[1] ZHANG Z R, LIU H, ZHU S P et al. Application of CFD in ship engineering design practice and ship hydrodynamics[J]. Journal of Hydrodynamics, Ser. B, 18, 315-322(2006).

[4] MARRONE S, COLAGROSSI A, ANTUONO M et al. A 2D+t SPH model to study the breaking wave pattern generated by fast ships[J]. Journal of Fluids and Structures, 27, 1199-1215(2011).

[5] LYU H G, SUN P N, HUANG X T et al. On removing the numerical instability induced by negative pressures in SPH simulations of typical fluid-structure interaction problems in ocean engineering[J]. Applied Ocean Research, 117, 102938(2021).

[8] ZHANG A M, SUN P N, MING F R et al. Smoothed particle hydrodynamics and its applications in fluid-structure interactions[J]. Journal of Hydrodynamics, Ser. B, 29, 187-216(2017).

[9] YE T, PAN D Y, HUANG C et al. Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications[J]. Physics of Fluids, 31, 011301(2019).

[10] GÓMEZ-GESTEIRA M, CERQUEIRO D, CRESPO C et al. Green water overtopping analyzed with a SPH model[J]. Ocean Engineering, 32, 223-238(2005).

[12] WANG B L, GUO X Y, LIU H et al. Numerical simulations of wake signatures around high-speed ships[J]. Journal of Hydrodynamics, Ser. B, 26, 986-989(2015).

[13] REED A M, MILGRAM J H. Ship wakes and their radar images[J]. Annual Review of Fluid Mechanics, 34, 469-502(2002).

[14] CHEN C, ZHANG A M, CHEN J Q et al. SPH simulations of water entry problems using an improved boundary treatment[J]. Ocean Engineering, 238, 109679(2021).

[15] SUN P N, MING F R, ZHANG A M. Numerical simulation of interactions between free surface and rigid body using a robust SPH method[J]. Ocean Engineering, 98, 32-49(2015).

[17] LYU H G, DENG R, SUN P N et al. Study on the wedge penetrating fluid interfaces characterized by different density-ratios: Numerical investigations with a multi-phase SPH model[J]. Ocean Engineering, 237, 109538(2021).

[20] [20] VON KARMAN T H. The impact on seaplane floats during ling[J]. National Advisy Committee f Aeronatics, 1929.

[21] WANG S P, ZHANG A M, LIU Y L et al. Bubble dynamics and its applications[J]. Journal of Hydrodynamics, 30, 975-991(2018).

[22] MARRONE S, BOUSCASSE B, COLAGROSSI A et al. Study of ship wave breaking patterns using 3D parallel SPH simulations[J]. Computers & Fluids, 69, 54-66(2012).

[23] LANDRINI M, COLAGROSSI A, GRECO M et al. The fluid mechanics of splashing bow waves on ships: A hybrid BEM-SPH analysis[J]. Ocean Engineering, 53, 111-127(2012).

[25] LIU M B, LI S M. On the modeling of viscous incompressible flows with smoothed particle hydro-dynamics[J]. Journal of Hydrodynamics, 28, 731-745(2016).

[31] HASHIMOTO H, GRENIER N, SUEYOSHI M et al. Comparison of MPS and SPH methods for solving forced motion ship flooding problems[J]. Applied Ocean Research, 118, 103001(2022).

[32] ABDELRAZEK A M, KIMURA I, SHMIZU Y. Comparison between SPH and MPS methods for numerical simulations of free surface flow problems[J]. Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering), 70, I_67-I_72(2014).

[33] BAKTI F P, KIM M H, KIM K S et al. Comparative study of standard WC-SPH and MPS solvers for free surface academic problems[J]. International Journal of Offshore and Polar Engineering, 26, 235-243(2016).

[34] [34] ZHANG Y X, WAN D C. Comparison investigations of numerical simulations of incompressible viscous flows by SPH MPS[C]ASME 2010 29th International Conference on Ocean, Offshe Arctic Engineering. Shanghai, China: ASME, 2010: 837845.

