Tsunami modelling with adaptively refined finite volume methods

Acta Numerica

Volumn 20, Issue , 2011, Pages 211-289

  Leveque, Randall J ^a   George, David L ^b   Berger, Marsha J ^c  

^a UNIVERSITY OF WASHINGTON   (United States)

^b CASCADES VOLCANO OBSERVATORY   (United States)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79956136824     PISSN: 09624929     EISSN: 14740508     Source Type: Journal    
DOI: 10.1017/S0962492911000043     Document Type: Article

References (95)

1. B. F. Atwater et al. (2005), The Orphan Tsunami of 1700, University of Washington Press, Seattle.
2. D. S. Bale, R. J. LeVeque, S. Mitran and J. A. Rossmanith (2002), 'A wave propagation method for conservation laws and balance laws with spatially varying flux functions', SIAM J. Sci. Comput. 24, 955-978.
3. J. P. Bardet, C. E. Synolakis, H. L. Davies, F. Imamura and E. A. Okal (2003), 'Landslide tsunamis: Recent findings and research directions', Pure Appl. Geophys. 160, 1793-1809. (Pubitemid 37224682)
4. M. Berger and J. Oliger (1984), 'Adaptive mesh refinement for hyperbolic partial differential equations', J. Comput. Phys. 53, 484-512.
5. M. J. Berger and P. Colella (1989), 'Local adaptive mesh refinement for shock hydrodynamics', J. Comput. Phys. 82, 64-84.
6. M. J. Berger and R. J. LeVeque (1998), 'Adaptive mesh refinement using wavepropagation algorithms for hyperbolic systems', SIAM J. Numer. Anal. 35, 2298-2316. (Pubitemid 128464108)
7. M. J. Berger and I. Rigoutsos (1991), 'An algorithm for point clustering and grid generation', IEEE Trans. Sys. Man & Cyber. 21, 1278-1286.
8. M. J. Berger, D. A. Calhoun, C. Helzel and R. J. LeVeque (2009), 'Logically rectangular finite volume methods with adaptive refinement on the sphere', Phil. Trans. R. Soc. A 367, 4483-4496.
9. M. J. Berger, D. L. George, R. J. LeVeque and K. T. Mandli (2010), The GeoClaw software for depth-averaged flows with adaptive refinement. To appear in Advances in Water Resources. Available at: www.clawpack.org/links/awr11.
10. J. L. Bona, M. Chen and J.-C. Saut (2002), 'Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and linear theory', J. Nonlinear Sci. 12, 283-318. (Pubitemid 135699336)
11. N. Botta, R. Klein, S. Langenberg and S. Lützenkirchen (2004), 'Well balanced finite volume methods for nearly hydrostatic flows', J. Comput. Phys. 196, 539-565. (Pubitemid 38613256)
12. F. Bouchut (2004), Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources, Birkhäuser.
13. J. Bourgeois (2009), Geologic effects and records of tsunamis. In The Sea, Vol. 15 (E. N. Bernard and A. R. Robinson, eds), Harvard University Press, pp. 55- 92.
14. D. Burwell, E. Tolkova and A. Chawla (2007), 'Diffusion and dispersion characterization of a numerical tsunami model', Ocean Modelling 19, 10-30. (Pubitemid 47278924)
15. G. F. Carrier and H. Yeh (2005), 'Tsunami propagation from a finite source', CMES 10, 113-121. (Pubitemid 43258502)
16. G. F. Carrier, T. T. Wu and H. Yeh (2003), 'Tsunami run-up and draw-down on a plane beach', J. Fluid Mech. 475, 79-99. (Pubitemid 36251644)
17. M. J. Castro, P. G. LeFloch, M. L. Munoz and C. Parés (2008), 'Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes', J. Comput. Phys. 227, 8107-8129.
18. A. Costa and G. Macedonio (2005), 'Numerical simulation of lava flows based on depth-averaged equations', Geophys. Res. Lett. 32, L05304.
