In this paper, we critique the performance of the node control volume finite element (NCVFE) method for modeling multi-phase fluid flow in heterogeneous media. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them. Material properties are defined on elements, while transport is simulated on the control volumes. These two meshes are not aligned producing inaccurate results and artificial fluid smearing when modeling multi-phase fluid flow in heterogeneous media. We perform numerical tests to quantify and visualize the extent of this artificial fluid smearing in domains with different material properties. The domains are composed of tetrahedron finite elements. Large artificial fluid smearing is observed in coarse meshes; however, it decreases with the increase in mesh resolution. These findings prompt the use of high-resolution meshes for the method and the need for development of novel numerical methods to address this unphysical flow.

中文翻译：

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非均质多孔介质中多相流体流动建模的节点控制体积有限元法的性能

在本文中，我们批评了节点控制体积有限元 (NCVFE) 方法在模拟非均质介质中的多相流体流动时的性能。NCVFE 方法求解单元顶点处的压力，并围绕它们构建控制体积网格。材料属性是在元素上定义的，而传输是在控制体积上模拟的。在对非均质介质中的多相流体流动进行建模时，这两个网格未对齐会产生不准确的结果和人工流体涂抹。我们执行数值测试来量化和可视化这种人造流体在具有不同材料特性的域中涂抹的程度。域由四面体有限元组成。在粗网格中观察到大量人工流体涂抹；然而，它随着网格分辨率的增加而减小。