[38] SUN X S, SAKAI M, YAMADA Y. Three-dimensional simulation of a solid-liquid flow by the DEM-SPH method[J]. Journal of Computational Physics, 248, 147-176(2013).

[39] ROBB D M, GASKIN S J, MARONGIU J C. SPH-DEM model for free-surface flows containing solids applied to river ice jams[J]. Journal of Hydraulic Research, 54, 27-40(2016).

[40] KLOSS C, GONIVA C, HAGER A et al. Models, algorithms and validation for open source DEM and CFD-DEM[J]. Progress in Computational Fluid Dynamics, 12, 140-152(2012).

[43] COLAGROSSI A, LANDRINI M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics[J]. Journal of Computational Physics, 191, 448-475(2003).

[44] SUN P N, COLAGROSSI A, MARRONE S et al. Multi-resolution Delta-plus-SPH with tensile instability control: Towards high Reynolds number flows[J]. Computer Physics Communications, 224, 63-80(2018).

[45] CRESPO A C, DOMINGUEZ J M, BARREIRO A et al. GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods[J]. PLoS One, 6, e20685(2011).

[46] ZHANG Z F, WANG C, ZHANG A M et al. SPH-BEM simulation of underwater explosion and bubble dynamics near rigid wall[J]. Science China Technological Sciences, 62, 1082-1093(2019).

[47] GROENENBOOM P, CARTWRIGHT B, MCGUCKIN D. Recent features and industrial applications of the hybrid SPH-FE method[J]. International Journal of Computational Fluid Dynamics, 35, 106-128(2021).

[48] GINGOLD R A, MONAGHAN J J. Smoothed particle hydrodynamics: theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 181, 375-389(1977).

[49] MONAGHAN J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 110, 399-406(1994).

[50] NGUYEN V T, VU D T, PARK W G et al. Navier-Stokes solver for water entry bodies with moving Chimera grid method in 6DOF motions[J]. Computers & Fluids, 140, 19-38(2016).

[51] SUN P N, ZHANG A M, MARRONE S et al. An accurate and efficient SPH modeling of the water entry of circular cylinders[J]. Applied Ocean Research, 72, 60-75(2018).

[52] CHENG H, MING F R, SUN P N et al. Towards the modeling of the ditching of a ground-effect wing ship within the framework of the SPH method[J]. Applied Ocean Research, 82, 370-384(2019).

[53] LUO M, KHAYYER A, LIN P Z. Particle methods in ocean and coastal engineering[J]. Applied Ocean Research, 114, 102734(2021).

[54] LIU M B, LIU G R. Smoothed particle hydrodynamics (SPH): an overview and recent developments[J]. Archives of Computational Methods in Engineering, 17, 25-76(2010).

[55] COLAGROSSI A, ANTUONO M, LE TOUZÉ D. Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model[J]. Physical Review E, 79, 056701(2009).

[56] MARRONE S, ANTUONO M, COLAGROSSI A et al. δ-SPH model for simulating violent impact flows[J]. Computer Methods in Applied Mechanics and Engineering, 200, 1526-1542(2011).

[57] FEDERICO I, MARRONE S, COLAGROSSI A et al. Simulating 2D open-channel flows through an SPH model[J]. European Journal of Mechanics-B/Fluids, 34, 35-46(2012).

[58] WANG P P, ZHANG A M, MING F R et al. A novel non-reflecting boundary condition for fluid dynamics solved by smoothed particle hydrodynamics[J]. Journal of Fluid Mechanics, 860, 81-114(2019).

[59] CUMMINS S J, RUDMAN M. An SPH projection method[J]. Journal of Computational Physics, 152, 584-607(1999).

[60] CHOW A D, ROGERS B D, LIND S J et al. Incompressible SPH (ISPH) with fast Poisson solver on a GPU[J]. Computer Physics Communications, 226, 81-103(2018).

[61] CHOW A D, ROGERS B D, LIND S J et al. Numerical wave basin using incompressible smoothed particle hydrodynamics (ISPH) on a single GPU with vertical cylinder test cases[J]. Computers & Fluids, 179, 543-562(2019).