19. A. Dawson, D. Long and D. Smith (1988), 'The Storegga Slides: Evidence from eastern Scotland for a possible tsunami', Marine Geology, January 1988.
20. R. P. Denlinger and R. M. Iverson (2004a), 'Granular avalanches across irregular three-dimensional terrain 1: Theory and computation', J. Geophys. Res. 109, F01014.
21. R. P. Denlinger and R. M. Iverson (2004b), 'Granular avalanches across irregular three-dimensional terrain 2: Experimental tests', J. Geophys. Res. 109, F01015.
22. B. Einfeldt (1988), 'On Godunov-type methods for gas dynamics', SIAM J. Numer. Anal. 25, 294-318.
23. B. Einfeldt, C. D. Munz, P. L. Roe and B. Sjogreen (1991), 'On Godunov type methods near low densities', J. Comput. Phys. 92, 273-295.
24. S. Fomel and J. F. Claerbout (2009), 'Guest editors' introduction: Reproducible research', Comput. Sci. Engrg 11, 5-7.
25. J. M. Gallardo, C. Parés and M. Castro (2007), 'On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas', J. Comput. Phys. 227, 574-601.
26. E. L. Geist and T. Parsons (2006), 'Probabilistic analysis of tsunami hazards', Nat. Haz. 37, 277-314. (Pubitemid 43216620)
27. E. L. Geist, T. Parsons, U. S. ten Brink and H. J. Lee (2009), 'Tsunami probability', 15, 201-235.
28. G. Gelfenbaum and B. Jaffe (2003), 'Erosion and sedimentation from the 17 July, 1998 Papua New Guinea tsunami', Pure Appl. Geophys. 160, 1969-1999. (Pubitemid 37224690)
29. D. George (2010), 'Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959)', Int. J. Numer. Meth. Fluids.
30. D. L. George (2006), Finite volume methods and adaptive refinement for tsunami propagation and inundation. PhD thesis, University of Washington.
31. D. L. George (2008), 'Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation', J. Comput. Phys. 227, 3089-3113.
32. D. L. George and R. J. LeVeque (2006), 'Finite volume methods and adaptive refinement for global tsunami propagation and local inundation', Science of Tsunami Hazards 24, 319-328.
33. F. I. González and Y. A. Kulikov (1993), Tsunami dispersion observed in the deep ocean. In Tsunamis in the World (S. Tinti, ed.), Vol. 1 of Advances in Natural and Technological Hazards Research, Kluwer, pp. 7-16.
34. F. I. González, E. L. Geist, B. Jaffe, U. Kanoglu et al. (2009), 'Probabilistic tsunami hazard assessment at Seaside, Oregon, for near- and far-field seismic sources', J. Geophys. Res. 114, C11023.
35. L. Gosse (2000), 'A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms', Comput. Math. Appl. 39, 135-159. (Pubitemid 30589005)
36. L. Gosse (2001), 'A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms', Math. Mod. Meth. Appl. Sci. 11, 339-365. (Pubitemid 33687726)
37. J. M. Greenberg and A. Y. LeRoux (1996), 'A well-balanced scheme for numerical processing of source terms in hyperbolic equations', SIAM J. Numer. Anal. 33, 1-16. (Pubitemid 126431700)
38. S. T. Grilli, M. Ioualalen, J. Asavanant, F. Shi, J. T. Kirby and P. Watts (2007), 'Source constraints and model simulation of the December 26, 2004, Indian Ocean Tsunami', J. Waterway, Port, Coastal, and Ocean Engineering 133, 414.
39. H. Haflidason, H. Sejrup, A. NygÅrd, J. Mienert and P. Bryn (2004), 'The Storegga Slide: Architecture, geometry and slide development', Marine Geology, January 2004.
40. J. Hammack and H. Segur (1978), 'Modelling criteria for long water waves', J. Fluid Mech. 84, 337-358.
41. A. Harten, P. D. Lax and B. van Leer (1983), 'On upstream differencing and Godunov-type schemes for hyperbolic conservation laws', SIAM Review 25, 35-61.
