[1] JOHANSEN J P, CASTRO A M, CARRICA P M. Full-scale two-phase flow measurements on Athena research vessel[J]. International Journal of Multiphase Flow, 36, 720-737(2010).

[3] BODAGHKHANI A, DOWDELL J R, COLBOURNE B et al. Measurement of spray-cloud characteristics with bubble image velocimetry for braking wave impact[J]. Cold Regions Science and Technology, 145, 52-64(2018).

[5] DEIKE L, MELVILLE W K, POPINET S. Air entrainment and bubble statistics in breaking waves[J]. Journal of Fluid Mechanics, 801, 91-129(2016).

[7] HU Z Z, MAI T, GREAVES D et al. Investigations of offshore breaking wave impacts on a large offshore structure[J]. Journal of Fluids and Structures, 75, 99-116(2017).

[9] MORI N, KAKUNO S. Aeration and bubble measurements of coastal breaking waves[J]. Fluid Dynamics Research, 40, 616-626(2008).

[10] KANNAN Y S, KARRI B, SAHU K C. Letter: entrapment and interaction of an air bubble with an oscillating cavitation bubble[J]. Physics of Fluids, 30, 041701(2018).

[11] LI S, ZHANG A M, HAN R et al. Experimental and numerical study of two underwater explosion bubbles: coalescence, fragmentation and shock wave emission[J]. Ocean Engineering, 190, 106414(2019).

[12] DEANE G B, STOKES M D. Scale dependence of bubble creation mechanisms in breaking waves[J]. Nature, 418, 839-844(2002).

[13] KIMMOUN O, BRANGER H. A particle image velocimetry investigation on laboratory surf-zone breaking waves over a sloping beach[J]. Journal of Fluid Mechanics, 558, 353-397(2007).

[14] WATANABE Y, SAEKI H. Velocity field after wave breaking[J]. International Journal for Numerical Methods in Fluids, 39, 607-637(2002).

[15] SHI F Y, KIRBY J T, MA G F. Modeling quiescent phase transport of air bubbles induced by breaking waves[J]. Ocean Modelling, 35, 105-117(2010).

[16] DERAKHTI M, KIRBY J T. Bubble entrainment and liquid-bubble interaction under unsteady breaking waves[J]. Journal of Fluid Mechanics, 761, 464-506(2014).

[17] LUBIN P, GLOCKNER S. Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments[J]. Journal of Fluid Mechanics, 767, 364-393(2015).

[18] WANG Z Y, YANG J M, STERN F. High-fidelity simulations of bubble, droplet and spray formation in breaking waves[J]. Journal of Fluid Mechanics, 792, 307-327(2016).

[19] CHAN W H R, MIRJALILI S, JAIN S S et al. Birth of microbubbles in turbulent breaking waves[J]. Physical Review Fluids, 4, 100508(2019).

[20] KIGER K T, DUNCAN J H. Air-entrainment mechanisms in plunging jets and breaking waves[J]. Annual Review of Fluid Mechanics, 44, 563-596(2012).

[22] 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).

[23] CASTILLO-OROZCO E, DAVANLOU A, CHOUDHURY P K et al. Droplet impact on deep liquid pools: Rayleigh jet to formation of secondary droplets[J]. Physical Review E, 92, 053022(2015).

[24] GRENIER N, LE TOUZÉ D, COLAGROSSI A. Viscous bubbly flows simulation with an interface SPH model[J]. Ocean Engineering, 69, 88-102(2013).

[26] LIU J R, ZHU C Y, FU T T et al. Systematic study on the coalescence and breakup behaviors of multiple parallel bubbles rising in power-law fluid[J]. Industrial & Engineering Chemistry Research, 53, 4850-4860(2014).

[27] RAMÍREZ-MUñOZ J, GAMA-GOICOCHEA A, SALINAS-RODRíGUEZ E. Drag force on interacting spherical bubbles rising in-line at large Reynolds number[J]. International Journal of Multiphase Flow, 37, 983-986(2011).

