High-Order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes

Ziyao Xu Michigan Technological University Yang Yang Michigan Technological University Hui Guo China University of petroleum

Numerical Analysis and Scientific Computing mathscidoc:1907.25002

Journal of Computational Physics, 390, (1), 323-341, 2019.8
Wormhole propagation, arising in petroleum engineering, is used to describe the distribution of acid and the increase of porosity in carbonate reservoir under dissolution of injected acid. The important physical features of porosity and acid concentration include their boundedness between $0$ and $1$, as well as the monotone increasing for porosity. How to keep these properties in the simulation is crucial to the robustness of the numerical algorithm. In this paper, we propose high-order bound-preserving discontinuous Galerkin methods to keep these important physical properties. The main technique is to introduce a new variable $r$ to replace the original acid concentration and use a consistent flux pair to deduce a ghost equation such that the positive-preserving technique can be applied on both original and deduced equations. A high-order slope limiter is used to keep a polynomial upper bound which changes over time for $r$. Moreover, the high-order accuracy is attained by the flux limiter. Numerical examples are given to demonstrate the high-order accuracy and bound-preserving property of the numerical technique.
Wormhole propagation, Bound-preserving, High-order, Discontinuous Galerkin method, Triangular meshes, Flux limiter
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@inproceedings{ziyao2019high-order,
  title={High-Order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes},
  author={Ziyao Xu, Yang Yang, and Hui Guo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190701051427239771382},
  booktitle={Journal of Computational Physics},
  volume={390},
  number={1},
  pages={323-341},
  year={2019},
}
Ziyao Xu, Yang Yang, and Hui Guo. High-Order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes. 2019. Vol. 390. In Journal of Computational Physics. pp.323-341. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190701051427239771382.
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