42. B. Higman, G. Gelfenbaum, P. Lynett, A. Moore and B. Jaffe (2007), Predicted sedimentary record of reflected bores. In Proc. Sixth International Symposium on Coastal Engineering and Science of Coastal Sediment Processes, ASCE, pp. 1-14.
43. K. Hirata, E. Geist, K. Satake, Y. Tanioka and S. Yamaki (2003), 'Slip distribution of the 1952 Tokachi-Oki earthquake (M 8.1) along the Kuril Trench deduced from tsunami waveform inversion', J. Geophys. Res.
44. K. Huntington, J. Bourgeois, G. Gelfenbaum, P. Lynett, B. Jaffe, H. Yeh and R. Weiss (2007), 'Sandy signs of a tsunami's onshore depth and speed', EOS 88, 577-578. www.agu.org/journals/eo/eo0752/2007EO52 tabloid.pdf.
45. A. In (1999), 'Numerical evaluation of an energy relaxation method for inviscid real fluids', SIAM J. Sci. Comput. 21, 340-365.
46. K. Jankaew, B. F. Atwater, Y. Sawai, M. Choowong, T. Charoentitirat, M. E. Martin and A. Prendergast (2008), 'Medieval forewarning of the 2004 Indian Ocean tsunami in Thailand', Nature 455, 1228-1231.
47. H. M. Kelsey, A. R. Nelson, E. Hemphill-Haley and R. C. Witter (2005), 'Tsunami history of an Oregon coastal lake reveals a 4600 yr record of great earthquakes on the Cascadia subduction zone', GSA Bulletin 117, 1009-1032. (Pubitemid 40950057)
48. Z. Kowalik, W. Knight, T. Logan and P. Whitmore (2005), 'Modeling of the global tsunami: Indonesian Tsunami of 26 December 2004.', Science of Tsunami Hazards 23, 40-56.
49. J. O. Langseth and R. J. LeVeque (2000), 'A wave-propagation method for threedimensional hyperbolic conservation laws', J. Comput. Phys. 165, 126-166.
50. R. J. LeVeque (1996), 'High-resolution conservative algorithms for advection in incompressible flow', SIAM J. Numer. Anal. 33, 627-665. (Pubitemid 126431732)
51. R. J. LeVeque (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge University Press.
52. R. J. LeVeque (2009), 'Python tools for reproducible research on hyperbolic problems', Comput. Sci. Engrg 11, 19-27.
53. R. J. LeVeque (2010), 'A well-balanced path-integral f-wave method for hyperbolic problems with source terms', J. Sci. Comput. doi:10.1007/s10915-010- 9411-0. www.clawpack.org/links/wbfwave10.
54. R. J. LeVeque and D. L. George (2004), High-resolution finite volume methods for the shallow water equations with bathymetry and dry states. In Proc. Long-Wave Workshop, Catalina (P. L.-F. Liu, H. Yeh and C. Synolakis, eds), Vol. 10, World Scientific, pp. 43-73. www.amath.washington.edu/∼rjl/pubs/ catalina04/.
55. R. J. LeVeque and M. Pelanti (2001), 'A class of approximate Riemann solvers and their relation to relaxation schemes', J. Comput. Phys. 172, 572-591. (Pubitemid 33082553)
56. P. L. Liu, H. Yeh and C. Synolakis, eds (2008), Advanced Numerical Models for Simulating Tsunami Waves and Runup, Vol. 10 of Advances in Coastal and Ocean Engineering, World Scientific.
57. P. Liu, P. Lynett, H. Fernando, B. Jaffe and H. Fritz (2005), 'Observations by the International Tsunami Survey Team in Sri Lanka', Science 308, 1595. (Pubitemid 40807501)
58. P. Liu, S. Woo and Y. Cho (1998), 'Computer programs for tsunami propagation and inundation'. ceeserver.cee.cornell.edu/pll-group/comcot.htm.
