On the Performance of the Node Control Volume Finite Element Method for Modeling Multi-phase Fluid Flow in Heterogeneous
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On the Performance of the Node Control Volume Finite Element Method for Modeling Multi‑phase Fluid Flow in Heterogeneous Porous Media Abdul Salam Abd1 · Ahmad S. Abushaikha1 Received: 28 October 2019 / Accepted: 14 September 2020 / Published online: 30 September 2020 © The Author(s) 2020
Abstract 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. Keywords Node control volume finite element method · Flow in heterogeneous and fractured porous media · Upstream mobility · Numerical simulation · Unstructured grid
1 Introduction Finite volume and finite element discretizations have been extensively studied for the past few decades for different flow systems in heterogeneous and fractured porous media (Chen and Ewing 1997; Stefansson et al. 2018; Abushaikha 2018; Abushaikha et al. 2017; Ahmed et al. 2019; Xia and Zhang 2006; Khoei and Haghighat 2011). One important finite element method is the node control volume finite element (NCVFE) method which was developed by Baliga and Patankar (1980) to numerically solve fluid dynamics problems. They subdivided the domain using irregular triangular elements with control volumes surrounding nodes (vertices), Fig. 1. The pressure is solved on the nodes, while * Ahmad S. Abushaikha [email protected] https://qasr.qa 1
Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University, Education City, Qatar Foundation, Doha, Qatar
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A. S. Abd, A. S. Abushaikha
Fig. 1 Triangle finite element mesh (dashed lines) with the corresponding node control volume mesh (solid lines) imposed on the vertices of elements. a The material properties (gray color) are defined on the elements, here representing a fracture (white is lower permeability matrix), b The pressure and transport variables are computed on the node control volumes (blue color). The control volume mesh spans both the fracture and matrix material properties promoting unphysical flow across the boundaries of elements
the velocity components are solved on the elements sequentially. The secondary control volum
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