[29] LEGENDRE D, MAGNAUDET J, MOUGIN G. Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid[J]. Journal of Fluid Mechanics, 497, 133-166(2003).

[30] PRINCE M J, BLANCH H W. Bubble coalescence and break-up in air-sparged bubble columns[J]. AIChE Journal, 36, 1485-1499(1990).

[31] WU M M, CUBAUD T, HO C. Scaling law in liquid drop coalescence driven by surface tension[J]. Physics of Fluids, 16, L51-L54(2004).

[33] BAHREINI M, DERAKHSHANDEH J F, RAMIAR A et al. Numerical study on multiple bubbles condensation in subcooled boiling flow based on CLSVOF method[J]. International Journal of Thermal Sciences, 170, 107121(2021).

[34] WEN X, ZHAO W W, WAN D C. A multiphase MPS method for bubbly flows with complex interfaces[J]. Ocean Engineering, 238, 109743(2021).

[35] ZHANG G Y, ZHAO W W, WAN D C. Partitioned MPS-FEM method for free-surface flows interacting with deformable structures[J]. Applied Ocean Research, 114, 102775(2021).

[36] CHEN X, WAN D C. Numerical simulation of three-dimensional violent free surface flows by GPU-based MPS method[J]. International Journal of Computational Methods, 16, 1843012(2019).

[37] WEN X, WAN D C. Numerical simulation of Rayleigh–Taylor instability by multiphase MPS method[J]. International Journal of Computational Methods, 16, 1846005(2019).

[39] ZHANG A M, NI B Y. Three-dimensional boundary integral simulations of motion and deformation of bubbles with viscous effects[J]. Computers & Fluids, 92, 22-33(2014).

[42] PELTONEN P, KANNINEN P, LAURILA E et al. Scaling effects on the free surface backward facing step flow[J]. Physics of Fluids, 33, 042106(2021).

[43] CHANSON H. Current knowledge in hydraulic jumps and related phenomena. A survey of experimental results[J]. European Journal of Mechanics-B/Fluids, 28, 191-210(2019).

[44] THORODDSEN S T, ETOH T G, TAKEHARA K. High-speed imaging of drops and bubbles[J]. Annual Review of Fluid Mechanics, 40, 257-285(2008).

[45] ZHANG X S, WANG J H, WAN D C. Euler–Lagrange study of bubble breakup and coalescence in a turbulent boundary layer for bubble drag reduction[J]. Physics of Fluids, 33, 037105(2021).

[46] ZHANG X S, WANG J H, WAN D C. Euler–Lagrange study of bubble drag reduction in turbulent channel flow and boundary layer flow[J]. Physics of Fluids, 32, 027101(2020).

[47] MA D, LIU M Y, ZU Y G et al. Two-dimensional volume of fluid simulation studies on single bubble formation and dynamics in bubble columns[J]. Chemical Engineering Science, 72, 61-77(2012).

[48] GOURICH B, VIAL C, ESSADKI A H et al. Identification of flow regimes and transition points in a bubble column through analysis of differential pressure signal–influence of the coalescence behavior of the liquid phase[J]. Chemical Engineering and Processing: Process Intensification, 45, 214-223(2016).

[49] KOUZBOUR S, GOURICH B, STIRIBA Y et al. Experimental analysis of the effects of liquid phase surface tension on the hydrodynamics and mass transfer in a square bubble column[J]. International Journal of Heat and Mass Transfer, 170, 121009(2021).

[50] CHAUMAT H, BILLET A M, DELMAS H. Hydrodynamics and mass transfer in bubble column: Influence of liquid phase surface tension[J]. Chemical Engineering Science, 62, 7378-7390(2007).

[51] SONG J H, JOHANSEN K, PRENTICE P. An analysis of the acoustic cavitation noise spectrum: the role of periodic shock waves[J]. The Journal of the Acoustical Society of America, 140, 2494-2505(2016).

[52] XU W L, LI J B, LUO J et al. Effect of a single air bubble on the collapse direction and collapse noise of a cavitation bubble[J]. Experimental Thermal and Fluid Science, 120, 110218(2021).

