A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

Chengxin Zhang; Chao Wang; Shouhai Chen; Fajie Wang

doi:10.32604/cmes.2023.024884

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ARTICLE

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

Chengxin Zhang¹, Chao Wang¹, Shouhai Chen^2,*, Fajie Wang^1,*
1 College of Mechanical and Electrical Engineering, National Engineering Research Center for Intelligent Electrical Vehicle Power System, Qingdao University, Qingdao, 266071, China
2 Hisense (Shandong) Air Conditioner Co., Ltd., Qingdao, 266100, China
* Corresponding Authors: Shouhai Chen. Email: ; Fajie Wang. Email:
(This article belongs to this Special Issue: Advances on Mesh and Dimension Reduction Methods)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2407-2424. https://doi.org/10.32604/cmes.2023.024884

Received 11 June 2022; Accepted 09 August 2022; Issue published 23 November 2022

Abstract

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two- and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

Keywords

Local knot method; transient heat conduction; dual reciprocity method; meshless method

Cite This Article

Zhang, C., Wang, C., Chen, S., Wang, F. (2023). A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains. CMES-Computer Modeling in Engineering & Sciences, 135(3), 2407–2424.

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