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Conservative local discontinuous Galerkin method for compressible miscible displacements in porous media

Fan Yu China University of Petroleum Hui Guo China University of Petroleum Nattaporn Chuenjarernx Michigan Technological University Yang Yang Michigan Technological University

Numerical Analysis and Scientific Computing mathscidoc:1907.25005

Journal of Scientific Computing, 73, 1249–1275, 2017.12
In [H. Guo, Q. Zhang, J. Wang, Applied Mathematics and Computation, 259 (2015), 88-105], a nonconservative local discontinuous Galerkin (LDG) method for both flow and transport equations was introduced for the one-dimensional coupled system of compressible miscible displacement problem. In this paper, we will continue our effort and develop a conservative LDG method for the problem in two space dimensions. Optimal error estimates in $L^{\infty}(0, T; L^{2})$ norm for not only the solution itself but also the auxiliary variables will be derived. The main difficulty is how to treat the inter-element discontinuities of two independent solution variables (one from the flow equation and the other from the transport equation) at cell interfaces. Numerical experiments will be given to confirm the accuracy and efficiency of the scheme.
local discontinuous Galerkin method; error estimate; compressible miscible displacement
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@inproceedings{fan2017conservative,
  title={Conservative local discontinuous Galerkin method for compressible miscible displacements in porous media},
  author={Fan Yu, Hui Guo, Nattaporn Chuenjarernx, and Yang Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190701094727552958385},
  booktitle={Journal of Scientific Computing},
  volume={73},
  pages={1249–1275},
  year={2017},
}
Fan Yu, Hui Guo, Nattaporn Chuenjarernx, and Yang Yang. Conservative local discontinuous Galerkin method for compressible miscible displacements in porous media. 2017. Vol. 73. In Journal of Scientific Computing. pp.1249–1275. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190701094727552958385.
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