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Title: Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method

Abstract

One of the most important questions in tsunami modeling is the estimation of tsunami run-up heights at different points along a coastline. Methods for numerical simulation of tsunami wave propagation in deep and shallow seas are well developed and have been widely used by many scientists (2001-2008). In this paper, we consider a two-dimensional nonlinear shallow water model of tsunami given by Tivon Jacobson is work [1]. u{sub t}+uu{sub x}+{nu}u{sub y} -c{sup 2}(h{sub x}+(h{sub b}){sub x}) {nu}{sub t}+u{nu}{sub x}+{nu}{nu}{sub y} = -c{sup 2}(h{sub y}+(h{sub b}){sub y}) h{sub t}+(hu){sub x}+(h{nu}){sub y} = 0 g-shore, h is surface elevation and s, t is time, u is velocity of cross-shore, {nu} is velocity of along-shore, h is surface elevation and h{sub b} is function of shore. This is a nondimensionalized model with the gravity g and constant reference depth H factored into c = {radical}(gH). We apply the Adomian Decompostion Method (ADM) to solve the tsunami model. This powerful method has been used to obtain explicit and numerical solutions of three types of diffusion-convection-reaction (DECR) equations. The ADM results for the tsunami model yield analytical solutions in terms of a rapidly convergent infinite power series. Symbolic computation, numerical results and graphs of solutionsmore » are obtained by Maple program.« less

Authors:
; ;  [1]
  1. Department of Mathematics, King Mongkut's University of Technology, North Bangkok (Thailand)
Publication Date:
OSTI Identifier:
21251344
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1048; Journal Issue: 1; Conference: International conference on numerical analysis and applied mathematics 2008, Psalidi, Kos (Greece), 16-20 Sep 2008; Other Information: DOI: 10.1063/1.2990991; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; APPROXIMATIONS; COMPUTERIZED SIMULATION; CONVECTION; DIFFUSION; FINITE ELEMENT METHOD; GRAVITATION; NONLINEAR PROBLEMS; POLYNOMIALS; SEAS; SHORES; SURFACES; TSUNAMIS; TWO-DIMENSIONAL CALCULATIONS; VELOCITY; WATER; WAVE EQUATIONS; WAVE PROPAGATION

Citation Formats

Waewcharoen, Sribudh, Boonyapibanwong, Supachai, and Koonprasert, Sanoe. Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method. United States: N. p., 2008. Web. doi:10.1063/1.2990991.
Waewcharoen, Sribudh, Boonyapibanwong, Supachai, & Koonprasert, Sanoe. Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method. United States. https://doi.org/10.1063/1.2990991
Waewcharoen, Sribudh, Boonyapibanwong, Supachai, and Koonprasert, Sanoe. 2008. "Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method". United States. https://doi.org/10.1063/1.2990991.
@article{osti_21251344,
title = {Application of 2D-Nonlinear Shallow Water Model of Tsunami by using Adomian Decomposition Method},
author = {Waewcharoen, Sribudh and Boonyapibanwong, Supachai and Koonprasert, Sanoe},
abstractNote = {One of the most important questions in tsunami modeling is the estimation of tsunami run-up heights at different points along a coastline. Methods for numerical simulation of tsunami wave propagation in deep and shallow seas are well developed and have been widely used by many scientists (2001-2008). In this paper, we consider a two-dimensional nonlinear shallow water model of tsunami given by Tivon Jacobson is work [1]. u{sub t}+uu{sub x}+{nu}u{sub y} -c{sup 2}(h{sub x}+(h{sub b}){sub x}) {nu}{sub t}+u{nu}{sub x}+{nu}{nu}{sub y} = -c{sup 2}(h{sub y}+(h{sub b}){sub y}) h{sub t}+(hu){sub x}+(h{nu}){sub y} = 0 g-shore, h is surface elevation and s, t is time, u is velocity of cross-shore, {nu} is velocity of along-shore, h is surface elevation and h{sub b} is function of shore. This is a nondimensionalized model with the gravity g and constant reference depth H factored into c = {radical}(gH). We apply the Adomian Decompostion Method (ADM) to solve the tsunami model. This powerful method has been used to obtain explicit and numerical solutions of three types of diffusion-convection-reaction (DECR) equations. The ADM results for the tsunami model yield analytical solutions in terms of a rapidly convergent infinite power series. Symbolic computation, numerical results and graphs of solutions are obtained by Maple program.},
doi = {10.1063/1.2990991},
url = {https://www.osti.gov/biblio/21251344}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1048,
place = {United States},
year = {2008},
month = {9}
}