[62] CRESPO A J C, DOMÍNGUEZ J M, ROGERS B D et al. DualSPHysics: open-source parallel CFD solver based on smoothed particle Hydrodynamics (SPH)[J]. Computer Physics Communications, 187, 204-216(2015).

[63] ZHANG C, REZAVAND M, ZHU Y J et al. SPHinXsys: an open-source multi-physics and multi-resolution library based on smoothed particle hydrodynamics[J]. Computer Physics Communications, 267, 108066(2021).

[64] VILA J P. On particle weighted methods and smooth particle hydrodynamics[J]. Mathematical Models and Methods in Applied Sciences, 9, 161-209(1999).

[65] ANTUONO M, COLAGROSSI A, MARRONE S. Numerical diffusive terms in weakly-compressible SPH schemes[J]. Computer Physics Communications, 183, 2570-2580(2012).

[66] ANTUONO M, SUN P N, MARRONE S et al. The δ-ALE-SPH model: An arbitrary Lagrangian-Eulerian framework for the δ-SPH model with particle shifting technique[J]. Computers & Fluids, 216, 104806(2021).

[67] NESTOR R M, BASA M, LASTIWKA M et al. Extension of the finite volume particle method to viscous flow[J]. Journal of Computational Physics, 228, 1733-1749(2009).

[68] LIND S J, XU R, STANSBY P K et al. Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves[J]. Journal of Computational Physics, 231, 1499-1523(2012).

[69] SUN P N, COLAGROSSI A, MARRONE S et al. The δ-plus-SPH model: Simple procedures for a further improvement of the SPH scheme[J]. Computer Methods in Applied Mechanics and Engineering, 315, 25-49(2017).

[70] SUN P N, COLAGROSSI A, MARRONE S et al. A consistent approach to particle shifting in the δ-plus-SPH model[J]. Computer Methods in Applied Mechanics and Engineering, 348, 912-934(2019).

[71] ZHANG G M, BATRA R C. Modified smoothed particle hydrodynamics method and its application to transient problems[J]. Computational Mechanics, 34, 137-146(2004).

[72] DILTS G A. Moving-least-squares-particle hydrodynamics—I. Consistency and stability[J]. International Journal for Numerical Methods in Engineering, 44, 1115-1155(1999).

[73] LIU M B, XIE W P, LIU G R. Modeling incompressible flows using a finite particle method[J]. Applied Mathematical Modelling, 29, 1252-1270(2005).

[74] WANG P P, ZHANG A M, MENG Z F et al. A new type of WENO scheme in SPH for compressible flows with discontinuities[J]. Computer Methods in Applied Mechanics and Engineering, 381, 113770(2021).

[75] MENG Z F, ZHANG A M, WANG P P et al. A targeted essentially non-oscillatory (TENO) SPH method and its applications in hydrodynamics[J]. Ocean Engineering, 243, 110100(2022).

[76] PURI K, RAMACHANDRAN P. Approximate Riemann solvers for the Godunov SPH (GSPH)[J]. Journal of Computational Physics, 270, 432-458(2014).

[77] COLAGROSSI A, SOUTO-IGLESIAS A, ANTUONO M et al. Smoothed-particle-hydrodynamics modeling of dissipation mechanisms in gravity waves[J]. Physical Review E, 87, 023302(2013).

[78] ZHU Y J, ZHANG C, YU Y C et al. A CAD-compatible body-fitted particle generator for arbitrarily complex geometry and its application to wave-structure interaction[J]. Journal of Hydrodynamics, 33, 195-206(2021).

[79] ADAMI S, HU X Y, ADAMS N A. A generalized wall boundary condition for smoothed particle hydrodynamics[J]. Journal of Computational Physics, 231, 7057-7075(2012).

[80] CHENG H, MING F R, SUN P N et al. Ship hull slamming analysis with smoothed particle hydrodynamics method[J]. Applied Ocean Research, 101, 102268(2020).

[81] DOMÍNGUEZ J M, FOURTAKAS G, ALTOMARE C et al. DualSPHysics: from fluid dynamics to multiphysics problems[J]. Computational Particle Mechanics, 1-29(2021).

