Topology optimization of non-Fourier heat conduction problems considering global thermal dissipation energy minimization

Zhao, Qinghai; Wang, Fajie; Tie-zhu, Zhang; Li, Xinqing

doi:10.1007/s00158-021-02924-0

Cited by 9 publications

(1 citation statement)

References 60 publications

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“…There are many kinds of conventional numerical methods applied to transient heat conduction problems, for instance, the finite element method (FEM) [3,4], the finite difference method (FDM) [5] and the boundary element method (BEM) [6,7]. Among them, the FEM has been widely used in engineering and scientific calculation, and its mature commercial software has been widely used to analyze and simulate practical problems.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang¹,

Wang²,

Chen³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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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.

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