[53] ZHENG C X, JAMES D L. Harmonic fluids[J]. ACM Transactions on Graphics, 28, 37(2009).

[54] FUSTER D, CONOIR J M, COLONIUS T. Effect of direct bubble-bubble interactions on linear-wave propagation in bubbly liquids[J]. Physical Review E, 90, 063010(2014).

[55] COSTA MARTINS J, SELEGHIM P JR. Propagation and attenuation of pressure waves in dispersed two-phase flows[J]. Journal of Fluids Engineering, 139, 011304(2017).

[56] ZHANG Y N, GUO Z Y, GAO Y H et al. Acoustic wave propagation in bubbly flow with gas, vapor or their mixtures[J]. Ultrasonics Sonochemistry, 40, 40-45(2018).

[57] XU X X, GONG J. A united model for predicting pressure wave speeds in oil and gas two-phase pipeflows[J]. Journal of Petroleum Science and Engineering, 60, 150-160(2008).

[58] COMMANDER K W, PROSPERETTI A. Linear pressure waves in bubbly liquids: comparison between theory and experiments[J]. The Journal of the Acoustical Society of America, 85, 732-746(1989).

[59] LOUISNARD O. A simple model of ultrasound propagation in a cavitating liquid. Part I: Theory, nonlinear attenuation and traveling wave generation[J]. Ultrasonics Sonochemistry, 19, 56-65(2012).

[60] FUSTER D, MONTEL F. Mass transfer effects on linear wave propagation in diluted bubbly liquids[J]. Journal of Fluid Mechanics, 779, 598-621(2015).

[61] DONG R R, KATZ J, HUANG T T. On the structure of bow waves on a ship model[J]. Journal of Fluid Mechanics, 346, 77-115(1997).

[62] ROTH G I, MASCENIK D T, KATZ J. Measurements of the flow structure and turbulence within a ship bow wave[J]. Physics of Fluids, 11, 3512-3523(1999).

[63] OLIVIERI A, PISTANI F, WILSON R et al. Scars and vortices induced by ship bow and shoulder wave breaking[J]. Journal of Fluids Engineering, 129, 1445-1459(2007).

[64] WILSON R V, CARRICA P M, STERN F. URANS simulations for a high-speed transom stern ship with breaking waves[J]. International Journal of Computational Fluid Dynamics, 20, 105-125(2006).

[65] [65] WANG J H, WAN D C. Breaking wave simulations of highspeed surface combatant using openfoam[C]Proceedings of the 8th International Conference on Computational Methods. Guilin: [s. n. ], 2017.

[66] CARRICA P M, HUANG J, NOACK R et al. Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant[J]. Computers & Fluids, 39, 1095-1111(2010).

[67] BROGLIA R, DURANTE D. Accurate prediction of complex free surface flow around a high speed craft using a single-phase level set method[J]. Computational Mechanics, 62, 421-437(2018).

[68] WANG J H, REN Z, WAN D C. Study of a container ship with breaking waves at high Froude number using URANS and DDES methods[J]. Journal of Ship Research, 64, 346-356(2020).

[70] BODAGHKHANI A, DEHGHANI S R, MUZYCHKA Y S et al. Understanding spray cloud formation by wave impact on marine objects[J]. Cold Regions Science and Technology, 129, 114-136(2016).

[71] BODAGHKHANI A, COLBOURNE B, MUZYCHKA Y S. Prediction of droplet size and velocity distribution for spray formation due to wave-body interactions[J]. Ocean Engineering, 155, 106-114(2018).

[72] MA J S, OBERAI A A, HYMAN M C et al. Two-fluid modeling of bubbly flows around surface ships using a phenomenological subgrid air entrainment model[J]. Computers & Fluids, 52, 50-57(2011).

[73] CASTRO A M, CARRICA P M. Eulerian polydispersed modeling of bubbly flows around ships with application to Athena R/V[J]. International Shipbuilding Progress, 60, 403-433(2013).

