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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A Proper Orthogonal Decomposition Analysis Method for Multimedia Heat Conduction Problems
Xiaowei Gao,
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
Industrial Equipment,
School of Aeronautics and Astronautics,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: xwgao@dlut.edu.cn
Search for other works by this author on:
Jinxiu Hu,
Jinxiu Hu
Department of Mechanical Engineering,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: dzyxhjx@126.com
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: dzyxhjx@126.com
Search for other works by this author on:
Shizhang Huang
Shizhang Huang
School of Aeronautics and Astronautics,
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: szhdlut@qq.com
Dalian University of Technology,
Dalian, Liaoning 116023, China
e-mail: szhdlut@qq.com
Search for other works by this author on:
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
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
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
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. Jul 2016, 138(7): 071301 (11 pages)
Published Online: April 19, 2016
Article history
Received:
December 6, 2014
Revised:
March 1, 2016
Citation
Gao, X., Hu, J., and Huang, S. (April 19, 2016). "A Proper Orthogonal Decomposition Analysis Method for Multimedia Heat Conduction Problems." ASME. J. Heat Transfer. July 2016; 138(7): 071301. https://doi.org/10.1115/1.4033081
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