A Shallow Water Model for Computing Inland Inundation Due to Indonesian Tsunami 2004 Using a Moving Coastal Boundary
In this paper, a two-dimensional mathematical model is developed for estimating the extent of inland inundation due to Indonesian tsunami of 2004 along the coastal belts of Peninsular Malaysia and Thailand. The model consists of the shallow water equations together with open and coastal boundary conditions. In order to route the water wave towards the land, the coastal boundary is treated as a time dependent moving boundary. For computation of tsunami inundation, the initial tsunami wave is generated in the deep ocean with the strength of the Indonesian tsunami of 2004. Several numerical experiments are carried out by changing the slope of the beach to examine the extent of inundation with slope. The simulated inundation is found to decrease with the increase of the slope of the orography. Correlation between inundation / recession and run-up are found to be directly proportional to each other.
[1] Aida, I., "Numerical Computation of a Tsunami Based on a Fault Origin
Model of an Earthquake", J. Seismol. Soc. Japan, 27, 141-154, 1974.
[2] Ammon, C. J., Ji, C., Thio, H.-K., Robinson, D., Ni, S., Hjorleifsdottir,
V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet,
J. & Wald, D., "Rupture Process of the 2004 Sumatra-Andaman
Earthquake", Science, 308(5725), 1133 - 1139, 2005.
[3] Arreaga-Vargas, P., Ortiz, M. & Farreras, S.F., "Mapping the Possible
Tsunami Hazard as the First Step Towards a Tsunami Resistant
Community in Esmeraldas, Ecuador. In K. Satake (Ed.), Tsunamis: Case
Studies and Recent Developments (pp. 203 - 215). Netherlands:
Springer, 2005.
[4] Cho, Y.-S., Jin, S.-B., & Lee, H.-J.,"Safety analysis of Ulchin Nuclear
Power Plant against Nihonkai-Chubu Earthquake Tsunami", Nuclear
Engineering and Design, 228(1-3), 393-400, 2004.
[5] Dube, S. K., Sinha, P.C., & Roy, G.D. , "The Effect of a Continuously
Deforming Coastline on the Numerical Simulation of Storm Surge in
Bangladesh", Mathematics and Computers in Simulation, 28, 41 - 56,
1986.
[6] Inan, A., & Balas, L. A, "Moving Boundary Wave Run-Up Model. In Y.
Shi, Albada, G.D.v., Dongarra", J., & Sloot, P.M.A. (Ed.),
Computational Science - ICCS (pp. 38-45). Berlin / Heidelberg:
Springer, 2007.
[7] Karim, M. F., Roy, G.D., Ismail, A.I.M., & Meah, M.A. , "A Shallow
Water Model for Computing Tsunami along the West Coast of
Peninsular Malaysia and Thailand Using Boundary-Fitted Curvilinear
Grids" Science of Tsunami Hazards, 26(1), 21 - 41, 2007.
[8] Kowalik, Z., Knight, W., & Whitmore, P. M.., "Numerical Modeling of
the Tsunami: Indonesian Tsunami of 26 December 2004",Sc. Tsunami
Hazards, 23(1), 40 - 56, 2005.
[9] Lynch, F. R., & Gray, W.G., "Finite Element Simulation of Flow in
Deforming Regions, 1980. J. Comput. Phys., 36, 135 - 153, 1980.
[10] Okada, Y., "Surface Deformation due to Shear and Tensile Faults in a
Half Space", Bull, Seism. Soc. Am., 75, 1135 - 1154, 1985.
[11] Papadopoulos, G. A., Caputo, R., McAdoo, B., Pavlides, S., Karastathis,
V., Fokaefs, A., Orfanogiannaki, K. & Valkaniotis, S.," The large
tsunami of 26 December 2004: Field observations and eyewitnesses
accounts from Sri Lanka, Maldives Is. and Thailand", Earth Planets
Space, 58, 233 - 241, 2006.
[12] Roy, G. D., Karim, M. F., & Ismail, A. M., "A 1-D Shallow Water
Model for Computing Inland Inundation due to Long Waves Using a
Moving Boundary", Far East J. Appl. Math., 28(3), 395 - 408, 2007.
[13] Tanioka, Y., Yudhicara, Kususose, T., Kathiroli, S., Nishimura, Y.,
Iwasaki, S. & Satake, K. "Rapture process of 2004 great Sumatra-
Andaman earthquake estimated from tsunami waveforms," Earth Planets
Space, 58, 203 - 209, 2006.
[14] Viana-Baptista, M. A., Soares, P.M., Miranda, J.M. & Luis, J.F.,
"Tsunami Propagation along Tagus Estuary (Lisbon, Portugal)
Preliminary Results", Science of Tsunami Hazards, 24(5), 329 - 338,
2006.
[15] Wijetunge, J. J., "Tsunami on 26 December 2004: Spatial distribution of
tsunami height and the extent of inundation in Sri-Lanka, Science of
Tsunami Hazard, 24(3) 225-239, 2006.
[1] Aida, I., "Numerical Computation of a Tsunami Based on a Fault Origin
Model of an Earthquake", J. Seismol. Soc. Japan, 27, 141-154, 1974.
