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An \(h-\)Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model

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Abstract

In this paper, we apply local discontinuous Galerkin methods to the compressible wormhole propagation. With high velocity, Darcy–Forchheimer model is used instead of classical Darcy framework. Optimal error estimates for the pressure, velocity, porosity and concentration in different norms are established on non-uniform rectanglular grids. To capture the propagation of the wormhole accurately and save computations, adaptive mesh is applied. Numerical experiments are presented to verify the theoretical analysis and show the good performance of the LDG scheme for compressible wormhole propagation.

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Acknowledgements

This work is supported by NSF Grant DMS-1818467, National Natural Science Foundation of China Grants 11801569 and 11571367, the Fundamental Research Funds for the Central Universities 18CX05003A, 18CX02021A and YJ201601010.

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Authors and Affiliations

  1. College of Science, China University of Petroleum, Qingdao, 266580, China

    Lulu Tian, Hui Guo & Rui Jia

  2. Michigan Technological University, Houghton, MI, 49931, USA

    Yang Yang

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  1. Lulu Tian
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  2. Hui Guo
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  3. Rui Jia
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Correspondence to Hui Guo.

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Lulu Tian was supported by National Natural Science Foundation of China 11801569 and Natural Science Foundation of Shandong Province (CN) ZR2018BA011. The second author was supported by National Natural Science Foundation of China Grants 11571367 and the Fundamental Research Funds for the Central Universities 18CX05003A. The last author was supported by NSF Grant DMS-1818467. This work is also supported by the National Natural Science Foundation of China (41974133).

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Tian, L., Guo, H., Jia, R. et al. An \(h-\)Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model. J Sci Comput 82, 43 (2020). https://doi.org/10.1007/s10915-020-01135-x

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