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Real-Time Reliable Simulation of Heat Transfer Phenomena

[+] Author Affiliations
G. Rozza

Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

D. B. P. Huynh

National University of Singapore, Singapore

N. C. Nguyen, A. T. Patera

Massachusetts Institute of Technology, Cambridge, MA

Paper No. HT2009-88212, pp. 851-860; 10 pages
doi:10.1115/HT2009-88212
From:
  • ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences
  • Volume 3: Combustion, Fire and Reacting Flow; Heat Transfer in Multiphase Systems; Heat Transfer in Transport Phenomena in Manufacturing and Materials Processing; Heat and Mass Transfer in Biotechnology; Low Temperature Heat Transfer; Environmental Heat Transfer; Heat Transfer Education; Visualization of Heat Transfer
  • San Francisco, California, USA, July 19–23, 2009
  • Conference Sponsors: Heat Transfer Division
  • ISBN: 978-0-7918-4358-1 | eISBN: 978-0-7918-3851-8
  • Copyright © 2009 by ASME

abstract

In this paper we discuss the application of the certified reduced basis method and the associated software package rbMIT© to “worked problems” in steady and unsteady conduction. Each worked problem is characterized by an input parameter vector — material properties, boundary conditions and sources, and geometry — and desired outputs — selected fluxes and temperatures. The methodology and associated rbMIT© software, as well as the educational worked problem framework, consists of two distinct stages: an Offline (or “Instructor”) stage in which a new heat transfer worked problem is first created; and an Online (or “Lecturer”/“Student”) stage in which the worked problem is subsequently invoked in (say) various in-class, project, or homework settings. In the very inexpensive Online stage, given an input parameter value, the software returns both (i) an accurate reduced basis output prediction, and (ii) a rigorous bound for the error in the reduced basis prediction relative to an underlying expensive high-fidelity finite element discretization; as required in the educational context, the response is both rapid and reliable. We present illustrative results for two worked problems: a steady thermal fin, and unsteady thermal analysis of a delamination crack.

Copyright © 2009 by ASME

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