Abstract
This work presents a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving a single-phase compressible flow in highly heterogeneous media. To discretize this problem, we first construct a fine-grid approximation using the Finite Element Method with a backward Euler time approximation. After time discretization, we use Newton’s method to handle the non-linearity in the resulting equations. To solve the linear system efficiently, we shall use the framework of CEM-GMsFEM by constructing multiscale basis functions on a suitable coarse-grid approximation. These basis functions are given by solving a class of local energy minimization problems over the eigenspaces that contain local information on heterogeneity. In addition, oversampling techniques provide exponential decay outside the corresponding local oversampling regions. Finally, we will provide two numerical experiments on a 3D case to show the performance of the proposed approach.
Eric Chung’s research is partially supported by the Hong Kong RGC General Research Fund (Project number: 14304021).
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Poveda, L.A., Fu, S., Chung, E.T. (2023). Constraint Energy Minimizing Generalized Multiscale Finite Element Method for Highly Heterogeneous Compressible Flow. In: Mikyška, J., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2023. ICCS 2023. Lecture Notes in Computer Science, vol 10477. Springer, Cham. https://doi.org/10.1007/978-3-031-36030-5_22
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DOI: https://doi.org/10.1007/978-3-031-36030-5_22
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