A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements

HOU Junjian; GUO Zhuangzhi; ZHONG Yudong; HE Wenbin; ZHOU Fang; XIE Guizhong

doi:10.21656/1000-0887.410394

Volume 42 Issue 11

Nov. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(11): 1169-1176

HOU Junjian, GUO Zhuangzhi, ZHONG Yudong, HE Wenbin, ZHOU Fang, XIE Guizhong. A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1169-1176. doi: 10.21656/1000-0887.410394

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A Boundary Element Method for Steady-State Heat Transfer Problems Based on a Novel Type of Interpolation Elements

doi: 10.21656/1000-0887.410394

HOU Junjian^{1, 2
,},
GUO Zhuangzhi^{1, 2},
ZHONG Yudong^{1, 2
,},
HE Wenbin^{1, 2},
ZHOU Fang^{1, 2},
XIE Guizhong^{1, 2}

1.
College of Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, P.R.China
2.
Henan Engineering Research Center of New Energy Vehicle Lightweight Design and Manufacturing, Zhengzhou 450002, P.R.China

Received Date: 2020-12-24
Rev Recd Date: 2021-05-07

Available Online: 2021-12-07

Publish Date: 2021-11-30

Abstract

Abstract

To improve the computational accuracy of the boundary element method (BEM) for solving the steady-state heat problems, a new method was studied with a new element interpolation method (called expansion element interpolation method). The novel expansion interpolation element was obtained through configuration of virtual nodes at the boundary of the traditional discontinuous element, to transform the original discontinuous element into a higher-order continuous element. The interpolation function constructed with the virtual node and the internal source node can accurately work in the continuous and discontinuous physical fields on the boundary, and the interpolation accuracy increases by 2 orders compared with that of the original discontinuous element. In addition, the boundary integral equation is only valid at the internal source nodes of the traditional discontinuous element and contains only the degrees of freedom of the source nodes, while the degrees of freedom of the virtual node can be eliminated through the relationship between the virtual node and the internal source node, so the size of the final linear system equations will not increase. This new interpolation element inherits the advantages of the traditional continuous and discontinuous elements and overcomes their disadvantages. The numerical results show that, the proposed method helps solve the steady-state heat transfer problem with high computational accuracy and convergence.
- boundary element method,
- boundary integral equation,
- steady-state heat transfer,
- interpolation element

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References(18)

References

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