**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30121

##### Tsunami Inundation Modeling in a Boundary Fitted Curvilinear Grid Model Using the Method of Lines Technique

**Authors:**
M. Ashaque Meah,
M. Shah Noor,
M Asif Arefin,
Md. Fazlul Karim

**Abstract:**

A numerical technique in a boundary-fitted curvilinear grid model is developed to simulate the extent of inland inundation along the coastal belts of Peninsular Malaysia and Southern Thailand due to 2004 Indian ocean tsunami. Tsunami propagation and run-up are also studied in this paper. The vertically integrated shallow water equations are solved by using the method of lines (MOL). For this purpose the boundary-fitted grids are generated along the coastal and island boundaries and the other open boundaries of the model domain. A transformation is used to the governing equations so that the transformed physical domain is converted into a rectangular one. The MOL technique is applied to the transformed shallow water equations and the boundary conditions so that the equations are converted into ordinary differential equations initial value problem. Finally the 4^{th} order Runge-Kutta method is used to solve these ordinary differential equations. The moving boundary technique is applied instead of fixed sea side wall or fixed coastal boundary to ensure the movement of the coastal boundary. The extent of intrusion of water and associated tsunami propagation are simulated for the 2004 Indian Ocean tsunami along the west coast of Peninsular Malaysia and southern Thailand. The simulated results are compared with the results obtained from a finite difference model and the data available in the USGS website. All simulations show better approximation than earlier research and also show excellent agreement with the observed data.

**Keywords:**
Open boundary condition,
moving boundary condition,
boundary-fitted curvilinear grids,
far field tsunami,
Shallow Water Equations,
tsunami source,
Indonesian tsunami of 2004.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1131247

**References:**

[1] Y. S. Cho, S B. Jin, and H. J. Lee, “Safety analysis of Ulchin Nuclear Power Plant against Nihonkai-Chubu Earthquake Tsunami”, Nuclear Engineering and Design, Vol. 228(1-3), 2004, pp 393-400.

[2] Y. S. Cho, and J. M. Kim, “Moving Boundary Treatment in Run-up process of Tsunami”, Journal of Coastal Research, SI 56, Proceedings of the 10th International Coastal Symposium, Lisbon, Portugal, 2009, pp 482-486.

[3] S. K. Dube, P. C. Sinha, and G. D. Roy, “Numerical simulation of storm surges in Bangladesh using a bay–river coupled model”, Coastal Eng., Vol. 10,1986, pp 85–101.

[4] E. L. Geist, V. V. Titov, andC. E. Synolakis, “Tsunami: wave of change”, Scientific American, Vol. 294, 2006, pp 56 – 63.

[5] A. Inan, and L. A. Balas, “Moving Boundary Wave Run-Up Model” In Y. Shi, Albada, G. D. V., Dongarra, J., & Sloot, P.M.A. (Ed.), Berlin Heidelberg: Springer, Computational Science – ICCS, 2007, pp 38-45.

[6] A. I. M. Ismail, M. F. Karim,G. D. Roy, and M. A. Meah, “Numerical Modeling of Tsunami via the Method of Lines”, International Journal of Mathematical, Physics and Engineering Sciences, Vol. 1(4), 2007, pp 213 - 222.

[7] M. F. Karim, G. D. Roy, A. I. M. Ismail, and M. A. Meah, “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, Vol. 26 (1), 2007, pp 21 – 41.

[8] M. F. Karim, G. D. Roy, and A. I. M. Ismail, “A Study of Open Boundary Conditions for Far Field Tsunami Computation”, WSEAS Transactions on Environment and Development, vol 4 (4), 2008, pp 334–349.

[9] M. F. Karim, and A. I. M. Ismail., “Estimation of expected maximum water level due to tide and tsunami interaction along the coastal belts of Penang Island in Peninsular Malaysia”, Journal of Science of Tsunami Hazards,Vol. 29 (2), 2010, pp 127 – 138.

[10] M. F. Karim, M. A. Meah, and A. I. M. Ismail, “A Shallow Water Model for Computing Inland Inundation due to Indonesian Tsunami 2004 using a Moving Coastal Boundary”, World Academy of Science, Engineering and Technology, vol 72, 2012, pp 1777 – 1782.

[11] M. F. Karim, D. S. Sankar, and E. Yunus, “On the open sea propagation of 2004 global tsunami generated by the sea bed deformation”, International Journal of Applied Engineering Research, Vol. 11 (4), 2016,pp 2686-2692.

[12] Z. Kowalik, W. Knight, and P. M. Whitmore, “Numerical Modeling of the Tsunami: Indonesian Tsunami of 26 December 2004”, Journal of Science of Tsunami Hazards, Vol. 23(1), 2005, pp 40 – 56.

[13] M. A. Meah, M. F. Karim, M. S. Noor, N. N. Papri, M. K. Hossen, and M. Ismoin, “Combined Effect of Moving and Open Boundary Conditions in the Simulation of Inland Inundation Due to Far Field Tsunami” International Journal of Computer, Electrical, Automation, Control and Information Engineering, Vol. 10(2), 2016, pp 219 – 227.

[14] M. A. Meah, M. F. Karim, M. S. Noor, M. K. Hossen, and M. E. Al-Islam, “The method of lines technique in a boundary-fitted curvilinear grid model to simulate 2004 Indian Ocean Tsunami”, International Research Journal of Engineering Science, Technology and Innovation, Vol. 2(3), 2013, pp 40-50.

[15] M. A. Meah , A. I. M Ismail, M. F. Karim, and M. S. Islam, “Simulation of the Effect of Far Field Tsunami Through an Open Boundary Condition in a Boundary-Fitted Curvilinear Grid System” Journal of Science of Tsunami Hazards, Vol. 31(1), 2012, pp 1 – 18.

[16] G. D. Roy, M. F. Karim, and A. I. M. Ismail, “A 1-D Shallow Water Model for Computing Inland Inundation due to Long Waves Using a Moving Boundary”, Far East Journal of Applied Mathematics, Vol. 28(3), 2007, pp 395-408.

[17] G. A. Papadopoulos, R. Caputo, B. McAdoo, S. Pavlides, V. Karastathis, A. Fokaefs, K. Orfanogiannaki, and S. Valkaniotis, “The large tsunami of 26 December 2004: Field observations and eyewitnesses accounts from Sri Lanka”, Maldives Is. and Thailand, Earth Planets Space, Vol. 58, 2006, pp 233 – 241.

[18] K. Satake, “Tsunamis. In W. Lee, Kanamori, H., Jennings, P. & Kisslinger, C. (Ed.)”, International handbook of Earthquake and Engineering Seismology (pp. 436 - 451.). Amsterdam: Academic Press, 2002.

[19] M. N. O. Sadiku, and R. C. Gorcia, “Method of lines solutions of axisymmetric problems”, Southeastcon 2000, Proceedings of the IEEE, Vol.7 (9), 2000, pp 527-530.

[20] B. Uslu, J. C. Borrero, L. A. Dengler, and C.E. Synolakis, “Tsunami inundation at Crescent City, California generated by earthquakes along the Cascadia Subduction Zone”, Geophys. Res. Lett., Vol.34, 2007, L20601, doi:10.1029/2007GL030188.

[21] M. A. Viana-Baptista, P.M. Soares, J. M. Miranda, and J. F. Luis, “Tsunami Propagation along Tagus Estuary” (Lisbon, Portugal) Preliminary Results. Science of Tsunami Hazards, Vol. 24(5), 2006, pp 329 – 338.