论文标题
在线保守广义的多尺度有限元方法用于流模型
Online conservative generalized multiscale finite element method for flow models
论文作者
论文摘要
在本文中，我们考虑了在异质多孔介质中的两相流量模型的背景下，使用通用多尺度有限元方法（GMSFEM）考虑了在线丰富程序。椭圆方程的系数称为渗透性，是模型中异质性的主要来源。椭圆压方程是使用在线GMSFEM求解的，并与需要质量局部保护的双曲线传输方程相结合。为了满足保护属性，我们旨在通过使用后处理技术在多尺度函数的空间内构建保守的通量。为了提高在线GMSFEM中压力和速度解决方案的准确性，我们采用系统的在线丰富程序。在线结构引起的压力准确性的增加是由保守的通量场和耦合传输方程中所需的饱和解决方案继承的。尽管压力方程的系数取决于可能随时间变化的饱和度，但我们可以使用初始系数构建一个近似空间，而无需进一步更新的初始系数。展出了与四种不同类型的异质通透性系数相对应的数值结果，以测试所提出的方法。
In this paper, we consider an online enrichment procedure using the Generalized Multiscale Finite Element Method (GMsFEM) in the context of a two-phase flow model in heterogeneous porous media. The coefficient of the elliptic equation is referred to as the permeability and is the main source of heterogeneity within the model. The elliptic pressure equation is solved using online GMsFEM, and is coupled with a hyperbolic transport equation where local conservation of mass is necessary. To satisfy the conservation property, we aim at constructing conservative fluxes within the space of multiscale basis functions through the use of a postprocessing technique. In order to improve the accuracy of the pressure and velocity solutions in the online GMsFEM we apply a systematic online enrichment procedure. The increase in pressure accuracy due to the online construction is inherited by the conservative flux fields and the desired saturation solutions from the coupled transport equation. Despite the fact that the coefficient of the pressure equation is dependent on the saturation which may vary in time, we may construct an approximation space using the initial coefficient where no further basis updates follow. Numerical results corresponding to four different types of heterogeneous permeability coefficients are exhibited to test the proposed methodology.
