Adaptation of a mesh at numerical simulation of tsunami waves

M. A. Nosov

Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 63-76.

Résumé

The principles and method of adaptation of an unstructured mesh to distribution of ocean depths for long-wave models of tsunamis are described. It is shown that for adequate reproduction of tsunami waves within a long-wave theory the perturbation entered into model has to be smoothed or filtered for elimination of the short-period components subject to phase dispersion. The explicit formula for calculation of cut-off period for the filter is suggested. Estimates of the relative computing effectiveness of use of the unstructured mesh adapted to distribution of ocean depths in comparison with the regular grids are performed. It is shown that use of unstructured mesh can provide an increase in computing effectiveness up to several thousand times.

Détail

Keywords: tsunami waves, long-wave theory, numerical simulation, unstructured mesh.
Mots-clés : phase dispersion

Bibliographie

[1] M.A. Nosov, “Tsunami waves of seismic origin: The modern state of knowledge”, Izvestiya-Atmospheric and Oceanic Physics, 50:5 (2014), 474–484 | DOI | DOI

[2] B.W. Levin, M.A. Nosov, Physics of Tsunamis, Second Edition, Springer, Cham–Heidelberg–New York–Dordrecht–London, 2016, 388 pp.

[3] F. Imamura, A.C. Yalciner, G. Ozyurt, Tsunami Modelling Manual (TUNAMI model), Revision due on APRIL 2006, 58 pp.

[4] V.V. Titov, F.I. Gonzalez, H.O. Mofjeld, A.J. Venturato, NOAA Time Seattle Tsunami Mapping Project: Procedures, Data Sources, and Products, NOAA Technical Memorandum OAR PMEL-124, 2003, 21 pp.

[5] P.L.F. Liu, S.B. Woo, Y.S. Cho, Computer programs for tsunami propagation and inundation, Tech. rep., Cornell University, 1998, 104 pp. | Zbl

[6] A.I. Zaytsev, A.G. Chernov, A.C. Yalciner, E.N. Pelinovsky, A.A. Kurkin, MANUAL Tsunami Simulation / Visualization Code NAMI DANCE versions 4.9, 2010

[7] Yu.I. Shokin, V.V. Babailov, S.A. Beisel, L.B. Chubarov, S.V. Eletsky, Z.I. Fedotova, V.K. Gusyakov, “Mathematical Modeling in application to regional tsunami warning systems operations”, Computational Science and High Performance Computing III, Notes on numerical fluid mechanics and multidisciplinary design, 101, Springer, 2008, 52–68 | DOI | MR

[8] S. Harig, C. Chaeroni, W.S. Pranowo, J. Behrens, “Tsunami simulations on several scales: Comparison of approaches with unstructured meshes and nested grids”, Ocean Dynamics, 58 (2008), 429–440 | DOI

[9] Y. Yamazaki, Z. Kowalik, K.F. Cheung, “Depth-integrated, non-hydrostatic model for wave breaking and run-up”, Int. J. Numer. Meth. Fluids, 61 (2009), 473–497 | DOI | MR | Zbl

[10] R.J. LeVeque, D.L. George, M.J. Berger, “Tsunami modelling with adaptively refined finite volume methods”, Acta Numerica, 20 (2011), 211–289 | DOI | MR | Zbl

[11] I.V. Fine, A.B. Rabinovich, B.D. Bornhold, R.E. Thomson, E.A. Kulikov, “The Grand Banks land-slide-generated tsunami of November 18, 1929: Preliminary analysis and numerical modeling”, Marine Geology, 215 (2005), 45–57 | DOI

[12] Y. Fujii, K. Satake, “Tsunami Source of the 2004 Sumatra-Andaman Earthquake Inferred from Tide Gauge and Satellite Data”, Bulletin of the Seismological Society of America, 97:1A (2007), S192–S207 | DOI

[13] Z. Kowalik, W. Knight, T. Logan, P. Whitmore, “The tsunami of 26 December, 2004: numerical modeling and energy considerations”, Pure Appl. Geophys., 164 (2007), 379–393 | DOI

[14] D.J. Nicolsky, E.N. Suleimani, R.A. Hansen, “Validation and Verification of a Numerical Model for Tsunami Propagation and Runup”, Pure Appl. Geophys., 168:6–7 (2011), 1199–1222 | DOI

[15] M.A. Nosov, A.V. Moshenceva, S.V. Kolesov, “Horizontal motions of water in the vicinity of a tsunami source”, Pure Appl. Geophys., 170:9–10 (2013), 1647–1660 | DOI

[16] O.V. Bulatov, T.G. Elizarova, “Regularized shallow water equations for numerical simulation of flows with a moving shoreline”, Computational Mathematics and Mathematical Physics, 56:4 (2016), 661–679 | DOI | DOI | MR | Zbl

