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Original Articles

Simulation of Tsunami Propagation Using Adaptive Cartesian Grids

, &
Pages 1550016-1-1550016-30 | Received 24 Jul 2014, Accepted 28 Jul 2015, Published online: 10 Jan 2018

References

  • Abadie, S. M. , Harris, J. C. , Grilli, S. T. & Fabre, R. [2012] “Numerical modeling of tsunami waves generated by the Sank collapse of the Cumbre Vieja Volcano (La Palma, Canary islands): Tsunami source and near field effects,” J. Geophys. Res. 117, C05030.
  • Arcos, M. E. M. & LeVeque, R. J. [2014] “Validating velocities in the geoclaw tsunami model using observations near hawaii from the 2011 Tohoku tsunami,” Pure Appi. Geophys 172, 849–867.
  • Berger, M. J. & LeVeque, R. J. [1998] “Adaptive mesh refinement using wave-propagation algorithms for hyperbolic systems,” SIAM J. Numer. Anal. 35, 2298–2316.
  • Berger, M. J. & Oliger, J. [1984] “Adaptive mesh refinement for hyperbolic partial differential equations,” J. Comput. Phys. 53 (3), 484–512.
  • Bradford, S. F. & Sanders, B. F. [2002] “Finite-volume model for shallow-water flooding of arbitrary topography,” J. Hydraul. Eng. 128, 289–298.
  • Briggs, M. , Synolakis, C. , Harkins, G. & Green, D. [1995] “Laboratory experiments of tsunami runup on a circular island,” Pure Appl. Geophys. 144, 569–593.
  • Bussing, T. R. & Murmant, E. M. [1988] “Finite-volume method for the calculation of compressible chemically reacting flows,” AIAA J. 26, 1070–1078.
  • Choi, B. H. , Kim, D. C. , Pelinovsky, E. & Woo, S. B. [2007] “Three-dimensional simulation of tsunami run-up around conical island,” Coastal Eng. 54, 618–629.
  • Clain, S. & Clauzon, V. [2010] “L∞ stability of the MUSCL methods,” Numer. Math. 116, 31–64.
  • Courant, R. , Friedrichs, K. & Lewy, H. [1928] “Ueber die partiellen differenzengleichungen der mathematischen physik,” Math. Ann. 100 (1), 32–74.
  • Fujii, Y. , Satake, K. , Sakai, S. , Shinohara, M. & Kanazawa, T. [2011] “Tsunami source of the 2011 off the pacific coast of tohoku earthquake,” Earth Planets Space 63 (7), 815–820.
  • Funke, S. , Pain, C. , Kramer, S. & Piggott, M. [2011] “A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models,” Adv. Water Resources 34, 1483–1495.
  • George, D. L. & LeVeque, R. J. [2008] High-Resolution Methods and Adaptive Refinement for Tsunami Propagation and Inundation, Hyperbolic Problems: Theory, Numerics, Applications (Springer-Verlag, Berlin, Heidelberg).
  • Hinkelmann, R. [2005] Efficient Numerical Methods and Information-Processing Techniques for Modeling Hydro- and Environmental Systems (Springer, Berlin, Heidelberg).
  • Hooper, A. , Pietrzak, J. , Simons, W. , Cui, H. , Riva, R. , Naeije, M. , Terwisscha van Scheltinga, A. , Schrama, E. , Stelling, G. & Socquet, A. [2013] “Importance of horizontal seafloor motion on tsunami height for the 2011 mw = 9.0 tohoku-oki earthquake,” Earth Planetary Sci. Lett. 361, 469–479.
  • Horrillo, J. , Wood, A. , Kim, G.-B. & Parambath, A. [2013] “A simplified 3-D Navier-Stokes numerical model for landslide-tsunami: Application to the gulf of Mexico,” J. Geophys. Res. Oceans 118 (12), 6934–6950.
  • Hou, J. , Simons, F. , Mahgoub, M. & Hinkelmann, R. [2013] “A robust well-balanced model on unstructured grids for shallow water flows with wetting and drying over complex topography,” Computer Methods Appl. Mech. Eng. 257, 126–149.
  • Hubbard, M. E. & Dodd, N. [2002] “A 2d numerical model of wave run-up and overtopping,” Coastal Eng. 47, 1–26.
