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:: Volume 8, Issue 30 (12-2017) ::
JPG 2017, 8(30): 17-38 Back to browse issues page
Improvement in the SPH-Paddle Wave Maker Approach for Real Tsunami Waves Modeling
Ehdan Rastgoftar, Mahmood Reza Akbarpour Jannat *, Babak Banijamali
Iranian National Institute for Oceanography and Atmospheric Science (INIOAS) , akbarpour@inio.ac.ir
Abstract:   (762 Views)
The present study focused on generation of representative waves of tsunamis using GPU-based SPH numerical method. In this regard, solitary waves, as traditional representative of leading waves of tsunamis, were firstly generated in SPH model by a piston wave-maker moving based on an implicit equation solved by numerical code. Since it was proved that solitary waves are remarkably shorter and steeper than real-world tsunami waves, a new approach was also presented to reproduce the very long wave of a real tsunami. In this method, the tsunami time series was approximated by a theoretical relation based on the combination of several solitons. The relation was then used to solve the linearized trajectory equation of a wave-maker for generation of the intended time series of tsunami wave in the SPH model. The generation of solitary wave in SPH model was evaluated by comparing different simulated waves with analytical ones and it was seen that the solitary waves are successfully generated. In order to consider the accuracy of SPH formulation for simulation of the solitary wave evolution, an experimental case of breaking solitary wave propagation over a composite beach was also simulated. Although numerical results demonstrated a slight spurious wave-height decay, the SPH model satisfactorily reproduced the entire evolution phases of the solitary wave including wave propagation over a flat bottom, wave shoaling on a slope and wave breaking. For verification of the proposed approach in reproduction of real-world tsunami measurements, the time series of surface elevation record of the 2004 Indian Ocean tsunami was generated in SPH model. The results demonstrated that the tsunami record is successfully generated using the piston wave-maker. Thus, the presented approach can be regarded as a suitable method for representing the very long wave of the tsunami instead of the traditional options.
Keywords: Solitary wave, Tsunami time series, Smoothed Particle Hydrodynamics (SPH) method, Paddle wave maker
Full-Text [PDF 1144 kb]   (247 Downloads)    
Type of Study: Applied Research | Subject: Modeling & Simulation
Received: 2017/08/2 | Accepted: 2017/10/16 | ePublished: 2020/07/25
References
1. Altomare, C., et al. (2014) "A hybrid numerical model for coastal engineering problems." Proc. 34th Conf. Coast. Eng. Seoul, Korea, 2014 34: [DOI:10.9753/icce.v34.waves.60]
2. Batchelor, G.K. (1967) "An Introduction to Fluid Dynamics." Book 631.
3. Boussinesq, J. (1872) "Théorie des ondes et de remous qui se propagent…." Journal de Mathématiques Pures et Appliquées, Vol. 17, pp. 55-108.
4. Chan IC, Liu PLF (2012) On the runup of long waves on a plane beach. J Geophys Res 117:C08006. [DOI:10.1029/2012JC007994]
5. Crespo, A.J.C., Gomez-Gesteira, M., and Dalrymple, R.A. (2007) "Boundary conditions generated by dynamic particles in SPH methods." Computers, Materials, & Continua, Vol. 5, No. 3, pp. 173-184.
6. Crespo, A. J, Gomez-Gesteira, M., and Dalrymple, R.A. (2008) "Modeling Dam Break Behavior over a Wet Bed by a SPH Technique." Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 134, No. 6, pp. 330-320. [DOI:10.1061/(ASCE)0733-950X(2008)134:6(313)]
7. Crespo, A.J.C., et al (2015) "DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH)." Computer Physics Communications, Vol. 187, pp. 204-216. [DOI:10.1016/j.cpc.2014.10.004]
8. Dalrymple, R.A., and Rogers, B.D. (2006) "Numerical modeling of water waves with the SPH method." Coastal Engineering, Vol. 53, No (2-3), pp. 141-147. [DOI:10.1016/j.coastaleng.2005.10.004]
9. Dao, M.H., Xu, H., Chan, E.S., and Tkalich, P. (2013) "Modelling of tsunami-like wave run-up, breaking and impact on a vertical wall by SPH method." Nat Hazards Earth Syst Sci 13:3457-3467 [DOI:10.5194/nhess-13-3457-2013]
10. Gingold, R.A., and Monaghan, J.J. (1977) "Smoothed particle hydrodynamics: theory and application to non-spherical stars." Monthly Notices of the Royal Astronomical Society, Vol. 181, pp. 375-389. [DOI:10.1093/mnras/181.3.375]
11. Gomez-Gesteira, M., and Dalrymple, R.A. (2004) "Using a Three-Dimensional Smoothed Particle Hydrodynamics Method for Wave Impact on a Tall Structure." Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 130, No. 2, pp. 63-69. [DOI:10.1061/(ASCE)0733-950X(2004)130:2(63)]
12. Gomez-Gesteira, M., et al. (2005) "Green water overtopping analyzed with a SPH model." Ocean Engineering, Vol. 32, pp. 223-238. [DOI:10.1016/j.oceaneng.2004.08.003]
13. Gomez-Gesteira, M., et al. (2012) "SPHysics-development of a free-surface fluid solver-Part 1: Theory and formulations." Computers & Geosciences, Vol. 48, pp. 289-299. [DOI:10.1016/j.cageo.2012.02.029]
14. Goring, D. (1978) "Tsunamis-the propagation of long waves onto a shelf." W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA., Report No. KH-R-38.
