×

An improved incompressible SPH model for simulation of wave-structure interaction. (English) Zbl 1365.76257

Summary: An improved two-dimensional Incompressible Smoothed Particle Hydrodynamics (ISPH) model is developed to simulate free surface flow interaction with structures. In this model, the improved mirror particle treatment for solid boundaries is developed, in which the mirror parameters and mirroring rules are redefined. The proposed mirror particle treatment is more accurate with less artificial oscillations of pressure. The improvement of pressure computations is verified by a benchmark test of dam break flow and the comparisons with the documented data showed satisfactory agreement. A series of numerical simulations have been conducted to further verify the applicability of the model for simulations of wave interaction with coastal structures of various shapes. These include linear wave reflection from an impermeable breakwater, solitary wave passing a rectangular obstacle and periodic wave train decompositions over a submerged shelf. In these simulations, the total particle number employed is up to 150,000 and rather good agreement has been obtained when the numerical results are compared to available analytical, experimental, and other numerical data found in literatures.

MSC:

76M28 Particle methods and lattice-gas methods
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs

Software:

PARDISO
Full Text: DOI

References:

[1] Liu, G. R.; Liu, M. B., Smoothed particle hydrodynamics: a meshfree particle method (2003), World Scientific: World Scientific Singapore · Zbl 1046.76001
[2] Ferrari, A.; Fraccarollo, L.; Dumbser, M.; Toro, E. F.; Armanini, A., Three-dimensional flow evolution after a dambreak, J Fluid Mech, 663, 456-477 (2010) · Zbl 1205.76228
[3] Monaghan, J. J.; Kos, A., Solitary waves on a Cretan beach, J Wtrwy Port Coast Ocean Eng, 125, 3, 145-154 (1999)
[4] Roubtsova, V.; Kahawita, R., The SPH technique applied to free surface flows, Comput Fluids, 35, 1359-1371 (2006) · Zbl 1177.76327
[5] Angela, F.; Michael, D.; Eleuterio, F. T.; Aronne, A., A new 3D parallel SPH scheme for free surface flows, Comput Fluids, 38, 1203-1217 (2009) · Zbl 1242.76270
[6] Ferrari, A.; Dumbser, M.; Toro, E. F.; Armanini, A., A new 3D parallel SPH scheme for free surface flows, Comput Fluids, 38, 6, 1203-1217 (2009) · Zbl 1242.76270
[7] Shao, S. D.; Lo, E. Y.M., Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Adv Water Resour, 26, 787-800 (2003)
[8] Cummins, S. J.; Rudman, M., An SPH projection method, J Comput Phys, 152, 584-607 (1999) · Zbl 0954.76074
[9] Shao, S. D., Incompressible SPH simulation of water entry of a free-falling object, Int J Numer Methods Fluids, 59, 91-115 (2009) · Zbl 1391.76633
[10] Maruzewski, P.; Le Touze, D.; Oger, G.; Avellan, F., SPH high-performance computing simulations of rigid solids impacting the free-surface of water, J Hydraul Res, 47, 126-134 (2009)
[11] Lin, P. Z., A fixed-grid model for simulation of a moving body in free surface flows, Comput Fluids, 36, 549-561 (2007) · Zbl 1177.76260
[12] Shao, S. D., Incompressible SPH flow model for wave interactions with porous media, Coast Eng, 57, 304-316 (2010)
[13] Li, J.; Liu, H. X.; Gong, K.; Tan, S. K.; Shao, S. D., SPH modeling of solitary wave fissions over uneven bottoms, Coast Eng, 60, 261-275 (2012)
[14] Gao, R.; Ren, B.; Wang, G. Y.; Wang, Y. X., Numerical modelling of regular wave slamming on subface of open-piled structures with the corrected SPH method, Appl Ocean Res, 34, 173-186 (2012)
[15] Andrea, A.; Jean-Christophe, M.; Francis, L.; Julien, L.; Joëlle, C., SPH truncation error in estimating a 3D function, Comput Fluids, 44, 279-296 (2011) · Zbl 1271.76261
[16] Monaghan, J. J., Simulating free surface flow with SPH, J Comput Phys, 110, 399-406 (1994) · Zbl 0794.76073
[17] Libersky, L. D.; Petschek, A. G.; Carney, T. C., High strain Lagrangian hydrodynamics a three dimensional SPH code for dynamic material response, J Comput Phys, 109, 1, 65-67 (1993) · Zbl 0791.76065
