This study presents that an emulator of a particle method has the potential to be applied for the statistical analysis of tsunami run-up phenomena. The emulator follows a Gaussian process to model a particle method specifically for estimating wave heights of tsunami run-up in front of buildings on the ground. In general, Gaussian processes have the advantage of designing statistical emulators to reduce the computational cost required by simulators. Although statistical analysis using computational models requires a considerable number of simulations, Gaussian process emulators can address this challenge. In contrast, particle methods are advantageous for simulating free-surface flow problems including tsunami run-up. The mesh-free methods discretize the Navier–Stokes and continuity equations without mesh generations as opposed to mesh methods, and thus they can simulate tsunami behaviors near ground buildings. In this study, we simplify tsunami run-up as three-dimensional dam-break problems where the collapse of a water column owing to gravity moves in a slope and impacts on two buildings. Although these problems are not exactly tsunami run-up phenomena, the study intends to show the possibility of applying the Gaussian process emulator for such phenomena. The sensitivity analysis of the wave heights is carried out using the emulator to observe how the run-up heights are influenced by the initial size of the water column. Consequently, it predicts the tendency of the wave heights based on the initial settings and demonstrates the effectiveness of the emulator for the run-up analysis. In addition, this study illustrates the frequency and quartiles of the run-up heights near ground structures, which can be applied for tsunami evacuation planning.
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Tsunami wo yosoku suru shikumi. Japan Meteorological Agency. https://www.data.jma.go.jp/svd/eqev/data/tsunami/ryoteki.html. Accessed 10 Nov 2020 (in Japanese)
Arikawa T (2015) Consideration of characteristics of pressure on seawall by solitary waves based on hydraulic experiments. J Japan Soc Civ Eng Ser B2 (Coast Eng) 71(2):I\_889-I\_894 (in Japanese)
Synolakis C (1987) The run-up of solitary waves. J Fluid Mech 185:523–545
Synolakis C (1991) Tsunami run-up on steep slopes: how good linear theory really is. Nat Hazards 4:221–234
Asakura R, Iwase K, Ikeya T, Takao M, Kaneto T, Fujii, N, Ohmori M (2003) The tsunami wave force acting on land structures. In: Proceedings of the 28th international conference on coastal engineering, pp 1191–1202 (in Japanese)
Arimitsu T, Ooe K, Kawasaki K (2012) Hydraulic experiment on evaluation method of tsunami wave pressure using inundation depth and velocity in front of land structure. J Japan Soc Civ Eng Ser B2 (Coast Eng) 68(2):I\_776-I\_780 (in Japanese)
Asai M, Goda T, Oguni K, Isobe D, Kashiyama K, Isshiki M (2014) Evaluation of tsunami fluid force acted on tsunami refuge building by using a stabilized ISPH. J Japan Soc Civ Eng Ser A2 (Appl Mech (AM)) 70(2):I\_649-I\_658 (in Japanese)
Suwa T, Imamura F, Sugawara D (2014) Development of a tsunami simulator integrating the smoothed-particle hydrodynamics method and the nonlinear shallow water wave model. J Japan Soc Civ Eng Ser A2 (Appl Mech (AM)) 70(2):I\_016-I\_020 (in Japanese)
Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82:1013–1024
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Notices R Astron Soc 181(3):375–389
Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30:543–574
Cummins S, Rudman M (1999) An SPH projection method. J Comput Phys 152(2):584–607
Lo EYM, Shao S (2002) Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Appl Ocean Res 24(5):275–286
Shao S, Lo EYM (2003) Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv Water Resour 26(7):787–800
Koshizuka S, Oka Y (1996) Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 123:421–434
Koshizuka S, Nobe A, Oka Y (1998) Numerical analysis of breaking waves using the moving particle semi-implicit method. Int J Numer Method Fluids 26:751–769
Koshizuka S, Shibata K, Kondo M, Matsunaga T (2018) Moving particle semi-implicit method: a meshfree particle method for fluid dynamics. Academic Press, Chippenham
