Development of FTCS Artificial Dissipation for Dam Break 2D Modelling

Avis Mellivera, Khilmi Zain, Mohammad Bagus Adityawan, Dhemi Harlan, Mohammad Farid, Bagus Pramono Yakti

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.


 



Keywords


Dam Break, Hansen Filter, FTCS

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References


Adityawan, M. B., and Tanaka, H. (2012): Bed stress assessment under solitary wave run-up, Earth, Planets and Space, 64(10), 945–954.

Brufau, P., and Garcı́a-Navarro, P. (2003): Unsteady Free Surface Flow Simulation Over Complex Topography with A Multidimensional Upwind Technique, Journal of Computational Physics, 186(2), 503–526.

Delis, A. I., and Katsaounis, Th. (2005): Numerical solution of the two-dimensional shallow water equations by the application of relaxation methods, Applied Mathematical Modelling, 29(8), 754–783.

Delis, A. I., and Skeels, C. P. (1998): TVD schemes for open channel flow, International Journal for Numerical Methods in Fluids, 26(7), 791-809.

Farid, M., Yakti, B. P., Rizaldi, A., and Adityawan, M. B. (2016): Finite Difference Numerical Scheme for Simulating Dam Break Flow, The 5th HATHI International Seminar on Water Resilience in a Changing World.

Ginting, B., and Mundani, R.-P. (2019): Comparison of Shallow Water Solvers: Applications for Dam-Break and Tsunami Cases with Reordering Strategy for Efficient Vectorization on Modern Hardware, Water, 11(4), 639.

Harlan, D., Adityawan, M. B., Natakusumah, D. K., and Lely Hardianti Zendrato, N. (2019): Application of Numerical Filter to a Taylor Galerkin Finite Element Model for Movable Bed Dam Break Flows, International Journal of GEOMATE, 16(57).

Kawahara, M., and Umetsu, T. (1986): Finite Ement Method for Moving Boundary Problems in River Flow, International Journal for Numerical Methods in Fluids, 6(6), 365–386.

Lai, W., and Khan, A. A. (2011): Discontinuous Galerkin Method for 1D Shallow Water Flow with Water Surface Slope Limiter, 5(3), 10.

Welahettige, P., Vaagsaether, K., and Lie, B. (2018): A Solution Method for One-Dimensional Shallow Water Equations Using Flux Limiter Centered Scheme for Open Venturi Channel, The Journal of Computational Multiphase Flows, 10(4), 228–238.

Yakti, Bagus Pramono., Adityawan, M.B., Farid, Mohammad., Suryadi, Yadi., Nugroho, Joko., Hadihardaja, Iwan Kridasantausa. (2018): Modeling of Flood Propagation due to the Failure of Way Ela Natural Dam, MATEC Web of Conferences 147, 03009.




DOI: http://dx.doi.org/10.5614%2Fjts.2020.27.1.1

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