[77] PELTZER R D, GRIFFIN O M, BARGER W R et al. High‐resolution measurement of surface‐active film redistribution in ship wakes[J]. Journal of Geophysical Research: Oceans, 97, 5231-5252(1992).

[78] SOLOVIEV A, MAINGOT C, AGOR M et al. 3D sonar measurements in wakes of ships of opportunity[J]. Journal of Atmospheric and Oceanic Technology, 29, 880-886(2012).

[79] [79] KOUZOUBOV A, WOOD S, ELLEM R. Acoustic imaging of surface ship wakes[C]Proceedings of the Internoise 2014 43rd International Congress on Noise Control Engineering: Improving the Wld Through Noise Control. Melbourne, Australia: [s. n. ], 2014: 36853694.

[80] SHEN L, ZHANG C, YUE D K P. Free-surface turbulent wake behind towed ship models: experimental measurements, stability analyses and direct numerical simulations[J]. Journal of Fluid Mechanics, 469, 89-120(2002).

[81] [81] FU T C, FULLERTON A M, RATCLIFFE T, et al. A detailed study of transom breaking waves[R]. [S. l. ]: Naval Surface Warfare Center Carderock Division, 2009.

[82] [82] FU T C, FULLERTON A M, DRAZEN D, et al. A detailed study of transom breaking waves. Part II: NSWCCD50TR2010003[R]. [S. l. ]: Naval Surface Warfare Center Carderock Division, 2010.

[84] CASTRO A M, LI J J, CARRICA P M. A mechanistic model of bubble entrainment in turbulent free surface flows[J]. International Journal of Multiphase Flow, 86, 35-55(2016).

[85] HENDRICKSON K, WEYMOUTH G D, YU X M et al. Wake behind a three-dimensional dry transom stern. Part Ⅰ. Flow structure and large-scale air entrainment[J]. Journal of Fluid Mechanics, 875, 854-883(2019).

[86] HENDRICKSON K, YUE D K P. Wake behind a three-dimensional dry transom stern. Part Ⅱ. Analysis and modelling of incompressible highly variable density turbulence[J]. Journal of Fluid Mechanics, 875, 884-913(2019).

[87] STANSBERG C T, PAKOZDI C, ABRAHAMSEN B et al. Hydrodynamic model tests and numerical modelling: exploring the challenging physics in storm waves[J]. Marintek Review, 1, 1-12(2014).

[88] SUN S Y, WU G X, XU G. Breaking wave impact on a floating body with air bubble effect[J]. Journal of Fluids and Structures, 82, 16-34(2018).

[89] YAO X L, HUANG X H, SHI Z Y et al. Reducing bubble generation and sweepdown effect on a research vessel with a moonpool[J]. Proceedings of the Institution of Mechanical Engineers. Part M: Journal of Engineering for the Maritime Environment, 235, 303-310(2021).

[90] POPINET S. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries[J]. Journal of Computational Physics, 190, 572-600(2003).

[91] BORTHWICK A, LEON S C, JÓZSA J. Adaptive quadtree model of shallow-flow hydrodynamics[J]. Journal of Hydraulic Research, 39, 413-424(2001).

[92] POPINET S. An accurate adaptive solver for surface-tension-driven interfacial flows[J]. Journal of Computational Physics, 228, 5838-5866(2009).

[93] THORAVAL M J, TAKEHARA K, ETOH T G et al. Von Kármán vortex street within an impacting drop[J]. Physical Review Letters, 108, 264506(2012).

[94] [94] Center AF flash user''s guide[Z]. Flash Center f Computational Science University of Chicago, 2021.

[95] FUSTER D, BAGUÉ A, BOECK T et al. Simulation of primary atomization with an octree adaptive mesh refinement and VOF method[J]. International Journal of Multiphase Flow, 35, 550-565(2009).

[96] SUI Y, SPELT P D M. Validation and modification of asymptotic analysis of slow and rapid droplet spreading by numerical simulation[J]. Journal of Fluid Mechanics, 715, 283-313(2013).

[97] BERGER M J, OLIGER J. Adaptive mesh refinement for hyperbolic partial differential equations[J]. Journal of Computational Physics, 53, 484-512(1984).

