Higher order multiscale finite element method for heat transfer modeling
Authors:
- Marek Klimczak,
- Witold Cecot
Abstract
In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.
- Record ID
- CUTb0dbfa92b4944984ae66682d066bdd22
- Publication categories
- ;
- Author
- Journal series
- Materials, ISSN , e-ISSN 1996-1944, Biweekly
- Issue year
- 2021
- Vol
- 14
- No
- 14
- Pages
- [1-17]
- Article number
- 3827
- Other elements of collation
- schem.; wykr.; Bibliografia (na s.) - 16-17; Bibliografia (liczba pozycji) - 52; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 14, Iss. 14, Spec. Iss.
- Substantive notes
- Special Issue: Computational Mechanics of Structures and Materials
- Keywords in English
- heat transfer, multiscale finite element method, homogenization
- DOI
- DOI:10.3390/ma14143827 Opening in a new tab
- URL
- https://www.mdpi.com/1996-1944/14/14/3827/htm Opening in a new tab
- Related project
- Połączenie wieloskalowej metody elementów skończonych z nieciągłym podejściem Petrowa-Galerkina. . Project leader at PK: , ,
Projects financed by NSC [Projekty finansowane przez NCN] - Language
- eng (en) English
- License
- Score (nominal)
- 140
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTb0dbfa92b4944984ae66682d066bdd22/
- URN
urn:pkr-prod:CUTb0dbfa92b4944984ae66682d066bdd22
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.