59. P. Lynett and P. L. Liu (2002), 'A numerical study of submarine-landslidegenerated waves and run-up', Proc. Royal Soc. London Ser. A 458, 2885-2910.
60. C. L. Mader and M. L. Gittings (2002), 'Modeling the 1958 Lituya Bay mega tsunami, II', Science of Tsunami Hazards 20, 241.
61. K. T. Mandli (2010), Personal communication.
62. L. Mansinha and D. Smylie (1971), 'The displacement fields of inclined faults', Bull. Seism. Soc. Amer. 61, 1433-1438.
63. M. E. Martin, R. Weiss, J. Bourgeois, T. K. Pinegina, H. Houston and V. V. Titov (2008), 'Combining constraints from tsunami modeling and sedimentology to untangle the 1969 Ozernoi and 1971 Kamchatskii tsunamis', Geophys. Res. Lett. 35, L01610.
64. D. G. Masson, C. B. Harbitz, R. B. Wynn, G. Pedersen and F. Løvholt (2006), 'Submarine landslides: processes, triggers and hazard prediction', Philos. Trans. Royal Soc. A: Math. Phys. Engrg Sci. 364, 2009.
65. D. S. McCulloch (1966), Slide-induced waves, seiching and ground fracturing caused by the earthquake of March 27, 1964, at Kenai Lake, Alaska. USGS Professional Paper 543-A. www.dggs.dnr.state.ak.us/pubs/pubs?reqtype= citation&ID=3884.
66. C. Meinig, S. E. Stalin, A. I. Nakamura, F. González and H. B. Milburn (2006), Technology developments in real-time tsunami measuring, monitoring and forecasting. In OCEANS, 2005: Proc. MTS/IEEE, pp. 1673-1679.
67. Z. Merali (2010), 'Why scientific computing does not compute', Nature 467, 775-777.
68. D. J. Miller (1960), Giant waves in Lituya Bay, Alaska. USGS Professional Paper 354-C. www.dggs.dnr.state.ak.us/pubs/pubs?reqtype=citation&ID=3852.
69. S. Noelle, N. Pankrantz, G. Puppo and J. R. Natvig (2006), 'Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows', J. Comput. Phys. 213, 474-499. (Pubitemid 43240121)
70. Y. Okada (1985), 'Surface deformation due to shear and tensile faults in a halfspace', Bull. Seism. Soc. Amer. 75, 1135-1154.
71. Y. Okada (1992), 'Internal deformation due to shear and tensile faults in a halfspace', Bull. Seism. Soc. Amer. 82, 1018-1040. (Pubitemid 23386858)
72. V. V. Ostapenko (1999), 'Numerical simulation of wave flows caused by a shoreside landslide', J. Applied Mech. Tech. Phys. 40, 647-654.
73. M. Pelanti, F. Bouchut and A. Mangeney (2008), 'A Roe-type scheme for two-phase shallow granular flows over variable topography', M2AN 42, 851-885.
74. M. Pelanti, F. Bouchut and A. Mangeney (2011), 'A Riemann solver for singlephase and two-phase shallow flow models based on relaxation: Relations with Roe and VFRoe solvers', J. Comput. Phys. 230, 515-550.
75. D. B. Percival, D. W. Denbo, M. C. Eblé, E. Gica, H. O. Mofjeld, M. C. Spillane, L. Tang and V. V. Titov (2010), 'Extraction of tsunami source coefficients via inversion of DART buoy data', Natural Hazards doi:10.1007/s11069-010-9688-1.
76. G. Plafker, R. Kachadoorian, E. B. Eckel and L. R. Mayo (1969), Effects of the earthquake of March 27, 1964 on various communities. USGS Professional Paper 542G. www.dggs.dnr.state.ak.us/pubs/pubs?reqtype=citation&ID=3883.
77. J. J. Quirk (2003), Computational science: 'Same old silence, same old mistakes' 'Something more is needed . . . '. In Adaptive Mesh Refinement: Theory and Applications (T. Plewa, T. Linde and V. G. Weirs, eds), Vol. 41 of Lecture Notes in Computational Science and Engineering, Springer, pp. 3-28.
