Numerical simulation of tsunami propagation with Finite Difference Method and Runge Kutta 4^th Order Method (study case : south coast of Java island)

Abstract

Tsunamis are disasters that cause so much damage. In the history of the tsunami, Indonesia has been hit by tsunami several times, based on data from the National Disaster Management Agency (BNBP), as of 1629 - 2007, Indonesia was recorded 184 times affected by large and small tsunami disasters. Based on these data, it is very important for Indonesia to increase security against the tsunami disaster. Also, the tsunami in Indonesia occurred due to earthquakes, volcanic eruptions, and landslides in the sea. This study discussed about to the tsunami with a location located in the southern of Java, precisely in the area of Central Java, considering that in 2017 there was friction between the Indies and Eurasian plates which caused an earthquake measuring 6.9 magnitude, but did not cause a tsunami. In this study, a tsunami wave propagation simulation was carried out with the aim of knowing how long it would take the waves to the shoreline and how high the waves would be when they were on the shoreline. The model used is a tsunami model created by Imamura by solving differential equations using finite difference and Runge-Kutta 4th order. Based on the simulation results with the initial determination of a 5 m tsunami wave centered at a distance of 25 km from the shoreline, Tsunami waves with a height of 8.7 m will arrive at the shoreline at 140 seconds. With wave height is 8.7 m at the shoreline, the water will enter the land or can also be called the tsunami disaster. At that time, residents are expected to have been evacuated from the coastal area. In addition, based on numerical simulations that have been carried out, information is obtained that the computation time of the method is faster than the computation time of the Runge-Kutta method with differences in altitude results that are quite small and can be tolerated. This shows that the Finite Difference method can be applied to tsunami disaster mitigation software because it has a fairly fast computing time compared to the Runge-Kutta 4th order method.

Disaster mitigation preparedness of Semeru volcano eruption

“…In these simulations, complex parameter combinations, consisting of solid and fluid particles with varying physical properties, are frequently associated with geophysical flows and exhibit diverse and intricate dynamic characteristics in the results of numerical analyses [30]. The finite difference method in numerical simulations is particularly suitable for software applications, especially in modeling disaster mitigation, as it offers faster computing times than the Runge-Kutta 4 th -order method [32].…”