Smoothed particle hydrodynamics (SPH): An overview and recent developments

Archives of Computational Methods in Engineering

Volumn 17, Issue 1, 2010, Pages 25-76

  Liu, M B ^a   Liu, G R ^b  

^a INSTITUTE OF MECHANICS   (China)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION SCHEME; GENERAL APPROACH; LAGRANGIAN FORMULATIONS; MESHFREE PARTICLE METHOD; NUMERICAL ASPECTS; NUMERICAL TECHNIQUES; SMOOTHED PARTICLE HYDRODYNAMICS; SMOOTHING KERNELS; SPH METHODS;

DIFFERENTIAL EQUATIONS; FLUID DYNAMICS; HYDRODYNAMICS; MOTION ESTIMATION; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

NUMBER THEORY;

EID: 77952876665     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-010-9040-7     Document Type: Article

References (399)

1. Chung TJ (2002) Computational fluid dynamics. Cambridge University Press, Cambridge.
2. Anderson JD (2002) Computational fluid dynamics: the basics with applications. McGraw Hill, New York.
3. Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth-Heinemann, Stonham.
4. Liu GR (2002) Meshfree methods: moving beyond the finite element method. CRC Press, Boca Raton.
5. Hirsch C (1988) Numerical computation of internal & external flows: fundamentals of numerical discretization. Wiley, New York.
6. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore.
7. Liu GR, Gu YT (2005) An Introduction to meshfree methods and their programming. Springer, Dordrecht, p 479.
8. Zhang SZ (1976) Detonation and its applications. Press of National Defense Industry, Beijing.
9. Zukas JA (1990) High velocity impact dynamics. Wiley, New York.
10. Hockney RW, Eastwood JW (1988) Computer simulation using particles. Institute of Physics Publishing, Bristol.
11. Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford University Press, Oxford.
12. Li S, Liu WK (2002) Meshfree and particle methods and their applications. Appl Mech Rev 55(1): 1-34.
13. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139(1-4): 3-47.
14. Idelsohn SR, Onate E (2006) To mesh or not to mesh? That is the question. Comput Methods Appl Mech Eng 195(37-40): 4681-4696.
15. Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79(3): 763-813.
16. Liu GR (2008) A generalized Gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods. Int J Comput Methods 5(2): 199-236.
17. Liu GR (2009) A G space theory and weakened weak (W2) form for a unified formulation of compatible and incompatible methods, part I: theory. Int J Numer Methods Eng. doi: 10. 1002/nme. 2719.
18. Liu GR (2009) A G space theory and weakened weak (W2) form for a unified formulation of compatible and incompatible methods, part II: applications to solid mechanics problems. Int J Numer Methods Eng. doi: 10. 1002/nme. 2720.
19. Liu GR (2009) On the G space theory. Int J Comput Methods 6(2): 257-289.
20. Liu GR, Nguyen-Thoi T, H. N-X, Lam KY (2008) A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems. Comput Struct 87: 14-26.
21. Liu GR, Zhang GY (2008) Upper bound solution to elasticity problems: a unique property of the linearly conforming point interpolation method (LC-PIM). Int J Numer Methods Eng 74: 1128-1161.
22. Liu GR, Nguyen-Thoi T, Lam KY (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses in solids. J Sound Vib 320: 1100-1130.
23. Zhang GY, Liu GR, Nguyen TT, Song CX, Han X, Zhong ZH, Li GY (2007) The upper bound property for solid mechanics of the linearly conforming radial point interpolation method (LC-RPIM). Int J Comput Methods 4(3): 521-541.
24. Liu GR, Zhang GY (2009) A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method. Int J Comput Methods 6(1): 147-179.
25. Liu GR, Zhang GY (2008) Edge-based Smoothed Point Interpolation Methods. Int J Comput Methods 5(4): 621-646.
26. Liu GY, Zhang GY (2009) A novel scheme of strain-constructed point interpolation method for static and dynamic mechanics problems. Int J Appl Mech 1(1): 233-258.
27. Liu GR, Xu X, Zhang GY, Nguyen-Thoi T (2009) A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh. Int J Numer Methods Eng 77: 1439-1467.
28. Liu GR, Xu X, Zhang GY, Gu YT (2009) An extended Galerkin weak form and a point interpolation method with continuous strain field and superconvergence using triangular mesh. Comput Mech 43: 651-673.
29. Nguyen-Thoi T, Liu GR, Lam KY, Zhang GY (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics problems using 4-node tetrahedral elements. Int J Numer Methods Eng 78: 324-353.
30. Liu GR, Nguyen-Thoi T, Lam KY (2008) A novel Alpha finite element method (FEM) for exact solution to mechanics problems using triangular and tetrahedral elements. Comput Methods Appl Mech Eng 197: 3883-3897.
31. Liu GR, Nguyen-Xuan H, Nguyen TT, Xu X (2009) A novel weak form and a superconvergent alpha finite element method for mechanics problems using triangular meshes. J Comput Phys 228(11): 3911-4302.
32. Liu GR, Zhang J, Lam KY (2008) A gradient smoothing method (GSM) with directional correction for solid mechanics problems. Comput Mech 41: 457-472.
33. Liu GR, Xu XG (2008) A gradient smoothing method (GSM) for fluid dynamics problems. Int J Numer Methods Fluids 58: 1101-1133.
34. Xu XG, Liu GR (2008) An adaptive gradient smoothing method (GSM) for fluid dynamics problems. Int J Numer Methods Fluids doi: 10. 1002/fld. 2032.
35. Xu XG, Liu GR, Lee KH (2009) Application of gradient smoothing method (GSM) for steady and unsteady incompressible flow problems using irregular triangles. Int J Numer Methods Fluids (submitted).
36. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82(12): 1013-1024.
37. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics-theory and application to non-spherical stars. Mon Not R Astron Soc 181: 375-389.
38. Liu MB, Liu GR, Lam KY (2003) Constructing smoothing functions in smoothed particle hydrodynamics with applications. J Comput Appl Math 155(2): 263-284.
39. Fulk DA, Quinn DW (1996) An analysis of 1-D smoothed particle hydrodynamics kernels. J Comput Phys 126(1): 165-180.
40. Frenkel D, Smit B (2002) Understanding molecular simulation: from algorithms to applications. Academic Press, New York.
41. Hoogerbrugge PJ, Koelman J (1992) Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys Lett 19: 155.
42. Groot RD (1997) Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. J Chem Phys 107(11): 4423.
43. Gingold RA, Monaghan JJ (1982) Kernel estimates as a basis for general particle method in hydrodynamics. J Comput Phys 46: 429-453.
44. Hu XY, Adams NA (2006) Angular-momentum conservative smoothed particle dynamics for incompressible viscous flows. Phys Fluids 18: 101702.
45. Swegle JW, Hicks DL, Attaway SW (1995) Smoothed particle hydrodynamics stability analysis. J Comput Phys 116(1): 123-134.
46. Morris JP (1996) Analysis of Smoothed Particle Hydrodynamics with Applications. Monash University.
47. Monaghan JJ (1982) Why particle methods work. SIAM J Sci Stat Comput 3(4): 422-433.
48. Monaghan JJ (1985) Particle methods for hydrodynamics. Comput Phys Rep 3: 71-124.
49. Monaghan JJ (1992) Smooth particle hydrodynamics. Annu Rev Astron Astrophys 30: 543-574.
50. Johnson GR (1996) Artificial viscosity effects for SPH impact computations. Int J Impact Eng 18(5): 477-488.
51. Johnson GR, Beissel SR (1996) Normalized smoothing functions for SPH impact computations. Int J Numer Methods Eng 39(16): 2725-2741.
52. Randles PW, Libersky LD (1996) Smoothed particle hydrodynamics: some recent improvements and applications. Comput Methods Appl Mech Eng 139(1): 375-408.
53. Chen JK, Beraun JE, Carney TC (1999) A corrective smoothed particle method for boundary value problems in heat conduction. Int J Numer Methods Eng 46: 231-252.
54. Chen JK, Beraun JE (2000) A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems. Comput Methods Appl Mech Eng 190: 225-239.
55. Liu MB, Liu GR, Lam KY (2003) A one-dimensional meshfree particle formulation for simulating shock waves. Shock Waves 13(3): 201-211.
