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68. M. Sussman, E.G. Pucket, A coupled level set and volume-of-fluid method for computing 3D
axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301–337 (2000)
69. D. Enright, R. Fedkiw, J. Ferziger et al., A hybrid particle level set method for improved
interface capturing. J. Comput. Phys. 183(1), 83–116 (2002)
70. B.D. Nichols, C.W. Hirt, R.S. Hotchkiss, SOLA-VOF: A Solution Algorithm for Transient
Fluid Flow with Multiple Free Boundaries (Los Alamos Scientific Lab, 1980)
71. A.J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comput. 22(104),
745–762 (1968)
72. D.S. Kershaw, The incomplete Cholesky—conjugate gradient method for the iterative solution
of systems of linear equations. J. Comput. Phys. 26(1), 43–65 (1978)
73. S. Fujinaga, H. Takenaka, T. Narikiyo et al., Direct observation of keyhole behaviour during
pulse modulated high-power Nd: YAG laser irradiation. J. Phys. D: Appl. Phys. 33(5), 492–497
(2000)
74. A. Matsunawa, J.D. Kim, N. Seto et al., Dynamics of keyhole and molten pool in laser welding.
J. Laser Appl. 10(6), 247–254 (1998)
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on molten metal, in ICALEO 2003, Jacksonville, FL, United States (2003)
76. J. Kroos, U. Gratzke, M. Vicanek et al., Dynamic behaviour of the keyhole in laser welding.
J. Phys. D: Appl. Phys. 26(3), 481–486 (1993)
77. T. Klein, M. Vicanek, J. Kroos et al., Oscillations of the keyhole in penetration laser beam
welding. J. Phys. D: Appl. Phys. 27(10), 2023–2030 (1994)
78. T. Klein, M. Vicanek, G. Simon, Forced oscillations of the keyhole in penetration laser beam
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79. J.Y. Lee, H.K. Sung, D.F. Farson et al., Mechanism of keyhole formation and stability in
stationary laser welding. J. Phys. D: Appl. Phys. 35(13), 1570–1576 (2002)
80. S. Katayama, M. Mizutani, A. Matsunawa, Development of porosity prevention procedures
during laser welding, in Proceedings of SPIE, Osaka, Japan (2002), pp. 281–288
81. S. Katayama, Y. Kawahito, Elucidation of phenomena in high power fiber laser welding,
development of prevention procedures of welding defects, in Proceedings of SPIE, vol. 7195
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82. V.V. Semak, W.D. Bragg, B. Damkroger et al., Transient model for the keyhole during laser
welding. J. Phys. D: Appl. Phys. 32(15), L61–L64 (1999)
83. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free
surface evolution. Metall. Mater. Trans. A 33, 1817–1830 (2001)
84. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part II. Simulation of
keyhole evolution, velocity, temperature profile, and experimental verification. Metall. Mater.
Trans. A 33, 1831–1842 (2001)
85. X. Jin, P. Berger, T. Graf, Multiple reflections and Fresnel absorption in an actual 3D keyhole
during deep penetration laser welding. J. Phys. D: Appl. Phys. 39(21), 4703–4712 (2006)
86. R. Fabbro, S. Slimani, F. Coste et al., Study of keyhole behaviour for full penetration Nd-Yag
CW laser welding. J. Phys. D: Appl. Phys. 38(12), 1881–1887 (2005)
87. S. Pang, A three-dimensional sharp interface model for self-consistent keyhole and weld pool
dynamics in deep penetration laser welding. J. Phys. D: Appl. Phys. 44(2), (2011)
88. H. Ki, J. Mazumder, P.S. Mohanty, Modeling of laser keyhole welding: Part II. Simulation of
keyhole evolution, velocity, temperature profile, and experimental verification. Metall. Mater.
