup

Abstract

There are indisputable research supporting scientific argument that propagation of (tsunami) wave from intermediate depth towards shallower coastal area needs dispersive wave model. For tsunami wave simulation, efficiency of the numerical scheme is an important issue. In this paper, the two-layer non-hydrostatic model as developed previously in Pudjaprasetya et al. [2017] “A non-hydrostatic two-layer staggered scheme for transient waves due to anti-symmetric seabed thrust,” J. Earthquake Tsunami 11, 1–17, to study tsunami generation and propagation, is adopted. Restricting to 1+1 dimension, here, we focus on the performance of the scheme in simulating wave propagation in coastal areas, in particular predicting the run-up height. First, we conducted a simulation of harmonic wave over a sloping beach to conform the analytical shoreline motion by Carrier and Greenspan [1958] “Water waves of finite amplitude on a sloping beach,” J. Fluid Mech. 4, 97–109. The ability of the scheme in accommodating dispersion and non-linearity were shown via simulation of a solitary wave that propagates over a flat bottom. This solitary wave simulation provides an evaluation of the convergence aspect of the model. Further, several benchmark tests were conducted; a solitary wave over a sloping beach to mimic the experimental data by Synolakis [1986] “The run-up of solitary waves,” J. Fluid Mech. 185, 523–545, as well as solitary wave over a composite beach. Good agreement with laboratory data was obtained in terms of wave signal, whereas for relatively low amplitude, the solitary run-up height conforms the analytical formula. Moreover, the scheme is tested for simulating the Beji–Battjes experiment Beji, S. and Battjes, J. A. [1993] “Experimental investigation of wave propagation over a bar,” Coast. Eng. 19, 151–162. As well as wave focusing experiment by Kurnia et al. [2015] “Simulations for design and reconstruction of breaking waves in a wavetank,” Proc. ASME 2015 34th Int. Conf. Ocean, Offshore and Arctic Engineering, Newfoundland, Canada, 31 May–5 June 2015, pp. 2–7.

Staggered Conservative Scheme for 2-Dimensional Shallow Water Flows

“…Validation of the model against the 1d solution of Carrier Greenspan 1958 has been conducted in [29,30]. As such, here we conducted validation of run-up and run-down using another analytical N-wave solutions, also from Carrier et al, (2003) [31].…”