56. Liu MB, Liu GR (2006) Restoring particle consistency in smoothed particle hydrodynamics. Appl Numer Math 56(1): 19-36.
57. Liu MB, Xie WP, Liu GR (2005) Modeling incompressible flows using a finite particle method. Appl Math Model 29(12): 1252-1270.
58. Batra RC, Zhang GM (2004) Analysis of adiabatic shear bands in elasto-thermo-viscoplastic materials by modified smoothed-particle hydrodynamics (MSPH) method. J Comput Phys 201(1): 172-190.
59. Fang JN, Owens RG, Tacher L, Parriaux A (2006) A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J Non-Newton Fluid 139(1-2): 68-84.
60. Fang JN, Parriaux A (2008) A regularized Lagrangian finite point method for the simulation of incompressible viscous flows. J Comput Phys 227(20): 8894-8908.
61. Fang JN, Parriaux A, Rentschler M, Ancey C (2009) Improved SPH methods for simulating free surface flows of viscous fluids. Appl Numer Math 59(2): 251-271.
62. Dyka CT, Ingel RP (1995) An approach for tension instability in smoothed particle hydrodynamics (SPH). Comput Struct 57(4): 573-580.
63. Dyka CT, Randles PW, Ingel RP (1997) Stress points for tension instability in SPH. Int J Numer Methods Eng 40(13): 2325-2341.
64. Randles PW, Libersky LD, (2000) Normalized SPH with stress points. Int J Numer Methods Eng 48(10): 1445-1462.
65. Vignjevic R, Campbell J, Libersky L (2000) A treatment of zero-energy modes in the smoothed particle hydrodynamics method. Comput Methods Appl Mech Eng 184(1): 67-85.
66. Dilts GA (1999) Moving-Least-Squares-particle hydrodynamics. I: Consistency and stability. Int J Numer Methods Eng 44: 1115-1155.
67. Dilts GA (2000) Moving least square particle hydrodynamics ii: conservation and boundaries. Int J Numer Methods Eng 48: 1503-1524.
68. Bonet J, Kulasegaram S (2000) Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. Int J Numer Methods Eng 47(6): 1189-1214.
69. Chen JS, Pan C, Wu CT, Liu WK (1996) Reproducing kernel particle methods for large deformation analysis of nonlinear structures. Comput Methods Appl Mech Eng 139: 195-227.
70. Liu WK, Chen Y, Jun S, Chen JS, Belytschko T, Pan C, Uras RA, Chang CT (1996) Overview and applications of the reproducing kernel particle methods. Arch Comput Methods Eng 3(1): 3-80.
71. Rabczuk T, Belvtschko T, Xiao SP (2004) Stable particle methods based on Lagrangian kernels. Comput Methods Appl Mech Eng 193(12): 1035-1063.
72. Belytschko T, Krongauz Y, Dolbow J, Gerlach C (1998) On the completeness of the meshfree particle methods. Int J Numer Methods Eng 43(5): 785-819.
73. Zhang GM, Batra RC (2004) Modified smoothed particle hydrodynamics method and its application to transient problems. Comput Mech 34(2): 137-146.
74. Belytschko T, Guo Y, Liu WK, Xiao SP (2000) A unified stability analysis of meshless particle methods. Int J Numer Methods Eng 48: 1359-1400.
75. Fulk DA (1994) A numerical analysis of smoothed particle hydrodynamics. Air Force Institute of Technology.
76. Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68(8): 1703-1759.
77. Hernquist L (1993) Some cautionary remarks about smoothed particle hydrodynamics. Astrophys J 404(2): 717-722.
78. Century Dynamics Incorporated (1997) AUTODYN release notes version 3. 1. AUTODYN™ interactive non-linear dynamic analysis software.
79. Benz W (1990) Smooth particle hydrodynamics: a review. The numerical modelling of nonlinear stellar pulsations, problems and prospects. Kluwer Academic, Boston.
80. Morris JP (1996) A study of the stability properties of smooth particle hydrodynamics. Publ Astron Soc Aust 13(1): 97-102.
81. Omang M, Borve S, Trulsen J (2005) Alternative kernel functions for smoothed particle hydrodynamics in cylindrical symmetry. Shock Waves 14(4): 293-298.
82. Jin HB, Ding X (2005) On criterions for smoothed particle hydrodynamics kernels in stable field. J Comput Phys 202(2): 699-709.
83. Capuzzo-Dolcetta R, Di Lisio R (2000) A criterion for the choice of the interpolation kernel in smoothed particle hydrodynamics. Appl Numer Math 34(4): 363-371.
84. Cabezon RM, Garcia-Senz D, Relano A (2008) A one-parameter family of interpolating kernels for smoothed particle hydrodynamics studies. J Comput Phys 227(19): 8523-8540.
85. Monaghan JJ, Lattanzio JC (1985) A refined particle method for astrophysical problems. Astron Astrophys 149(1): 135-143.
86. Johnson GR, Stryk RA, Beissel SR (1996) SPH for high velocity impact computations. Comput Methods Appl Mech Eng 139(1-4): 347-373.
87. Swegle JW, Attaway SW, Heinstein MW, Mello FJ Hicks DL (1994) An analysis of smoothed particle hydrodynamics. Sandia National Labs., Albuquerque.
88. Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth-Heinemann, Bristol.
89. Chen JK, Beraun JE, Jih CJ (1999) An improvement for tensile instability in smoothed particle hydrodynamics. Comput Mech 23(4): 279-287.
90. Chen JK, Beraun JE, Jih CJ (1999) Completeness of corrective smoothed particle method for linear elastodynamics. Comput Mech 24(4): 273-285.
91. Hernquist L, Katz N (1989) TREESPH-a unification of SPH with the hierarchical tree method. Astrophys J Suppl Ser 70(2): 419-446.
92. Sod GA (1978) A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J Comput Phys 27: 1-31.
93. Fletcher CAJ (1991) Computational techniques for fluid dynamics, 1: fundamental and general techniques. Springer, Berlin.
94. Agertz O, Moore B, Stadel J, Potter D, Miniati F, Read J, Mayer L, Gawryszczak A, Kravtosov A, Nordlund A, Pearce F, Quilis V, Rudd D, Springel V, Stone J, Tasker E, Teyssier R, Wadsley J, Walder R (2007) Fundamental differences between SPH and grid methods. Mon Not R Astron Soc 380: 963-978.
95. Schussler M, Schmitt D (1981) Comments on smoothed particle hydrodynamics. Astron Astrophys 97(2): 373-379.
96. Espanol P (1998) Fluid particle model. Phys Rev E 57(3): 2930-2948.
97. Wang L, Ge W, Li J (2006) A new wall boundary condition in particle methods. Comput Phys Commun 174(5): 386-390.
98. Revenga M, Zuniga I, Espanol P (1998) Boundary models in DPD. Int J Mod Phys C 9(8): 1319-1328.
99. Liu MB, Meakin P, Huang H (2007) Dissipative particle dynamics simulation of pore-scale flow. Water Resour Res 43: W04411. doi: 10. 1029/2006WR004856.
100. Revenga M, Zuniga I, Espanol P (1998) Boundary models in DPD. Int J Mod Phys C 9(8): 1319-1328.
101. Revenga M, Zuniga I, Espanol P (1999) Boundary conditions in dissipative particle dynamics. Comput Phys Commun 121(122): 309-311.
102. Willemsen SM, Hoefsloot HCJ, Iedema PD (2000) No-slip boundary condition in dissipative particle dynamics. Int J Mod Phys C 11(5): 881-890.
103. Duong-Hong D, Phan-Thien N, Fan X (2004) An implementation of no-slip boundary conditions in DPD. Comput Mech 35(1): 24-29.
104. Crespo AJC, Gomez-Gesteira M, Dalrymple RA (2007) Boundary conditions generated by dynamic particles in SPH methods. Comput Mater Continua 5(3): 173-184.
105. Gong K, Liu H (2007). A new boundary treatment for smoothed particle hydrodynamics. In: Asian and Pacific coasts 2007, Nanjing, China.
106. Hieber SE, Koumoutsakos P (2008) An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers. J Comput Phys 227(19): 8636-8654.
107. Klessen R (1997) GRAPESPH with fully periodic boundary conditions: fragmentation of molecular clouds. Mon Not R Astron Soc 292(1): 11-18.