  • Imamura, F. [1996] Review of tsunami simulation with a finite difference method, in Long-Wave Runup Models, eds. Yeh, P. L. H. & Synolakis, C. (Word Scientific Publishing Co., Singapore), pp. 25–42.
  • Ji, H. , Lien, F.-S. & Yee, E. [2010] “A new adaptive mesh refinement data structure with an application to detonation,” J. Comput. Phys. 229 (23), 8981–8993.
  • Kazolea, M. , Delis, A. , Nikolos, I. & Synolakis, C. [2012] “An unstructured finite volume numerical scheme for extended 2D Boussinesq-type equations,” Coastal Eng. 69, 42–66.
  • Lay, T. , Yamazaki, Y. , Ammon, C. J. , Cheung, K. F. & Kanamori, H. [2011] “The 2011 Mw 9.0 off the pacific coast of tohoku earthquake: Comparison of deep-water tsunami signals with finite-fault rupture model predictions,” Earth Planets Space 63 (7), 797–801.
  • Lee, W.-K. , Borthwick, A. G. & Taylor, P. H. [2011] “A fast adaptive quadtree scheme for a two-layer shallow water model,” J. Comput. Phys. 230 (12), 4848–4870.
  • Liang, Q. [2011] “A structured but non-uniform cartesian grid-based model for the shallow water equations,” Int. J. Numer. Methods Fluids 66 (5), 537–554.
  • Liang, Q. [2012] “A simplified adaptive cartesian grid system for solving the 2D shallow water equations,” Int. J. Numer. Methods Fluids 69 (2), 442–458.
  • Liang, Q. & Borthwick, A. G. [2009] “Adaptive quadtree simulation of shallow flows with wet dry fronts over complex topography,” Computers Fluids 38, 221–234.
  • Liang, Q. , Hou, J. k. Xia, X. [2015] “Contradiction between the c-property and mass conservation in adaptive grid based shallow flow models: Cause and solution,” Int. J. Numer. Methods Fluids 78 (1), 17–36.
  • Liang, Q. & Marche, F. [2009] “Numerical resolution of well-balanced shallow water equations with complex source terms,” Adv. Water Resources 32, 873–884.
  • Liu, P. L. F. , Cho, Y.-S. , Briggs, M. J. , Kanoglu, U. & Synolakis, C. E. [1995] “Runup of solitary wave on a circular island,” J. Fluid Mech. 302, 259–285.
  • Liu, P. L.-F. , Yeh, H. & Synolakis, C. eds. [2008] Advanced Numerical Models for Simulating Tsunami Waves and Runup (World Scientific Publishing Co., Inc., Singapore).
  • Lynett, P. J. , Wu, T.-R. & Liu, P. L. F. [2002] “Modeling wave runup with depth-integrated equations,” Coastal Eng. 46, 89–107.
  • Matsuyama, M. & Tanaka, H. [2001] “An experimental study of the highest run-up height in 1993 Hokkaido Nansei-oki earthquake tsunami,” in Proc. Int. Tsunami Symp., Seattle, U.S.A., pp. 879–889.
  • Melgar, D. & Bock, Y. [2013] “Near-field tsunami models with rapid earthquake source inversions from land- and ocean-based observations: The potential for forecast and warning,” J. Geophys. Res. Solid Earth 118 (11), 5939–5955.
  • Nicolsky, D. J. , Suleimant, E. N. & Hansen, R. A. [2011] “Validation and verification of a numerical model for tsunami propagation and runup,” Pure Appl. Geophys. 168, 1199–1222.
  • Nikolos, I. & Delis, A. [2009] “An unstructured node-centered finite volume scheme for shallow water flows with wet/dry fronts over complex topography,” Computer Methods Appl. Mech. Eng. 198, 3723–3750.
  • Oishi, Y. , Imamura, F. & Sugawara, D. [2015] “Near-field tsunami inundation forecast using the parallel tsunami-n2 model: Application to the 2011 tohoku-oki earthquake combined with source inversions,” Geophys. Res. Lett. 42 (4), 1083–1091.
  • Okada, Y. [1985] “Surface deformation due to shear and tensile faults in a half-space,” Bull. Seismological Soc. Am. 74, 1135–1154.
