References
- Wilson HA. On convection of heat. Cambridge Philos Soc. 1904;12:406–423.
- Rosenthal D. The theory of moving sources of heat and its application to metal treatments. Trans ASME. 1946;11:849–865.
- Rykalin NN. Calculation of thermal processes in welding. Moscow: Mashgiz; 1951.
- Goldak J, Chakravarti A, Bibby M. A new finite element model for welding heat sources. Metall Trans B. 1984;15(2):299–305.
- Karkhin VA, Khomich PN, Michailov VG. Models for volume heat sources and functional-analytical technique for calculating the temperature fields in butt welding. Mathematical Modeling of Weld Phenomena 8/Cerjak H., H. K. D. H. Bhadeshia, Kozeschnik E. Graz: Verlag der Technischen Universitaet Graz; 2007. p. 819–834.
- Karkhin VA. Thermal processes in welding. 2nd ed. St. Petersburg: Saint Petersburg Polytechnic University; 2015.
- Carslow GS, Jaeger D. Thermal conductivity of solid bodies. Nauka: Moscow; 1964.
- Lankalapalli KN, Tu JF, Gartner M. A model for estimating penetration depth of laser welding processes. Appl Phys. 1996;29:1831–1841.
- Radaj D. Welding residual stresses and distortion. Calculation and measurement. Duesseldorf: DVS Verlag; 2003.
- Artinov A, Bachmann M, Rethmeier M. Equivalent heat source approach in a 3D transient heat transfer simulation of full-penetration high power laser beam welding of thick metal plates. Int J Heat Mass Transfer. 2018;122:1003–1013.
- Ai Y, Jiang P, Shao X, et al. A three-dimensional numerical simulation model for weld characteristics analysis in fiber laser keyhole welding. Int J Heat Mass Transfer. 2017;108:614–626.
- Cho WI, Na SJ, Thomy C, et al. Numerical simulation of molten pool dynamics in high power disk laser welding. J Mater Process Technol. 2012;212(1):262–275.
- Makhnenko VI, Petun LA, Prilutskiy VP, et al. Assessment of thermal processes near a moving weld pool. Avt.Svarka. 1969;11:1–6.
- Pavelic V, Tanbakuchi R, Uyehara OA, et al. Experimental and computed temperature histories in gas tungsten-arc welding of thin plates. Weld J. 1969;7:295–305.
- Karkhin VA, Plochikhine VV, Ilyin AS, et al. Inverse modeling of fusion welding processes. Weld World. 2002;46(11–12):2–13.
- Karkhin VA, Ilyin AS, Plochikhine VV. Solution inverse problem of heat conductivity with allowance for heat melting and crystallization. Svarochnoe Proizvodstvo. 2003;7:3–6.
- Pittner A, Karkhin V, Rethmeier M. Reconstruction of 3D transient temperature field for fusion welding processes on basis of discrete experimental data. Weld World. 2015;59(4):497–512.
- Faber TE. Fluid dynamics for physicists. Cambridge: Cambridge University Press; 1995.
- Wilcox DC. Turbulence modeling for CFD. La Canada (CA): DCW Industries; 1993.
- Brent AD, Voller VR, Reid KTJ. Enthalpyporosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal. Numeri Heat Transf A Appl. 1988;3:297–318.
- Larsson J. Numerical simulation of turbulent flows for turbine blade heat transfer applications [doctoral thesis]. Goteborg: Chalmers University of Technology; 1998.
- Makhnenko VI, Petun LA, Prilutskiy VP, et al. Estimation of thermal processes near a moving weld pool. Avt Svarka. 1969;11:1–6.
- Karkhin VA, Khomich PN, Yu IS. Calculation of thermal processes around a moving weld pool by the method of boundary elements. Svarka I Diagnostika. 2016;4:32–35.
- Karkhin VA, Khomich PN, Ginzburg SA, et al. Analysis of thermal processes near a moving weld pool by the method of boundary elements. Svarochnoe Proizvodstvo. 2017;8:3–8.
- Karkhin VA, Khomich PN, Panchenko OV, et al. Calculation of the temperature field according to the given geometry of the weld pool in fusion welding. Voprosy Materialovedeniya. 2017;2:208–216.
- Benergy P, Butterfield R. Method of boundary elements in applied sciences. Moscow: Mir; 1984.
- Brebbia K, Telles J, Vroubel L. Methods of boundary elements. Moscow: Mir; 1987.
- Hang M, Okada A. Computation of GMAW welding heat transfer with boundary element method. Adv Eng Software. 1993;16(1):1–5.
- Golovanov NN. Geometric modeling. Moscow: Physico-mathematical literature; 2002.