Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide

  • Didit Adytia School of Computing, Telkom University
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This paper focuses on the numerical modelling and simulation of tsunami waves triggered by an underwater landslide. The equation of motion for water waves is represented by the Nonlinear Shallow Water Equations (NSWE). Meanwhile, the motion of underwater landslide is modeled by incorporating a term for bottom motion into the NSWE. The model is solved numerically by using a finite volume method with a momentum conservative staggered grid scheme that is proposed by Stelling & Duinmeijer 2003 [12].  Here, we modify the scheme for the implementation of bottom motion. The accuracy of the implementation for representing wave runup and rundown is shown by performing the runup of harmonic wave as proposed by Carrier & Greenspan 1958 [2], and also solitary wave runup of Synolakis, 1986 [14], for both breaking and non-breaking cases. For the underwater landslide, result of the simulation is compared with simulation using the Boundary Integral Equation Model (BIEM) that is performed by Lynett and Liu, 2002 [9].


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Adytia, D., Tarwidi, D., Kifli, S.A., and Pudjaprasetya, S.R., “Staggered grid implementation of 1D Boussinesq model for simulating dispersive wave”. International Journal of Physics: Conference Series , vol. 971, no. 1, p. 012020. IOP Publishing. 2018.

Carrier, G.F. and Greenspan, H.P., “Water waves of finite amplitude on a sloping beach”. J. Fluid Mech. 4. pp. 97-109. 1958.

Dutykh, D. and Kalisch, H.. “Boussinesq modeling of surface waves due to underwater landslides”. arXiv preprint arXiv:1112.5083. 2011.

Fuhrman, D.R. and Madsen, P.A., “Tsunami generation, propagation, and run-up with a high-order Boussinesq model”. Coast. Eng. 56(7), pp.747-758. 2009.

Grilli, S. T., Skourup, J. & Svendsen, I. A. “An efficient boundary element method for nonlinear waves”. Engng Analysis Bound. Elem. 6, 97-107. 1989.

Hammack, J.L., “A note on tsunamis: their generation and propagation in an ocean of uniform depth”. J. Fluid Mech. 60(4), pp.769-799. 1973.

Harbitz, C.B., Løvholt, F. dan Bungum, H. . “Submarine landslide tsunamis: how extreme and how likely?” Natural Hazards, 72(3), pp.1341-1374. 2014.

Liam, L.S., Adytia, D. and van Groesen, E..” Embedded wave generation for dispersive surface wave models”. Ocean Eng. 80. Pp. 73-83. 2014.

Lynett, P. dan Liu, P.L.F. . “A numerical study of submarine–landslide–generated waves and run–up”. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. vol. 458, no. 2028, pp. 2885-2910. The Royal Society. 2002.

Pelinovsky, E., Kharif, C., Riabov, I. and Francius, M., “Modelling of tsunami propagation in the vicinity of the French coast of the Mediterranean”. Natural hazards, 25(2), pp.135-159. 2002.

Rynn, J.. “A preliminary assessment of tsunami hazard and risk in the Indonesian region”. Science of Tsunami Hazards, 20(4), p.193. 2002.

Stelling, G.S. dan Duinmeijer, S.A., “A staggered conservative scheme for every Froude number in rapidly varied shallow”. Journal of numerical methods in fluids, 43(12), pp.1329-1354. 2003.

Stelling, G.S. dan Zijlema, M., “Numerical modeling of wave propagation, breaking and run-up on a beach”. In Advanced Computational Methods in Science and Engineering,pp. 373-401. Springer, Berlin, Heidelberg. 2009.

Synolakis, C. E., “The runup of long waves”. Dissertation (Ph.D.), California Institute of Technology. 1986.

Tsuji, Y., Matsutomi, H., Imamura, F., Takeo, M., Kawata, Y., Matsuyama, M., Takahashi, T. dan Harjadi, P., “Damage to coastal villages due to the 1992 Flores Island earthquake tsunami”. Pure and Applied Geophysics, 144(3-4), pp.481-524. 1995.

How to Cite
Adytia, D. (2019). Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide. Indonesia Journal on Computing (Indo-JC), 4(1), 29-42.
Computational and Simulation