15. Goring, D., and Raichlen, F. (1980) "The Generation Of Long Waves In The Laboratory." Coast. Eng. Proc., Vol. 1, pp. 430-443. [DOI:10.1061/9780872622647.047]
16. Gotoh, H., Shibihara, T., and Sakai, T. (2001) "Sub-particle-scale model for the MPS method - Lagrangian flow model for hydraulic engineering." Computational Fluid Dynamics Journal, Vol. 9 (4), pp. 339-347.
17. Gotoh, H., Shao S., and Memita, T. (2004) "SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater." Coastal Engineering Journal, Vol. 46, pp. 39-63. [DOI:10.1142/S0578563404000872]
18. Gotoh, H., Okayasu, A., and Watanabe, Y. (2013) "Computational wave dynamics." World Scientific Publishing Co, p 234. ISBN: 978-981-4449-70-0 [DOI:10.1142/8714]
19. Gotoh, H., Khayyer, A., Ikari, H., Arikawa, T., Shimosako, K. (2014) "On enhancement of Incompressible SPH method for simulation of violent sloshing flows", Applied Ocean Research, Vol. 46, pp. 104-115, ISSN 0141-1187. [DOI:10.1016/j.apor.2014.02.005]
20. Grilli, S.T., Svendsen, I.A., and Subramanya, R. (1997) "Breaking Criterion and Characteristics for Solitary Wave on Slopes." Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 123, No. 3, pp. 102-112. [DOI:10.1061/(ASCE)0733-950X(1997)123:3(102)]
21. Hammack, J.L. (1973) "A note on tsunamis: their generation and propagation in an ocean of uniform depth." Journal of Fluid Mechanics, Vol. 60, No. 4, pp. 769-799. [DOI:10.1017/S0022112073000479]
22. Herault, A. (2010) "SPH on GPU with CUDA." Journal of Hydraulic Research, Vol. 48, pp. 74-79. [DOI:10.1080/00221686.2010.9641247]
23. Kanoglu, U., and Synolakis, C.E. (1998) "Long wave runup on piecewise linear topographies." Journal of Fluid Mechanics, Vol. 374, pp. 1-28. [DOI:10.1017/S0022112098002468]
24. Khayyer, A., Gotoh, H., Shao, S. (2009) "Enhanced predictions of wave impact pressure by improved incompressible SPH methods." Applied Ocean Research, Vol. 31 (2), pp. 111-131, ISSN 0141-1187. [DOI:10.1016/j.apor.2009.06.003]
25. Kim, S.K., Liu, P.L.F., and Liggett, J.A. (1983) "Boundary integral equation solutions for solitary wave generation, propagation and run-up." Coastal Engineering, Vol. 7, pp. 299-317. [DOI:10.1016/0378-3839(83)90001-7]
26. Laitone, E.V. (1963) "Higher approximation to non-linear water waves and the limiting heights of cnoidal, solitary, and Stokes' waves." Beach Erosion Board, U.S. Department of the Army, Corps of Engineers, Technical Memorandum No. 133.
