Tsunami wave propagation by voronoi diagram

  • Authors

    • V Yuvaraj Hindustan Institute of technology and science
    • S Rajasekaran Sri Sairam Institute of Technology
    • D Nagarajan , BS Abdhur Rahman University
    2018-06-27
    https://doi.org/10.14419/ijet.v7i3.12486
  • Tsunami Wave Propagation, Voronoi Diagram, Fast Marching Method, Finite Difference Methods, Reaching Time.
  • Cellular automata is the model applied in very complicated situations and complex problems. It involves the Introduction of voronoi diagram in tsunami wave propagation with the help of a fast-marching method to find the spread of the tsunami waves in the coastal regions. In this study we have modelled and predicted the tsunami wave propagation using the finite difference method. This analytical method gives the horizontal and vertical layers of the wave run up and enables the calculation of reaching time.

     

     

  • References

    1. [1] F. Diasa, D. Dutykhc, L. O’Briena, E. Renzia, T. Stefanakisb, On the modelling of tsunami generation and tsunami inundation, Procedia IUTAM 10 (2014) 338 – 355. https://doi.org/10.1016/j.piutam.2014.01.029.

      [2] B Gutenberg, Tsunamis and earthquakes, Bulletin of the Seismological Society of America 29 (1939) 517–526.

      [3] D Dutykh, D Mitsotakis, L B Chubarov, On the contribution of the horizontal sea-bed displacements into the tsunami generation process, Ocean Modeling 56 (2012) 43–56. https://doi.org/10.1016/j.ocemod.2012.07.002.

      [4] A Ezerky, N Abcha, E Pelinovsky, Physical simulation of resonant wave run-up on a beach, Nonlinear Processes Geophysics 20 (2013) 35–40. https://doi.org/10.5194/npg-20-35-2013.

      [5] P Brufau, M E Va´zquez-Ce´ndon, P Garcı´a-Navarro, A numerical model for the flooding and drying of irregular domains, International Journal for Numerical Methods in Fluids 39 (2003) 247–275. https://doi.org/10.1002/fld.285.

      [6] D L George, R J LeVeque, Finite volume methods and adaptive refinement for global tsunami propagation and local inundation, Sci. Tsunami Hazard 24 5 (2006) 319–328.

      [7] A I Adamatzky, Voronoi-Like Partition of Lattice in Cellular Automata, Mathematical Computation Modeling 23 4 (1996) 51-66. https://doi.org/10.1016/0895-7177(96)00003-9.

      [8] S Stifter, An axiomatic approach to Voronoi-diagrams in 3D, Journal of Computer and system science 43 (1991) 361-379. https://doi.org/10.1016/0022-0000(91)90019-2.

      [9] J Chen, Voronoi special dynamic model, Mapping press, (2002) 24-37.

      [10] Yongze Chen, Philip L.-F. Liu, Modified Boussinesq Equations and Associated Parabolic Model for Water Wave Propagation, Journal of Fluid Mechanics 228 (1995) 351-381. https://doi.org/10.1017/S0022112095001170.

      [11] W Kristina, O Bokhove, E Van Groesen, Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry, Nonlinear Processes Geophysics 21 (2014) 987-1005. https://doi.org/10.5194/npg-21-987-2014.

      [12] G Klopman, E Van Groesen, M A Dingemans, Variational approach to Boussinesq modelling of fully non-linear water waves, J. Fluid Mechanics 657 (2010) 36–63. https://doi.org/10.1017/S0022112010001345.

      [13] Kristina, W., Van Groesen, E., and Bokhove, O, Effective Coastal Boundary Conditions for Dispersive Tsunami Propagation, Memorandum 1983, Department of Applied Mathematics, University of Twente, Enschede, the Netherlands (2012).

      [14] S Aggelos, Dimakopoulos, Antonella Guercio, Giovanni Cuomo, Advanced numerical modelling of tsunami wave propagation, transformation and run-up, Proceedings of the Institution of Civil Engineers Engineering and Computational Mechanics 167 (2014) 3.

      [15] Phung DangHieua, Tanimoto Katsutoshia, Vu Thanh Ca, Numerical simulation of breaking waves using a two-phase flow model, Applied Mathematical Modelling, 28 11 (2004) 983-1005. https://doi.org/10.1016/j.apm.2004.03.003.

      [16] Tetsushi Nishida, Kokichi Sugihara, Masato Kimura, Stable marker-particle method for the Voronoi diagram in a flow field, Journal of Computational and Applied Mathematics 202 (2007) 377 – 391. https://doi.org/10.1016/j.cam.2006.01.035.

      [17] F Aurenhammer, H Edelsbrunner, An optimal algorithm for constructing the weighted Voronoi diagram in the plane, Pattern Recognition 17 (1984) 251–257. https://doi.org/10.1016/0031-3203(84)90064-5.

      [18] Cecilia Bohler, Rolf Klein, Andrzej Lingas, Chih-Hung Liu, Forest-like abstract Voronoi diagram in linear time, Computational Geometry: Theory and Applications 68 (2018) 134-145. https://doi.org/10.1016/j.comgeo.2017.06.013.

      [19] Santiago Garrido, Luis Moreno, Fernando Martin, and David Alvarez, Fast Marching subjected to a Vector Field - path planning method for Mars rovers, Experts system and its applications 78 C (2017) 334-346.

      [20] F. Harlow, J Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Physics Fluids 8 (1965). 2182–2189. https://doi.org/10.1063/1.1761178.

      [21] Li Jin, Donguk Kim, Lisen Mu, Deok-Soo Kim, Shi-Min Hu, A sweepline algorithm for Euclidean Voronoi diagrams of circles, Elsevier Computer-Aided Design 38 (2006) 260–272. https://doi.org/10.1016/j.cad.2005.11.001.

      [22] Tetsushi Nishida, Kokichi Sugihara, Voronoi diagram in the flow, Algorithms and Computation, 14th International Symposium, ISAAC 2003, Kyoto, December 2003, Lecture Notes in Computer Science, Springer 2906 (2003) 26–35.

      [23] Sugihara K, Voronoi diagrams in a river, International Journal of Computational Geometry and Application 2 (1992) 29–48. https://doi.org/10.1142/S0218195992000032.

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  • How to Cite

    Yuvaraj, V., Rajasekaran, S., & Nagarajan, D. (2018). Tsunami wave propagation by voronoi diagram. International Journal of Engineering & Technology, 7(3), 1233-1235. https://doi.org/10.14419/ijet.v7i3.12486