A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales
A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales
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DOI：
10.1115/1.1357165
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发表时间：
2001-03-01
影响因子：
2.6
通讯作者：
Fish, J
中科院分区：
文献类型：
--
作者：
Chen, W;Fish, J
建立了周期性非均匀介质中波传播的频散模型。该模型是基于高阶数学均匀化理论与多个空间和时间尺度。一个快速的空间尺度和一个缓慢的时间尺度被引入到帐户的快速空间波动，以及捕捉的长期行为的均匀化的解决方案。利用这种方法，成功地解决了传统的多尺度高阶均匀化方法中存在的问题。一个模型的初边值问题的解析求解和结果已被发现是在良好的协议与数值解的源问题在非均匀介质。
A dispersive model is developed for wave propagation in periodic heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale ai e introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution. By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved. A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a heterogeneous medium.