A Stable Scheme for the Numerical Computation of Long Wave Propagation in Temporal Laminates
A Stable Scheme for the Numerical Computation of Long Wave Propagation in Temporal Laminates
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DOI：
10.1006/jcph.2002.6991
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发表时间：
2002-03
影响因子：
4.1
通讯作者：
Suzanne L. Weekes
中科院分区：
文献类型：
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作者：
Suzanne L. Weekes
时间层合板是一种材料，其参数在空间上是均匀的，但在时间上周期性地和不连续地变化。在这篇文章中，我们考虑波传播通过一个时间层压板的扰动移动通过介质的周期是大的相对？叠层的周期。值得注意的是，可以选择组成材料和混合系数，使得临时层压件中的有效速度大于各个相速度。我们表明，分析问题承认稳定的长波模式，但较短的波模式增长，因为他们通过层压层。在CFL条件下，使用标准迎风有限差分法计算通过该复合介质的波动，用于数值波在单个介质中的传播，将产生不断增长的短波模式。由于短波的增长，通过截断和四舍五入误差进入计算，因此数值结果会降低精度。一个新的CFL约束推导出的有限差分数值方案，这将使我们能够计算稳定的长波运动。数值结果给出了均匀化问题（？？0）。
A temporal laminate is a material whose parameters are homogeneous in space but vary periodically and discontinuously in time. In this article, we consider wave propagation through a temporal laminate where the period of the disturbance moving through the media is large relative to ? the period of the lamination. It is worth noting that the constituent materials and the mixing coefficient can be chosen so that the effective speed in a temporal laminate is greater than the individual phase speeds. We show that the analytic problem admits stable long wave modes, but shorter wave modes grow as they pass through the laminate layers. Computing wave motion through this composite medium using the standard upwind, finite-difference method under the CFL condition for numerical wave propagation in the individual media will produce growing short wave modes. Numerical results are degraded since accuracy is quickly lost due to the growth of short waves which enter into the computation through truncation and round-off error. A new CFL constraint is derived for a finite-difference numerical scheme which will allow us to compute the stable long wave motion. Numerical results are given for the direct numerical simulation of the homogenization problem (??0).