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Engineering with Computers

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28.06.2020 | Original Article

An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems

verfasst von: Bing-Bing Xu, Xiao-Wei Gao, Miao Cui

Erschienen in: Engineering with Computers | Ausgabe 2/2022

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Abstract

Our purpose is to establish a numerical method meeting the requirements of efficiency, stability, accuracy and easy-using. Faced with these demands, in this paper, a hybrid method combining the advantages of 2 weak-form meshless methods is proposed for solving steady and transient heat conduction problems with temperature-dependent thermophysical properties in heterogeneous media. In the process of the calculation for an arbitrary model discretized by the hybrid method, two different weak-form methods are used for the nodes categorized as: (1) boundary nodes, (2) near boundary interior nodes and (3) interior nodes. A Galerkin free element method (GFREM) is proposed for the interior nodes of the Cartesian grid; and the local radial point interpolation method (LRPIM) is used for the other two types of nodes. The GFREM using the Cartesian grid can greatly improve the accuracy and efficiency of the hybrid scheme. Special decomposition technology to determine the irregular integral domain for LRPIM can increase the flexibility for complex models. In addition, the full implicit finite difference scheme and Newton–Raphson method are used for solving transient nonlinear problems. And non-crossing interface integral domain and support domain are employed for heterogeneous media. Compared with other methods, numerical results show better accuracy, stability and efficiency from the numerical experiments.

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Titel: An efficient and accurate hybrid weak-form meshless method for transient nonlinear heterogeneous heat conduction problems
verfasst von: Bing-Bing Xu
Xiao-Wei Gao
Miao Cui
Publikationsdatum: 28.06.2020
Verlag: Springer London
Erschienen in: Engineering with Computers / Ausgabe 2/2022
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-020-01050-7

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