Real-Time Reliable Simulation of Heat Transfer Phenomena

In this paper we discuss the application of the certified reduced basis method and the associated software package rbMIT (c) 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(c) 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 \emph{and} reliable. We present illustrative results for two worked problems: a steady thermal fin, and unsteady thermal analysis of a delamination crack.


Published in:
Proceedings of the ASME HT 2009 summer conference
Presented at:
ASME -American Society of Mechanical Engineers - Heat Transfer Summer Conference, paper HT2009-88212, S. Francisco, CA, USA, 19-23 July 2009
Year:
2009
Publisher:
NewYork, ASME
Keywords:
Note:
presented in the Educational Section of the conference. EPFL-IACS report 06.2009, peer reviewed
Laboratories:




 Record created 2009-05-07, last modified 2018-03-17

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