BIE formulation for axisymmetric transient heat conduction applications

References

• B. Yu, W. A. Yao, and Q. Gao, “A precise integration boundary-element method for solving transient heat conduction problems with variable thermal conductivity,” Numer. Heat Transf. B, vol. 65, no. 5, pp. 472–493, 2014. DOI: 10.1080/10407790.2013.873311.
   Web of Science ®Google Scholar
• G. Y. Li, S. P. Guo, J. M. Zhang, Y. Li, and L. Han, “Transient heat conduction analysis of functionally graded materials by a multiple reciprocity boundary face method,” Eng. Anal. Bound. Elem., vol. 60, pp. 81–88, 2015. DOI: 10.1016/j.enganabound.2015.03.006.
   Web of Science ®Google Scholar
• S. P. Guo, X. J. Li, J. M. Zhang, G. F. Bin, and W. Huang, “A triple reciprocity method in Laplace transform boundary element method for three-dimensional transient heat conduction problems,” Int. J. Heat Mass Transf., vol. 114, pp. 258–267, 2017. DOI: 10.1016/j.ijheatmasstransfer.2017.06.073.
   Web of Science ®Google Scholar
• D. Nardini and C. A. Brebbia, “A new approach to free vibration analysis using boundary elements,” Appl. Math. Model., vol. 7, no. 3, pp. 157–162, 1983. DOI: 10.1016/0307-904X(83)90003-3.
   Web of Science ®Google Scholar
• Y. Ochiai, “Three-dimensional heat conduction analysis of inhomogeneous materials by triple-reciprocity boundary element method,” Eng. Anal. Bound. Elem., vol. 51, pp. 101–108, 2015. DOI: 10.1016/j.enganabound.2014.10.014.
   Web of Science ®Google Scholar
• A. J. Nowak and C. A. Brebbia, “The multiple-reciprocity method-A new approach for transforming BEM domain integrals to the boundary,” Eng. Anal. Bound. Elem., vol. 6, no. 3, pp. 164–167, 1989. DOI: 10.1016/0955-7997(89)90032-5.
   Web of Science ®Google Scholar
• X. W. Gao, “The radial integration method for evaluation of domain integrals with boundary-only discretization,” Eng. Anal. Bound. Elem, vol. 26, no. 10, pp. 905–916, 2002. DOI: 10.1016/S0955-7997(02)00039-5.
   Web of Science ®Google Scholar
• W. Z. Feng, K. Yang, M. Cui. and X. W. Gao, “Analytically-integrated radial integration BEM for solving three-dimensional transient heat conduction problems,” Int. Commun. Heat Mass Transf., vol. 79, pp. 21–30, 2016. DOI: 10.1016/j.icheatmasstransfer.2016.10.010.
   Web of Science ®Google Scholar
• X. W. Gao, “A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity,” Int. J. Numer. Meth. Engng., vol. 66, no. 9, pp. 1411–1431, 2006. DOI: 10.1002/nme.1602.
   Web of Science ®Google Scholar
• X. W. Gao, “An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals,” Comput. Methods Appl. Mech. Eng., vol. 199, no. 45–48, pp. 2856–2864, 2010. DOI: 10.1016/j.cma.2010.05.008.
   Web of Science ®Google Scholar
• K. Yang and X. W. Gao, “Radial integration BEM for transient heat conduction problems,” Eng. Anal. Bound. Elem., vol. 34, no. 6, pp. 557–563, 2010. DOI: 10.1016/j.enganabound.2010.01.008.
   Web of Science ®Google Scholar
• H. F. Peng, M. Cui, and X. W. Gao, “A boundary element method without internal cells for solving viscous flow problems,” Eng. Anal. Bound. Elem., vol. 37, no. 2, pp. 293–300, 2013. DOI: 10.1016/j.enganabound.2012.09.014.
   Web of Science ®Google Scholar
• W. Z. Feng, J. Liu, and X. W. Gao, “An improved direct method for evaluating hyper singular stress boundary integral equations in BEM,” Eng. Anal. Bound. Elem., vol. 61, pp. 274–281, 2015. DOI: 10.1016/j.enganabound.2015.08.002.
   Web of Science ®Google Scholar
• M. Cui, B. B. Xu, W. Z. Feng, Y. Zhang, X. W. Gao, and H. F. Peng, “A radial integration boundary element method for solving transient heat conduction problems with heat sources and variable thermal conductivity,” Numer. Heat Transf. B-Fund., vol. 73, no. 1, pp. 1–18, 2018. DOI: 10.1080/10407790.2017.1420319.
   Web of Science ®Google Scholar
• W. Z. Feng, H. Y. Li, L. F. Gao, W. Qian, and K. Yang, “Hypersingular flux interface integral equation for multi-medium heat transfer analysis,” Int. Commun. Heat Mass Transf., vol. 138, pp. 852–865, 2019. DOI: 10.1016/j.ijheatmasstransfer.2019.04.055.
   Web of Science ®Google Scholar
• H. F. Peng, K. Liu, M. Cui, and X. W. Gao, “A meshless BEM for solving transient non-homogeneous convection-diffusion problem with variable velocity and source term,” Eng. Anal. Bound. Elem., vol. 121, pp. 65–75, 2020. DOI: 10.1016/j.enganabound.2020.09.009.
   Web of Science ®Google Scholar
• K. Yang, H. Y. Li, H. F. Peng, and X. W. Gao, “New interface integration BEM for solving Multi-medium nonlinear heat transfer problems,” Eng. Anal. Bound. Elem., vol. 117, pp. 66–75, 2020. DOI: 10.1016/j.enganabound.2020.03.015.
   Web of Science ®Google Scholar
• A. A. Becker, Boundary Element Method in Engineering. New York: McGraw-Hill, 1992.
   Google Scholar
• X. W. Gao, H. F. Peng, K. Yang, and J. Wang, Advanced Boundary Element Method—Theory and Codes (In Chinese). China: Scientific Publisher of China, 2015.
   Google Scholar