[2] Ammon, C. J., Ji, C., Thio, H.-K., Robinson, D., Ni, S., Hjorleifsdottir,
V., Kanamori, H., Lay, T., Das, S., Helmberger, D., Ichinose, G., Polet,
J. & Wald, D., "Rupture Process of the 2004 Sumatra-Andaman
Earthquake", Science, 308(5725), 1133 - 1139, 2005.
[3] Arreaga-Vargas, P., Ortiz, M. & Farreras, S.F., "Mapping the Possible
Tsunami Hazard as the First Step Towards a Tsunami Resistant
Community in Esmeraldas, Ecuador. In K. Satake (Ed.), Tsunamis: Case
Studies and Recent Developments (pp. 203 - 215). Netherlands:
Springer, 2005.
[4] Cho, Y.-S., Jin, S.-B., & Lee, H.-J.,"Safety analysis of Ulchin Nuclear
Power Plant against Nihonkai-Chubu Earthquake Tsunami", Nuclear
Engineering and Design, 228(1-3), 393-400, 2004.
[5] Dube, S. K., Sinha, P.C., & Roy, G.D. , "The Effect of a Continuously
Deforming Coastline on the Numerical Simulation of Storm Surge in
Bangladesh", Mathematics and Computers in Simulation, 28, 41 - 56,
1986.
[6] Inan, A., & Balas, L. A, "Moving Boundary Wave Run-Up Model. In Y.
Shi, Albada, G.D.v., Dongarra", J., & Sloot, P.M.A. (Ed.),
Computational Science - ICCS (pp. 38-45). Berlin / Heidelberg:
Springer, 2007.
[7] Karim, M. F., Roy, G.D., Ismail, A.I.M., & Meah, M.A. , "A Shallow
Water Model for Computing Tsunami along the West Coast of
Peninsular Malaysia and Thailand Using Boundary-Fitted Curvilinear
Grids" Science of Tsunami Hazards, 26(1), 21 - 41, 2007.
[8] Kowalik, Z., Knight, W., & Whitmore, P. M.., "Numerical Modeling of
the Tsunami: Indonesian Tsunami of 26 December 2004",Sc. Tsunami
Hazards, 23(1), 40 - 56, 2005.
[9] Lynch, F. R., & Gray, W.G., "Finite Element Simulation of Flow in
Deforming Regions, 1980. J. Comput. Phys., 36, 135 - 153, 1980.
[10] Okada, Y., "Surface Deformation due to Shear and Tensile Faults in a
Half Space", Bull, Seism. Soc. Am., 75, 1135 - 1154, 1985.
[11] Papadopoulos, G. A., Caputo, R., McAdoo, B., Pavlides, S., Karastathis,
V., Fokaefs, A., Orfanogiannaki, K. & Valkaniotis, S.," The large
tsunami of 26 December 2004: Field observations and eyewitnesses
accounts from Sri Lanka, Maldives Is. and Thailand", Earth Planets
Space, 58, 233 - 241, 2006.
[12] Roy, G. D., Karim, M. F., & Ismail, A. M., "A 1-D Shallow Water
Model for Computing Inland Inundation due to Long Waves Using a
Moving Boundary", Far East J. Appl. Math., 28(3), 395 - 408, 2007.
[13] Tanioka, Y., Yudhicara, Kususose, T., Kathiroli, S., Nishimura, Y.,
Iwasaki, S. & Satake, K. "Rapture process of 2004 great Sumatra-
Andaman earthquake estimated from tsunami waveforms," Earth Planets
Space, 58, 203 - 209, 2006.
[14] Viana-Baptista, M. A., Soares, P.M., Miranda, J.M. & Luis, J.F.,
"Tsunami Propagation along Tagus Estuary (Lisbon, Portugal)
Preliminary Results", Science of Tsunami Hazards, 24(5), 329 - 338,
2006.
[15] Wijetunge, J. J., "Tsunami on 26 December 2004: Spatial distribution of
tsunami height and the extent of inundation in Sri-Lanka, Science of
Tsunami Hazard, 24(3) 225-239, 2006.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58621", author = "Md. Fazlul Karim and Mohammed Ashaque Meah and Ahmad Izani M. Ismail", title = "A Shallow Water Model for Computing Inland Inundation Due to Indonesian Tsunami 2004 Using a Moving Coastal Boundary", abstract = "In this paper, a two-dimensional mathematical model is developed for estimating the extent of inland inundation due to Indonesian tsunami of 2004 along the coastal belts of Peninsular Malaysia and Thailand. The model consists of the shallow water equations together with open and coastal boundary conditions. In order to route the water wave towards the land, the coastal boundary is treated as a time dependent moving boundary. For computation of tsunami inundation, the initial tsunami wave is generated in the deep ocean with the strength of the Indonesian tsunami of 2004. Several numerical experiments are carried out by changing the slope of the beach to examine the extent of inundation with slope. The simulated inundation is found to decrease with the increase of the slope of the orography. Correlation between inundation / recession and run-up are found to be directly proportional to each other.
", keywords = "Inland Inundation, Shallow Water Equations,
Tsunami, Moving Coastal Boundary.", volume = "6", number = "12", pages = "1714-6", }
