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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2016, Volume 19, Number 2, Pages 153–165
DOI: https://doi.org/10.15372/SJNM20160203 (Mi sjvm609) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A numerical algorithm for computing tsunami wave amplitude

S. I. Kabanikhinab, O. I. Krivorotkoab

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev pr., Novosibirsk, 630090, Russia
b Novosibirsk State University, 2 Pirogova str., Novosibirsk, 630090, Russia
Full-text PDF (1446 kB) Citations (7)
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DOI: https://doi.org/10.15372/SJNM20160203
Abstract: A numerical algorithm for computing tsunami wave front amplitude is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved by the Godunov approach and the bicharacteristic method. The qualitative comparison of the two above methods is described. Then a change in variables associated with the eikonal solution is introduced. At the last step, using the expansion of the fundamental solution of shallow water equations in the sum of singular and regular parts, we obtain the Cauchy problem for the wave amplitude. This approach allows one to reduce computer costs. The numerical results are presented.
Key words: shallow water equations, tsunami amplitude, fundamental solution, eikonal equation, finite difference approach.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Foundation for Basic Research 15-01-09230
16-31-00189
Received: 17.09.2015
English version:
Numerical Analysis and Applications, 2016, Volume 9, Issue 2, Pages 118–128
DOI: https://doi.org/10.1134/S1995423916020038
Bibliographic databases:
Document Type: Article
UDC: 517.9+519.6
Language: Russian
Citation: S. I. Kabanikhin, O. I. Krivorotko, “A numerical algorithm for computing tsunami wave amplitude”, Sib. Zh. Vychisl. Mat., 19:2 (2016), 153–165; Num. Anal. Appl., 9:2 (2016), 118–128
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    • This publication is cited in the following 7 articles:
    1. Z. I. Fedotova, G. S. Khakimzyanov, “O svoistvakh raznostnykh skhem dlya resheniya nelineino-dispersionnykh uravnenii povyshennoi tochnosti. I. Sluchai odnoi prostranstvennoi peremennoi”, Sib. zhurn. vychisl. matem., 26:4 (2023), 451–467  mathnet  crossref
    2. Z. I. Fedotova, G. S. Khakimzyanov, “On the Properties of Difference Schemes for Solving Nonlinear Dispersive Equations of Increased Accuracy. I. The Case of One Spatial Variable”, Numer. Analys. Appl., 16:4 (2023), 375  crossref
    3. A L Leontyev, M I Chumak, A V Nikitina, I V Chumak, “Application of FPGA technologies for modeling hydrophysical processes in reservoirs with complex bottom topography”, IOP Conf. Ser.: Mater. Sci. Eng., 1029:1 (2021), 012076  crossref
    4. A. A. Uspenskii, P. D. Lebedev, “Properties of Non Stationer Pseudo Vertex With the Break of Smoothness of the Target Set Boarder Curvature in the Dirichlet Problem to Eikonal Type Equation”, Sib. Electron. Math. Rep., 17 (2020), 2028–2044  mathnet  crossref  mathscinet  zmath  isi
    5. S. I. Kabanikhin, O. I. Krivorotko, “An algorithm for source reconstruction in nonlinear shallow-water equations”, Comput. Math. Math. Phys., 58:8 (2018), 1334–1343  mathnet  crossref  crossref  isi  elib
    6. D. A. Lozhnikov, V. E. Nazaikinskii, “Method for the analysis of long water waves taking into account reflection from a gently sloping beach”, Pmm-J. Appl. Math. Mech., 81:1 (2017), 21–28  crossref  mathscinet  isi  elib  scopus
    7. S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Characteristics with Singularities and the Boundary Values of the Asymptotic Solution of the Cauchy Problem for a Degenerate Wave Equation”, Math. Notes, 100:5 (2016), 695–713  mathnet  crossref  crossref  mathscinet  isi  elib
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