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A POD Analysis Method for Multi-Media Heat Conduction Problems

[+] Author Affiliations
Xiao-Wei Gao, Jin-Xiu Hu, Shi-Zhang Huang

Dalian University of Technology, Dalian, Liaoning, China

Paper No. IMECE2014-36561, pp. V08BT10A012; 8 pages
doi:10.1115/IMECE2014-36561
From:
  • ASME 2014 International Mechanical Engineering Congress and Exposition
  • Volume 8B: Heat Transfer and Thermal Engineering
  • Montreal, Quebec, Canada, November 14–20, 2014
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4956-9
  • Copyright © 2014 by ASME

abstract

In this paper, a new POD-based 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 Proper Orthogonal Decomposition (POD) technique is applied to facilitate reduced-order modeling of the unsteady heat conduction behavior. The snapshot matrix is constructed medium by medium by collecting individual medium solutions at different instants in time through a column-wise manner. By means of expressing physical variables in terms of reduced modes at individual medium level, a system of differential equations about 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 any desired time steps. A numerical example is given to demonstrate the efficiency of the proposed method.

Copyright © 2014 by ASME

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