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Galerkin-based quasi-smooth manifold element (QSME) method for anisotropic heat conduction problems in composites with complex geometry

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Abstract

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method (FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element (QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional (2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity. The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom (DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

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Abbreviations

c :

specific heat capacity

g :

heat source

h :

heat convection coefficient

J :

Jacobian matrix

k :

thermal conductivity tensor

L i :

area coordinates

N :

element approximation function vector

q :

heat flux

q n :

heat flux normal to the boundary

T :

temperature

T ∞ :

ambient temperature

T e :

element degree of freedom (DOF) vector

t :

time variable

x :

spatial coordinate.

Ω:

solving domain

ΓT :

temperature boundary

Γq :

heat flux boundary

Γc :

convection boundary

ρ :

mass density

λ :

penalty factor

η i :

weight for boundary integration.

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Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410083, China

    Pan Wang, Xiangcheng Han, Weibin Wen & Jun Liang

  2. Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081, China

    Xiangcheng Han & Jun Liang

  3. School of Science, Harbin Institute of Technology, Shenzhen, 518055, Guangdong Province, China

    Baolin Wang

Authors
  1. Pan Wang
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  2. Xiangcheng Han
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  4. Baolin Wang
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  5. Jun Liang
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Corresponding authors

Correspondence to Weibin Wen or Jun Liang.

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Conflict of interest The authors declare no conflict of interest.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 12102043, 12072375, and U2241240) and the Natural Science Foundation of Hunan Province of China (Nos. 2023JJ40698 and 2021JJ40710)

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Wang, P., Han, X., Wen, W. et al. Galerkin-based quasi-smooth manifold element (QSME) method for anisotropic heat conduction problems in composites with complex geometry. Appl. Math. Mech.-Engl. Ed. 45, 137–154 (2024). https://doi.org/10.1007/s10483-024-3072-8

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  • DOI: https://doi.org/10.1007/s10483-024-3072-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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