Trans. A 33(6), 1831–1842 (2002)
89. J. Zhou, H.L. Tsai, T.F. Lehnhoff, Investigation of transport phenomena and defect formation
in pulsed laser keyhole welding of zinc-coated steels. J. Phys. D: Appl. Phys. 39(24), 5338
(2006)
90. N.S. Hosseini Motlagh, P. Parvin, M. Jandaghi et al., The influence of different volume ratios
of He and At in shielding gas mixture on the power waste parameters for Nd: YAG and CO 2
laser welding. Opt. Laser Technol. 54, 191–198 (2013)
Bibliography
67. H. Zhao, A fast sweeping method for Eikonal equations. Math. Comput. 74(250), 603–627
(2005)
68. M. Sussman, E.G. Pucket, A coupled level set and volume-of-fluid method for computing 3D
axisymmetric incompressible two-phase flows. J. Comput. Phys. 162(2), 301–337 (2000)
69. D. Enright, R. Fedkiw, J. Ferziger et al., A hybrid particle level set method for improved
interface capturing. J. Comput. Phys. 183(1), 83–116 (2002)
70. B.D. Nichols, C.W. Hirt, R.S. Hotchkiss, SOLA-VOF: A Solution Algorithm for Transient
Fluid Flow with Multiple Free Boundaries (Los Alamos Scientific Lab, 1980)
71. A.J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comput. 22(104),
745–762 (1968)
72. D.S. Kershaw, The incomplete Cholesky—conjugate gradient method for the iterative solution
of systems of linear equations. J. Comput. Phys. 26(1), 43–65 (1978)
73. S. Fujinaga, H. Takenaka, T. Narikiyo et al., Direct observation of keyhole behaviour during
pulse modulated high-power Nd: YAG laser irradiation. J. Phys. D: Appl. Phys. 33(5), 492–497
(2000)
74. A. Matsunawa, J.D. Kim, N. Seto et al., Dynamics of keyhole and molten pool in laser welding.
J. Laser Appl. 10(6), 247–254 (1998)
75. M. Mizutani, S. Katayama, Keyhole behavior and pressure distribution during laser irradiation
on molten metal, in ICALEO 2003, Jacksonville, FL, United States (2003)
76. J. Kroos, U. Gratzke, M. Vicanek et al., Dynamic behaviour of the keyhole in laser welding.
J. Phys. D: Appl. Phys. 26(3), 481–486 (1993)
77. T. Klein, M. Vicanek, J. Kroos et al., Oscillations of the keyhole in penetration laser beam
welding. J. Phys. D: Appl. Phys. 27(10), 2023–2030 (1994)
78. T. Klein, M. Vicanek, G. Simon, Forced oscillations of the keyhole in penetration laser beam
welding. J. Phys. D: Appl. Phys. 29(2), 322–332 (1996)
79. J.Y. Lee, H.K. Sung, D.F. Farson et al., Mechanism of keyhole formation and stability in
stationary laser welding. J. Phys. D: Appl. Phys. 35(13), 1570–1576 (2002)
80. S. Katayama, M. Mizutani, A. Matsunawa, Development of porosity prevention procedures
during laser welding, in Proceedings of SPIE, Osaka, Japan (2002), pp. 281–288
81. S. Katayama, Y. Kawahito, Elucidation of phenomena in high power fiber laser welding,
development of prevention procedures of welding defects, in Proceedings of SPIE, vol. 7195
(2009), p. 71951R
82. V.V. Semak, W.D. Bragg, B. Damkroger et al., Transient model for the keyhole during laser
welding. J. Phys. D: Appl. Phys. 32(15), L61–L64 (1999)
83. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part I. Mathematical modeling, numerical methodology, role of recoil pressure, multiple reflections, and free
surface evolution. Metall. Mater. Trans. A 33, 1817–1830 (2001)
84. H. Ki, P.S. Mohanty, J. Mazumder, Modeling of laser keyhole welding: Part II. Simulation of
keyhole evolution, velocity, temperature profile, and experimental verification. Metall. Mater.
Trans. A 33, 1831–1842 (2001)
85. X. Jin, P. Berger, T. Graf, Multiple reflections and Fresnel absorption in an actual 3D keyhole
during deep penetration laser welding. J. Phys. D: Appl. Phys. 39(21), 4703–4712 (2006)
86. R. Fabbro, S. Slimani, F. Coste et al., Study of keyhole behaviour for full penetration Nd-Yag
CW laser welding. J. Phys. D: Appl. Phys. 38(12), 1881–1887 (2005)
87. S. Pang, A three-dimensional sharp interface model for self-consistent keyhole and weld pool
dynamics in deep penetration laser welding. J. Phys. D: Appl. Phys. 44(2), (2011)
88. H. Ki, J. Mazumder, P.S. Mohanty, Modeling of laser keyhole welding: Part II. Simulation of
keyhole evolution, velocity, temperature profile, and experimental verification. Metall. Mater.
Trans. A 33(6), 1831–1842 (2002)
89. J. Zhou, H.L. Tsai, T.F. Lehnhoff, Investigation of transport phenomena and defect formation
in pulsed laser keyhole welding of zinc-coated steels. J. Phys. D: Appl. Phys. 39(24), 5338
(2006)
90. N.S. Hosseini Motlagh, P. Parvin, M. Jandaghi et al., The influence of different volume ratios
of He and At in shielding gas mixture on the power waste parameters for Nd: YAG and CO 2
laser welding. Opt. Laser Technol. 54, 191–198 (2013)