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Local Discontinuous Galerkin Method with Implicit–Explicit Time Marching for Incompressible Miscible Displacement Problem in Porous Media

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Abstract

In this paper, we shall present two fully-discrete local discontinuous Galerkin methods, coupled with multi-step implicit–explicit time discretization up to second order, for solving the two-dimensional incompressible miscible displacement problem. To avoid the solving of nonlinear algebraic systems, the extrapolation linearization is adopted to diffusion–dispersion tensor. Under weak temporal-spatial conditions, the optimal error estimates in \(L^{\infty }(L^{2})\) norm for both concentration and velocity are derived. Numerical experiments are also given to demonstrate the theoretical results.

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu Province, People’s Republic of China

    Haijin Wang

  2. College of Science, China University of Petroleum, Qingdao, 266580, Shandong Province, People’s Republic of China

    Jingjing Zheng, Fan Yu & Hui Guo

  3. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu Province, People’s Republic of China

    Qiang Zhang

Authors
  1. Haijin Wang
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  2. Jingjing Zheng
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  3. Fan Yu
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  4. Hui Guo
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  5. Qiang Zhang
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Correspondence to Qiang Zhang.

Additional information

H. Wang: Research supported by NSFC Grants 11601241 and 11671199, Natural Science Foundation of Jiangsu Province Grant BK20160877, and NUPTSF Grant NY215067. J. Zheng, F. Yu and H. Guo: Research supported by NSFC Grant 11571367 and the Fundamental Research Funds for the Central Universities. Q. Zhang: Research supported by NSFC Grants 11671199 and 11571290.

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Wang, H., Zheng, J., Yu, F. et al. Local Discontinuous Galerkin Method with Implicit–Explicit Time Marching for Incompressible Miscible Displacement Problem in Porous Media. J Sci Comput 78, 1–28 (2019). https://doi.org/10.1007/s10915-018-0752-4

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  • DOI: https://doi.org/10.1007/s10915-018-0752-4

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