  • Popinet, S. [2003] “Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries,” J. Comput. Phys. 190 (2), 572–600.
  • Popinet, S. [2011] “Quadtree-adaptive tsunami modelling,” Ocean Dyn. 61, 1261–1285.
  • Popinet, S. [2012] “Adaptive modelling of long-distance wave propagation and fine-scale flooding during the Tohoku tsunami,” Nat. Hazards Earth Syst. Sci. 12, 1213–1227.
  • Rogers, B. , Fujihara, M. &c Borthwick, A. G. L. [2001] “Adaptive q-tree godunov-type scheme for shallow water equations,” Int. J. Numer. Methods Fluids 35 (3), 247–280.
  • Satake, K. , Fujii, Y. , Harada, T. & Namegaya, Y. [2013] “Time and space distribution of coseismic slip of the 2011 tohoku earthquake as inferred from tsunami waveform data,” Bull. Seismol. Soc. Am. 103 (2B), 1473–1492.
  • Synolakis, C. E. [1986] The runup of long waves, PhD Thesis, California Institute of Technology, Pasadena, California.
  • Synolakis, C. E. , Bernard, E. N. , Titov, V. V. , Kanoglu, U. & Gonzalez, F. I. [2007] Standards, criteria, and procedures for NOAA evaluation of tsunami numerical models, NOAA Technical Memorandum OAR PMEL-135. NOAA/Pacific Marine Environmental Laboratory, Seattle, WA.
  • Tang, L. , Titov, V. V. , Bernard, E. N. , Wei, Y. , Chamberlin, C. D. , Newman, J. C. , Mofjeld, H. O. , Areas, D. , Eble, M. C. , Moore, C. et al. [2012] “Direct energy estimation of the 2011 Japan tsunami using deep-ocean pressure measurements,” J. Geophys. Res. 117, C08008.
  • Titov, V. V. & Synolakis, C. E. [1995] “Modeling of breaking and nonbreaking long-wave evolution and runup using vtcs-2,” J. Waterway Port Coastal Ocean Eng. 121, 308–316.
  • Titov, V. V. & Synolakis, C. E. [1998] “Numerical modeling of tidal wave runup,” J. Waterway Port Coastal Ocean Eng. 124, 157–161.
  • van Leer, B. [1984] “On the relation between the upwind-differencing schemes of godunov, engquistosher and roe,” SIAM J. Sci. Stat. Comput. 5, 1–20.
  • Wang, X. & Liu, P. L.-F. [2006] “An analysis of 2004 Sumatra earthquake fault plane mechanisms and Indian ocean tsunami,” J. Hydraul. Res. 44 (2), 147–154.
  • Watanabe, Y. , Mitobe, Y. , Saruwatari, A. , Yamada, T. & Niida, Y. [2012] “Evolution of the 2011 Tohoku earthquake tsunami on the Pacific coast of Hokkaido,” Coast. Eng. J. 54 (01), 1250002.
  • Wei, Y. , Bernard, E. N. , Tang, L. , Weiss, R. , Titov, V. V. , Moore, C. , Spillane, M. , Hopkins, M. & Kangolu, U. [2008] “Real-time experimental forecast of the peruvian tsunami of August 2007 for U.S. coastlines,” Geophys. Res. Lett. 35 (4), L04609.
  • Wei, Y. , Chamberlin, C. , Titov, V. V. , Tang, L. & Bernard, E. N. [2012] “Modeling of the 2011 Japan tsunami: Lessons for near-field forecast,” Pure Appl. Geophys. 170 (6–8), 1309–1331.
  • Yiu, K. , Greaves, D. , Cruz, S. , Saalehi, A. & Borthwick, A. [1996] “Quadtree grid generation: Information handling, boundary fitting and CFD applications,” Computers Fluids 25 (8), 759–769.
  • Zhang, Y. J. & Baptista, A. M. [2008] “An efficient and robust tsunami model on unstructured grids, part i: Inundation benchmarks,” Pure Appl. Geophys. 165 (11–12), 2229–2248.
  • Zhou, J. G. , Causon, D. M. , Ingrain, D. M. & Mingham, C. G. [2002] “Numerical solutions of the shallow water equations with discontinuous bed topography,” Int. J. Numer. Methods Fluids 38 (8), 769–788.
  • Zijlema, M. , Stelling, G. & Smit, P. [2011] “SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters,” Coastal Eng. 58 (10), 992–1012.

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