108. Randles PW, Libersky LD (2005) Boundary conditions for a dual particle method. Comput Struct 83(17-18): 1476-1486.
109. Yildiz M, Rook RA, Suleman A (2009) SPH with the multiple boundary tangent method. Int J Numer Methods Eng 77(10): 1416-1438.
110. Takeda H, Miyama SM, Sekiya M (1994) Numerical simulation of viscous flow by smoothed particle hydrodynamics. Prog Theor Phys 92(5): 939-960.
111. Morris JP, Fox PJ, Zhu Y (1997) Modeling low Reynolds number incompressible flows using SPH. J Comput Phys 136(1): 214-226.
112. Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2): 399-406.
113. Campbell PM (1989) Some new algorithms for boundary value problems in smooth particle hydrodynamics. Technical Report, Mission Research Corp, Albuquerque, NM.
114. Libersky LD, Petschek AG, Carney TC, Hipp JR, Allahdadi FA (1993) High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J Comput Phys 109(1): 67-75.
115. Rapaport DC (2004) The art of molecular dynamics simulation. Cambridge University Press, Cambridge.
116. Liu MB, Meakin P, Huang H (2007) Dissipative particle dynamics simulation of fluid motion through an unsaturated fracture and fracture junction. J Comput Phys 222(1): 110-130.
117. Tartakovsky AM, Meakin P (2005) Simulation of unsaturated flow in complex fractures using smoothed particle hydrodynamics. Vadose Zone J 4(3): 848-855.
118. Liu MB, Meakin P, Huang H (2007) Dissipative particle dynamics simulation of multiphase fluid flow in microchannels and microchannel networks. Phys Fluids 19(3): 033302.
119. Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191(2): 448-475.
120. Owen JM, Villumsen JV, Shapiro PR, Martel H (1998) Adaptive smoothed particle hydrodynamics: methodology, II. Astrophys J Suppl Ser 116(2): 155-209.
121. Shapiro PR, Martel H, Villumsen JV, Owen JM (1996) Adaptive smoothed particle hydrodynamics, with application to cosmology: methodology. Astrophys J Suppl Ser 103(2): 269-330.
122. Fulbright MS, Benz W, Davies MB (1995) A method of smoothed particle hydrodynamics using spheroidal kernels. Astrophys J 440(1): 254-262.
123. Liu MB, Liu GR (2005) Meshfree particle simulation of micro channel flows with surface tension. Comput Mech 35(5): 332-341.
124. Liu MB, Liu GR, Lam KY (2006) Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength. Shock Waves 15(1): 21-29.
125. Swegle JW, Attaway SW (1995) On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations. Comput Mech 17(3): 151-168.
126. Attaway SW, Hendrickson BA, Plimpton SJ, Gardner DR, Vaughan CT, Brown KH, Heinstein MW (1998) A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D. Comput Mech 22(2): 143-159.
127. Campbell J, Vignjevic R, Libersky L (2000) A contact algorithm for smoothed particle hydrodynamics. Comput Methods Appl Mech Eng 184(1): 49-65.
128. Drumm C, Tiwari S, Kuhnert J, Bart HJ (2008) Finite pointset method for simulation of the liquid-liquid flow field in an extractor. Comput Chem Eng 32(12): 2946-2957.
129. Huang H, Dyka CT, Saigal S (2004) Hybrid particle methods in frictionless impact-contact problems. Int J Numer Methods Eng 61: 2250-2272.
130. Li Y, Liu GR, Luan MT, Ky Dai, Zhong ZH, Li GY, Han X (2007) Contact analysis for solids based on linearly conforming radial point interpolation method. Comput Mech 39(4): 537-554.
131. Limido J, Espinosa C, Salauen M, Lacome JL (2007) SPH method applied to high speed cutting modelling. Int J Mech Sci 49(7): 898-908.
132. Mehra V, Chaturvedi S (2006) High velocity impact of metal sphere on thin metallic plates: a comparative smooth particle hydrodynamics study. J Comput Phys 212(1): 318-337.
133. Parshikov AN, Medin SA (2002) Smoothed particle hydrodynamics using interparticle contact algorithms. J Comput Phys 180(1): 358-382.
134. Parshikov AN, Medin SA, Loukashenko II, Milekhin VA (2000) Improvements in SPH method by means of interparticle contact algorithm and analysis of perforation tests at moderate projectile velocities. Int J Impact Eng 24(8): 779-796.
135. Plimpton S, Attaway S, Hendrickson B, Swegle J, Vaughan C, Gardner D (1998) Parallel transient dynamics simulations: algorithms for contact detection and smoothed particle hydrodynamics. J Parallel Distrib Comput 50(1-2): 104-122.
136. Prochazka PP, Kravtsov AN, Peskova S (2008) Blast impact on structures of underground parking. Undergr Spaces Des Eng Environ Asp 102: 11-19.
137. Sauer RA, Li SF (2008) An atomistically enriched continuum model for nanoscale contact mechanics and Its application to contact scaling. J Nanosci Nanotechnol 8(7): 3757-3773.
138. Schieback C, Burzle F, Franzrahe K, Neder J, Henseler P, Mutter D, Schwierz N, Nielaba P (2009) Computer simulations of complex many-body systems. In: High performance computing in science and engineering '08, Stuttgart, Germany.
139. Seo S, Min O, Lee J (2008) Application of an improved contact algorithm for penetration analysis in SPH. Int J Impact Eng 35(6): 578-588.
140. Vignjevic R, Campbell J (1999) A penalty approach for contact in smoothed particle hydrodynamics. Int J Impact Eng 23(1): 945-956.
141. Vignjevic R, De Vuyst T, Campbell JC, Source C (2006) A frictionless contact algorithm for meshless methods. Comput Model Eng 13(1): 35.
142. Belytschko T, Neal MO (1991) Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Methods Eng 31(3): 547-572.
143. Liu MB, Liu GR, Lam KY, Zong Z (2003) Smoothed particle hydrodynamics for numerical simulation of underwater explosion. Comput Mech 30(2): 106-118.
144. Liu MB, Liu GR, Lam KY, Zong Z (2001) A new technique to treat material interfaces for smoothed particle hydrodynamics. In: Computational mechanics-new frontiers for new millennium. Elsevier Science, Amsterdam.
145. Monaghan JJ (2000) SPH without a tensile instability. J Comput Phys 159(2): 290-311.
146. Vignjevic R, De Vuyst T, Campbell J (2002) The use of a homogeneous repulsive force for contact treatment in sph. In: WCCM V, Vienna, Austria.
147. Balsara DS (1995) von Neumann stability analysis of smoothed particle hydrodynamics suggestions for optimal algorithms. J Comput Phys 121(2): 357-372.
148. Belytschko T, Xiao S (2002) Stability analysis of particle methods with corrected derivatives. Comput Math Appl 43(3-5): 329-350.
149. Bonet J, Kulasegaram S (2001) Remarks on tension instability of Eulerian and Lagrangian corrected smooth particle hydrodynamics (CSPH) methods. Int J Numer Methods Eng 52: 1203-1220.
150. Lanson N, Vila JP (2007) Renormalized meshfree schemes, I: consistency, stability, and hybrid methods for conservation laws. SIAM J Numer Anal 46(4): 1912-1934.
151. Randles PW, Petschek AG, Libersky LD, Dyka CT (2003) Stability of DPD and SPH. In: Meshfree methods for partial differential equations. Springer, Berlin.
152. Sigalotti LDG, Lopez H (2008) Adaptive kernel estimation and SPH tensile instability. Comput Math Appl 55(1): 23-50.
153. Gray JP, Monaghan JJ, Swift RP (2001) SPH elastic dynamics. Comput Methods Appl Mech Eng 190(49): 6641-6662.
154. Beissel S, Belytschko T (1996) Nodal integration of the element-free Galerkin method. Comput Methods Appl Mech Eng 139(1-4): 49-74.
155. Melean Y, Sigalotti LDG, Hasmy A (2004) On the SPH tensile instability in forming viscous liquid drops. Comput Phys Commun 157(3): 191-200.
156. Benz W (1988) Applications of smooth particle hydrodynamics (SPH) to astrophysical problems. Comput Phys Commun 48(1): 97-105.