78. P. J. Roache (1998), Verification and Validation in Computational Science and Engineering, Hermosa Publishers, Albuquerque, NM.
79. T. Saito, T. Matsuzawa, K. Obara and T. Baba (2010), 'Dispersive tsunami of the 2010 Chile earthquake recorded by the high-sampling-rate ocean-bottom pressure gauges', Geophys. Res. Lett. 37, L22303.
80. K. Satake, K. Shimazaki, Y. Tsuji and K. Ueda (1996), 'Time and size of a giant earthquake in Cascadia inferred from Japanese tsunami records of January 1700', Nature 379, 246-249.
81. K. Satake, K. Wang and B. Atwater (2003), 'Fault slip and seismic moment of the 1700 Cascadia earthquake inferred from Japanese tsunami descriptions', J. Geophys. Res. 108, 2535.
82. C. Synolakis, J. Bardet, J. Borrero, H. Davies, E. Okal, E. Silver, S. Sweet and D. Tappin (2002), 'The slump origin of the 1998 Papua New Guinea tsunami', Proc. Royal Soc. London Ser. A: Math. Phys. Engrg Sci. 458, 763.
83. C. E. Synolakis and E. N. Bernard (2006), 'Tsunami science before and beyond Boxing Day 2004', Philos. Trans. Royal Soc. A: Math. Phys. Engrg Sci. 364, 2231.
84. C. E. Synolakis, E. N. Bernard, V. V. Titov, U. Kâno¢glu and F. I. González (2008), 'Validation and verification of tsunami numerical models', Pure Appl. Geophys. 165, 2197-2228.
85. W. C. Thacker (1981), 'Some exact solutions to the nonlinear shallow water wave equations', J. Fluid Mech. 107, 499-508.
86. V. V. Titov and C. E. Synolakis (1995), 'Modeling of breaking and nonbreaking long wave evolution and runup using VTCS-2', J. Waterways, Ports, Coastal and Ocean Engineering 121, 308-316. (Pubitemid 26463828)
87. V. V. Titov and C. E. Synolakis (1998), 'Numerical modeling of tidal wave runup', J. Waterways, Ports, Coastal and Ocean Engineering 124, 157-171. (Pubitemid 28425027)
88. V. V. Titov, F. I. Gonzalez, E. N. Bernard, M. C. Eble, H. O. Mofjeld, J. C. Newman and A. J. Venturato (2005), 'Real-time tsunami forecasting: Challenges and solutions', Nat. Hazards 35, 35-41.
89. E. F. Toro (2001), Shock-Capturing Methods for Free-Surface Shallow Flows, Wiley.
90. X. Wang and P. L. Liu (2007), 'Numerical simulations of the 2004 Indian Ocean tsunamis: Coastal effects', J. Earthquake Tsunami 1, 273-297.
91. P. Watts, S. Grilli, J. Kirby, G. J. Fryer and D. R. Tappin (2003), 'Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model', Nat. Haz. Earth Sys. Sci. 3, 391-402. (Pubitemid 38362775)
92. R. Weiss, H. Fritz and K. Wünnemann (2009), 'Hybrid modeling of the megatsunami runup in Lituya Bay after half a century', Geophys. Res. Lett. 36, L09602.
93. H. Yeh, R. K. Chadha, M. Francis, T. Katada, G. Latha, C. Peterson, G. Raghuramani and J. P. Singh (2006), 'Tsunami runup survey along the southeast Indian coast', Earthquake Spectra 22, S173-S186.
94. H. Yeh, P. L. Liu and C. Synolakis, eds (1996), Long-Wave Runup Models, World Scientific.
95. H. Yeh, P. Liu, M. Briggs and C. Synolakis (1994), 'Propagation and amplification of tsunamis at coastal boundaries', Nature 372, 353-355. (Pubitemid 24364361)