[82] GAROOSI F, HOOMAN K. Numerical simulation of multiphase flows using an enhanced volume-of-fluid (VOF) method[J]. International Journal of Mechanical Sciences, 215, 106956(2022).

[83] DI MASCIO A, BROGLIA R, MUSCARI R. On the application of the single-phase level set method to naval hydrodynamic flows[J]. Computers & Fluids, 36, 868-886(2007).

[84] TAGLIAFIERRO B, MANCINI S, ROPERO-GIRALDA P et al. Performance assessment of a planing hull using the smoothed particle hydrodynamics method[J]. Journal of Marine Science and Engineering, 9, 244(2021).

[85] VEEN D, GOURLAY T. A combined strip theory and smoothed particle hydrodynamics approach for estimating slamming loads on a ship in head seas[J]. Ocean Engineering, 43, 64-71(2012).

[86] ANDRILLON Y, ALESSANDRINI B. A 2D+T VOF fully coupled formulation for the calculation of breaking free-surface flow[J]. Journal of Marine Science and Technology, 8, 159-168(2004).

[87] MINTU S, MOLYNEUX D, COLBOURNE B. Full-scale SPH simulations of ship-wave impact generated sea spray[J]. Ocean Engineering, 241, 110077(2021).

[88] MONAGHAN J J, KOCHARYAN A. SPH simulation of multi-phase flow[J]. Computer Physics Communications, 87, 225-235(1995).

[89] FONTY T, FERRAND M, LEROY A et al. Mixture model for two-phase flows with high density ratios: a conservative and realizable SPH formulation[J]. International Journal of Multiphase Flow, 111, 158-174(2019).

[90] FONTY T, FERRAND M, LEROY A et al. Air entrainment modeling in the SPH method: a two-phase mixture formulation with open boundaries[J]. Flow, Turbulence and Combustion, 105, 1149-1195(2020).

[91] ALTOMARE C, DOMÍNGUEZ J M, CRESPO A J C et al. Long-crested wave generation and absorption for SPH-based DualSPHysics model[J]. Coastal Engineering, 127, 37-54(2017).

[92] HE M, KHAYYER A, GAO X F et al. Theoretical method for generating solitary waves using plunger-type wavemakers and its smoothed particle hydrodynamics validation[J]. Applied Ocean Research, 106, 102414(2021).

[93] ANTUONO M, COLAGROSSI A, MARRONE S et al. Propagation of gravity waves through an SPH scheme with numerical diffusive terms[J]. Computer Physics Communications, 182, 866-877(2011).

[94] SUN P N, LUO M, LE TOUZÉ D et al. The suction effect during freak wave slamming on a fixed platform deck: smoothed particle hydrodynamics simulation and experimental study[J]. Physics of Fluids, 31, 117108(2019).

[95] REN B, WEN H J, DONG P et al. Numerical simulation of wave interaction with porous structures using an improved smoothed particle hydrodynamic method[J]. Coastal Engineering, 88, 88-100(2014).

[96] REN B, HE M, DONG P et al. Nonlinear simulations of wave-induced motions of a freely floating body using WCSPH method[J]. Applied Ocean Research, 50, 1-12(2015).

[97] SHAO S D, JI C M, GRAHAM D I et al. Simulation of wave overtopping by an incompressible SPH model[J]. Coastal Engineering, 53, 723-735(2006).

[99] [99] LE TOUZ D, MARSH A, OGER G, et al. SPH simulation of green water ship flooding scenarios[J]. Journal of Hydrodynamics, Ser. B, 2010, 22(5 Supp. 1): 231236.

[100] AREU-RANGEL O S, HERNÁNDEZ-FONTES J V, SILVA R et al. Green water loads using the wet dam-break method and SPH[J]. Ocean Engineering, 219, 108392(2021).

[101] ZHAO X Z, HU C H. Numerical and experimental study on a 2-D floating body under extreme wave conditions[J]. Applied Ocean Research, 35, 1-13(2012).

[102] ZHAO X Z, YE Z T, FU Y N et al. A CIP-based numerical simulation of freak wave impact on a floating body[J]. Ocean Engineering, 87, 50-63(2014).

