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Research Papers: Conduction

A Proper Orthogonal Decomposition Analysis Method for Multimedia Heat Conduction Problems

[+] Author and Article Information
Xiaowei Gao

State Key Laboratory of Structural Analysis for
Industrial Equipment,
School of Aeronautics and Astronautics,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: xwgao@dlut.edu.cn

Jinxiu Hu

Department of Mechanical Engineering,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: dzyxhjx@126.com

Shizhang Huang

School of Aeronautics and Astronautics,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: szhdlut@qq.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received December 6, 2014; final manuscript received March 1, 2016; published online April 19, 2016. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 138(7), 071301 (Apr 19, 2016) (11 pages) Paper No: HT-14-1783; doi: 10.1115/1.4033081 History: Received December 06, 2014; Revised March 01, 2016

In this paper, a new proper orthogonal decomposition (POD) analysis method is proposed for numerical analysis of thermal mechanical engineering problems consisting of multiple media. After the creation of a heat conduction solution database for each medium, the “snapshot” approach of the POD technique is applied to facilitate reduced-order modeling (ROM) of the unsteady heat conduction behavior. The snapshot matrix is constructed medium by medium by collecting individual medium solutions at different instances in time through a columnwise manner. By means of expressing physical variables in terms of reduced modes at the individual medium level, a system of differential equations with respect to time is formed by utilizing the consistency conditions of the physical variables on interface boundaries. The solutions of the problem can be obtained by solving the system of equations at different time stops. Two numerical examples are given to demonstrate the efficiency of the proposed method.

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Figures

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Fig. 5

Proportion of eigenvalue for the left subdomain

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Fig. 2

FEM model of the rectangular plate with a hole

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Fig. 3

Mesh of left subdomain

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Fig. 4

Mesh of right subdomain

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Fig. 1

Geometry, media, and constant boundary condition of the rectangular plate with a hole

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Fig. 10

Temperature versus time at different points denoted in Fig. 2 for constant boundary condition

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Fig. 11

Temperature versus time at different points for boundary condition 2

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Fig. 12

Temperature versus time at different points for boundary condition 3

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Fig. 13

Absolute error versus time at different points for constant boundary condition

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Fig. 6

Relative error using truncated modes for the left subdomain

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Fig. 7

Proportion of eigenvalue for the right subdomain

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Fig. 8

Relative error using truncated modes for the right subdomain

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Fig. 9

The POD modes of temperature field for left and right subdomains (the first five)

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Fig. 14

Absolute error versus time at different points for boundary condition 2

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Fig. 15

Absolute error versus time at different points for boundary condition 3

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Fig. 16

Comparison of real and fictitious temperature on the interface of the rectangular plate with a hole

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Fig. 26

Absolute error versus time at different points for constant boundary condition

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Fig. 27

Absolute error versus time at different points for boundary condition 2

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Fig. 28

Absolute error versus time at different points for boundary condition 3

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Fig. 17

Geometry and constant boundary conditions of the cylinder parts

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Fig. 18

FEM model and two media of the cylinder parts

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Fig. 19

Proportion of eigenvalue for the upper subdomain

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Fig. 20

Relative error using truncated modes for the upper subdomain

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Fig. 21

Proportion of eigenvalue for the lower subdomain

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Fig. 22

Relative error using truncated modes for the lower subdomain

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Fig. 23

Temperature versus time at different points for constant boundary condition

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Fig. 24

Temperature versus time at different points for boundary condition 2

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Fig. 25

Temperature versus time at different points for boundary condition 3

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