Finite Element Analysis of Tsunami by Viscous Shallow-Water Equations

Hiroshi Dan; Hiroshi Kanayama

doi:10.20965/jaciii.2012.p0508

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JACIII Vol.16 No.4 pp. 508-513

doi: 10.20965/jaciii.2012.p0508

(2012)

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Finite Element Analysis of Tsunami by Viscous Shallow-Water Equations

Hiroshi Dan and Hiroshi Kanayama

Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

Received:

December 12, 2011

Accepted:

March 31, 2012

Published:

June 20, 2012

Keywords:

tsunami, viscous shallow-water equations, Navier-Stokes equations, finite element method

Abstract

In this paper, viscous shallow-water equations are derived from three-dimensional Navier-Stokes equations under the hydrostatic assumption. The viscous shallow-water equations are approximated by the finite element method based on our numerical scheme developed in 1978. This approach is used to simulate a tsunami in Hakata Bay. Results show a reasonable estimate of the tsunami arrival time.

Cite this article as:

H. Dan and H. Kanayama, “Finite Element Analysis of Tsunami by Viscous Shallow-Water Equations,” J. Adv. Comput. Intell. Intell. Inform., Vol.16 No.4, pp. 508-513, 2012.

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References

[1] National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism, Japan and Building Research Institute, Incorporated Administrative Agency, Japan, “Quick Report of the Field Survey and Research on The 2011 off the Pacific Coast of Tohoku Earthquake,” Technical Note, No.636, Building Research Data, No.132, 2011. (in Japanese)
[2] C. Goto and K. Sato, “Development of Tsunami Numerical Simulation System for Sanriku Coast in Japan,” Report of the Port and Harbour Research Institute, Vol.32, No.2, pp. 3-44, 1993. (in Japanese)
[3] T. Takahashi, “Application of Numerical Simulation to Tsunami Disaster Prevention,” J. of Japan Society of Computational Fluid Dynamics, Vol.12, No.2, pp. 23-32, 2004. (in Japanese)
[4] The Central Disaster Prevention Council, “Special Investigation Council concerning Tounankai and Nankai Earthquakes, etc.” (in Japanese)
[5] E. Ulutas, “The 2011 Off the Pacific Coast of Tohoku-oki Earthquake and Tsunami: Influence of the Source Characteristics on the Maximum Tsunami Heights,” Proc. of the Int. Symp. on Engineering Lessons Learned from the 2011 Great East Japan Earthquake, pp. 602-611, 2012.
[6] F. Imamura, A. C. Yalciner, and G. Ozyurt, “Tsunami Modelling Manual,” 2006,
http://www.tsunami.civil.tohoku.ac.jp/hokusai3/J/projects/manual-ver-3.1.pdf. (accessed 2012-03-27).
[7] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations I – Derivation and Conservation Laws –,” Memoirs of Numerical Mathematics 8/9, pp. 39-64, 1981/1982.
[8] H. Kanayama and K. Ohtsuka, “Finite Element Analysis on the Tidal Current and COD Distribution in Mikawa Bay,” Coastal Engineering in Japan, Vol.21, pp. 157-171, 1978.
[9] H. Kanayama and H. Dan, “A Finite Element Scheme for Two-Layer Viscous Shallow-Water Equations,” Japan J. of Industrial and Applied Mathematics, Vol.23, Vol.2, pp. 163-191, 2006.
[10] H. Kanayama and T. Ishikawa, “A Finite Element Scheme of the Two Layer Viscous Shallow Water Equations,” Proc. of 16th Computational Fluid Dynamics Symp., D29-1, 2002. (in Japanese)
[11] K. Murakami, “Calculation of Vertical Circulation in Stratified Waters by 2-Level and 2-Layer Models,” Proc. of Coastal Engineering, JSCE, Vol.36, pp. 204-208, 1989. (in Japanese)
[12] H. Kanayama and H. Dan, “Two-Layer Viscous Shallow-Water Equations and Conservation Laws,” J. of Computational Science and Technology, Vol.3, No.1, pp. 373-384, 2009.
[13] M. Tabata, “A Finite Element Approximation Corresponding to the Upwind Finite Differencing,” Memoirs of Numerical Mathematics, Vol.4, pp. 47-63, 1977.
[14] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations II – A Linearized System –,” Bulletin of University of Electro-Communications, Vol.1, No.2, pp. 347-355, 1988.
[15] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations III – A Finite Element Scheme –,” Bulletin of University of Electro-Communications, Vol.2, No.1, pp. 47-62, 1989.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism, Japan and Building Research Institute, Incorporated Administrative Agency, Japan, “Quick Report of the Field Survey and Research on The 2011 off the Pacific Coast of Tohoku Earthquake,” Technical Note, No.636, Building Research Data, No.132, 2011. (in Japanese)

