[2] [2] COLE R H.Underwater explosion$$M$$.New Jersey:Princeton University Press,1948.

[3] [3] ANH Tu Nguyen.The application of CEL technique to simulate the behavior of an underwater explosion bubble in the vicinity of a rigid wall$$J$$.Applied Mechanics and Materials,2020,4796:126-139.

[4] [4] CHEN G Q,ZHANG A M,HUANG X.On the interaction between bubbles and the free surface with high density ratio 3D lattice Boltzmann method$$J$$.Theoretical and Applied Mechanics Letters,2018,8(4):252-256.

[5] [5] JAYAPRAKASH A,SINGH S,CHAHINE G.Experimental and numerical investigation of single bubble dynamics in a two-phase bubbly medium$$J$$.Journal of Fluids Engineering,2011,133(12):121305.

[7] [7] HUNG C F,HWANGFU J J.Experimental study of the behavior of mini-charge underwater explosion bubbles near different boundaries$$J$$.Journal of Fluid Mechanics,2010,651：55-80.

[8] [8] BETHE H A.On the theory of shock waves for an arbitrary equation of state［C］∥JOHNSON J N,CHéRET R.Classic Papers in Shock Compression Science.High-Pressure Shock Compression of Condensed Matter.New York,NY：Springer,1998：421-495.

[12] [12] ZHANG A M,WANG S P,HUANG C,et al.Influences of initial and boundary conditions on underwater explosion bubble dynamics$$J$$.European Journal of Mechanics-B/ Fluids,2013,42:69-91.

[13] [13] GEERS T L.Doubly asymptotic approximations for transient motions of submerged structures$$J$$.The Journal of the Acoustical Society of America,1987,64:1500-1508.

[16] [16] HAN R,WANG S P,YAO X L.Dynamics of an air bubble induced by an adjacent oscillating bubble$$J$$.Engineering Analysis with Boundary Elements,2016,62:65-77.

[17] [17] BESANT W H.Hydrostatics and hydrodynamics$$M$$.London：Cambridge University Press,1859.

[18] [18] RAYLEIGH J W.On the pressure developed in a liquid during the collapse of a spherical cavity$$J$$.Philos Mag,1917,34:94-98.

[19] [19] GEERS T L,HUNTER K S.An integrated wave-effects model for an underwater explosion bubble$$J$$.The Journal of the Acoustical Society of America,2002,111(4):1584-1601.

[20] [20] NOLTINGK B E,NEPPIRAS E A.Cavitation produced by ultrasonics$$J$$.Proc Phys Soc.London,1950,63B:674-685.

[21] [21] GILMORE F R.The growth and collapse of a spherical bubble in a viscous compressible liquid$$J$$.Hydro Lab Calif inst Tech Report,1952,26(4)：62-83.

[22] [22] HICKS A N.Explosion induced hull whipping$$M$$.Advances in marine structures,Elsevier Applied Science Publishers,1986:390-410.

[23] [23] VERNON T A.Whipping response of ship hulls form underwater explosion bubble loading$$R$$.AD-A178096,1986.

[25] [25] KLASEBOERE,KHOO B C.A modified Rayleigh-Plesset model for a non-spherically symmetric oscillating bubble with applications to boundary integral methods$$J$$.Engineering Analysis with Boundary Elements,2006,30(1):59-71.

[26] [26] LIU Y L,ZHANG A M,TIAN Z L.Approximation of underwater explosion bubble by singularities based on BEM$$J$$.Ocean Engineering,2014,75(1):46-52.

[27] [27] HARKIN A,KAPER T J,NADIM A.Coupled pulsation and translation of two gas bubbles in a liquid$$J$$.Journal of Fluid Mechanics,2001,445:377-411.

[28] [28] KELLER J B,KOLODNER I I.Damping of underwater explosion bubble oscillations$$J$$.Journal of Applied Physics,1956,27(10)：1152-1161.

[29] [29] PROSPERETTI A,LEZZI A.Bubble dynamics in a compressible liquid.Part 1:first-order theory$$J$$.Journal of Fluid Mechanics,1986,168:457-478.

[30] [30] LEZZI A,PROSPERETTI A.Bubble dynamics in a compressible liquid.Part 2:second-order theory$$J$$.Journal of Fluid Mechanics,1987,185:289-321

[31] [31] WANG Q X,BLAKE J R.Non-spherical bubble dynamics in a compressible liquid.Part 1:travelling acoustic wave$$J$$.Journal of Fluid Mechanics,2010,659:191-224.

[32] [32] WANG Q X,BLAKE J R.Non-spherical bubble dynamics in a compressible liquid.Part 2:acoustic standing wave$$J$$.Journal of Fluid Mechanics,2011,679:559-581.

[33] [33] WANG Q X.Non-spherical bubble dynamics of underwater explosions in a compressible fluid［J］.Physics of Fluids(1994-present),2013,25(7):072104.

[36] [36] BRETT J M,YIANNAKOPOULOS G,VAN Der SCHAAF P J.Time-resolved measurement of the deformation of submerged cylinders subjected to loading from a nearby explosion$$J$$.International Journal of Impact Engineering,2000,24(9):875-890.

[38] [38] O′DANIEL J L,HARRIS G,ILAMNI R,et al.Underwater explosion bubble jetting effects on infrastructure$$R$$.DTIC Document,2011.

