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Numerical analysis of incompressible wormhole propagation with mass-preserving characteristic mixed finite element procedure

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Abstract

In this article, we construct a new combined characteristic mixed finite element procedure to simulate the incompressible wormhole propagation. In this procedure, we use the classical mixed finite element method to solve the pressure equation and a modified mass-preserving characteristic finite element method for the solute transport equation, and solve the porosity function straightly by the given concentration. This combined method not only keeps mass balance globally but also preserves maximum principle for the porosity. We considered the corresponding convergence and derive the optimal L2-norm error estimate. Finally, we present some numerical examples to confirm theoretical analysis.

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Acknowledgments

The authors would like to thank the editor and referees for their valuable comments and suggestions which greatly improved the quality of this paper.

Funding

This work was supported by the Major Scientific and Technological Projects of CNPC (ZD2019-183-008), the Natural Science Foundation of Shandong Province (ZR2019MA015), and the Fundamental Research Funds for the Central Universities (20CX05011A).

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Authors and Affiliations

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

    Jiansong Zhang, Yun Yu, Bingjie Ji & Yue Yu

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  1. Jiansong Zhang
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  2. Yun Yu
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  3. Bingjie Ji
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  4. Yue Yu
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Correspondence to Jiansong Zhang.

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Zhang, J., Yu, Y., Ji, B. et al. Numerical analysis of incompressible wormhole propagation with mass-preserving characteristic mixed finite element procedure. Numer Algor 89, 323–340 (2022). https://doi.org/10.1007/s11075-021-01116-7

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  • DOI: https://doi.org/10.1007/s11075-021-01116-7

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