[98] TRYGGVASON G, BUNNER B, ESMAEELI A et al. A front-tracking method for the computations of multiphase flow[J]. Journal of Computational Physics, 169, 708-759(2001).

[99] OSHER S, SETHIAN J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics, 79, 12-49(1988).

[100] SUSSMAN M, SMEREKA P, OSHER S. A Level set approach for computing solutions to incompressible two-phase flow[J]. Journal of Computational Physics, 114, 146-159(1994).

[101] HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 39, 201-225(1981).

[102] [102] JAMTVEIT B, MEAKIN P. Growth, dissolution, pattern fmation in geosystems[M]. Boston: Kluwer Academic Publishers, 1999.

[103] UNVERDI S O, TRYGGVASON G. A front-tracking method for viscous, incompressible, multi-fluid flows[J]. Journal of Computational Physics, 100, 25-37(1992).

[104] LEUNG S, ZHAO H K. A grid based particle method for moving interface problems[J]. Journal of Computational Physics, 228, 2993-3024(2009).

[105] SETHIAN J A, SMEREKA P. Level set methods for fluid interfaces[J]. Annual Review of Fluid Mechanics, 35, 341-372(2003).

[106] SCARDOVELLI R, ZALESKI S. Direct numerical simulation of free-surface and interfacial flow[J]. Annual Review of Fluid Mechanics, 31, 567-603(1999).

[107] ANDERSON D M, MCFADDEN G B, WHEELER A A. Diffuse-interface methods in fluid mechanics[J]. Annual Review of Fluid Mechanics, 30, 139-165(1998).

[108] [108] YOUNGS D L. Timedependent multimaterial flow with large fluid disttion[M]MTON K W, BAINES M J. Numerical Methods f Fluid Dynamics. New Yk: Academic Press, 1982.

[109] XIAO F, HONMA Y, KONO T. A simple algebraic interface capturing scheme using hyperbolic tangent function[J]. International Journal for Numerical Methods in Fluids, 48, 1023-1040(2005).

[110] YOKOI K. Efficient implementation of THINC scheme: a simple and practical smoothed VOF algorithm[J]. Journal of Computational Physics, 226, 1985-2002(2007).

[111] ZHAO Y C, CHEN H C. A new coupled level set and volume-of-fluid method to capture free surface on an overset grid system[J]. International Journal of Multiphase Flow, 90, 144-155(2017).

[112] FUSTER D, ARRUFAT T, CRIALESI-ESPOSITO M et al. A momentum-conserving, consistent, volume-of-fluid method for incompressible flow on staggered grids[J]. Computers & Fluids, 104785(2021).

[113] GHODS S, HERRMANN M. A consistent rescaled momentum transport method for simulating large density ratio incompressible multiphase flows using Level set methods[J]. Physica Scripta, 2013, 014050(2013).

[114] RUDMAN M. A volume-tracking method for incompressible multifluid flows with large density variations[J]. International Journal for Numerical Methods in Fluids, 28, 357-378(1998).

[115] [115] BUSSMANN M, KOTHE D B, SICILIAN J M. Modeling high density ratio incompressible interfacial flows[C]Proceedings of ASME 2002 Joint U. S. European Fluids Engineering Division Conference. Montreal, Canada: ASME, 2002.

[116] VAUDOR G, MÉNARD T, ANISZEWSKI W et al. A consistent mass and momentum flux computation method for two phase flows. Application to atomization process[J]. Computers & Fluids, 152, 204-216(2017).

[117] XAVIER T, ZUZIO D, AVERSENG M et al. Toward direct numerical simulation of high speed droplet impact[J]. Meccanica, 55, 387-401(2020).

[118] ANISZEWSKI W, SAADE Y, ZALESKI S et al. Planar jet stripping of liquid coatings: numerical studies[J]. International Journal of Multiphase Flow, 132, 103399(2020).

[119] BRACKBILL J U, KOTHE D B, ZEMACH C. A continuum method for modeling surface tension[J]. Journal of Computational Physics, 100, 335-354(1992).

