周期性材料非经典热传导时空间多尺度分析方法

研究了一种空间-时间多尺度的方法,来分析周期性材料中非傅立叶热传导问题。计算模型是根据空间-时间尺度的高阶均匀化理论建立的,通过引入放大空间尺度和缩小时间尺度,研究了由空间非均匀性引起的非傅立叶热传导的波动效应和非局部效应。合并不同阶的均匀化非傅立叶热传导方程,消去缩小时间尺度参数,得到四阶微分方程。并进一步用C0连续修正了高阶非局部热传导方程的有限元近似解,使问题的求解避免了对有限元离散的C1连续性要求。给出的数值算例讨论了各种情况下方法的正确性与有效性。 

NONCLASSICAL HEAT CONDUCTION ANALYSIS IN PERIODIC STRUCTURES WITH MULTIPLE SPATIAL AND TEMPORAL SCALES ANALYSIS METHOD

A spatial and temporal multiple scale method is studied to simulate the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials . The model is derived from the higher-order homogenization theory with multiple spatial and temporal scales. Amplified spatial and reduced temporal scales are respectively introduced to account for fluctuations of non-Fourier heat conduction due to material heterogeneity and nonlocal effect of the homogenized solution. By combining various orders of homogenized non-Fourier heat conduction equations, the reduced time dependence is eliminated and the fourth-order differential equations are derived. To avoid the necessity of C~1- continuity in finite element implementation, the C~0-continuous mixed finite element approximation of the resulting nonlocal equations of non-Fourier heat conduction is put forward. Numerical examples are computed to demonstrate the efficiency and validity of the theories and model developed.