[2] [2] C. Goto and K. Sato, “Development of Tsunami Numerical Simulation System for Sanriku Coast in Japan,” Report of the Port and Harbour Research Institute, Vol.32, No.2, pp. 3-44, 1993. (in Japanese)

[3] [3] T. Takahashi, “Application of Numerical Simulation to Tsunami Disaster Prevention,” J. of Japan Society of Computational Fluid Dynamics, Vol.12, No.2, pp. 23-32, 2004. (in Japanese)

[4] [4] The Central Disaster Prevention Council, “Special Investigation Council concerning Tounankai and Nankai Earthquakes, etc.” (in Japanese)

[5] [5] E. Ulutas, “The 2011 Off the Pacific Coast of Tohoku-oki Earthquake and Tsunami: Influence of the Source Characteristics on the Maximum Tsunami Heights,” Proc. of the Int. Symp. on Engineering Lessons Learned from the 2011 Great East Japan Earthquake, pp. 602-611, 2012.

[6] [6] F. Imamura, A. C. Yalciner, and G. Ozyurt, “Tsunami Modelling Manual,” 2006,
http://www.tsunami.civil.tohoku.ac.jp/hokusai3/J/projects/manual-ver-3.1.pdf. (accessed 2012-03-27).

[7] [7] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations I – Derivation and Conservation Laws –,” Memoirs of Numerical Mathematics 8/9, pp. 39-64, 1981/1982.

[8] [8] H. Kanayama and K. Ohtsuka, “Finite Element Analysis on the Tidal Current and COD Distribution in Mikawa Bay,” Coastal Engineering in Japan, Vol.21, pp. 157-171, 1978.

[9] [9] H. Kanayama and H. Dan, “A Finite Element Scheme for Two-Layer Viscous Shallow-Water Equations,” Japan J. of Industrial and Applied Mathematics, Vol.23, Vol.2, pp. 163-191, 2006.

[10] [10] H. Kanayama and T. Ishikawa, “A Finite Element Scheme of the Two Layer Viscous Shallow Water Equations,” Proc. of 16th Computational Fluid Dynamics Symp., D29-1, 2002. (in Japanese)

[11] [11] K. Murakami, “Calculation of Vertical Circulation in Stratified Waters by 2-Level and 2-Layer Models,” Proc. of Coastal Engineering, JSCE, Vol.36, pp. 204-208, 1989. (in Japanese)

[12] [12] H. Kanayama and H. Dan, “Two-Layer Viscous Shallow-Water Equations and Conservation Laws,” J. of Computational Science and Technology, Vol.3, No.1, pp. 373-384, 2009.

[13] [13] M. Tabata, “A Finite Element Approximation Corresponding to the Upwind Finite Differencing,” Memoirs of Numerical Mathematics, Vol.4, pp. 47-63, 1977.

[14] [14] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations II – A Linearized System –,” Bulletin of University of Electro-Communications, Vol.1, No.2, pp. 347-355, 1988.

[15] [15] H. Kanayama and T. Ushijima, “On the Viscous Shallow-Water Equations III – A Finite Element Scheme –,” Bulletin of University of Electro-Communications, Vol.2, No.1, pp. 47-62, 1989.