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针对拟周期复合材料结构的热传导问题,基于多尺度渐近分析,建立了一种高精度高阶多尺度计算模型(包括低阶和高阶细观单胞模型、宏观均匀化模型和宏-细观关联的二阶双尺度渐近解)。通过点点意义下的局部误差分析,证明了二阶双尺度解可以保证热通量的局部平衡,从而精确捕捉拟周期复合材料结构细观尺度的振荡行为。然后,通过积分意义下的全局误差分析,得到了二阶双尺度渐近解的显式误差估计。进一步,基于有限元方法、有限差分方法和插值方法,发展了可以有效求解拟周期复合材料结构热传导问题的多尺度数值算法。最后,通过数值实验验证了所建立的高阶多尺度计算方法的有效性,特别是该方法的高精度计算性能。
Abstract:In this paper, a comprehensive computational framework is established based on multiscale asymptotic analysis for analyzing the heat conduction performances of quasi-periodic composite structures, integrating lower-and higher-order microscopic unit cell models, a homogenized macroscopic model, and a second-order two-scale asymptotic solution with macro-micro correlations. Subsequently, local error analysis demonstrates that the second-order two-scale solution ensures local heat flux balance, accurately capturing the micro-scale oscillating behavior of quasiperiodic composite structures. Furthermore, global error analysis in the integral sense provides explicit error estimates for the second-order two-scale solution. Additionally, a multi-scale numerical algorithm is developed, combining the finite element method, finite difference method, and interpolation method, to effectively solve the heat conduction problem. Finally, numerical experiments confirm the effectiveness of the proposed method, in particular, its high-precision computational performance is thoroughly validated.
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基本信息:
DOI:10.12194/j.ntu.20241125001
中图分类号:TB33
引用信息:
[1]丁奕菲,董灏.拟周期复合材料结构热传导问题的高阶多尺度计算方法及误差估计[J].南通大学学报(自然科学版),2026,25(02):43-52.DOI:10.12194/j.ntu.20241125001.
基金信息:
国家自然科学基金面上项目(12471387); 陕西省科协青年人才托举计划项目(20220506); 西安电子科技大学2024年学科交叉拓展特支计划项目(TZJH2024008); 中央高校基本科研业务费项目(ZYTS24071)
2025-04-24
2025-04-24
2025-04-24