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Numerical simulation of the tsunami run-up on the coast using the method of large particles

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Abstract

An approach to the computer simulation of a tsunami run-up on the coast is presented, based on nested grids and the large-particle method. The computational algorithms are based on the classical equations of shallow-water theory. The main elements of the developed computational technology are described and the results are given of the verification and validation of numerical algorithms, as well as the mathematical model and of one- and two-dimensional test problems. The capabilities of the algorithms developed by the authors are demonstrated for the calculation of the defining parameters of the tsunami run-up on the coast in the vicinity of the town of Severo-Kurilsk (November 5, 1952).

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References

  1. N. Mori, T. Takahashi, and The 2011 Tohoku Earthquake Tsunami Joint Survey Group, “Nationwide post event survey and analysis of the 2011 Tohoku earthquake tsunami,” Coast. Eng. J. 54, 1–27 (2012).

    Article  Google Scholar 

  2. H. Kawai, M. Sato, K. Kawaguchi, and K. Seki, “The 2011 off the Pacific coast of Tohoku earthquake tsunami observed by GPS buoys,” J. Jpn. Soc. Civil Eng., Ser. B2 67, 1291–1295 (2011).

    Google Scholar 

  3. G. Oger, M. Doring, B. Alessandrini, and P. Ferrant, “Two-dimensional SPH simulations of wedge water entries,” J. Comput. Phys. 213, 803–822 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  4. O. M. Belotserkovskii and Yu. M. Davydov, Large Particle Method in Gasdynamics (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  5. M. de Leffe, D. le Touze, and B. Alessandrini, “SPH modeling of shallow-water coastal flows,” J. Hydraul. Res. 48 (extra iss.), 118–125 (2010).

    Article  Google Scholar 

  6. V. S. Kosykh, L. B. Chubarov, V. K. Gusyakov, D. A. Kamaev, V. M. Grigor’eva, and S. A. Beisel, “Methods for calculating the maximum height of the tsunami waves in the protected areas of the Far East coast of the Russian Federation,” Inform. Sbornik: Rezult. Ispyt. Nov. Usovershenst. Tekhnol. Modelei Metodov Gidrometeorol. Prognozov, No. 40, 115–134 (2013).

    Google Scholar 

  7. V. K. Gusiakov, “Residual displacements on the surface of elastic half-space,” in Conditionally Correct Problems of Mathematical Physics in Interpretation of Geophysical Observations (Vychisl. Tsentr Sib. Otdel. RAN, Novosibirsk, 1978), pp. 23–51 [in Russian].

    Google Scholar 

  8. R. W. MacCormack, “The effect of viscosity in hypervelocity impact cratering,” J. Spacecraft Rockets 40, 757–763, 2003.

    Article  Google Scholar 

  9. A. D. Rychkov, S. A. Beisel, and L. B. Chubarov, “Computer Program: Module for calculation of runup of tsunami waves on a coast RunUp-LP,” State Registration Certificate of Computer Program No. 2013617980.

  10. L. B. Chubarov, V. V. Babailov, and S. A. Beisel, “Program for calculating parameters of seismogenetic tsunami waves MGC,” State Registration Certificate of Computer Program No. 2011614598.

  11. Long-Wave Runup Models, Ed. by H. Yeh, P. Liu, and C. E. Synolakis (World Scientific, Singapore, 1996).

    Google Scholar 

  12. C. E. Synolakis, “The runup of solitary waves,” J. Fluid Mech. 185, 523–545 (1987).

    Article  MATH  Google Scholar 

  13. C. E. Synolakis, “Tsunami runup on steep slopes: how good linear theory really is,” Natural Hazards 4, 221–234 (1991).

    Article  Google Scholar 

  14. Z. I. Fedotova, “Numerical method validation for modeling of long waves runup on a coast,” Vychisl. Tekhnol. 7(5), 58–76 (2002).

    MathSciNet  MATH  Google Scholar 

  15. S. P. Bautin, S. L. Deryabin, A. F. Sommer, G. S. Khakimzyanov, and N. Yu. Shokina, “Use of analytic solutions in the statement of difference boundary conditions on a movable shore line,” Russ. J. Numer. Anal. Math. Model. 26, 353–377 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  16. N. M. Borisova, A. V. Gusev, and V. V. Ostapenko, “Propagation of discontinuous waves along a dry bed,” Fluid Dynam. 41, 606–618 (2006).

    Article  MATH  Google Scholar 

  17. Coastal and Hydraulics Laboratory. http://chl.erdc.usace.army.mil/chl.aspx?p=s&a=Projects;35/

  18. GEBCO General Bathymetric Chart of the Oceans. www.gebco.net/data-and-products/gridded-bathymetry-data/

  19. Index of /srtm/version2-1/SRTM3/Eurasia. http://dds.cr.usgs.gov/srtm/version2-1/SRTM3/Eurasia/

  20. C-MAP M-AN-C013.12 Kamchatka peninsula and Kuril islands.

  21. E. F. Savarenskii, V. G. Tishchenko, A. E. Sviatlovskii, A. D. Dobrovolskii, and A. V. Zhivago, “Tsunami of November 4–5, 1952,” Bull. Soveta Seismol. AN SSSR, No. 4, 36–37 (1958).

    Google Scholar 

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Correspondence to L. B. Chubarov.

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Original Russian Text © Yu.I. Shokin, S.A. Beisel, A.D. Rychkov, L.B. Chubarov, 2015, published in Matematicheskoe Modelirovanie, 2015, Vol. 27, No. 1, pp. 99–112.

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Shokin, Y.I., Beisel, S.A., Rychkov, A.D. et al. Numerical simulation of the tsunami run-up on the coast using the method of large particles. Math Models Comput Simul 7, 339–348 (2015). https://doi.org/10.1134/S2070048215040109

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  • DOI: https://doi.org/10.1134/S2070048215040109

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