157. Frederic AR, James CL (1999) Smoothed particle hydrodynamics calculations of stellar interactions. J Comput Appl Math 109: 213-230.
158. Hultman J, Pharayn A (1999) Hierarchical, dissipative formation of elliptical galaxies: is thermal instability the key mechanism? Hydrodynamic simulations including supernova feedback multi-phase gas and metal enrichment in cdm: structure and dynamics of elliptical galaxies. Astron Astrophys 347: 769-798.
159. Thacker RJ, Couchman HMP (2001) Star formation, supernova feedback, and the angular momentum problem in numerical cold dark matter cosmogony: halfway there. Astrophys J 555(1): L17-L20.
160. Monaghan JJ, Lattanzio JC (1991) A simulation of the collapse and fragmentation of cooling molecular clouds. Astrophys J 375(1): 177-189.
161. Berczik P (2000) Modeling the star formation in galaxies using the chemo-dynamical SPH code. Astrophys Space Sci 271(2): 103-126.
162. Lee WH, Kluzniak W (1999) Newtonian hydrodynamics of the coalescence of black holes with neutron stars, II: tidally locked binaries with a soft equation of state. Mon Not R Astron Soc 308(3): 780-794.
163. Lee WH (2000) Newtonian hydrodynamics of the coalescence of black holes with neutron stars, III: irrotational binaries with a stiff equation of state. Mon Not R Astron Soc 318(2): 606-624.
164. Senz DG, Bravo E, Woosley SE (1999) Single and multiple detonations in white dwarfs. Astron Astrophys 349: 177-188.
165. Monaghan JJ (1990) Modelling the universe. Astron Soc Aust Proc 8(3): 233-237.
166. Hong JM, Lee HY, Yoon JC, Kim CH (2008) Bubbles alive. ACM Trans Graph 27(3).
167. Monaghan JJ, Kocharyan A (1995) SPH simulation of multi-phase flow. Comput Phys Commun 87: 225-235.
168. Hu XY, Adams NA (2006) A multi-phase SPH method for macroscopic and mesoscopic flows. J Comput Phys 213(2): 844-861.
169. Garg R, Narayanan C, Lakehal D, Subramaniam S (2007) Accurate numerical estimation of interphase momentum transfer in Lagrangian-Eulerian simulations of dispersed two-phase flows. Int J Multiph Flow 33(12): 1337-1364.
170. Liu J, Koshizuka S, Oka Y (2005) A hybrid particle-mesh method for viscous, incompressible, multiphase flows. J Comput Phys 202(1): 65-93.
171. Password F (2003) Cosmological smoothed particle hydrodynamics simulations: a hybrid multiphase model for star formation. Mon Not R Astron Soc 339(2): 289-311.
172. Ritchie BW, Pa Thomas (2001) Multiphase smoothed-particle hydrodynamics. Mon Not R Astron Soc 323(3): 743-756.
173. Hu XY, Adams NA (2009) A constant-density approach for incompressible multi-phase SPH. J Comput Phys 228(6): 2082-2091.
174. Hu XY, Adams NA (2007) An incompressible multi-phase SPH method. J Comput Phys 227(1): 264-278.
175. Dalrymple RA, Rogers BD (2006) Numerical modeling of water waves with the SPH method. Coast Eng 53(2-3): 141-147.
176. Crespo AJC, Gomez-Gesteira M, Dalrymple RA (2007) 3D SPH simulation of large waves mitigation with a dike. J Hydraul Res 45(5): 631-642.
177. Shao SD, Gotoh H (2004) Simulating coupled motion of progressive wave and floating curtain wall by SPH-LES model. Coast Eng J 46(2): 171-202.
178. Gotoh H, Shao SD, Memita T (2004) SPH-LES model for numerical investigation of wave interaction with partially immersed breakwater. Coast Eng 46(1): 39-63.
179. Shao SD (2006) Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling. Int J Numer Methods Fluids 50(5): 597-621.
180. Gomez-Gesteira M, Dalrymple RA (2004) Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure. J Waterw Port C 130(2): 63-69.
181. Crespo AJC, Gomez-Gesteira M, Carracedo P, Dalrymple RA (2008) Hybridation of generation propagation models and SPH model to study severe sea states in Galician Coast. J Mar Syst 72(1-4): 135-144.
182. Crespo AJC, Gomez-Gesteira M, Dalrymple RA (2008) Modeling dam break behavior over a wet bed by a SPH technique. J Waterw Port C 134(6): 313-320.
183. Gotoh H, Sakai T (2006) Key issues in the particle method for computation of wave breaking. Coast Eng 53(2-3): 171-179.
184. Issa R, Violeau D (2008) Modelling a plunging breaking solitary wave with eddy-viscosity turbulent SPH models. Comput Mater Continua 8(3): 151-164.
185. Khayyer A, Gotoh H, Shao SD (2008) Corrected incompressible SPH method for accurate water-surface tracking in breaking waves. Coast Eng 55(3): 236-250.
186. Monaghan JJ, Kos A, Issa N (2003) Fluid motion generated by impact. J Waterw Port C 129(6): 250-259.
187. Panizzo A (2005). SPH modelling of underwater landslide generated waves. In: Proceedings of the 29th international conference on coastal engineering 2004, Lisbon, Portugal.
188. Qiu LC (2008) Two-dimensional SPH simulations of landslide-generated water waves. J Hydraul Eng ASCE 134(5): 668-671.
189. Rogers BD, Dalrymple RA (2005) SPH modeling of breaking waves. In: Proceedings of the 29th international conference on coastal engineering 2004, Lisbon, Portugal.
190. Shao SD (2009) Incompressible SPH simulation of water entry of a free-falling object. Int J Numer Methods Fluids 59(1): 91-115.
191. Shao SD, Ji CM, Graham DI, Reeve DE, James PW, Chadwick AJ (2006) Simulation of wave overtopping by an incompressible SPH model. Coast Eng 53(9): 723-735.
192. Violeau D, Buvat C, Abed-Meraim K, de Nanteuil E (2007) Numerical modelling of boom and oil spill with SPH. Coast Eng 54(12): 895-913.
193. Yim SC, Yuk D, Panizzo A, Di Risio M, Liu PLF (2008) Numerical simulations of wave generation by a vertical plunger using RANS and SPH models. J Waterw Port C 134(3): 143-159.
194. Zou S, Dalrymple RA (2005) Sediment suspension modeling by smoothed particle hydrodynamics. In: Proceedings of the 29th international conference on coastal engineering 2004, Lisbon, Portugal.
195. Bulgarelli UP (2005) The application of numerical methods for the solution of some problems in free-surface hydrodynamics. J Ship Res 49(4): 288-301.
196. Iglesias AS, Rojas LP, Rodriguez RZ (2004) Simulation of anti-roll tanks and sloshing type problems with smoothed particle hydrodynamics. Ocean Eng 31(8-9): 1169-1192.
197. Kim Y (2007) Experimental and numerical analyses of sloshing flows. J Eng Math 58(1-4): 191-210.
198. Lohner R, Yang C, Onate E (2006) On the simulation of flows with violent free surface motion. Comput Methods Appl Mech Eng 195(41-43): 5597-5620.
199. Rhee SH, Engineer L (2005) Unstructured grid based Reynolds-averaged Navier-Stokes method for liquid tank sloshing. J Fluid Eng 127: 572.
200. Souto-Iglesias A, Delorme L, Perez-Rojas L, Abril-Perez S (2006) Liquid moment amplitude assessment in sloshing type problems with smooth particle hydrodynamics. Ocean Eng 33(11-12): 1462-1484.
201. Bursik M, Martinez-Hackert B, Delgado H, Gonzalez-Huesca A (2003) A smoothed-particle hydrodynamic automaton of landform degradation by overland flow. Geomorphology 53(1-2): 25-44.
202. Zhu Y, Fox PJ, Morris JP (1999) A pore-scale numerical model for flow through porous media. Int J Numer Anal Methods 23(9): 881-904.
203. Zhu Y, Fox PJ (2002) Simulation of pore-scale dispersion in periodic porous media using smoothed particle hydrodynamics. J Comput Phys 182(2): 622-645.
204. Tartakovsky AM, Meakin P (2006) Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics. Adv Water Resour 29(10): 1464-1478.