[121] SUSSMAN M, SMITH K M, HUSSAINI M Y et al. A sharp interface method for incompressible two-phase flows[J]. Journal of Computational Physics, 221, 469-505(2007).

[122] LIU X D, FEDKIW R P, KANG M. A boundary condition capturing method for Poisson's equation on irregular domains[J]. Journal of Computational Physics, 160, 151-178(2000).

[123] CUMMINS S J, FRANCOIS M M, KOTHE D B. Estimating curvature from volume fractions[J]. Computers & Structures, 83, 425-434(2005).

[124] PESKIN C S. Flow patterns around heart valves: a numerical method[J]. Journal of Computational Physics, 10, 252-271(1972).

[125] GOLDSTEIN D, HANDLER R, SIROVICH L. Modeling a no-slip flow boundary with an external force field[J]. Journal of Computational Physics, 105, 354-366(1993).

[126] SAIKI E M, BIRINGEN S. Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method[J]. Journal of Computational Physics, 123, 450-465(1996).

[127] [127] MOHDYUSOF J. Combined immersedboundaryBspline methods f simulations of flows in complex geometries[R]. [S. l. ]: Annual Research Briefs, Center f Turbulence Research, 1997: 317327.

[128] [128] MAJUMDAR S, IACCARINO G, DURBIN P. RANS solvers with adaptive structured boundary nonconfming grids[R]. Stanfd: Center f Turbulence Research, 2001.

[129] TSENG Y H, FERZIGER J H. A ghost-cell immersed boundary method for flow in complex geometry[J]. Journal of Computational Physics, 192, 593-623(2003).

[130] LIU C, HU C H. Block-based adaptive mesh refinement for fluid structure interactions in incompressible flows[J]. Computer Physics Communications, 232, 104-123(2018).

[131] ZHANG C, ZHANG W, LIN N S et al. A two-phase flow model coupling with volume of fluid and immersed boundary methods for free surface and moving structure problems[J]. Ocean Engineering, 74, 107-124(2013).

[132] ZHANG C, LIN N S, TANG Y H et al. A sharp interface immersed boundary/VOF model coupled with wave generating and absorbing options for wave-structure interaction[J]. Computers & Fluids, 89, 214-231(2014).

[133] YANG J M, STERN F. Sharp interface immersed-boundary/Level-set method for wave–body interactions[J]. Journal of Computational Physics, 228, 6590-6616(2009).

[134] LIU C, HU C H. An efficient immersed boundary treatment for complex moving object[J]. Journal of Computational Physics, 274, 654-680(2014).

[138] [138] LI J J. Contributions to modeling of bubble entrainment f ship hydrodynamics applications[D]. Iowa City: University of Iowa, 2015.

[139] BALDY S. A generation-dispersion model of ambient and transient bubbles in the close vicinity of breaking waves[J]. Journal of Geophysical Research:Oceans, 98, 18277-18293(1993).

[140] [140] CLIFT R, GRACE J R, WEBER M E. Bubbles, s particles[M]. San Diego: Academic Press, 1978.

[141] MA G F, SHI F Y, KIRBY J T. A polydisperse two-fluid model for surf zone bubble simulation[J]. Journal of Geophysical Research: Oceans, 116, C05010(2011).

[142] CARRICA P M, DREW D, BONETTO F et al. A polydisperse model for bubbly two-phase flow around a surface ship[J]. International Journal of Multiphase Flow, 25, 257-305(1999).

[143] RAPP R J, MELVILLE W K. Laboratory measurements of deep-water breaking waves[J]. Philosophical Transactions of the Royal Society A, 331, 735-800(1990).

[144] MA J S, OBERAI A A, DREW D A et al. A comprehensive sub-grid air entrainment model for RaNS modeling of free-surface bubbly flows[J]. The Journal of Computational Multiphase Flows, 3, 41-56(2011).

[145] MORAGA F J, CARRICA P M, DREW D A et al. A sub-grid air entrainment model for breaking bow waves and naval surface ships[J]. Computers & Fluids, 37, 281-298(2008).