27. Lee, E.S. (2009) "Application of weakly compressible and truly incompressible SPH to 3-D water collapse in waterworks." Journal of Hydraulic Research, Vol. 48, pp. 50-60. [DOI:10.3826/jhr.2010.0003]
28. Liang, D., et al. (2013) "Comparison between Boussinesq and shallow-water models in predicting solitary wave runup on plane beaches." Coastal Engineering Journal, Vol. 55, No. 04, 1350014. [DOI:10.1142/S0578563413500149]
29. Lo, E.Y.M., and Shao, S. (2002) "Simulation of near-shore solitary wave mechanics by an incompressible SPH method." Applied Ocean Research. 24, 275-286. [DOI:10.1016/S0141-1187(03)00002-6]
30. Lopez, D., Marivela, R., and Garrote, L. (2010) "Smoothed particle hydrodynamics model applied to hydraulic structures: a hydraulic jump test case." Journal of Hydraulic Research, Vol. 48, pp. 142-158. [DOI:10.1080/00221686.2010.9641255]
31. Lucy, L.B. (1977) "A numerical approach to the testing of the fission hypothesis." Astronomical Journal, Vol. 82, pp. 1013-1024. [DOI:10.1086/112164]
32. Lynett, P.J., Wu, T.R., and Liu, P.L.F. (2002) "Modeling wave runup with depth-integrated equations." Coastal Engineering, Vol. 46, pp. 89-107. [DOI:10.1016/S0378-3839(02)00043-1]
33. Lynett, P.J. (2007) "Effect of a Shallow Water Obstruction on Long Wave Runup and Overland Flow Velocity." Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 133, pp. 455-462. [DOI:10.1061/(ASCE)0733-950X(2007)133:6(455)]
34. Madsen PA, Fuhrman DR, Schaffer HA (2008) On the solitary wave paradigm for tsunamis. J Geophys Res Ocean. [DOI:10.1029/2008JC004932]
35. McCowan, J. (1891) "On the Solitary Wave," London, Edinburgh, and Dublin Philosophical Magazine, Vol. 32, pp. 45-58. [DOI:10.1080/14786449108621390]
36. Monaghan, J.J. (1994) "Simulating free surface flows with SPH." Journal of Computational Physics. Vol. 110, No. 2, pp. 399-406. [DOI:10.1006/jcph.1994.1034]
37. Monaghan, J.J., and Kos, A. (1999) "Solitary Waves on a Cretan Beach." Journal of Waterway, Port, Coastal, and Ocean Engineering. 125, pp. 145-155. [DOI:10.1061/(ASCE)0733-950X(1999)125:3(145)]
38. Oger, G., et al. (2006) "Two-dimensional SPH simulations of wedge water entries." Journal of Computational Physics, Vol. 213, pp. 803-822. [DOI:10.1016/j.jcp.2005.09.004]
39. Rogers, B.D., and Dalrymple, R.A. (2008) "SPH modeling of tsunami waves." Adv. Coast. Ocean Eng. 10, 75-100. [DOI:10.1142/9789812790910_0003]
40. Russell, J. (1844) "Report on waves." Fourteenth Meet. B. Assoc. Adv. Sci. 1, 311.
41. Shao, S. (2005) "SPH simulation of solitary wave interaction with a curtain-type breakwater." Journal of Hydraulic Research, Vol. 48, pp. 366-375. [DOI:10.1080/00221680509500132]
42. Schimmels S, Sriram V, Didenkulova I (2016) Tsunami generation in a large scale experimental facility. Coast Eng 110:32-41. [DOI:10.1016/j.coastaleng.2015.12.005]
43. St-Germain, P., et al. (2014) "Smoothed-Particle Hydrodynamics Numerical Modeling of Structures Impacted by Tsunami Bores." J. Waterw. Port, Coastal, Ocean Eng. 140 (2014) 66-81. [DOI:10.1061/(ASCE)WW.1943-5460.0000225]
44. Svendsen, I.A. (1974) "Cnoidal waves over a gently sloping bottom." Ph. D. Thesis, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark.
45. Synolakis, C.E. (1987) "The runup of solitary waves." Journal of Fluid Mechanics, Vol. 185, pp. 523-545. [DOI:10.1017/S002211208700329X]
46. Synolakis, C.E., et al. (2008) "Validation and verification of tsunami numerical models." Pure and Applied Geophysics, Vol. 165, pp. 2197-2228. [DOI:10.1007/s00024-004-0427-y]
47. Synolakis, C.E., and Kanoglu, U. (2009) "Tsunami hydrodynamic modeling: standards and guidelines." Nonlinear wave dynamics, Lynett, P. J., Ed., World Scientific, Singapore, pp. 127-145. [DOI:10.1142/9789812709042_0006]
48. Wei, Z., et al. (2015) "SPH modeling of dynamic impact of tsunami bore on bridge piers." Coastal Engineering, Vol. 104, pp. 26-42. [DOI:10.1016/j.coastaleng.2015.06.008]
49. Weiss, R., et al. (2010) "Three-dimensional modeling of long-wave runup: simulation of tsunami inundation with GPU-SPHYSICS." Coastal Eng. Proc., 1(32), 8. [DOI:10.9753/icce.v32.currents.8]
50. Wendland, H. (1995) "Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree." Advances in Computational Mathematics, Vol. 4, No. 1, pp. 389-396. [DOI:10.1007/BF02123482]
51. Xie, J., Nistor, I., and Murty, T. (2012) "A corrected 3-D SPH method for breaking tsunami wave modelling." Nat Hazards 60:81-100. [DOI:10.1007/s11069-011-9954-x]
52. Zheng, X., Lv, X., Ma, Q., Duan, W., Khayyer, A., Shao, S. (2017) "An improved solid boundary treatment for wave-float interactions using ISPH method." International Journal of Naval Architecture and Ocean Engineering, ISSN 2092-6782.
53. Zelt, J.A. (1991) "The run-up of nonbreaking and breaking solitary waves." Coastal Engineering, Vol. 15, pp. 205-246. [DOI:10.1016/0378-3839(91)90003-Y]
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Rastgoftar E, Akbarpour Jannat M R, Banijamali B. Improvement in the SPH-Paddle Wave Maker Approach for Real Tsunami Waves Modeling. JPG. 2017; 8 (30) :17-38
URL: http://jpg.inio.ac.ir/article-1-585-en.html
Volume 8, Issue 30 (12-2017) Back to browse issues page
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