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.
- Heat Transfer Division
Real-Time Reliable Simulation of Heat Transfer Phenomena
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Rozza, G, Huynh, DBP, Nguyen, NC, & Patera, AT. "Real-Time Reliable Simulation of Heat Transfer Phenomena." Proceedings of the 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. pp. 851-860. ASME. https://doi.org/10.1115/HT2009-88212
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