Fast numerical upscaling of heat equation for fibrous materials

Handle URI:
http://hdl.handle.net/10754/598317
Title:
Fast numerical upscaling of heat equation for fibrous materials
Authors:
Iliev, Oleg; Lazarov, Raytcho; Willems, Joerg
Abstract:
We are interested in numerical methods for computing the effective heat conductivities of fibrous insulation materials, such as glass or mineral wool, characterized by low solid volume fractions and high contrasts, i.e., high ratios between the thermal conductivities of the fibers and the surrounding air. We consider a fast numerical method for solving some auxiliary cell problems appearing in this upscaling procedure. The auxiliary problems are boundary value problems of the steady-state heat equation in a representative elementary volume occupied by fibers and air. We make a simplification by replacing these problems with appropriate boundary value problems in the domain occupied by the fibers only. Finally, the obtained problems are further simplified by taking advantage of the slender shape of the fibers and assuming that they form a network. A discretization on the graph defined by the fibers is presented and error estimates are provided. The resulting algorithm is discussed and the accuracy and the performance of the method are illusrated on a number of numerical experiments. © Springer-Verlag 2010.
Citation:
Iliev O, Lazarov R, Willems J (2010) Fast numerical upscaling of heat equation for fibrous materials. Computing and Visualization in Science 13: 275–285. Available: http://dx.doi.org/10.1007/s00791-010-0144-2.
Publisher:
Springer Nature
Journal:
Computing and Visualization in Science
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
Aug-2010
DOI:
10.1007/s00791-010-0144-2
Type:
Article
ISSN:
1432-9360; 1433-0369
Sponsors:
There search of R.Lazarov was supported in partsby NSF Grant DMS-0713829, by the European School for IndustrialMathematics (ESIM) sponsored through the Erasmus Mundus programof the EU, and by award KUS-C1-016-04, made by King Abdullah Uni-versity of Science and Technology (KAUST). O. Iliev was supportedby DAAD-PPP D/07/10578, and J. Willems was supported by DAAD-PPPD/07/10578andtheStudienstiftungdesdeutschenVolkes(GermanNational Academic Foundation).
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Full metadata record

DC FieldValue Language
dc.contributor.authorIliev, Olegen
dc.contributor.authorLazarov, Raytchoen
dc.contributor.authorWillems, Joergen
dc.date.accessioned2016-02-25T13:18:36Zen
dc.date.available2016-02-25T13:18:36Zen
dc.date.issued2010-08en
dc.identifier.citationIliev O, Lazarov R, Willems J (2010) Fast numerical upscaling of heat equation for fibrous materials. Computing and Visualization in Science 13: 275–285. Available: http://dx.doi.org/10.1007/s00791-010-0144-2.en
dc.identifier.issn1432-9360en
dc.identifier.issn1433-0369en
dc.identifier.doi10.1007/s00791-010-0144-2en
dc.identifier.urihttp://hdl.handle.net/10754/598317en
dc.description.abstractWe are interested in numerical methods for computing the effective heat conductivities of fibrous insulation materials, such as glass or mineral wool, characterized by low solid volume fractions and high contrasts, i.e., high ratios between the thermal conductivities of the fibers and the surrounding air. We consider a fast numerical method for solving some auxiliary cell problems appearing in this upscaling procedure. The auxiliary problems are boundary value problems of the steady-state heat equation in a representative elementary volume occupied by fibers and air. We make a simplification by replacing these problems with appropriate boundary value problems in the domain occupied by the fibers only. Finally, the obtained problems are further simplified by taking advantage of the slender shape of the fibers and assuming that they form a network. A discretization on the graph defined by the fibers is presented and error estimates are provided. The resulting algorithm is discussed and the accuracy and the performance of the method are illusrated on a number of numerical experiments. © Springer-Verlag 2010.en
dc.description.sponsorshipThere search of R.Lazarov was supported in partsby NSF Grant DMS-0713829, by the European School for IndustrialMathematics (ESIM) sponsored through the Erasmus Mundus programof the EU, and by award KUS-C1-016-04, made by King Abdullah Uni-versity of Science and Technology (KAUST). O. Iliev was supportedby DAAD-PPP D/07/10578, and J. Willems was supported by DAAD-PPPD/07/10578andtheStudienstiftungdesdeutschenVolkes(GermanNational Academic Foundation).en
dc.publisherSpringer Natureen
dc.subjectEffective heat conductivityen
dc.subjectFibrous materialsen
dc.subjectNumerical upscalingen
dc.titleFast numerical upscaling of heat equation for fibrous materialsen
dc.typeArticleen
dc.identifier.journalComputing and Visualization in Scienceen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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