Multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains

TL;DR

This paper introduces a multiscale computational method using second-order two-scale solutions for heat conduction in composite structures with various periodic configurations, validated by numerical examples.

Contribution

The paper develops a novel SOTS-based multiscale method and provides error analysis and a finite element algorithm for heat conduction in complex composite structures.

Findings

The SOTS solutions effectively model heat conduction in diverse composite structures.

Error estimates confirm the accuracy of the SOTS approximate solutions.

Numerical examples demonstrate the method's feasibility and effectiveness.

Abstract

This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on asymptotic homogenization method. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing SOTS solutions. Furthermore, the error estimates for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.