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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Verfasserangaben:O. Iliev, R. Lazarov, J. Willems
URN (Permalink):urn:nbn:de:hbz:386-kluedo-15660
Schriftenreihe (Bandnummer):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (142)
Sprache der Veröffentlichung:Englisch
Jahr der Fertigstellung:2008
Jahr der Veröffentlichung:2008
Veröffentlichende Institution:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Datum der Publikation (Server):25.06.2008
Freies Schlagwort / Tag:effective heat conductivity; fibrous materials; graph laplacian; numerical upscaling
Fachbereiche / Organisatorische Einheiten:Fraunhofer (ITWM)
DDC-Sachgruppen:5 Naturwissenschaften und Mathematik / 510 Mathematik
Lizenz (Deutsch):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011