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B. Yu, Yuhuan Tong, Pengmin Hu, Q. Gao (2020)
A novel inversion approach for identifying the shape of cavity by combining Gappy POD with direct inversion schemeInternational Journal of Heat and Mass Transfer, 150
Chuanbao Nie, Bo Yu (2019)
Inversing heat flux boundary conditions based on precise integration FEM without iteration and estimation of thermal stress in FGMsInternational Journal of Thermal Sciences
E. Divo, A. Kassab, Franklin Rodríguez (2003)
PARALLEL DOMAIN DECOMPOSITION APPROACH FOR LARGE-SCALE THREE-DIMENSIONAL BOUNDARY-ELEMENT MODELS IN LINEAR AND NONLINEAR HEAT CONDUCTIONNumerical Heat Transfer, Part B: Fundamentals, 44
L. Wrobel, C. Brebbia (1987)
The dual reciprocity boundary element formulation for diffusion problemsApplied Mechanics and Engineering, 65
M. Ingber, C. Schmidt, J. Tanski, J. Phillips (2003)
BOUNDARY-ELEMENT ANALYSIS OF 3-D DIFFUSION PROBLEMS USING A PARALLEL DOMAIN DECOMPOSITION METHODNumerical Heat Transfer, Part B: Fundamentals, 44
Yan Gu, Qingsong Hua, Chuanzeng Zhang, Xiaoqiao He (2019)
The generalized finite difference method for long-time transient heat conduction in 3D anisotropic composite materialsApplied Mathematical Modelling
M. Mohammadi, M. Hematiyan, L. Marin (2010)
Boundary element analysis of nonlinear transient heat conduction problems involving non-homogenous and nonlinear heat sources using time-dependent fundamental solutionsEngineering Analysis With Boundary Elements, 34
A. Fic, R. Białecki, A. Kassab (2005)
Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element MethodNumerical Heat Transfer, Part B: Fundamentals, 48
Bingbing Xu, Xiaowei Gao, M. Cui (2020)
An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problemsEngineering with Computers
Qianghua Zhu, Yuanbo Liang, Xiaowei Gao (2020)
A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 1: Basic algorithmNumerical Heat Transfer, Part B: Fundamentals, 77
R. Białecki, G. Kuhn (1993)
Boundary element solution of heat conduction problems in multizone bodies of non-linear materialInternational Journal for Numerical Methods in Engineering, 36
Q. Gao, C. Nie (2021)
An accurate and efficient Chebyshev expansion method for large-scale transient heat conduction problemsComputers & Structures
M. Guillot, S. McCool (2015)
Effect of boundary condition approximation on convergence and accuracy of a finite volume discretization of the transient heat conduction equationInternational Journal of Numerical Methods for Heat & Fluid Flow, 25
Liangxian Gu, Yifan Wang, S. Shi, Dai Cunxi (2016)
An approximate analytical method for nonlinear transient heat transfer through a metallic thermal protection systemInternational Journal of Heat and Mass Transfer, 103
O. Balima, Y. Favennec, D. Petit (2007)
Model Reduction for Heat Conduction with Radiative Boundary Conditions using the Modal Identification MethodNumerical Heat Transfer, Part B: Fundamentals, 52
A. Khosravifard, M. Hematiyan, L. Marin (2011)
Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation methodApplied Mathematical Modelling, 35
H. Thakur, K. Singh, P. Sahoo (2010)
Meshless Local Petrov-Galerkin Method for Nonlinear Heat Conduction ProblemsNumerical Heat Transfer, Part B: Fundamentals, 56
A. Gaonkar, S. Kulkarni (2015)
Application of multilevel scheme and two level discretization for POD based model order reduction of nonlinear transient heat transfer problemsComputational Mechanics, 55
M. Ingber, Chingshyang Chen, J. Tanski (2004)
A mesh free approach using radial basis functions and parallel domain decomposition for solving three‐dimensional diffusion equationsInternational Journal for Numerical Methods in Engineering, 60
H. Cui, Q. Gao, Xiaolan Li, H. Ouyang (2019)
An efficient and accurate method for transient heat conduction in a periodic structure with moving heat sourcesInternational Journal of Numerical Methods for Heat & Fluid Flow, 30
Yasong Sun, Xinyu Li, Jiazi Zhao, Yang Hu, Xin Jing, Jing Ma, Ruirui Zhou (2022)
Investigation of transient coupled conduction and radiation heat transfer in the linearly anisotropic scattering cylindrical medium by spectral collocation methodInternational Journal of Thermal Sciences
K. Erhart, E. Divo, A. Kassab (2006)
A parallel domain decomposition boundary element method approach for the solution of large-scale transient heat conduction problemsEngineering Analysis With Boundary Elements, 30
Akhilendra Singh, I. Singh, R. Prakash (2006)
Numerical Solution of Temperature-Dependent Thermal Conductivity Problems Using a Meshless MethodNumerical Heat Transfer, Part A: Applications, 50