[103] SUI Y T, ZHANG A M, MING F R et al. Experimental investigation of oblique water entry of high-speed truncated cone projectiles: Cavity dynamics and impact load[J]. Journal of Fluids and Structures, 104, 103305(2021).

[104] GHAZANFARIAN J, SAGHATCHI R, GORJI-BANDPY M. Turbulent fluid-structure interaction of water-entry/exit of a rotating circular cylinder using SPH method[J]. International Journal of Modern Physics C, 26, 1550088(2015).

[105] ZHANG H S, ZHANG Z L, HE F et al. Numerical investigation on the water entry of a 3D circular cylinder based on a GPU-accelerated SPH method[J]. European Journal of Mechanics-B/Fluids, 94, 1-16(2022).

[106] YANG Q Z, XU F, YANG Y et al. Two-phase SPH model based on an improved Riemann solver for water entry problems[J]. Ocean Engineering, 199, 107039(2020).

[107] DI MASCIO A, ANTUONO M, COLAGROSSI A et al. Smoothed particle hydrodynamics method from a large eddy simulation perspective[J]. Physics of Fluids, 29, 035102(2017).

[109] WU Q G, NI B Y, BAI X L et al. Experimental study on large deformation of free surface during water exit of a sphere[J]. Ocean Engineering, 140, 369-376(2017).

[110] CHU X S, YAN K, WANG Z et al. Numerical simulation of water-exit of a cylinder with cavities[J]. Journal of Hydrodynamics, Ser. B, 22, 877-881(2010).

[111] SUN P N, LE TOUZÉ D, OGER G et al. An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase flows. Part 1: numerical scheme and validations with basic 1D and 2D benchmarks[J]. Journal of Computational Physics, 426, 109937(2021).

[113] PENG Y X, ZHANG A M, MING F R. Numerical simulation of structural damage subjected to the near-field underwater explosion based on SPH and RKPM[J]. Ocean Engineering, 222, 108576(2021).

[114] [114] BENZ W. Smooth particle hydrodynamics: a review[M]BUCHLER J R. The numerical modelling of nonlinear stellar pulsations. Ddrecht: Springer, 1990: 269288.

[116] XIE W F, LIU T G, KHOO B C. Application of a one-fluid model for large scale homogeneous unsteady cavitation: The modified Schmidt model[J]. Computers & Fluids, 35, 1177-1192(2006).

[117] SUN P N, LE TOUZÉ D, OGER G et al. An accurate SPH volume adaptive scheme for modeling strongly-compressible multiphase flows. Part 2: extension of the scheme to cylindrical coordinates and simulations of 3D axisymmetric problems with experimental validations[J]. Journal of Computational Physics, 426, 109936(2021).

[118] ZHANG A M, YANG W S, HUANG C et al. Numerical simulation of column charge underwater explosion based on SPH and BEM combination[J]. Computers & Fluids, 71, 169-178(2013).

[119] FANG X L, COLAGROSSI A, WANG P P et al. An accurate and robust axisymmetric SPH method based on Riemann solver with applications in ocean engineering[J]. Ocean Engineering, 244, 110369(2022).

[120] MAY D A, MONAGHAN J J. Can a single bubble sink a ship?[J]. American Journal of Physics, 71, 842-849(2003).

[122] JOSHI S, FRANC J P, GHIGLIOTTI G et al. SPH modelling of a cavitation bubble collapse near an elasto-visco-plastic material[J]. Journal of the Mechanics and Physics of Solids, 125, 420-439(2019).

[123] PINEDA S, MARONGIU J C, AUBERT S et al. Simulation of a gas bubble compression in water near a wall using the SPH-ALE method[J]. Computers & Fluids, 179, 459-475(2019).

[124] YIN J Y, ZHANG Y X, ZHANG Y N. Numerical study of a laser generated cavitation bubble based on FVM and CLSVOF method[J]. IOP Conference Series:Earth and Environmental Science, 240, 072021(2019).

[125] MÜLLER S, BACHMANN M, KRÖNINGER D et al. Comparison and validation of compressible flow simulations of laser-induced cavitation bubbles[J]. Computers & Fluids, 38, 1850-1862(2009).

