NUMERICAL MODEL OF WAVE RUN-UP ON A BEACH - Erwina, Novry
The study of wave run-up on a beach has an important role in tsunami mitigation. Run-up is the maximum vertical extent of wave uprush on a beach or structure, measured from the still water level. The inundation area of a tsunami event is directly related to its run-up. When waves arrives at a shore, the height of wave run-up depends on the bottom topography profiles, as well as the characteristics of the incoming waves. In this dissertation, a comprehensive study regarding wave run-up is conducted. The discussion is focused on the validation of numerical scheme simulating wave run-up. The numerical scheme used here is the momentum conservative scheme for hydrostatics Shallow Water Equations (SWE), first introduced by Stelling & Duijnmejer (2003). Basically, this scheme is a finite volume method for ShallowWater Equation that is applied on a staggered grid scheme. This scheme can accommodate computation that involve wet-dry area, so it is suitable to simulate waves run -up and run-down phenomena. Starting with the run-up study of a one dimensional cases, the validation of the proposed scheme was carried out by comparing the numerical result with Carrier- Greenspan analytical solution for monochromatic waves. Then, a solitary wave run-up simulation was performed to compare the numerical results to the experimental results of Synolakis (1987). The comparison of run-up height shows a good agreement, especially when the ratio of amplitudo to depth is less than 0:04, which is a non-breaking wave case. Thus, we conclude that the momentum conservative scheme can be used to estimate wave run-up reasonably well. For the run up study of two dimensional cases, the momentum conservative scheme is implemented to solve the two dimensional SWE. This scheme was validated with experimental data from literature, those are wave run-up on conical island and those of Monai Valley. These are two important benchmark tests for numerical model of tsunami. Comparison results show that the momentum conservative scheme can simulate wave run-up in two dimensional topography well. Thus, the proposed momentum conservative scheme is ready to be used to predict run-up wave using real topography.