[146] [146] TAVAKOLINEJAD M. Air bubble entrainment by breaking bow waves simulated by a 2D+ T technique[D]. Maryl: University of Maryl, College Park, 2010.

[147] LI J J, MARTIN J E, CARRICA P M. Large-scale simulation of ship bubbly wake during a maneuver in stratified flow[J]. Ocean Engineering, 173, 643-658(2019).

[148] HERRMANN M. A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure[J]. Journal of Computational Physics, 229, 745-759(2010).

[149] HSIAO C T, MA J S, CHAHINE G L. Multiscale tow-phase flow modeling of sheet and cloud cavitation[J]. International Journal of Multiphase Flow, 90, 102-117(2017).

[150] [150] PATKAR S, AANJANEYA M, KARPMAN D, et al. A hybrid LagrangianEulerian fmulation f bubble generation dynamics[C]Proceedings of the 12th ACM SIGGRAPHEurographics Symposium on Computer Animation. Anaheim, Califnia: ACM, 2013: 105114.

[151] [151] HSIAO C T, WU X G, MA J S, et al. Numerical experimental study of bubble entrainment due to a hizontal plunging jet[J] International Shipbuilding Progress, 2013, 60(1234): 435469.

[152] MA J S, HSIAO C T, CHAHINE G L. A physics based multiscale modeling of cavitating flows[J]. Computers & Fluids, 145, 68-84(2017).

[153] [153] JAIN D, KUIPERS J A M, DEEN N G. Numerical study of coalescence breakup in a bubble column using a hybrid volume of fluid discrete bubble model approach[J] Chemical Engineering Science, 2014, 119: 134146.

[154] LI L M, LI B K, LIU Z Q. Modeling of gas-steel-slag three-phase flow in ladle metallurgy. Part II. Multi-scale mathematical model[J]. ISIJ International, 57, 1980-1989(2017).

[155] TOMAR G, FUSTER D, ZALESKI S et al. Multiscale simulations of primary atomization[J]. Computers & Fluids, 39, 1864-1874(2010).

[156] LING Y, ZALESKI S, SCARDOVELLI R. Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model[J]. International Journal of Multiphase Flow, 76, 122-143(2015).

[157] ZUZIO D, ESTIVALÈZES J L, DIPIERRO B. An improved multiscale Eulerian-Lagrangian method for simulation of atomization process[J]. Computers & Fluids, 176, 285-301(2018).

[158] ZHANG X S, WANG J H, WAN D C. An improved multi-scale two phase method for bubbly flows[J]. International Journal of Multiphase Flow, 133, 103460(2020).

[159] YAN K, CHE D F. A coupled model for simulation of the gas-liquid two-phase flow with complex flow patterns[J]. International Journal of Multiphase Flow, 36, 333-348(2021).

[160] BUSCAGLIA G C, BOMBARDELLI F A, GARCÍA M H. Numerical modeling of large-scale bubble plumes accounting for mass transfer effects[J]. International Journal of Multiphase Flow, 28, 1763-1785(2002).

[161] XIANG M, CHEUNG S C P, TU J Y et al. A multi-fluid modelling approach for the air entrainment and internal bubbly flow region in hydraulic jumps[J]. Ocean Engineering, 91, 51-63(2014).

[162] CHANSON H. Convective transport of air bubbles in strong hydraulic jumps[J]. International Journal of Multiphase Flow, 36, 798-814(2010).

[163] LI J J, CASTRO A M, CARRICA P M. A pressure-velocity coupling approach for high void fraction free surface bubbly flows in overset curvilinear grids[J]. International Journal for Numerical Methods in Fluids, 79, 343-369(2015).

[164] LI J J, CARRICA P M. A population balance cavitation model[J]. International Journal of Multiphase Flow, 138, 103617(2021).

[165] LI J J, CARRICA P M. An approach to couple velocity/pressure/void fraction in two-phase flows with incompressible liquid and compressible bubbles[J]. International Journal of Multiphase Flow, 102, 77-94(2018).