H. Chu, Chieh-Li Chen (2008)
Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problemCommunications in Nonlinear Science and Numerical Simulation, 13
C. Farhat, F. Roux (1991)
A method of finite element tearing and interconnecting and its parallel solution algorithmInternational Journal for Numerical Methods in Engineering, 32
P. Nakshatrala, K. Nakshatrala, D. Tortorelli (2009)
A time‐staggered partitioned coupling algorithm for transient heat conductionInternational Journal for Numerical Methods in Engineering, 78
K. Nakshatrala, K. Hjelmstad, D. Tortorelli (2008)
A FETI‐based domain decomposition technique for time‐dependent first‐order systems based on a DAE approachInternational Journal for Numerical Methods in Engineering, 75
Xiaohua Zhang, Hui Xiang (2015)
A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problemsInternational Journal of Heat and Mass Transfer, 84
Qianghua Zhu, Yuanbo Liang, Xiaowei Gao (2020)
A proper orthogonal decomposition analysis method for transient nonlinear heat conduction problems. Part 2: Advanced algorithmNumerical Heat Transfer, Part B: Fundamentals, 77
Genghui Jiang, Hua‐Yu Liu, Kai Yang, Xiaowei Gao (2020)
A fast reduced-order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problemsComputer Methods in Applied Mechanics and Engineering, 368
Jiannan Tang, Mei Huang, Mengling Yang, Yuanyuan Zhao, Xiaoping Ouyang (2018)
A procedure for solving transient nonlinear thermal problems of high burn-up nuclear fuel rods in a light water reactorApplied Thermal Engineering
B. Yu, Pengmin Hu, A. Saputra, Yan Gu (2021)
The scaled boundary finite element method based on the hybrid quadtree mesh for solving transient heat conduction problemsApplied Mathematical Modelling, 89
H. Cui, Q. Gao, Xiaolan Li, H. Ouyang (2020)
A Novel Method for Transient Heat Conduction in a Quasi-Periodic Structure With Nonlinear DefectsJournal of Heat Transfer-transactions of The Asme, 142
Zhiqiang Yang, J. Cui, Yi Sun, J. Ge (2015)
Multiscale computation for transient heat conduction problem with radiation boundary condition in porous materialsFinite Elements in Analysis and Design, 102
S. Feng, X. Cui, A. Li, G. Xie (2016)
A face-based smoothed point interpolation method (FS-PIM) for analysis of nonlinear heat conduction in multi-material bodiesInternational Journal of Thermal Sciences, 100
M. Girault, D. Petit (2005)
Identification methods in nonlinear heat conduction. Part I: Model reductionInternational Journal of Heat and Mass Transfer, 48
O. Balima, Y. Favennec, M. Girault, D. Petit (2006)
Comparison between the modal identification method and the POD‐Galerkin method for model reduction in nonlinear diffusive systemsInternational Journal for Numerical Methods in Engineering, 67
Ł. Brodzik, A. Frąckowiak (2019)
Optimization of the heat flow by solving inverse problem in the protective layer of the TPS panelInternational Journal of Numerical Methods for Heat & Fluid Flow
Yuanbo Liang, Xiaowei Gao, Bingbing Xu, Qianghua Zhu, Z. Wu (2020)
A new alternating iteration strategy based on the proper orthogonal decomposition for solving large-scaled transient nonlinear heat conduction problemsJ. Comput. Sci., 45
Lin Cheng, G. Wagner (2021)
An optimally-coupled multi-time stepping method for transient heat conduction simulation for additive manufacturingComputer Methods in Applied Mechanics and Engineering, 381
K. Cole, J. Beck, A. Haji-sheikh, B. Litkouhi (1992)
Heat Conduction Using Green's Function
Q. Gao, H. Cui (2018)
Efficient and accurate method for 2D periodic structures based on the physical features of the transient heat conductionInternational Journal of Thermal Sciences, 127
J. Álvarez-Hostos, Erick Gutierrez-Zambrano, Joselynne Salazar-Bove, E. Puchi-Cabrera, A. Bencomo (2019)
Solving heat conduction problems with phase-change under the heat source term approach and the element-free Galerkin formulationInternational Communications in Heat and Mass Transfer
This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources.Design/methodology/approachBased on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique.FindingsWithin a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure.Originality/valueAn efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.
International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing
Published: Jan 3, 2023
Keywords: Nonlinear; Transient heat conduction; Radiation boundary condition; Green’s function; Quasi-superposition principle
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