论文标题
统一插值方法与移动贴片的自适应分区
Adaptive Partition of Unity Interpolation Method with Moving Patches
论文作者
论文摘要
Aiton和Driscoll使用Chebyshev本地插值剂引入的Unity插值方法的自适应分区被探索，以插值功能，该功能具有尖锐的梯度，代表两种中等问题。对于在向量字段下进化的函数，可以移动统一贴片（封面）的分区并调整大小以遵循局部配置文件的变化动力学。该方法针对无线性无分流矢量字段的选定的1D和2D两中性问题进行了测试。在这种情况下，每个贴片中有助于整个域的音量保存的音量分数可以保持高精度，直到机器精确度。可以从该方法中受益的应用程序包括音量跟踪和多相流建模。
The adaptive partition of unity interpolation method, introduced by Aiton and Driscoll, using Chebyshev local interpolants, is explored for interpolating functions with sharp gradients representing two-medium problems. For functions that evolve under vector fields, the partition of unity patches (covers) can be shifted and resized to follow the changing dynamics of local profiles. The method is tested for selected 1D and 2D two-medium problems with linear divergence-free vector fields. In those cases, the volume fraction in each patch contributing to volume conservation throughout the domain can be kept in high accuracy down to machine precisions. Applications that could benefit from the method include volume tracking and multiphase flow modeling.