205. Cleary PW, Prakash M (2004) Discrete-element modelling and smoothed particle hydrodynamics: potential in the environmental sciences. Philos Trans R Soc A 362(1822): 2003-2030.
206. Ghazali JN, Kamsin A (2008) A real time simulation and modeling of flood hazard. In: 12th WSEAS international conference on systems, Heraklion, Greece.
207. Kipfer P, Westermann R (2006) Realistic and interactive simulation of rivers. In: Graphics interface 2006, Quebec, Canada.
208. Bui HH, Fukagawa R, Sako K (2006) Smoothed particle hydrodynamics for soil mechanics. Taylor & Francis, London.
209. Bui HH, Fukagawa R, Sako K, Ohno S (2008) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. Int J Numer Anal Methods 32(12): 1537-1570.
210. Bui HH, Sako K, Fukagawa R (2007) Numerical simulation of soil-water interaction using smoothed particle hydrodynamics (SPH) method. J Terramech 44(5): 339-346.
211. Gallati M, Braschi G, Falappi S (2005) SPH simulations of the waves produced by a falling mass into a reservoir. Nuovo Cimento C 28(2): 129-140.
212. Herrera PA, Massabo M, Beckie RD (2009) A meshless method to simulate solute transport in heterogeneous porous media. Adv Water Resour 32(3): 413-429.
213. Hui HH, Fukagawa R, Sako K (2006) Smoothed particle hydrodynamics for soil mechanics. Terramechanics 26: 49-53.
214. Laigle D, Lachamp P, Naaim M (2007) SPH-based numerical investigation of mudflow and other complex fluid flow interactions with structures. Comput Geosci 11(4): 297-306.
215. Maeda K, Sakai H (2007) Seepage failure analysis with evolution of air bubbles by SPH. In: New frontiers in Chinese and Japanese geotechniques, proceedings of the 3rd Sino-Japan geotechnical symposium, Chongqing, China.
216. McDougall S, Hungr O (2004) A model for the analysis of rapid landslide motion across three-dimensional terrain. Can Geotech J 41(6): 1084-1097.
217. McDougall S, Hungr O (2005) Dynamic modelling of entrainment in rapid landslides. Can Geotech J 42(5): 1437-1448.
218. Moresi L, Muhlhous H, Dufour F (2001) An overview of numerical methods for Earth simulations.
219. Morris JP, Zhu Y, Fox PJ (1999) Parallel simulations of pore-scale flow through porous media. Comput Geotech 25(4): 227-246.
220. Pastor M, Haddad B, Sorbino G, Cuomo S, Drempetic V (2009) A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. Int J Numer Anal Methods 33(2).
221. Sakai H, Maeda K (2006) Seepage failure of granular ground accounting for soil-water-gas interaction. In: Geomechanics and geotechnics of particulate media, proceedings of the international symposium on geomechanics and geotechnics of particulate media, Ube, Yamaguchi, Japan.
222. Cleary PW (1998) Modelling confined multi-material heat and mass flows using SPH. Appl Math Model 22(12): 981-993.
223. Jeong JH, Jhon MS, Halow JS, van Osdol J (2003) Smoothed particle hydrodynamics: applications to heat conduction. Comput Phys Commun 153(1): 71-84.
224. Jiang F, Sousa ACM (2006) SPH numerical modeling for ballistic-diffusive heat conduction. Numer Heat Transfer B, Fundam 50(6): 499-515.
225. Jiang FM, Sousa ACM (2006) SPH numerical modeling for ballistic-diffusive heat conduction. Numer Heat Transfer B, Fundam 50(6): 499-515.
226. Rook R, Yildiz M, Dost S (2007) Modeling transient heat transfer using SPH and implicit time integration. Numer Heat Transfer B, Fundam 51(1): 1-23.
227. Sousa ACM, Jiang FM (2007) SPH as an inverse numerical tool for the prediction of diffusive properties in porous media. Diffus Solids Liq Heat Transfer, Microstruct Prop 553: 171-189.
228. Gutfraind R, Savage SB (1998) Flow of fractured ice through wedge-shaped channels: smoothed particle hydrodynamics and discrete-element simulations. Mech Mater 29(1): 1-17.
229. Oger L, Savage SB (1999) Smoothed particle hydrodynamics for cohesive grains. Comput Methods Appl Mech Eng 180(1): 169-183.
230. Ji SY, Li H, Shen HT, Wang RX, Yue QJ (2007) A hybrid Lagrangian-Eulerian numerical model for sea-ice dynamics. Acta Oceanol Sin 26: 12-24.
231. Ji SY, Shen HT, Wang ZL, Shen HH, Yue QJ (2005) A viscoelastic-plastic constitutive model with Mohr-Coulomb yielding criterion for sea ice dynamics. Acta Oceanol Sin 24(4): 54-65.
232. Schafer C, Speith R, Kley W (2007) Collisions between equal-sized ice grain agglomerates. Astron Astrophys 470(2): 733-739.
233. Shen HT, Su JS, Liu LW (2000) SPH simulation of river ice dynamics. J Comput Phys 165(2): 752-770.
234. Wang RX, Ji SY, Shen HT, Yue QJ (2005) Modified PIC method for sea ice dynamics. China Ocean Eng 19(3): 457-468.
235. Tartakovsky A, Meakin P (2005) Modeling of surface tension and contact angles with smoothed particle hydrodynamics. Phys Rev E 72(2): 26301.
236. Nugent S, Posch HA (2000) Liquid drops and surface tension with smoothed particle applied mechanics. Phys Rev E 62(4): 4968-4975.
237. Apfel RE, Tian Y, Jankovsky J, Shi T, Chen X, Holt RG, Trinh E, Croonquist A, Thornton KC, Sacco JA (1997) Free oscillations and surfactant studies of superdeformed drops in microgravity. Phys Rev Lett 78(10): 1912-1915.
238. Fang HS, Bao K, Wei JA, Zhang H, Wu EH, Zheng LL (2009) Simulations of droplet spreading and solidification using an improved SPH model. Numer Heat Transfer A, Appl 55(2): 124-143.
239. Lopez H, Sigalotti L, Di G (2006) Oscillation of viscous drops with smoothed particle hydrodynamics. Phys Rev E 73(5): 51201.
240. Melean Y, Sigalotti LD (2005) Coalescence of colliding van der Waals liquid drops. Int J Heat Mass Transfer 48: 4041-4061.
241. Melean Y, Sigalotti LDG (2005) Coalescence of colliding van der Waals liquid drops. Int J Heat Mass Transfer 48(19-20): 4041-4061.
242. Wang W, Huang Y, Grujicic M, Chrisey DB (2008) Study of impact-induced mechanical effects in cell direct writing using smooth particle hydrodynamic method. J Manuf Sci E, Trans ASME 130(2).
243. Zhang MY, Zhang H, Zheng LL (2007) Application of smoothed particle hydrodynamics method to free surface and solidification problems. Numer Heat Transfer A, Appl 52(4): 299-314.
244. Zhang MY, Zhang H, Zheng LL (2008) Simulation of droplet spreading, splashing and solidification using smoothed particle hydrodynamics method. Int J Heat Mass Transfer 51(13-14): 3410-3419.
245. Zhang MY, Zhang H, Zheng LL (2009) Numerical investigation of substrate melting and deformation during thermal spray coating by SPH method. Plasma Chem Plasma Process 29(1): 55-68.
246. Zhou GZ, Ge W, Li JH (2008) A revised surface tension model for macro-scale particle methods. Powder Technol 183(1): 21-26.
247. Liu MB, Liu GR, Lam KY, Zong Z (2003) Meshfree particle simulation of the detonation process for high explosives in shaped charge unlined cavity configurations. Shock Waves 12(6): 509-520.
248. Liu MB, Liu GR, Zong Z, Lam KY (2003) Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology. Comput Fluids 32(3): 305-322.
249. Liu MB, Liu GR, Lam KY (2002) Investigations into water mitigation using a meshless particle method. Shock Waves 12(3): 181-195.
250. Liu MB, Liu GR (2004) Smoothed particle hydrodynamics: some recent developments in theory and applications. J Beijing Polytech Univ 30: 61-71.
251. Liu MB, Liu GR, Lam KY, Zong Z (2003) Computer simulation of shaped charge detonation using meshless particle method. Fragblast 7(3): 181-202.
