论文标题
高度异质介质中多相传输的混合多尺度有限元方法的比较
A comparison of mixed multiscale finite element methods for multiphase transport in highly heterogeneous media
论文作者
论文摘要
在本文中，我们从系统地审查并比较了高度异质介质中的多相传输的两种混合多尺度有限元方法（MMSFEM）。特别是，我们将使用有限的全局信息考虑混合的多尺度有限元方法，简单地用MMSFEM表示，以及具有剩余驱动在线多尺度函数的混合通用多尺度有限元方法（MGMSFEM）。这两种方法均在混合多尺度有限元方法的框架下，其中在粗网格中求解了速度的经过精心构造的多尺度函数的粗网格方程。两种方法中的多尺度基础功能都包括本地和全球媒体信息。就使用有限的全局信息而言，在MSFEM方面，在每个本地社区中仅使用一个多尺度基函数，而MGMSFEM中使用了多个基础。我们将使用基准三维SPE10模型测试和比较这两种方法。每种情况报告的CPU时间将考虑一系列粗网格大小和基本功能的不同组合（离线和在线）。在我们的数值实验中，我们通过上述两种方法观察到良好的精度。最后，我们将在准确性和计算成本方面讨论和比较两种方法的优点和缺点。
In this paper, we systemically review and compare two mixed multiscale finite element methods (MMsFEM) for multiphase transport in highly heterogeneous media. In particular, we will consider the mixed multiscale finite element method using limited global information, simply denoted by MMsFEM, and the mixed generalized multiscale finite element method (MGMsFEM) with residual driven online multiscale basis functions. Both methods are under the framework of mixed multiscale finite element methods, where the pressure equation is solved in the coarse grid with carefully constructed multiscale basis functions for the velocity. The multiscale basis functions in both methods include local and global media information. In terms of MsFEM using limited global information, only one multiscale basis function is utilized in each local neighborhood while multiple basis are used in MGMsFEM. We will test and compare these two methods using the benchmark three-dimensional SPE10 model. A range of coarse grid sizes and different combinations of basis functions (offline and online) will be considered with CPU time reported for each case. In our numerical experiments, we observe good accuracy by the two above methods. Finally, we will discuss and compare the advantages and disadvantages of the two methods in terms of accuracy and computational costs.
