Simulasi Dampak Penghalang pada Gelombang Tsunami Menggunakan Persamaan Air Dangkal dengan Metode Beda Hingga

Ahmad Zaenal Arifin

Abstract


ABSTRAK

Tsunami menjadi salah satu bencana alam yang paling berbahaya di daerah sekitar pesisir. Dampak dari gelombang tsunami menyebabkan kerugian yang besar bagi manusia, adanya banyak korban jiwa dan juga besarnya kerugian dalam bidang ekonomi. Artikel ini menunjukkan simulasi dengan pendekatan numerik metode beda hingga untuk menunjukkan dampak keberadan barrier sebagai penghalang gelombang tsunami. Gelombang tsunami dapat direpresntasikan dengan menggunakan persamaan air dangkal. Persamaan air dangkal secara umum digunakan dalam menggambarkan masalah fluida yang didasari oleh konservasi fisik dan juga dapat digunakan untuk menggambarkan terjadinya gelombang tsunami. Persamaan air dangkal berbentuk persamaan diferensial parsial sehingga dapat diselesaikan menggunakan metode beda hingga. Hasil simulasi persamaan air dangkal menunjukan bahwa persamaan air dangkal dapat merepresentasikan gelombang tsunami dengan konstruksi penghalang dan diketahui bahwa pembangunan sebuah penghalang dapat memecah gelombang tsunami dan dapat mengurangi kekuatan gelombang.

 

ABSTRACT

One of the most dangerous natural disasters in the coastal area is Tsunami. The tsunami waves impact caused considerable losses to humans, many casualties, and significant losses in the economic field. This article shows a simulation using the numerical approach of finite difference methods to deliver the barrier's impact is a tsunami wave barrier. Tsunami waves can be represented using the shallow water equation. The shallow water equation is generally used to describe fluid problems based on physical conservation and define tsunami waves. The shallow water equation is in the form of a partial differential equation to be solved using the finite difference method. The shallow water equation's simulation results show that the shallow water equation can represent a tsunami wave with a barrier construction. It is known that the construction of a barrier can break the tsunami waves and reduce the strength of the waves.


Keywords


Tsunami; Shallow Water Equation; Finite-Different Method

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References


T. W. Wibowo, D. Mardiatno, and S. Sunarto, “Pemetaan Risiko Tsunami terhadap Bangunan secara Kuantitatif,” Maj. Geogr. Indones., vol. 31, no. 2, pp. 68–78, 2017.

A. J. Santoso, F. K. S. Dewi, and T. A. P. Sidhi, “Natural disaster detection using wavelet and artificial neural network,” in 2015 Science and Information Conference (SAI), 2015, pp. 761–764.

H. Guo, “Understanding global natural disasters and the role of earth observation,” Int. J. Digit. Earth, vol. 3, no. 3, pp. 221–230, 2010.

H. Latief, N. T. Puspito, and F. Imamura, “Tsunami catalog and zones in Indonesia,” J. Nat. Disaster Sci., vol. 22, no. 1, pp. 25–43, 2000.

E. Krausmann and A. M. Cruz, “Impact of the 11 March 2011, Great East Japan earthquake and tsunami on the chemical industry,” Nat. hazards, vol. 67, no. 2, pp. 811–828, 2013.

K. D. Marano, D. J. Wald, and T. I. Allen, “Global earthquake casualties due to secondary effects: a quantitative analysis for improving rapid loss analyses,” Nat. hazards, vol. 52, no. 2, pp. 319–328, 2010.

A. Suppasri, N. Shuto, F. Imamura, S. Koshimura, E. Mas, and A. C. Yalciner, “Lessons learned from the 2011 Great East Japan tsunami: performance of tsunami countermeasures, coastal buildings, and tsunami evacuation in Japan,” Pure Appl. Geophys., vol. 170, no. 6, pp. 993–1018, 2013.

M. Esteban et al., “Awareness of coastal floods in impoverished subsiding coastal communities in Jakarta: Tsunamis, typhoon storm surges and dyke-induced tsunamis,” Int. J. disaster risk Reduct., vol. 23, pp. 70–79, 2017.

B. V Boshenyatov and K. N. Zhiltsov, “Simulation of the interaction of tsunami waves with underwater barriers,” in AIP Conference Proceedings, 2016, vol. 1770, no. 1, p. 30088.

A. Tan, A. K. Chilvery, M. Dokhanian, and S. H. Crutcher, “Tsunami Propagation Models Based on First Principles,” Ed. by Gloria I. Lopez, p. 107, 2012.

M. del Jesus, J. L. Lara, and I. J. Losada, “Numerical Modeling of Tsunami Waves Interaction with Porous and Impermeable Vertical Barriers,” J. Appl. Math., vol. 2012, 2012.

S. Gerintya, “Gempa dan Tsunami: Mitigasi Buruk, Kerugian Tinggi - Tirto.ID.” https://tirto.id/gempa-dan-tsunami-mitigasi-buruk-kerugian-tinggi-c31k (accessed Feb. 20, 2021).

