Simulasi Sistem Persamaan Gelombang Air Dangkal Menggunakan Metode Numeris Lax-Friedrichs
Keywords:
Gelombang air dangkal, Gelombang air tenang, Gelombang Tsunami, Metode Lax-Friedrichs, TopografiAbstract
The shallow water wave equation system is a system of hyperbolic partial differential equations that describes wave conditions where the wavelength is much longer than the amplitude—for instance, in tsunami waves, floodwaters, and disturbed still water. The Lax-Friedrichs finite volume method is a numerical method used to solve hyperbolic partial differential equations. This research aims to apply the Lax-Friedrichs finite volume method to the shallow water wave equation system to observe how topography influences wave height and velocity. The cases simulated in this study include the movement of tsunami waves and disturbed still water. The simulation results indicate that differences in topography lead to distinct changes in the patterns of wave height and velocity.
Keywords: Disturbed still water waves, Lax-Friedrichs method, Shallow water waves, Topography, Tsunami waves
ABSTRAK
Sistem persamaan gelombang air dangkal merupakan suatu sistem persamaan diferensial parsial hiperbolik yang menggambarkan keadaan gelombang dimana panjang gelombang jauh lebih panjang dibanding amplitudo, contohnya pada gelombang tsunami, gelombang air banjir, dan gelombang air tenang yang terkena gangguan. Metode volume hingga Lax-Friedrichs merupakan salah satu metode numerik untuk menyelesaikan persamaan diferensial parsial hiperbolik. Penelitian ini bertujuan menerapkan metode volume hingga Lax-Friedrichs pada sistem persamaan gelombang air dangkal, untuk melihat bagaimana pengaruh topografi pada ketinggian dan kecepatan gelombang. Kasus yang disimulasikan pada penelitian ini yaitu pergerakan gelombang tsunami dan gelombang air tenang yang terkena gangguan. Hasil simulasi menunjukkan bahwa perbedaan topografi menyebabkan perbedaan perubahan pola ketinggian dan kecepatan gelombang.
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