[17] S. Watada, S. Kusumoto, K. Satake, “Traveltime delay and initial phase reversal of distant tsunamis coupled with the self-gravitating elastic earth”, J. Geophys. Res. Solid Earth, 119 (2014), 4287–4310 | DOI

[18] Ye.A. Kulikov, F.I. Gonzalez, “Recovery of the shape of a tsunami signal at the source from measurements of oscillations in the ocean level by a remote hydrostatic pressure sensor”, Trans. (Doklady) Russian Acad. Sci., Earth Sci. Sect., 345A (1995), 585–591

[19] T. Ohmachi, H. Tsukiyama, H. Matsumoto, “Simulation of tsunami induced by dynamic displacement of seabed due to seismic faulting”, Bulletin of the Seismological Society of America, 91:6 (2001), 1898–1909 | DOI

[20] M.A. Nosov, S.V. Kolesov, “Elastic oscillations of water column in the 2003 Tokachi-oki tsunami source: in-situ measurements and 3-D numerical modelling”, Nat. Hazards Earth Syst. Sci., 7 (2007), 243–249 | DOI

[21] B.H. Choi, E. Pelinovsky, D.C. Kim, I. Didenkulova, S.B. Woo, “Two- and three-dimensional computation of solitary wave runup on non-plane beach”, Nonlin. Processes Geophys., 15 (2008), 489–502 | DOI

[22] A. Bolshakova, S. Inoue, S. Kolesov, H. Matsumoto, M. Nosov, T. Ohmachi, “Hydroacoustic effects in the 2003 Tokachi-oki tsunami source”, Russ. J. Earth. Sci., 12 (2011), ES2005 | DOI

[23] G. Ma, F. Shi, J.T. Kirby, “Shock-capturing non-hydrostatic model for fully dispersive surface wave processes”, Ocean Modeling, 43–44 (2012), 22–35

[24] T. Maeda, T. Furumura, “FDM simulation of seismic waves, ocean acoustic waves, and tsunamis based on tsunami-coupled equations of motion”, Pure Appl. Geophys., 170:1–2 (2013), 109–127 | DOI

[25] F. Lovholt, G. Pedersen, S. Glimsdal, “Coupling of Dispersive Tsunami Propagation and Shallow Water Coastal Response”, The Open Oceanography Journal, 4 (2010), 71–82

[26] F. Shi, J.T. Kirby, J.C. Harris, J.D. Geiman, S.T. Grilli, “A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation”, Ocean Modelling, 43–44 (2012), 36–51 | DOI

[27] A. Piatanesi, S. Tinti, E. Bortolucci, “Finite-element simulations of the 28 December 1908 Messina straits (Southern Italy) tsunami”, Phys. Chem. Earth (A), 24 (1999), 145–150 | DOI

[28] R.A. Walters, “Design considerations for a finite element coastal ocean model”, Ocean Modelling, 15 (2006), 90–100 | DOI

[29] Y.J. Zhang, A.M. Baptista, “An Efficient and Robust Tsunami Model on Unstructured Grids. Part I: In-undation Benchmarks”, Pure Appl. Geophys., 165 (2008), 2229–2248 | DOI

[30] A. Androsov, J. Behrens, S. Danilov, “Tsunami Modelling with Unstructured Grids. Interaction between Tides and Tsunami Waves”, Computational Science and High Performance Computing IV Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 115, 2011, 191–206 | DOI | MR

[31] S. Popinet, “Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami”, Nat. Hazards Earth Syst. Sci., 12 (2012), 1213–1227 | DOI

[32] Q. Liang, J. Hou, R. Amouzgar, “Simulation of Tsunami Propagation Using Adaptive Cartesian Grids”, Coastal Engineering Journal, 57:4 (2015), 1550016 | DOI

[33] E.A. Kulikov, A.B. Rabinovich, R.E. Thomson, B.D. Bornhold, “The landslide tsunami of November 3, 1994. Skagway Harbor. Alaska”, J. Geophys. Res., 101:C3 (1996), 6609–6615 | DOI

[34] M.A. Nosov, S.V. Kolesov, “Optimal Initial Conditions for Simulation of Seismotectonic Tsunamis”, Pure and Applied Geophysics, 168:6–7 (2011), 1223–1237 | DOI

[35] I.V. Fine, E.A. Kulikov, “Raschet smeshchenii poverkhnosty okeana v ochege tsunami, vyzyvaemykh mgnovennoi verticalnoi podvizhkoi dna pri podvodnom zemletriasenii”, Vychislitelnye Tekhnologii, 16:2 (2011), 111–118

[36] M.A. Nosov, K.A. Sementsov, “Calculation of the initial elevation at the tsunami source using analytical solutions”, Izvestiya - Atmospheric and Oceanic Phys., 50:5 (2014), 539–546 | DOI | DOI

[37] H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge, UK, 1993, 764 pp. | MR | Zbl