Abstract
This one-dimensional simulation is performed to find the convergence of different fluxes on the water wave using shallow water equation. There are two cases where the topography is flat and not flat. The water level and grid of each simulation are made differently for each case, so that the water waves that occur can be analyzed. Many methods can be used to approximate the shallow water equation, one of the most used is the finite volume method. The finite volume method offers several numerical solutions for approximate shallow water equation, including Rusanov and HLLE. The derivation result of the numerical solution is used to approximate the shallow water equation. Differences in numerical and topographic solutions produce different waves. On flat topography, the rusanov flux has an average error of 0.06403 and HLLE flux with an average error of 0.06163. While the topography is not flat, the rusanov flux has a 1.63250 error and the HLLE flux has an error of 1.56960.
Highlights
Jurnal ini fokus pada simulasi gelombang air dan mencari konvergensi dari dua fluks numerik yang berbeda
This one-dimensional simulation is performed to find the convergence of different fluxes on the water wave using shallow water equation
Some approximate godunov schemes to compute shallow-water equations with topography
Summary
Jurnal ini fokus pada simulasi gelombang air dan mencari konvergensi dari dua fluks numerik yang berbeda. Kemudian skema keseimbangan ini telah diperluas ke persamaan air dangkal dengan topografi (LeRoux, 1998; Bon, 1997) dan gesekan Chinnayya and LeRoux (1999) didalamnya. Beberapa solusi fluks numerik telah dipaparkan seperti Riemann flux, Lax–Friedrichs approximation, Roe scheme, Engquist–Osher, Harten–Lax–van Leer (HLLE) flux functions, atau Rusanov flux (Bassi and Rebay, 1997). Namun jurnal ini akan memaparkan perhitungan secara numerik dengan metode beda volume menggunakan fluks Rusanov dan Harten-Lax-van Leer-Einfeldt (HLLE) untuk mendekati nilai dari persamaan air dangkal. Simulasi ini dibangun untuk membandingkan hasil perhitungan solusi numerik untuk mendekati solusi reference dari persamaan air dangkal (SWE). Solusi reference diperoleh dari hasil simulasi menggunakan fluks HLLE dengan pembagian sel sebanyak 3200. Dimana U adalah vektor permukaan air, F adalah pengatur fluks, dan Sb adalah vektor pembentuk dasar permukaan air
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