[18] Randles, P. W.; Libersky, L. D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput Methods Appl Mech, 139, 375-408 (1996) · Zbl 0896.73075
[19] Liu, G. R.; Gu, Y. T., A local radial point interpolation method (LRPIM) for free vibration analyses of 2D solids, J Sound Vib, 246, 1, 29-46 (2001)
[20] Morris, J. P.; Fox, P. J.; Zhu, Y., Modeling low Reynolds number incompressible flows using SPH, J Comput Phys, 136, 214-226 (1997) · Zbl 0889.76066
[21] Fourey, G.; Oger, G.; Le Touze, D.; Alessandrini, B., Violent fluid-structure interaction simulations using a coupled SPH/FEM method, Mater Sci Eng, 1-8 (2010)
[22] Yildiz, M.; Rook, R. A.; Suleman, A., SPH with the multiple boundary tangent method, Int J Numer Methods Eng, 77, 1416-1438 (2009) · Zbl 1156.76427
[23] Lo, E. Y.M.; Shao, S. D., Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Appl Ocean Res, 24, 275-286 (2002)
[24] Cho, Y. S.; Lee, J. I.; Kim, Y. T., Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem, Ocean Eng, 31, 1325-1335 (2004)
[25] Lin, P. Z., A multiple-layer \(σ\)-coordinate model for simulation of wave-structure interaction, Comput Fluids, 35, 147-167 (2006) · Zbl 1160.76323
[27] Ohyama, T.; Kioka, W.; Tada, A., Applicability of numerical models to nonlinear dispersive waves, Coast Eng, 24, 297-313 (1995)
[28] Li, T. Q.; Troch, P.; Rouck, J. D., Wave overtopping over a sea dike, J Comput Phys, 198, 686-726 (2004) · Zbl 1116.76327
[29] Chorin, A. J., Numerical solution of the Navier-Stokes equations, Math Comput, 22, 745-762 (1968) · Zbl 0198.50103
[30] Liu, D. M.; Lin, P. Z., A numerical study of three-dimensional liquid sloshing in tanks, J Comput Phys, 227, 3921-3939 (2007) · Zbl 1317.76061
[31] Monaghan, J. J., Smoothed particle hydrodynamics, Annu Rev Astron Astrophys, 30, 543-574 (1992)
[33] Khayyer, A.; Gotoh, H., Development of CMPS method for accurate water-surfacetracking in breaking waves, Coast Eng J, 50, 2, 179-207 (2008)
[34] Khayyer, A.; Gotoh, H., Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure, Coast Eng, 56, 4, 419-440 (2009)
[35] Khayyer, A.; Gotoh, H.; Shao, S. D., Enhanced predictions of wave impact pressure by improved incompressible SPH methods, Appl Ocean Res, 31, 111-131 (2009)
[38] Schenk, O.; Gartner, K., Two-level scheduling in PARDISO: improved scalability on shared memory multiprocessing systems, Parallel Comput, 28, 187-197 (2002) · Zbl 0982.68195
[39] Schenk, O.; Gartner, K., Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener Comp Syst, 20, 475-487 (2003) · Zbl 1062.65035
[40] Molteni, D.; Colagrossi, A., A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH, Comput Phys Commun, 180, 861-872 (2009) · Zbl 1198.76108
[41] Lee, T. H.; Zhou, Z. Q.; Cao, Y. S., Numerical simulations of hydraulic jumps in water sloshing and water impacting, J Fluid Eng, 124, 215-226 (2002)
[42] Van der Meer, J. W.; Briganti, R.; Zanuttigh, B.; Wang, B., Wave transmission and reflection at low crested structures: design formulae, oblique wave attack and spectral change, Coast Eng, 52, 10-11, 915-929 (2005)
[43] Gotoh, H.; Shao, S. D.; Memita, T., SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater, Coast Eng J, 46, 1, 39-63 (2004)
[44] Lin, P. Z., Numerical modeling of water waves (2008), Routledge: Taylor & Francis
[45] Huang, C. J.; Dong, C. M., On the interaction of a solitary wave and a submerged dike, Coast Eng, 43, 265-286 (2001)
[46] Jia, W.; Nakamura, Y., Incompressible flow solver of arbitrarily moving bodies with rigid surface, JSME Int J Ser B, 39, 2, 315-325 (1996)
[47] Chang, K. A.; Hsu, T. J.; Liu, P. L.-F., Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle. Part I. Solitary waves, Coast Eng, 44, 13-26 (2001)
[48] Ohyama, T.; Nadaoka, K., Transformation of nonlinear wave train passing over submerged shelf without breaking, Coast Eng, 24, l-22 (1994)
[49] Beji, S.; Battjes, J. A., Experimental investigation of wave propagation over a bar, Coast Eng, 19, 151-162 (1993)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.