Convergence of the CEM-GMsFEM for compressible flow in highly heterogeneous media

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Leonardo A. Poveda
  • Shubin Fu
  • Eric T. Chung
  • Lina Zhao

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)153-163
Journal / PublicationComputers and Mathematics with Applications
Volume151
Online published5 Oct 2023
Publication statusPublished - 1 Dec 2023

Abstract

This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM hinges on two crucial steps: First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. Then the basis functions are obtained by solving local energy minimization problems over the oversampling domains using the auxiliary space. The basis functions have exponential decay outside the corresponding local oversampling regions. The convergence of the proposed method is provided, and we show that this convergence only depends on the coarse grid size and is independent of the heterogeneities. An online enrichment guided by a posteriori error estimator is developed to enhance computational efficiency. Several numerical experiments on a three-dimensional case to confirm the theoretical findings are presented, illustrating the performance of the method and giving efficient and accurate numerical solutions. © 2023 Elsevier Ltd.

Research Area(s)

  • Compressible flow, Constraint energy minimization, Highly heterogeneous, Local spectral problems, Multiscale finite element methods

Citation Format(s)

Convergence of the CEM-GMsFEM for compressible flow in highly heterogeneous media. / Poveda, Leonardo A.; Fu, Shubin; Chung, Eric T. et al.
In: Computers and Mathematics with Applications, Vol. 151, 01.12.2023, p. 153-163.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review