[2] 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).

[3] 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).

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

[5] ZHONG S Y, SUN P N, PENG Y X et al. An SPH study of slamming and splashing at the bow of SYSU vessel[J]. Ocean Engineering, 269, 113581(2023).

[6] 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).

[7] LYU H G, SUN P N, MIAO J M et al. 3D multi-resolution SPH modeling of the water entry dynamics of free-fall lifeboats[J]. Ocean Engineering, 257, 111648(2022).

[8] WANG S, SOARES C G. Review of ship slamming loads and responses[J]. Journal of Marine Science and Application, 16, 427-445(2017).

[9] HERMUNDSTAD O A, MOAN T. Numerical and experimental analysis of bow flare slamming on a Ro–Ro vessel in regular oblique waves[J]. Journal of Marine Science and Technology, 10, 105-122(2005).

[10] BARJASTEH M, ZERAATGAR H, JAVAHERIAN M J. An experimental study on water entry of asymmetric wedges[J]. Applied Ocean Research, 58, 292-304(2016).

[11] DERAKHSHANIAN M S, HAGHDEL M, ALISHAHI M M et al. Experimental and numerical investigation for a reliable simulation tool for oblique water entry problems[J]. Ocean Engineering, 160, 231-243(2018).

[12] XIE H, REN H L, DENG B L et al. Experimental drop test investigation into slamming loads on a truncated 3D bow flare model[J]. Ocean Engineering, 169, 567-585(2018).

[13] LI Y, NIELSEN P V. CFD and ventilation research[J]. Indoor Air, 21, 442-453(2011).

[14] ZHANG G Y, ZHAO W W, WAN D C. Numerical simulations of sloshing waves in vertically excited square tank by improved MPS method[J]. Journal of Hydrodynamics, 34, 76-84(2022).

[15] WEN X, ZHAO W W, WAN D C. Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method[J]. Journal of Hydrodynamics, 33, 938-949(2021).

[16] SUN H, FALTINSEN O M. Water entry of a bow-flare ship section with roll angle[J]. Journal of Marine Science and Technology, 14, 69-79(2009).

[17] YU P Y, LI H, ONG M C. Numerical study on the water entry of curved wedges[J]. Ships and Offshore Structures, 13, 885-898(2018).

[19] GHADIMI P, CHEKAB M A F, DASHTIMANESH A. Numerical simulation of water entry of different arbitrary bow sections[J]. Journal of Naval Architecture and Marine Engineering, 11, 117-129(2014).

[20] PAIK K J, CARRICA P M, LEE D et al. Strongly coupled fluid–structure interaction method for structural loads on surface ships[J]. Ocean Engineering, 36, 1346-1357(2009).

[22] [22] CHEN C C, HUANG C H, CHEN K C, et al. Slamming loads calculation f an oil tanker[C]ASME 2014 33rd International Conference on Ocean, Offshe Arctic Engineering. San Francisco: American Society of Mechanical Engineers, 2014: V002T08A044. doi: 10.1115OMAE201423715.

[24] DOMÍNGUEZ J M, CRESPO A J C, HALL M et al. SPH simulation of floating structures with moorings[J]. Coastal Engineering, 153, 103560(2019).

[25] KANEHIRA T, MUTSUDA H, DRAYCOTT S et al. Numerical re-creation of multi-directional waves in a circular basin using a particle based method[J]. Ocean Engineering, 209, 107446(2020).

[26] ZHA R S, PENG H, QIU W. An improved higher-order moving particle semi-implicit method for simulations of two-dimensional hydroelastic slamming[J]. Physics of Fluids, 33, 037104(2021).

[27] KAWAMURA K, HASHIMOTO H, MATSUDA A et al. SPH simulation of ship behaviour in severe water-shipping situations[J]. Ocean Engineering, 120, 220-229(2016).

[28] ROSELLI R A R, VERNENGO G, BRIZZOLARA S et al. SPH simulation of periodic wave breaking in the surf zone–a detailed fluid dynamic validation[J]. Ocean Engineering, 176, 20-30(2019).

