Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide

Abstract

This paper focuses on the numerical modelling and simulation of tsunami waves triggered by an underwater landslide. The equation of motion for water waves is represented by the Nonlinear Shallow Water Equations (NSWE). Meanwhile, the motion of underwater landslide is modeled by incorporating a term for bottom motion into the NSWE. The model is solved numerically by using a finite volume method with a momentum conservative staggered grid scheme that is proposed by Stelling & Duinmeijer 2003 [12].  Here, we modify the scheme for the implementation of bottom motion. The accuracy of the implementation for representing wave runup and rundown is shown by performing the runup of harmonic wave as proposed by Carrier & Greenspan 1958 [2], and also solitary wave runup of Synolakis, 1986 [14], for both breaking and non-breaking cases. For the underwater landslide, result of the simulation is compared with simulation using the Boundary Integral Equation Model (BIEM) that is performed by Lynett and Liu, 2002 [9].