Numerical solution of the one dimentional shallow water wave equations using finite difference method : Lax-Friedrichs scheme

• Main Authors: Riestiana, V. A., Setiyowati, R., Kurniawan, V. Y.
• Format: Conference Proceeding
• Language: English
• Subjects: Coasts; Conservation equations; Finite difference method; Mathematical models; Shallow water; Topography; Water waves; Wave equations; Wave height
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/5.0039545

Tsunami is an example of long waves that can be mathematically modeled using shallow water wave equations. Shallow water wave equation consists of two equation obtained from conservation equations. The 2D shallow water wave equation assumes two-dimentional probrem that is as a function of two space variables (x and y) with non- negative time variable (t). The 1D shallow water wave equation is obtainde from the 2D shallow water wave equation by assuming that the y variable is ignored. Finite difference method can be used generally to determine the numerical solution of a nonlinear shallow water wave equation. Finite difference method has several schemes, one of them is Lax-Friedrichs scheme. In this research, we reconstruct the 1D shallow water wave equation with non-flat topography. Then, we determine numerical solution using finite different method : Lax-Friedrichs scheme. In this research, the initial wave amplitude is 45 meters and the topographic function is taken close to the topography of Sunda Strait. Numerical simulation results show that the maximum wave height at coastline (x = 50000) is 6.2702 meters with t = 798.2460 seconds. At t = 1000 seconds, maximum wave height is 5.28897 meters and reached the point of x = 39950 meters or 10.05 kilometers from the coastline.