Simulasi Aliran di Perairan Dangkal dengan Menggunakan Metoda Volume Hingga pada Sistem Grid tak Beraturan
DOI:
https://doi.org/10.5614/jts.2004.11.2.1Keywords:
Metoda volume hingga, Disipasi buatan, Grid tidak beraturan, Cell-centre.Abstract
Abstrak. Pada paper ini dikembangkan model numerik menggunakan skema numerik ekspisit dengan metoda volume hingga bertipe sell terpusat pada sistem grid tidak beraturan. Skema metoda volume hingga yang digunakan, pertama sekali diperkenalkan oleh Jameson [1] untuk menyelesaikan persamaan-persamaan Euler. Jameson menggunakan metoda tersebut untuk penyelesaian aliran viskos dan non viskos, aliran laminar viskos serta aliran turbulen pada berbagai bentuk sayap pesawat. Dalam paper ini skema tersebut dimodifikasi untuk menyelesaikan persamaan perairan dangkal (Shallow-water Equations). Model numerik ini digunakan pada aliran-aliran tunak dan tidak tunak dengan aliran subkritis dan superkritis serta simulasi loncatan hidrolik. Model numerik ini diselesaikan secara eksplisit, dimana diskritisasi ruang diselesaikan dengan metoda volume hingga bertipe sel terpusat (cell-center finite volume method) dan diskritisasi waktu digunakan metoda Runge-Kutta bertingkat banyak (multi-stage Runge-Kutta method). Untuk mengatasi osilasi numerik yang timbul digunakan disipasi numerik buatan yang diperkenalkan oleh Jameson [1]. Untuk beberapa uji kasus, hasil simualsi di bandingkan dengan perhitungan analitik serta dibandingkan dengan hasil dari penelitian yang telah dilakukan sebelumnya. Dari analisa hasil simulasi, didapatkan bahwa dari perbandingan antara hasil eksperimen dan numerik memperlihatkan bahwa sulusi numerik adalah akurat dam dapat diandalkan.Abstract. In this paper, it has been developed a numerical model using a general explicit numerical scheme base on the Finite Volume Method with cell-centre type on unstructured grid system. The Finite Volume scheme to be presented is developed on the basis of the finite volume scheme proposed by Jameson [1] for the solution of Euler equations. The proposed method is applied to solve some two-dimensional inviscid, laminar viscous and turbulent flows around various airfoils. In this paper, the scheme it has been modified to solve some two-dimensional depth average free-surface flows (Shallow-water Equations). This numerical model has been applied to depth averaged steady and unsteday flows for subcritical and supercritical free-surface flow and hydraulic jump simulations. This numerical model is solved by explicit way, where spatial discretisation is solved by cell-center finite volume metod and time discretisation is solved by multi-stage Runge-Kutta method. To make the computation stabel and cure from numerical oscilation an artificail disipation is introduced to the scheme. For some test cases, the calculated results are compared with experimental data that has been investigated. From simulation results analysis, the comparisons with measurements as well as with numerical solution show that the numerical method is comparatively accurate, fast, and reliable.
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