[126] LI T, ZHANG A M, WANG S P et al. Bubble interactions and bursting behaviors near a free surface[J]. Physics of Fluids, 31, 042104(2019).

[127] TIAN Z L, LIU Y L, ZHANG A M et al. Analysis of breaking and re-closure of a bubble near a free surface based on the Eulerian finite element method[J]. Computers & Fluids, 170, 41-52(2018).

[128] [128] LIBERSKY L D, PETSCHEK A G. Smooth particle hydrodynamics with strength of materials[M]. Advances in the freeLagrange method including contributions on adaptive gridding the smooth particle hydrodynamics method. Springer, Berlin, Heidelberg, 1991: 248257.

[129] MAUREL B, COMBESCURE A. A SPH shell formulation for plasticity and fracture analysis in explicit dynamics[J]. International Journal for Numerical Methods in Engineering, 76, 949-971(2008).

[130] CALEYRON F, COMBESCURE A, FAUCHER V et al. Dynamic simulation of damage-fracture transition in smoothed particles hydrodynamics shells[J]. International Journal for Numerical Methods in Engineering, 90, 707-738(2012).

[131] MING F R, ZHANG A M, WANG S P. Smoothed particle hydrodynamics for the linear and nonlinear analyses of elastoplastic damage and fracture of shell[J]. International Journal of Applied Mechanics, 7, 1550032(2015).

[132] MING F R, ZHANG A M, XUE Y Z et al. Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions[J]. Ocean Engineering, 117, 359-382(2016).

[133] [133] CALEYRON F. Simulation numérique par la méthode SPH de fuites de fluide consécutives à la déchirure d''un réservoir sous impact[D]. Villeurbanne, France: INSA de Lyon, 2011.

[134] HUANG Y H, ZHANG Z G, PENG Y X et al. A three-dimensional beam formulation for large deformation and an accurate implementation of the free boundary[J]. International Journal of Non-Linear Mechanics, 134, 103736(2021).

[135] PENG Y X, ZHANG A M, MING F R. A thick shell model based on reproducing kernel particle method and its application in geometrically nonlinear analysis[J]. Computational Mechanics, 62, 309-321(2018).

[136] PENG Y X, ZHANG A M, LI S F et al. A beam formulation based on RKPM for the dynamic analysis of stiffened shell structures[J]. Computational Mechanics, 63, 35-48(2019).

[137] GUO K, SUN P N, CAO X Y et al. A 3-D SPH model for simulating water flooding of a damaged floating structure[J]. Journal of Hydrodynamics, Ser. B, 29, 831-844(2017).

[138] CHENG H, ZHANG A M, MING F R. Study on coupled dynamics of ship and flooding water based on experimental and SPH methods[J]. Physics of Fluids, 29, 107101(2017).

[139] MING F R, ZHANG A M, CHENG H et al. Numerical simulation of a damaged ship cabin flooding in transversal waves with smoothed particle hydrodynamics method[J]. Ocean Engineering, 165, 336-352(2018).

[140] CAO X Y, TAO L B, ZHANG A M et al. Smoothed particle hydrodynamics (SPH) model for coupled analysis of a damaged ship with internal sloshing in beam seas[J]. Physics of Fluids, 31, 032103(2019).

[141] CAO X Y, MING F R, ZHANG A M et al. Multi-phase SPH modelling of air effect on the dynamic flooding of a damaged cabin[J]. Computers & Fluids, 163, 7-19(2018).

[142] HUANG C, ZHAO L, NIU J P et al. Coupled particle and mesh method in an Euler frame for unsteady flows around the pitching airfoil[J]. Engineering Analysis with Boundary Elements, 138, 159-176(2022).

[143] MARRONE S, DI MASCIO A, LE TOUZÉ D. Coupling of smoothed particle hydrodynamics with finite volume method for free-surface flows[J]. Journal of Computational Physics, 310, 161-180(2016).

[144] ZHUANG Y, WAN D C. Parametric study of a new HOS-CFD coupling method[J]. Journal of Hydrodynamics, 33, 43-54(2021).