252. Alia A, Souli M (2006) High explosive simulation using multi-material formulations. Appl Therm Eng 26(10): 1032-1042.
253. Bromm V, Yoshida N, Hernquist L (2003) The first supernova explosions in the universe. Astrophys J 596(2): L135-L138.
254. Busegnies Y, Francois J, Paulus G (2007) Unidimensional SPH simulations of reactive shock tubes in an astrophysical perspective. Shock Waves 16(4-5): 359-389.
255. Liu MB, Liu GR, Lam KY (2003) Comparative study of the real and artificial detonation models in underwater explosions. Electron Model 25(2): 113-124.
256. Mair HU (1999) Review: hydrocodes for structural response to underwater explosions. Shock Vib 6(2): 81-96.
257. Swegle JW (1992) Report at Sandia National Laboratories.
258. Libersky LD, Petschek AG (1991) Smooth particle hydrodynamics with strength of materials. In: Advances in the free-Lagrange method including contributions on adaptive gridding and the smooth particle hydrodynamics method, proceedings of the next free-Lagrange conference, Jackson Lake Lodge, Moran, WY, USA.
259. Zhou CE, Liu GR, Ky Lou (2007) Three-dimensional penetration simulation using smoothed particle hydrodynamics. Int J Comput Methods 4(4): 671-691.
260. Benz W, Asphaug E (1995) Simulations of brittle solids using smooth particle hydrodynamics. Comput Phys Commun 87(1): 253-265.
261. Cleary P, Ha J, Alguine V, Nguyen T (2002) Flow modelling in casting processes. Appl Math Model 26(2): 171-190.
262. Cleary PW, Ha J, Ahuja V (2000) High pressure die casting simulation using smoothed particle hydrodynamics. Int J Cast Met Res 12(6): 335-355.
263. Chen JS, Pan C, Roque C, Wang HP (1998) A Lagrangian reproducing kernel particle method for metal forming analysis. Comput Mech 22(3): 289-307.
264. Cleary PW, Ha J (2000) Three dimensional modelling of high pressure die casting. Int J Cast Met Res 12(6): 357-365.
265. Cleary PW, Prakash M, Ha J (2006) Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. J Mater Process Technol 177(1-3): 41-48.
266. Cleary PW, Prakash M, Ha J, Stokes N, Scott C (2007) Smooth particle hydrodynamics: status and future potential. Prog Comput Fluid Dyn 7(2-4): 70-90.
267. Ha J, Cleary PW (2000) Comparison of SPH simulations of high pressure die casting with the experiments and VOF simulations of Schmid and Klein. Int J Cast Met Res 12(6): 409-418.
268. Ha J, Cleary PW (2005) Simulation of high pressure die filling of a moderately complex industrial object using smoothed particle hydrodynamics. Int J Cast Met Res 18(2): 81-92.
269. Hu W, Yao LG, Hua ZZ (2007) Parallel point interpolation method for three-dimensional metal forming simulations. Eng Anal Bound Elem 31(4): 326-342.
270. Prakash M, Cleary PW, Grandfield J, Rohan P, Nguyen V (2007) Optimisation of ingot casting wheel design using SPH simulations. Prog Comput Fluid Dyn 7(2-4): 101-110.
271. Ala G, Francomano E, Tortofici A, Toscano E, Viola F (2007) Corrective meshless particle formulations for time domain Maxwell's equations. J Comput Appl Math 210(1-2): 34-46.
272. Ala G, Francomano E, Tortorici A, Toscano E, Viola F (2006) Smoothed particle electromagnetics: a mesh-free solver for transients. J Comput Appl Math 191(2): 194-205.
273. Ala G, Francomano E, Tortorici A, Toscano E, Viola F, di Ingegneria Elettrica D, e delle Telecomunicazioni E (2007) A mesh-free particle method for transient full-wave simulation. IEEE Trans Magn 43(4): 1333-1336.
274. Borve S, Omang M, Trulsen J (2001) Regularized smoothed particle hydrodynamics: a new approach to simulating magnetohydrodynamic shocks. Astrophys J 561(1): 82-93.
275. Dolag K, Bartelmann M, Lesch H (1999) SPH simulations of magnetic fields in galaxy clusters. Astron Astrophys 348(2): 351-363.
276. Francomano E, Tortorici A, Toscano E, Ala G, Viola F (2009) On the use of a meshless solver for PDEs governing electromagnetic transients. Appl Math Comput 209(1): 42-51.
277. Jiang FM, Oliveira MSA, Sousa ACM (2006) SPH simulation of transition to turbulence for planar shear flow subjected to a streamwise magnetic field. J Comput Phys 217(2): 485-501.
278. Meglicki Z (1994) Verification and accuracy of smoothed particle magnetohydrodynamics. Comput Phys Commun 81(1-2): 91-104.
279. Pimenta LCA, Mendes ML, Mesquita RC, Pereira GAS (2007) Fluids in electrostatic fields: an analogy for multirobot control. IEEE Trans Magn 43(4): 1765-1768.
280. Price DJ, Monaghan JJ (2004) Smoothed particle magnetohydrodynamics, I: algorithm and tests in one dimension. Mon Not R Astron Soc 348(1): 123-138.
281. Price DJ, Monaghan JJ (2004) Smoothed particle magnetohydrodynamics, II: variational principles and variable smoothing-length terms. Mon Not R Astron Soc 348(1): 139-152.
282. Price DJ, Monaghan JJ (2004) Smoothed particle magnetohydrodynamics: some shocking results. Astrophys Space Sci 292(1): 279-283.
283. Antoci C, Gallati M, Sibilla S (2007) Numerical simulation of fluid-structure interaction by SPH. Comput Struct 85(11-14): 879-890.
284. Prakash M, Cleary PW, Ha J, Noui-Mehidi MN, Blackburn H, Brooks G (2007) Simulation of suspension of solids in a liquid in a mixing tank using SPH and comparison with physical modelling experiments. Prog Comput Fluid Dyn 7(2): 91-100.
285. Anghileri M, Castelletti LML, Tirelli M (2005) Fluid structure interaction of water filled tanks during the impact with the ground. Int J Impact Eng 31(3): 235-254.
286. Chikazawa Y, Koshizuka S, Oka Y (2001) A particle method for elastic and visco-plastic structures and fluid-structure interactions. Comput Mech 27(2): 97-106.
287. Guilcher PM, Ducrozet G, Doring M, Alessandrini B, Ferrant P (2006) Numerical simulation of wave-body interactions using a modified SPH solver. In: Proceedings of the sixteenth international offshore and polar engineering conference, San Francisco, CA.
288. Hosseini SM, Amanifard N (2007) Presenting a modified SPH algorithm for numerical studies of fluid-structure interaction problems. IJE Trans B, Appl 20: 167-178.
289. Muller M (2004) Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. Technol Health Care 12(1): 25-31.
290. Hieber SE (2004) Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs. Technol Health Care 12(4): 305-314.
291. Tanaka N, Takano T (2005) Microscopic-scale simulation of blood flow using SPH method. Int J Comput Methods 2(4): 555-568.
292. Tsubota K, Wada S, Yamaguchi T (2006) Simulation study on effects of hematocrit on blood flow properties using particle method. J Biomech Sci Eng 1(1): 159-170.
293. Rosswog S, Wagner P (2002) Towards a macroscopic modeling of the complexity in traffic flow. Phys Rev E 65(3): 36106.
294. Benson DJ (1992) Computational methods in Lagrangian and Eulerian hydrocodes. Comput Methods Appl Mech Eng 99(2-3): 235-394.
295. Walters WP, Zukas JA (1989) Fundamentals of shaped charges. Wiley, New York.
296. Anderson CE (1987) An overview of the theory of hydrocodes. Int J Impact Eng 5(1-4): 33-59.
297. Anghileri M, Castelletti LML, Invernizzi F, Mascheroni M (2005) A survey of numerical models for hail impact analysis using explicit finite element codes. Int J Impact Eng 31(8): 929-944.
298. Attaway SW, Heinstein MW, Swegle JW (1993) Coupling of smooth particle hydrodynamics with the finite element method. In: IMPACT-4: structural mechanics in reactor technology conference, Berlin, Germany.
299. Batra RC, Zhang GM (2008) Modified Smoothed Particle Hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test. J Comput Phys 227(3): 1962-1981.
