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Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Wansheng Gao
  • Ludovic Chamoin
  • Insa Neuweiler

External Research Organisations

  • École normale supérieure Paris-Saclay (ENS Paris-Saclay)

Details

Original languageEnglish
Article number116321
JournalJournal of Computational and Applied Mathematics
Volume457
Early online date15 Oct 2024
Publication statusE-pub ahead of print - 15 Oct 2024

Abstract

Due to its non-intrusive nature and ease of implementation, the Non-Intrusive Reduced Basis (NIRB) two-grid method has gained significant popularity in numerical computational fluid dynamics simulations. The efficiency of the NIRB method hinges on separating the procedure into offline and online stages. In the offline stage, a set of high-fidelity computations is performed to construct the reduced basis functions, which is time-consuming but is only executed once. In contrast, the online stage adapts a coarse-grid model to retrieve the expansion coefficients of the reduced basis functions. Thus it is much less costly than directly solving a high-fidelity model. However, coarse grids in heterogeneous porous media of flow models are often accompanied by upscaled hydraulic parameters (e.g. hydraulic conductivity), thus introducing upscaling errors. In this work, we introduce the two-scale idea to the existing NIRB two-grid method: when dealing with coarse-grid models, we also employ upscaled model parameters. Both the discretization and upscaling errors are compensated by the rectification post-processing. The numerical examples involve flow and heat transport problems in heterogeneous hydraulic conductivity fields, which are generated by self-affine random fields. Our research findings indicate that the modified NIRB method can effectively capture the large-scale features of numerical solutions, including pressure, velocity, and temperature. However, accurately retrieving velocity fields with small-scale features remains highly challenging.

Keywords

    Flow and transport problems, Heterogeneous porous media, Model order reduction, NIRB, Parameter upscaling

ASJC Scopus subject areas

Cite this

Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media. / Gao, Wansheng; Chamoin, Ludovic; Neuweiler, Insa.
In: Journal of Computational and Applied Mathematics, Vol. 457, 116321, 15.03.2025.

Research output: Contribution to journalArticleResearchpeer review

Gao W, Chamoin L, Neuweiler I. Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media. Journal of Computational and Applied Mathematics. 2025 Mar 15;457:116321. Epub 2024 Oct 15. doi: 10.1016/j.cam.2024.116321
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