B. N. P. Bencana, “Risiko Bencana Indonesia,” Badan Nas. Penanggulangan Bencana Jakarta, 2016.

A. Kurniasih, J. Marin, and R. Setyawan, “Belajar dari Simeulue: Memahami Sistem Peringatan Dini Tsunami di Indonesia,” J. Geosains dan Teknol., vol. 3, no. 1, pp. 21–30, 2020.

K. Hu, C. G. Mingham, and D. M. Causon, “Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations,” Coast. Eng., vol. 41, no. 4, pp. 433–465, 2000.

P. Lin and P. L.-F. Liu, “Internal wave-maker for Navier-Stokes equations models,” J. Waterw. port, coastal, Ocean Eng., vol. 125, no. 4, pp. 207–215, 1999.

P. Higuera, J. L. Lara, and I. J. Losada, “Realistic wave generation and active wave absorption for Navier–Stokes models: Application to OpenFOAM®,” Coast. Eng., vol. 71, pp. 102–118, 2013.

N. Thurey, M. Muller-Fischer, S. Schirm, and M. Gross, “Real-time breaking waves for shallow water simulations,” in 15th Pacific Conference on Computer Graphics and Applications (PG’07), 2007, pp. 39–46.

D. Muliyati et al., “Simulation of ocean waves in coastal areas using the shallow-water equation,” in Journal of Physics: Conference Series, 2019, vol. 1402, no. 7, p. 77025.

P. A. Clarkson and E. L. Mansfield, “On a shallow water wave equation,” Nonlinearity, vol. 7, no. 3, p. 975, 1994.

Y. Zhou, “Wave breaking for a shallow water equation,” Nonlinear Anal. Theory, Methods Appl., vol. 57, no. 1, pp. 137–152, 2004.

H. Ozmen-Cagatay, S. Kocaman, and H. Guzel, “Investigation of dam-break flood waves in a dry channel with a hump,” J. Hydro-environment Res., vol. 8, no. 3, pp. 304–315, 2014.

G. Di Baldassarre, G. Schumann, P. D. Bates, J. E. Freer, and K. J. Beven, “Flood-plain mapping: a critical discussion of deterministic and probabilistic approaches,” Hydrol. Sci. Journal–Journal des Sci. Hydrol., vol. 55, no. 3, pp. 364–376, 2010.

A. M. Abdelrazek, I. Kimura, and Y. Shimizu, “Numerical simulation of a small-scale snow avalanche tests using non-Newtonian SPH model,” 土木学会論文集 A2, vol. 70, no. 2, p. I_681-I_690, 2014.

E. Bovet, B. Chiaia, and L. Preziosi, “A new model for snow avalanche dynamics based on non-Newtonian fluids,” Meccanica, vol. 45, no. 6, pp. 753–765, 2010.

D. Dutykh, C. Acary‐Robert, and D. Bresch, “Mathematical Modeling of Powder‐Snow Avalanche Flows,” Stud. Appl. Math., vol. 127, no. 1, pp. 38–66, 2011.

S. D. Gedney, “Introduction to the finite-difference time-domain (FDTD) method for electromagnetics,” Synth. Lect. Comput. Electromagn., vol. 6, no. 1, pp. 1–250, 2011.

D. F. S. Mary and D. Lee, “Analysis of an implicit finite difference solution to an underwater wave propagation problem,” J. Comput. Phys., vol. 57, no. 3, pp. 378–390, 1985.

J. A. Liggett and D. A. Woolhiser, “Difference solutions of the shallow-water equation,” J. Eng. Mech. Div., vol. 93, no. 2, pp. 39–72, 1967.

Y. Xing and C.-W. Shu, “High order finite difference WENO schemes with the exact conservation property for the shallow water equations,” J. Comput. Phys., vol. 208, no. 1, pp. 206–227, 2005.

M. Asai, Y. Miyagawa, N. Idris, A. Muhari, and F. Imamura, “Coupled tsunami simulations based on a 2d shallow-water equation-based finite difference method and 3d incompressible smoothed particle hydrodynamics,” J. Earthq. Tsunami, vol. 10, no. 05, p. 1640019, 2016.

E. Kreyszig, Advanced Engineering Mathematics. United States of America: Luarie Rosatone, 2011.

E. A. Karjadi, M. Badiey, J. T. Kirby, and C. Bayindir, “The effects of surface gravity waves on high-frequency acoustic propagation in shallow water,” IEEE J. Ocean. Eng., vol. 37, no. 1, pp. 112–121, 2011.

S. Elgar and R. T. Guza, “Shoaling gravity waves: Comparisons between field observations, linear theory, and a nonlinear model,” J. Fluid Mech., vol. 158, pp. 47–70, 1985.

F. Alcrudo and P. Garcia‐Navarro, “A high‐resolution Godunov‐type scheme infinite volumes for the 2D shallow‐water equations,” Int. J. Numer. Methods Fluids, vol. 16, no. 6, pp. 489–505, 1993.




DOI: https://doi.org/10.34312/jjom.v3i2.10068



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