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Higher Order Multiscale Finite Element Method for Heat Transfer Modeling.
Marek Klimczak1, Witold Cecot1
1Faculty of Civil Engineering, Cracow University of Technology, Warszawska 24 Street, 31-155 Cracow, Poland.
Materials (Basel, Switzerland)
|July 24, 2021
Summary
This study introduces an improved multiscale finite element method (MsFEM) for modeling heat transfer in complex materials. The enhanced MsFEM achieves accurate results with fewer computational resources, demonstrating its effectiveness for heterogeneous composites.
Area of Science:
- Computational Science
- Materials Science
- Heat Transfer
Background:
- Modeling steady-state heat transfer in heterogeneous materials presents significant computational challenges.
- Existing multiscale methods often require scale separation or are limited in approximation order.
Purpose of the Study:
- To develop and validate a novel multiscale finite element method (MsFEM) approach for enhanced steady-state heat transfer modeling.
- To investigate the performance of higher-order MsFEM with modified shape functions for composite materials.
Main Methods:
- Improved multiscale finite element method (MsFEM) incorporating modified higher-order shape functions.
- Application to steady-state heat transfer problems in heterogeneous materials.
- Numerical validation against direct finite-element solutions.
Main Results:
- The higher-order MsFEM demonstrated high accuracy and efficiency, comparable to direct solutions.
- Significant reduction in the number of degrees of freedom was achieved, especially for challenging cases like metal foams.
- The method showed good p-convergence in terms of degrees of freedom and computational time.
Conclusions:
- The modified higher-order MsFEM is a robust and efficient tool for modeling heat transfer in heterogeneous materials.
- The approach offers broad applicability to composite materials without requiring distinct scale separation.
- This method provides a significant advantage in computational efficiency for complex thermal analysis.
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