[39] [39] ZHANG A M,CUI P,CUI J,et al.Experimental study on bubble dynamics subject to buoyancy$$J$$.Journal of Fluid Mechanics,2015,776:137-160.

[40] [40] KLASEBOER E,HUNG K C,WANG C,et al.Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure$$J$$.Journal of Fluid Mechanics,2005,537:387-413.

[44] [44] LAUTERBORN W,BOLLE H.Experimental investigations of cavitation-bubble collapse in the neighborhood of a solid boundary$$J$$.Journal of Fluid Mechanics,1975,72(2):391-399.

[45] [45] GIBSON D C.Cavitaion adjacent to plane boundaries$$C$$∥Proc 3rd Conf Hydraulic Fluid Mech.Syndey,P R,Austr Inst Eng.,1968:210-214.

[46] [46] MITCHELL T M,HAMMITT F G.Asymmetric cavitation bubble collapse$$J$$.J Fluids Engng.Trans ASME,1973,195:29-37.

[47] [47] PHILIPP A,LAUTERBORN W.Cavitation erosion by single laser-produced bubbles$$J$$.Journal of Fluid Mechanics,1998,361:75-116.

[48] [48] LI Shuai,ZHANG A-Man,HAN Rui,et al.Experimental and numerical study of two underwater explosion bubbles:Coalescence,fragmentation and shock wave emission$$J$$.Ocean Engineering,2019,190,106414.

[49] [49] TIPTON R E,STEINBERG D J,TOMITA Y.Bubble explosion and collapse near a rigid wall$$J$$.JSME Intl J Series II,1992,35:67-75.

[50] [50] CHAHINE GL.Interaction between an oscillating bubble and a free surface$$J$$.Trans ASME,Journal of Fluids Engineering,1977,99(77):709-716.

[51] [51] DADVAND A,DAWOODIAN M,KHOO B C,et al.Spark-generated bubble collapse near or inside a circular aperture and the ensuing vortex ring and droplet formation$$J$$.Acta Mechanica Sinica,2013,29(5):657-666.

[55] [55] ZHANG S,WANG S,ZHANG A.Experimental study on the interaction between bubble and free surface using a high-voltage spark generator$$J$$.Physics of Fluids,2016,28(3):032109.

[57] [57] BLAKE J,TAIB B,DOHERTY G.Transient cavities near boundaries.Part 1.Rigid boundary$$J$$.Journal of Fluid Mechanics,1986,170:479-497.

[58] [58] ZHANG A M,SUN P N,MING F R.An SPH modeling of bubble rising and coalescing in three dimensions$$J$$.Computer Methods in Applied Mechanics and Engineering,2015,294：189-209.

[59] [59] AKIHIRO Y,HIROYUKI T.Numerical analysis of temperature fields inside non-spherical bubbles in the final stage of collapse$$Z$$.CAV2001：sessionB6.003.

[60] [60] LIU L T,YAO X L,ZHANG A M,et al.Research on the estimate formulas for underwater explosion bubble jet parameters$$J$$.Ocean Engineering,2018,164:563-576.

[62] [62] HARRIS P J.A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid$$J$$.International Journal for Numerical Methods in Engineering,1992,33(9):1813-1822.

[63] [63] WANG C,KHOO B C,YEO K S.Elastic mesh technique for 3D BIM simulation with an application to underwater explosion bubble dynamics$$J$$.Computers & Fluids,2003,32(9):1195-1212.

[65] [65] ZHANG A M,CUI P,CUI J,et al.Experimental study on bubble dynamics subject to buoyancy$$J$$.Journal of Fluid Mechanics,2015,776:137-160.

[66] [66] HSU Ching Yu,LIANG Cho Chung,NGUYEN Anh Tu,et al.A numerical study on the underwater explosion bubble pulsation and the collapse process$$J$$.Ocean Engineering,2014,81:29-38.

[67] [67] TIAN Zhao-li,LIU Yun-long,ZHANG A-man,et al.Jet development and impact load of underwater explosion bubble on solid wall$$J$$.Applied Ocean Research,2020,95(C):102013-102013.

[68] [68] LIU Yun-long,ZHANG A-man,TIAO Zhao-li,et al.Investigation of free-field underwater explosion with Eulerian finite element method$$J$$.Ocean Engineering,2018,166:182-190.

[70] [70] BEST J P.The formation of toroidal bubbles upon the collapse of transient cavities$$J$$.Journal of Fluid Mechanics,1993,251：79-107.

[71] [71] WANG Q X,YEO K S,KHOO B C,et al.Nonlinear interaction between gas bubble and free surface$$J$$.Computers & Fluids,1996,25(7):607-628.

[72] [72] LI S,LI Y B,ZHANG A M.Numerical analysis of the bubble jet impact on a rigid wall$$J$$.Applied Ocean Research,2015,50:227-236.

[75] [75] PHAN Thanh Hoang,NGUYEN Van Tu,PARK Warn Gyu.Numerical study on strong nonlinear interactions between spark-generated underwater explosion bubbles and a free surface$$J$$.International Journal of Heat and Mass Transfer,2020,163:120506-.

[76] [76] RUNGSIYAPHORNRAT S,KLASEBOER E,KHOO B,et al.The merging of two gaseous bubbles with an application to underwater explosions$$J$$.Computers & Fluids,2003,32(8):1049-1074.

[78] [78] BREMOND N,ARORA M,DAMMER S M,et al.Interaction of cavitation bubbles on a wall$$J$$.Physics of Fluids,2006,18(12):121505.