Development of FTCS Artificial Dissipation for Dam Break 2D Modelling

https://doi.org/10.5614/jts.2020.27.1.1

Authors

  • Avis Mellivera Bandung Institute of Technology
  • Khilmi Zain Bandung Institute of Technology
  • Mohammad Bagus Adityawan Bandung Institute of Technology
  • Dhemi Harlan Bandung Institute of Technology
  • Mohammad Farid Bandung Institute of Technology
  • Bagus Pramono Yakti Bandung Institute of Technology

Keywords:

Dam Break, Hansen Filter, FTCS

Abstract

Abstract

Dam is a useful infrastructure for human life. It helps supporting social and economic development. Damages to dams may cause negative impacts such as casualties and destruction.  Thus, mitigation for dam related disaster has to be performed. This study uses derivatives of 1D and 2D shallow water wave equations.  This equation is based on the principle of mass and momentum conservation. Furthermore, it is discretized using finite difference Forward Time Center Space (FTCS) scheme. Hansen's filter is used to reduce oscillation and maintain the stability of the calculation. The filter serves as an artificial dissipation to filter each point for each time step. Based on the analysis, simulation of 1D dam break using FTCS numerical scheme shows a similar flow pattern to the analytical solution. But, it is not stable and still shows a quite big oscillation. Hansen Filter can significantly reduce oscillation and increase accuracy. However, its application shows a less accurate wavefront and moveable bed situation. Overall it can be concluded that FTCS numerical scheme with numerical filter can be used to solve 2D shallow flow problems such as circular dam break simulation.

 

Abstrak

Bendungan adalah infrastruktur yang bermanfaat bagi kehidupan manusia untuk mendukung pembangunan sosial dan ekonomi. Selain bermanfaat, bendungan juga bisa berdampak negatif yaitu menyebabkan korban jiwa dan kerusakan. Oleh karena itu, mitigasi bencana terkait kegagalan bendungan perlu dilakukan. Penelitian ini dilakukan menggunakan turunan dari persamaan gelombang air dangkal 1D dan 2D. Persamaan ini merupakan gabungan dari prinsip konservasi massa dan momentum. Persamaan tersebut kemudian didiskritisasi menggunakan skema beda hingga Forward Time Center Space (FTCS). Filter Hansen digunakan untuk mengurangi osilasi dan menjaga stabilitas perhitungan. Filter berfungsi sebagai disipasi buatan untuk menyaring setiap titik pada setiap langkah waktu. Berdasarkan hasil analisis, dapat disimpulkan bahwa simulasi dam break 1D menggunakan skema numerik FTCS menunjukkan pola aliran yang mirip dengan solusi analitik tetapi tidak stabil dan masih menunjukkan osilasi yang cukup besar. Hansen Filter secara signifikan dapat mengurangi osilasi dan meningkatkan akurasi. Akan tetapi, aplikasinya menunjukkan muka gelombang dan situasi lapisan dasar yang kurang akurat. Secara keseluruhan dapat disimpulkan bahwa skema numerik FTCS dengan filter numerik dapat digunakan untuk menyelesaikan masalah aliran dangkal 2D seperti simulasi dam break.


 


Author Biographies

Avis Mellivera, Bandung Institute of Technology

Graduate School of Civil Engineering

Khilmi Zain, Bandung Institute of Technology

Graduate School of Civil Engineering

Mohammad Bagus Adityawan, Bandung Institute of Technology

Water Resource Engineering Research Group

Dhemi Harlan, Bandung Institute of Technology

Study Program of Water Resources Engineering and Management

Mohammad Farid, Bandung Institute of Technology

Center for Coastal and Marine Development

Bagus Pramono Yakti, Bandung Institute of Technology

Center for Water Resources Development

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Published

2020-04-14

Issue

Section

Articles