NDLI: Efficient analysis of transient heat transfer problems exhibiting sharp thermal gradients

Content Provider	Springer Nature Link
Author	O’Hara, P. Duarte, C. A. Eason, T. Garzon, J.
Copyright Year	2012
Abstract	In this paper, heat transfer problems with sharp spatial gradients are analyzed using the Generalized Finite Element Method with global-local enrichment functions (GFEM gl). With this approach, scale-bridging enrichment functions are generated on the fly, providing specially-tailored enrichment functions for the problem to be analyzed with no a-priori knowledge of the exact solution. In this work, a decomposition of the linear system of equations is formulated for both steady-state and transient heat transfer problems, allowing for a much more computationally efficient analysis of the problems of interest. With this algorithm, only a small portion of the global system of equations, i.e., the hierarchically added enrichments, need to be re-computed for each loading configuration or time-step. Numerical studies confirm that the condensation scheme does not impact the solution quality, while allowing for more computationally efficient simulations when large problems are considered. We also extend the GFEM gl to allow for the use of hexahedral elements in the global domain, while still using tetrahedral elements in the local domain, to allow for automatic localized mesh refinement without the use of constrained approximations. Simulations are run with the use of linear and quadratic hexahedral and tetrahedral elements in the global domain. Convergence studies indicate that the use of a different partition of unity (PoU) in the global (hexahedral elements) and local (tetrahedral elements) domains does not adversely impact the solution quality.
Starting Page	743
Ending Page	764
Page Count	22
File Format	PDF
ISSN	01787675
Journal	Computational Mechanics
Volume Number	51
Issue Number	5
e-ISSN	14320924
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-06-30
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Generalized finite elements Global-local finite elements Multi scale methods hp-Methods Transient analysis Theoretical and Applied Mechanics Computational Science and Engineering Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Ocean Engineering Computational Theory and Mathematics Mechanical Engineering Computational Mechanics Computational Mathematics

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