[29] SHADLOO M S, OGER G, LE TOUZÉ D. Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges[J]. Computers & Fluids, 136, 11-34(2016).

[31] HE F, ZHANG H S, HUANG C et al. Numerical investigation of the solitary wave breaking over a slope by using the finite particle method[J]. Coastal Engineering, 156, 103617(2020).

[33] 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).

[34] 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).

[35] LYU H G, SUN P N, HUANG X T et al. A review of SPH techniques for hydrodynamic simulations of ocean energy devices[J]. Energies, 15, 502(2022).

[36] ANTUONO M, COLAGROSSI A, MARRONE S et al. Free-surface flows solved by means of SPH schemes with numerical diffusive terms[J]. Computer Physics Communications, 181, 532-549(2010).

[37] 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).

[38] LIU M B, SHAO J R, CHANG J Z. On the treatment of solid boundary in smoothed particle hydrodynamics[J]. Science China Technological Sciences, 55, 244-254(2012).

[39] DILTS G A. Moving least-squares particle hydrodynamics II: conservation and boundaries[J]. International Journal for Numerical Methods in Engineering, 48, 1503-1524(2000).

[42] 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).

[43] YANG C, HAO Z B, HE M et al. Hydrodynamic investigation on the submerged tunnel suspended from a fixed platform using SPH method[J]. Ocean Engineering, 277, 114357(2023).

[44] WEN H J, REN B, DONG P et al. Numerical analysis of wave-induced current within the inhomogeneous coral reef using a refined SPH model[J]. Coastal Engineering, 156, 103616(2020).

[45] REN B, WEN H J, DONG P et al. Improved SPH simulation of wave motions and turbulent flows through porous media[J]. Coastal Engineering, 107, 14-27(2016).

[46] KAZEMI E, LUO M. A comparative study on the accuracy and conservation properties of the SPH method for fluid flow interaction with porous media[J]. Advances in Water Resources, 165, 104220(2022).

[47] 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).

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

[49] SHAO S D, LO E Y M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface[J]. Advances in Water Resources, 26, 787-800(2003).

[50] [50] LIU G R, LIU M B. Smoothed particle hydrodynamics: a meshfree particle method[M]. Singape: Wld Scientific, 2003.

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

[52] LYU H G, SUN P N, HUANG X T et al. SPHydro: promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineering[J]. Physics of Fluids, 35, 017116(2023).

[53] [53] CRESPO A J C, GÓMEZGESTEIRA M, DALRYMPLE R A. Boundary conditions generated by dynamic particles in SPH methods[J]. Computers, Materials & Continua, 2007, 5(3): 173184. doi: 10.3970cmc.2007.005.173.

[54] ZHANG A M, LI S M, CUI P et al. A unified theory for bubble dynamics[J]. Physics of Fluids, 35, 033323(2023).

[55] JALALISENDI M, OSMA S J, PORFIRI M. Three-dimensional water entry of a solid body: a particle image velocimetry study[J]. Journal of Fluids and Structures, 59, 85-102(2015).

[56] 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).

[57] 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).

[58] [58] GUILCHER P M, DUCZET G, ALESSRINI B, et al. Water wave propagation using SPH models[C]Proceedings 2nd International SPHERIC Wkshop. Madrid: [s.n.], 2007: 119−122.

[59] OMIDVAR P, NOROUZI H, ZARGHAMI A. Smoothed particle hydrodynamics for water wave propagation in a channel[J]. International Journal of Modern Physics C, 26, 1550085(2015).

[60] 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).

[62] MINTU S, MOLYNEUX D, COLBOURNE B. A theoretical model for ship-wave impact generated sea spray[J]. Journal of Offshore Mechanics and Arctic Engineering, 143, 041201(2021).

[63] [63] CLINE H E, LENSEN W E. System method f the display of surface structures contained within the interi region of a solid body: US, 4710876A[P]. 19871201.