Multiscale Simulation of 2D Heat Transfer in Composite Media Based on Global–Local Enrichment Functions

Guangzhong Liu (), Jiamin Guo, Yan Bao and Huan Ping
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Guangzhong Liu: School of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China
Jiamin Guo: School of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China
Yan Bao: Department of Civil Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Huan Ping: School of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China

Mathematics, 2025, vol. 13, issue 7, 1-19

Abstract: In this study, the extended finite element method (XFEM) was integrated into the generalized multiscale finite element method with global–local enrichment (GFEM gl ) to simulate 2D heat conduction in highly heterogeneous materials (i.e., matrixes with numerous randomly distributed inclusions or voids). This multiscale scheme was used to evaluate the effective thermal conductivity (ETC) of composites through simulation based on a representative volume element (RVE). In the proposed method, global–local enrichments are numerically constructed and incorporated into the global approximation in a hierarchical manner to integrate microstructure information into the macroscale problem. The XFEM is employed on a microscale mesh to avoid using a conformal mesh. RVEs containing numerous inclusions or voids with different volume fractions were numerically simulated using the proposed multiscale method, and the obtained results were compared with those of the standard single-scale XFEM and analytical models. The simulation results indicated that the proposed method has excellent accuracy and considerably lower computational cost.

Keywords: heat transfer; GFEM gl; XFEM; composite materials; effective thermal conductivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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