论文标题
高度异构压缩流的通用多尺度有限元法
Generalized multiscale finite element method for highly heterogeneous compressible flow
论文作者
论文摘要
在本文中，我们研究了高度异质多孔培养基中单相可压缩流的广义多尺度有限元方法（GMSFEM）。我们遵循GMSFEM的主要步骤，以构建依赖性的离线基础，以进行快速的粗网格模拟。基于平行计算的初始渗透率场，离线粗糙空间仅由一次有效构造一次。对两种类型的快照空间进行了严格的合并分析。分析表明，提出的多尺度方法的收敛速率取决于局部光谱问题的粗糙网状和特征值衰减。为了进一步提高多尺度方法的准确性，剩余的在线多尺度将添加到离线空间中。在线多尺度的构建基于由分析动机的精心设计错误指标。我们发现在线基础对于单数来源尤其重要。提出了对典型3D高度异构介质的丰富数值测试，以证明所提出的多尺度方法的令人印象深刻的计算优势。
In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation. The offline coarse space is efficiently constructed only once based on the initial permeability field with parallel computing. A rigorous convergence analysis is performed for two types of snapshot spaces. The analysis indicates that the convergence rates of the proposed multiscale method depend on the coarse meshsize and the eigenvalue decay of the local spectral problem. To further increase the accuracy of multiscale method, residual driven online multiscale basis is added to the offline space. The construction of online multiscale basis is based on a carefully design error indicator motivated by the analysis. We find that online basis is particularly important for the singular source. Rich numerical tests on typical 3D highly heterogeneous medias are presented to demonstrate the impressive computational advantages of the proposed multiscale method.