Shakibaeinia A, Jin Y (2010) A weakly compressible MPS method for modeling of open-boundary free-surface flow. Int J Numer Methods Fluids 63(10):1208–1232
Oochi M, Koshizuka S, Sakai M (2010) Explicit MPS algorithm for free surface flow analysis. Trans Japan Soc Comput Eng Science 2010:20100013 (in Japanese)
Oochi M, Yamada Y, Koshizuka S, Sakai M (2011) Validation of pressure calculation in Explicit MPS method. Trans Japan Soc Comput Eng Sci 2011:20110002 (in Japanese)
Yamada Y, Sakai M, Mizutani S, Koshizuka S, Oochi M, Murozono K (2011) Numerical simulation of three-dimensional free-surface flows with explicit moving particle simulation method. Trans At Energy Soc Japan 10(3):185–193 (in Japanese)
Ferrari A, Dumbser M, Toro EF (2009) A new 3D parallel SPH scheme for free surface flows. Comput Fluids 38:1203–1217
Chow AD, Rogers BD, Lind SJ, Stansby PK (2018) Incompressible SPH (ISPH) with fast Poisson solver on a GPU. Comput Phys Commun 226:81–103
Shibata K, Koshizuka S, Masaie I (2016) Cost reduction of particle simulations by an ellipsoidal particle model. Comput Methods Appl Mech Eng 307(1):411–450
Shibata K, Koshizuka S, Matsunaga T, Masaie I (2017) The overlapping particle technique for multi-resolution simulation of particle methods. Comput Methods Appl Mech Eng 325(1):434–462
Murotani K, Oochi M, Fujisawa T, Koshizuka S, Yoshimura S (2012) Distributed memory parallel algorithm for Explicit MPS using ParMETIS. Trans Japan Soc Comput Eng Sci 2012:20120012 (in Japanese)
Murotani K, Koshizuka S, Tamai T, Shibata K, Mitsume N, Yoshimura S, Tanaka S, Hasegawa K, Nagai N, Fujisawa T (2014) Development of hierarchical domain decomposition explicit MPS method and application to large-scale tsunami analysis with floating objects. J Adv Simul Sci Eng 1(1):16–35
Mizuno Y, Mitsume N, Yamada T, Yoshimura S (2019) Time-based dynamic load balancing algorithm for domain decomposition with particle method adopting three-dimensional polygon-wall boundary model. J Adv Simul Sci Eng 6(2):282–297
O’Hagan A (2006) Bayesian analysis of computer code outputs: a tutorial. Reliab Eng Syst Saf 91(10–11):1290–1300
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. The MIT Press, Massachusetts
Rougier J (2008) Efficient emulators for multivariate deterministic functions. J Comput Graph Stat 17(4):827–843
Rougier J, Maute A, Guillas S, Richmond AD (2009) Expert knowledge and multivariate emulation: the thermosphere-ionosphere electrodynamics general circulation model (TIE-GCM). Spec Issue Comput Model 51(4):414–424
Igarashi Y, Hori T, Murata S, Sato K, Baba T, Okada M (2016) Maximum tsunami height prediction using pressure gauge data by a Gaussian process at Owase in the Kii Peninsula, Japan. Mar Geophys Res 37(4):361–370
Oakley J, O’Hagan A (2002) Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika 89(4):769–784
Oakley J, O’Hagan A (2004) Probabilistic sensitivity analysis of complex models: a Bayesian approach. J R Stat Soc Stat Methodol Ser B 66(3):751–769
Sarri A, Guillas S, Dias F (2012) Statistical emulation of a tsunami model for sensitivity analysis and uncertainty quantification. Nat Hazards Earth Syst Sci 12(6):2003–2018
Mizuno Y, Koshizuka S (2020) Gaussian process emulation of particle method for estimating free-surface heights. J Fluid Sci Technol 15(3):JFST0021
Grezio A, Babeyko A, Baptista M, Behrens J, Costa A, Davies G, Geist EL, Glimsdal S, González FI, Griffin J, Harbitz CB, LeVeque RJ, Lorito S, Løvholt F, Omira R, Mueller C, Paris R, Parsons T, Polet J, Power W, Selva J, Sørensen MB, Thio H (2017) Probabilistic tsunami hazard analysis: multiple sources and global applications. Rev Geophys 55(4):1158–1198
Kohavi R (1995) A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the 14th international joint conference on artificial intelligence, vol 2, pp 1137–1143
This work was supported by JSPS KAKENHI Grant Numbers JP18K04576, JP21J12302.
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Mizuno, Y., Shibata, K. & Koshizuka, S. Statistical analysis of three-dimensional run-up heights using Gaussian process emulator of particle method. Comp. Part. Mech. (2021). https://doi.org/10.1007/s40571-021-00426-w
- EMPS method
- Free-surface flow
- Gaussian process regression
- Computational speed
- Sensitivity analysis
- Statistical emulation
- Tsunami evacuation planning