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A Graph-Laplacian approach for calculating the effective thermal conductivity of complicated fiber geometries

  • Abstract. An efficient approach to the numerical upscaling of thermal conductivities of fibrous media, e.g. insulation materials, is considered. First, standard cell problems for a second order elliptic equation are formulated for a proper piece of random fibrous structure, following homogenization theory. Next, a graph formed by the fibers is considered, and a second order elliptic equation with suitable boundary conditions is solved on this graph only. Replacing the boundary value problem for the full cell with an auxiliary problem with special boundary conditions on a connected subdomain of highly conductive material is justified in a previous work of the authors. A discretization on the graph is presented here, and error estimates are provided. The efficient implementation of the algorithm is discussed. A number of numerical experiments is presented in order to illustrate the performance of the proposed method.

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Author:O. Iliev, R. Lazarov, J. Willems
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15660
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (142)
Document Type:Report
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2008/06/25
Tag:effective heat conductivity; fibrous materials; graph laplacian; numerical upscaling
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011