300. Brown K, Attaway S, Plimpton S, Hendrickson B (2000) Parallel strategies for crash and impact simulations. Comput Methods Appl Mech Eng 184: 375-390.
301. De Vuyst T, Vignjevic R, Campbell JC (2005) Coupling between meshless and finite element methods. Int J Impact Eng 31(8): 1054-1064.
302. Fahrenthold EP, Koo JC (1997) Energy based particle hydrodynamics for hypervelocity impact simulation. Int J Impact Eng 20(1-5): 253-264.
303. Fawaz Z, Zheng W, Behdinan K (2004) Numerical simulation of normal and oblique ballistic impact on ceramic composite armours. Compos Struct 63(3-4): 387-395.
304. Fountzoulas CG, Gazonas GA, Cheeseman BA (2007) Computational modeling of tungsten carbide sphere impact and penetration into high-strength-low-alloy (HSLA)-100 steel targets. J Mech Mater Struct 2(10): 1965-1979.
305. Groenenboom PHL (1997) Numerical simulation of 2D and 3D hypervelocity impact using the SPH option in PAM-SHOCK(TM). Int J Impact Eng 20(1-5): 309-323.
306. Hayhurst CJ, Clegg RA (1997) Cylindrically symmetric SPH simulations of hypervelocity impacts on thin plates. Int J Impact Eng 20(1-5): 337-348.
307. Hayhurst CJ, Clegg RA Livingstone IA, Francis NJ (1996) The application of SPH techniques in Autodyn-2D to ballistic impact problems. In: 16th international symposium on ballistics, San Francisco, USA.
308. Hiermaier S, Schafer F (1999) Hypervelocity impact fragment clouds in high pressure gas numerical and experimental investigations. Int J Impact Eng 23(1): 391-400.
309. Ioan A, Brizzolara S, Viviani M, Couty N, Donner R, Hermundstad O, Kukkanen T, Malenica S, Temarel P (2007) Comparison of experimental and numerical impact loads on ship-like sections. In: Advancements in marine structures. Taylor & Francis, London.
310. Ji XY, Li YC, Huang XC, Chen G (2007) Coupled FE-SPH simulation of truncated-conical projectiles penetrating steel sheets. In: 7th international conference on shock & impact loads on structures, Beijing, China.
311. Johnson AF, Holzapfel M (2003) Modelling soft body impact on composite structures. Compos Struct 61(1-2): 103-113.
312. Johnson GR (1994) Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computations. Nucl Eng Des 150(2-3): 265-274.
313. Johnson GR, Beissel SR, Stryk RA (2000) A generalized particle algorithm for high velocity impact computations. Comput Mech 25(2): 245-256.
314. Johnson GR, Peterson EH, Stryrk RA (1993) Incorporation of an sph option into the epic code for a wide range of high velocity impact computations. Int J Impact Eng 14: 385-394.
315. Johnson GR, Stryk RA, Beissel SR, Holmquist TJ (2002) An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. Int J Impact Eng 27(10): 997-1013.
316. Kikuchi M, Miyamoto B (2006) Numerical simulation of impact crush/buckling of circular tube using SPH method. Key Eng Mater 306-308: 697-702.
317. Kitsionas S, Whitworth AP (2007) High-resolution simulations of clump-clump collisions using SPH with particle splitting. Mon Not R Astron Soc 378(2): 507-524.
318. Lam KY, Shen YG, Gong SW (2001) A study of axial impact of composite rods using SPH approach. Shock Vib 8(5): 303-312.
319. Lee M, Yoo YH (2001) Analysis of ceramic/metal armour systems. Int J Impact Eng 25(9): 819-829.
320. Libersky LD, Randles PW, Carney TC, Dickinson DL (1997) Recent improvements in SPH modeling of hypervelocity impact. Int J Impact Eng 20(6): 525-532.
321. Lukyanov AA, Reveles JR, Vignjevic R, Campbell J (2005) Simulation of hypervelocity debris impact and spacecraft shielding performance. In: Proceedings of the 4th European conference on space debris.
322. Ma S, Zhang X, Qiu XM (2009) Comparison study of MPM and SPH in modeling hypervelocity impact problems. Int J Impact Eng 36(2): 272-282.
323. Michel Y, Chevalier JM, Durin C, Espinosa C, Malaise F, Barrau JJ (2006) Hypervelocity impacts on thin brittle targets: experimental data and SPH simulations. Int J Impact Eng 33(1-12): 441-451.
324. Nizampatnam LS, Horn WJ (2008) Investigation of multi-material bird models for predicting impact loads. In: Proceedings of the Asme turbo expo, Berlin, Germany.
325. Park YK, Fahrenthold EP (2005) A kernel free particle-finite element method for hypervelocity impact simulation. Int J Numer Methods Eng 63(5): 737-759.
326. Rabczuk T, Eibl J (2006) Modelling dynamic failure of concrete with meshfree methods. Int J Impact Eng 32(11): 1878-1897.
327. Randles PW, Carney TC, Libersky LD, Renick JD, Petschek AG (1994) Calculation of oblique impact and fracture of tungsten cubes using smoothed particle hydrodynamics. Int J Impact Eng 17(4): 661-672.
328. Rosen P, Popescu V, Hoffmann C, Irfanoglu A (2008) A high-quality high-fidelity visualization of the September 11 attack on the World Trade Center. IEEE Trans Vis Comput Graph 14(4): 937-947.
329. Shintate K, Sekine H (2004) Numerical simulation of hypervelocity impacts of a projectile on laminated composite plate targets by means of improved SPH method. Compos Part A, Appl Sci 35(6): 683-692.
330. Stellingwerf RF, Wingate CA (1993) Impact modeling with smooth particle hydrodynamics. In: Conference: smooth particle hydrodynamics in astrophysics OAT workshop, Trieste, Italy.
331. Taylor EA (2001) Simulation of hollow shaped charge jet impacts onto aluminium whipple bumpers at 11 km/s. Int J Impact Eng 26(1-10): 773-784.
332. Vignjevic R, Lepage S, De Vuyst T (2005) Simulation of high velocity impacts on thin metallic targets II (discrete elements). WIT Trans Eng Sci 49: 575-582.
333. Wang P, Shao JL, Qin CS (2009) Effect of loading-wave-front width on micro-jet from aluminum surface. Acta Phys Sin 58(2): 1064-1070.
334. Zhang QM, Long RR, Liu ZF, Huang FL (2008) SPH simulations of hypervelocity impact of al spheres on multi-plate structures. Int J Mod Phys B 22(9-11): 1604-1611.
335. McCarthy MA, Xiao JR, Petrinic N, Kamoulakos A, Melito V (2004) Modelling of bird strike on an aircraft wing leading edge eade from fibre metal laminates, part 1: material modelling. Appl Compos Mater 11(5): 295-315.
336. Brown K, Attaway S, Plimpton S, Hendrickson B (2000) Parallel strategies for crash and impact simulations. Comput Methods Appl Mech Eng 184(2): 375-390.
337. Bicknell GV, Gingold RA (1983) On tidal detonation of stars by massive black holes. Astrophys J 273: 749-760.
338. Fulbright MS, Benz W, Davies MB (1995) A method of smoothed particle hydrodynamics using spheroidal kernels. Astrophys J 440: 254.
339. Chin GL (2001) Smoothed particle hydrodynamics and adaptive smoothed particle hydrodynamics with strength of materials. National University of Singapore, Singapore.
340. Hiermaier S, Konke D, Stilp AJ, Thoma K (1997) Computational simulation of the hypervelocity impact of Al-spheres on thin plates of different materials. Int J Impact Eng 20(1-5): 363-374.
341. Bangash MYH (1993) Impact and explosion. Blackwell Scientific, Oxford.
342. Cole RH (1948) Underwater explosions. Princeton University Press, Princeton.
343. Fickett WW (1966) Flow calculations for pulsating one-dimensional detonations. Phys Fluids 9: 903-916.
344. Mader CL (1998) Numerical modeling of explosives and propellants. CRC Press, New York.
345. Libersky LD, Randles PW (2006) Shocks and discontinuities in particle methods. Shock Compress Condens Matter 845: 1089-1092.
346. Ma S, Zhang X, Lian YP, Zhou X (2009) Simulation of high explosive explosion using adaptive material point method. Comput Model Eng 39(2): 101-123.
