A multiscale scaled boundary finite element method solving steady-state heat conduction problem with heterogeneous materials

Abstract

A new numerical model is proposed by bridging small and large scales via the numerical base functions constructed by Scaled Boundary Finite Element Method (SBFEM) for the multiscale heterogeneous analysis of steady-state heat conduction problems. Utilizing the advantages of polygonal Scaled Boundary Finite Element (SBFE) and image-based quadtree gridding, the construction of base functions can be conveniently and efficiently conducted particularly for the heterogeneous media with complex geometries or singularity of heat flux at the small-scale, and the solution accuracy at the large-scale can be improved by increasing nodes of coarse element only without increasing new nodes inside. Consequently, the SBFEM based solutions at the large-scale can be solved with a reduced order and sufficient accuracy, and the solutions at the small-scale can be achieved using SBFEM based base functions. Numerical examples are provided and the effectiveness of the proposed approach is stressed at both the large and small scales.

Keywords:

• Heterogeneous materials
• multiscale analysis
• numerical base functions
• SBFEM
• steady-state heat conduction

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Funding

The research leading to this paper was funded by the NSFC Grants [12072063, 11972109], The National Key Research and Development Program of China [2020YFB1708304], the Fundamental Research Funds for the Central Universities [DUT20LK09, DUT21YG129]. The authors are also grateful for the advices and supports from Prof. Chongmin Song from UNSW and Prof. Yonggang Zheng from DUT.