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Multiscale Hybridizable Discontinuous Galerkin Method for Flow Simulations in Highly Heterogeneous Media

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Abstract

We propose a multiscale hybridizable discontinuous Galerkin method for Darcy flow and two phase flow simulations in highly heterogeneous media. The multiscale space consists of offline and online multiscale basis functions. The offline basis functions are constructed by solving appropriate local spectral problem, and thus contain important local media information. The online basis functions are computed iteratively with the residuals of previous multiscale solution on selected local regions. Typically, the offline basis provides initial multiscale solution for constructing online basis. For the two phase flow simulations, we only compute the basis space for the initial permeability field and keep it fixed as time advancing. Numerical experiments show the multiscale solution can approximate the fine scale solution accurately for both types of flow simulations.

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Acknowledgements

Yanfang Yang’s work is supported by the National Natural Science Foundation of China (Grant No. 11901129).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, People’s Republic of China

    Yanfang Yang

  2. Department of Mathematics, Old Dominion University, Norfolk, USA

    Ke Shi

  3. Department of Mathematics, The Chinese University of Hong Kong, Sha Tin, Hong Kong SAR

    Shubin Fu

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  1. Yanfang Yang
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  2. Ke Shi
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  3. Shubin Fu
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Correspondence to Shubin Fu.

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Yang, Y., Shi, K. & Fu, S. Multiscale Hybridizable Discontinuous Galerkin Method for Flow Simulations in Highly Heterogeneous Media. J Sci Comput 81, 1712–1731 (2019). https://doi.org/10.1007/s10915-019-01058-2

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