复合材料结构温度相关非线性热辐射问题的高阶多尺度方法及其收敛性分析
A high-order multi-scale method and its convergence analysis for temperature-dependent nonlinear thermal radiation problems of composite structures
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中文总结 AI 辅助
针对复合材料结构温度相关非线性热辐射问题，建立含高阶校正项的多尺度模型与高效算法，推导收敛性并通过算例验证其精度高、计算成本低的优势。
中文摘要 AI 辅助
准确预测具有温度相关特性的复合材料结构中的非线性辐射热传递，对该类材料在高温领域的应用具有重要意义。本研究建立了一种高精度多尺度计算模型，该模型包含新型高阶校正项，可用于复合材料结构非线性热辐射的高保真模拟，实现热量的局部守恒。此外，推导了所得高阶多尺度解的显式收敛速率。进一步，开发了一种由离线和在线计算阶段组成的高效多尺度算法，用于复合材料结构非线性热辐射行为的高精度模拟，并获得了相应的收敛性分析。通过二维和三维数值算例验证了所提多尺度方法的竞争优势，不仅具有优异的数值精度，还降低了存储需求和计算时间方面的计算成本。
英文摘要
Accurate prediction of the nonlinear radiation thermal transfer in composite structures with temperature-dependent properties is significant in high-temperature applications of the materials. This study establishes a high-accuracy multi-scale computational model incorporating novel high-order correction terms for the high-fidelity simulation of nonlinear thermal radiation in composite structures, enabling local balance preserving of heat quantity. Moreover, an explicit convergence rate is also derived for the resulting high-order multi-scale solutions. Furthermore, an efficient multi-scale algorithm consisting of off-line and on-line computation stages is developed for high-accuracy simulation of nonlinear thermal radiation behavior in composite structures, and corresponding convergence analysis is also obtained. Two- and three-dimensional numerical examples are presented to validate the competitive advantages of the proposed multi-scale approach, not only exceptional numerical accuracy, but also reduced computational cost in both storage requirements and computational time.