347. Miyoshi H (2008) Numerical simulation of shaped charges using the SPH solver: jet formation and target penetration. Explos Shock Wave Hypervelocity Phenom Mater II.
348. Tanaka K (2008) Numerical studies of explosive welding by SPH. Explos Shock Wave Hypervelocity Phenom Mater II 566: 61-64.
349. Wataru K, Akiko M (2006) Explosion simulation by smoothed particle hydrodynamics. Comput Methods 2: 1397-1403.
350. Xu JX, Liu XL (2008) Analysis of structural response under blast loads using the coupled SPH-FEM approach. J Zhejiang Univ Sci A 9(9): 1184-1192.
351. Liu MB, Liu GR, Lam KY (2001) Simulation of the explosive detonation process by using SPH methodology. In: Computational fluids and solid mechanics. Elsevier Science, Amsterdam.
352. Dobratz BM (1981) LLNL explosive handbook. Lawrence Livermore National Laboratory, Livermore.
353. Chiesum JE, Shin YS (1997) Explosion gas bubbles near simple boundaries. Shock Vib 4(11): 11-25.
354. Karniadakis GE, Beskok A, Aluru A (2005) Microflows and nanoflows: fundamentals and simulation. Springer, Berlin.
355. Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Oxford University Press, Oxford.
356. Beskok A, Karniadakis GE (2001) Microflows: fundamentals and simulation. Springer, Berlin.
357. Pan L, Ng TY, Xu D, Liu GR, Lam KY (2002) Determination of temperature jump coefficient using the direct simulation Monte Carlo method. J Micromech Microeng 12(1): 41-52.
358. Pan LS, Liu GR, Khoo BC, Song B (2000) A modified direct simulation Monte Carlo method for low-speed microflows. J Micromech Microeng 10: 21-27.
359. Pan LS, Liu GR, Lam KY (1999) Determination of slip coefficient for rarefied gas flows using direct simulation Monte Carlo. J Micromech Microeng 9(1): 89-96.
360. Duong-Hong D, Wang JS, Liu GR, Chen YZ, Han J, Hadjiconstantinou NG (2007) Dissipative particle dynamics simulations of electroosmotic flow in nano-fluidic devices. Microfluid Nanofluid 3: 1-7.
361. Hoover WG, Hoover CG, Kum O, Castillo VM, Posch HA, Hess S (1996) Smooth particle applied mechanics. Comput Methods Sci Eng 2: 6572.
362. Hoover WG, Pierce TG, Hoover CG, Shugart JO, Stein CM, Edwards AL (1994) Molecular dynamics, smoothed-particle applied mechanics, and irreversibility. Comput Math Appl 28(10-12): 155-174.
363. Hoover WG, Hoover CG (2003) Links between microscopic and macroscopic fluid mechanics. Mol Phys 101(11): 1559-1573.
364. Espanol P (1997) Fluid particle dynamics: a synthesis of dissipative particle dynamics and smoothed particle dynamics. Europhys Lett 39(6): 605-610.
365. Espanol P, Revenga M (2003) Smoothed dissipative particle dynamics. Phys Rev E 67(2): 026705.
366. Liu MB, Liu GR, Lam KY (2003) Computer simulation of flip-chip underfill encapsulation process using meshfree particle method. Int J Comput Eng Sci 4(2): 405-408.
367. Li Q, Cai TM, He GQ, Hu CB (2006) Droplet collision and coalescence model. Appl Math Mech 27(1): 67-73.
368. Tartakovsky AM, Meakin P (2005) A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh Taylor instability. J Comput Phys 207(2): 610-624.
369. Tartakovsky AM, Meakin P, Scheibe TD, Eichler West RM (2007) Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. J Comput Phys 222(2): 654-672.
370. Tartakovsky AM, Redden G, Lichtner PC, Scheibe TD, Meakin P (2008) Mixing-induced precipitation: experimental study and multiscale numerical analysis. Water Resour Res 44(6).
371. Tartakovsky AM, Meakin P, Ward AL (2009) Smoothed particle hydrodynamics model of non-Aqueous phase liquid flow and dissolution. Transp Porous Media 76(1): 11-34.
372. Brackbill JU, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100(2): 335-354.
373. Morris JP (2000) Simulating surface tension with smoothed particle hydrodynamics. Int J Numer Methods Fluids 33(3): 333-353.
374. Lo YME, Shao S (2002) Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Appl Ocean Res 24(5): 275-286.
375. Shao S (2006) Incompressible SPH simulation of wave breaking and overtopping with turbulence modelling. Int J Numer Methods Fluids 50(5).
376. Shao S, Ji C (2006) SPH computation of plunging waves using a 2-D sub-particle scale (SPS) turbulence model. Int J Numer Methods Fluids 51(8).
377. Shao SD (2005) SPH simulation of solitary wave interaction with a curtain-type breakwater. J Hydraul Res 43(4): 366-375.
378. Frank J, Reich S (2003) Conservation properties of smoothed particle hydrodynamics applied to the shallow water equation. BIT 43(1): 41-55.
379. Ata R, Soulaimani A (2005) A stabilized SPH method for inviscid shallow water flows. Int J Numer Methods Fluids 47(2): 139-159.
380. Rodriguez-Paz M, Bonet J (2005) A corrected smooth particle hydrodynamics formulation of the shallow-water equations. Comput Struct 83(17-18): 1396-1410.
381. Idelsohn SR, Onate E, Pin FD (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61(7): 964-989.
382. Oger G, Alessandrini B, Ferrant P (2005) Capture of air cushion effects in a wedge water entry SPH simulation. In: Proceedings of the fifteenth international offshore and polar engineering conference.
383. Callati M, Braschi G, Falappi S (2005) SPH simulations of the waves produced by a falling mass into a reservoir. Nuovo Cimento C 28(2): 129-140.
384. Oger G, Doring M, Alessandrini B, Ferrant P (2006) Two-dimensional SPH simulations of wedge water entries. J Comput Phys 213(2): 803-822.
385. Delorme L, Iglesias AS, Perez SA (2005) Sloshing loads simulation in LNG tankers with SPH. In: International conference on computational methods in marine engineering, Barcelona.
386. Greco M, Landrini M, Faltinsen OM (2004) Impact flows and loads on ship-deck structures. J Fluids Struct 19(3): 251-275.
387. Liu MB, Liu GR, Zong Z (2008) An overview on smoothed particle hydrodynamics. Int J Comput Methods 5(1): 135-188.
388. Xu QX, Shen RY (2008) Fluid-structure interaction of hydrodynamic damper during the rush into the water channel. J Hydrodyn 20(5): 583-590.
389. Ataie-Ashtiani B, Shobeyri G (2008) Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics. Int J Numer Methods Fluids 56(2): 209-232.
390. Scanlon BR, Tyler SW, Wierenga PJ (1997) Hydrologic issues in arid, unsaturated systems and implications for contaminant transport. Rev Geophys 35(4): 461-490.
391. Nativ R, Adar E, Dahan O, Geyh M (1995) Water recharge and solute transport through the vadose zone of fractured chalk under desert conditions. Water Resour Res 31(2): 253-261.
392. Schwartz LM, Martys N, Bentz DP, Garboczi EJ, Torquato S (1993) Cross-property relations and permeability estimation in model porous media. Phys Rev E 48(6): 4584-4591.
393. Huang H, Meakin P, Liu MB (2005) Computer simulation of two-phase immiscible fluid motion in unsaturated complex fractures using a volume of fluid method. Water Resour Res. doi: 10. 1029/2005WR004204.
394. Huang H, Meakin P, Liu MB, McCreery GE (2005) Modeling of multiphase fluid motion in fracture intersections and fracture networks. Geophys Res Lett 32: L19402. doi: 10. 1029/2005GL023899.
395. Snyder LJ, Stewart WE (1966) Velocity and pressure profiles for Newtonian creeping flow in regular packed beds of spheres. AIChE J 12(1): 167-173.
396. Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1): 146-159.
397. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1): 201-225.
398. Unverdi SO, Tryggvason G (1992) A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys 100(1): 25-37.
399. Zhu Y, Fox PJ (2001) Smoothed particle hydrodynamics model for diffusion through porous media. Transp Porous Media 43(3): 441-471.