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Cell-Centered Finite Difference Method for the One-Dimensional Forchheimer Laws

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Abstract

Cell-centered finite difference method is introduced to solve the one-dimensional Forchheimer laws modeling incompressible fluids in porous media. Using this method, velocity and pressure can be approximated at the same time. Second-order accuracy error estimates for velocity and pressure are established. Numerical experiments are carried out to validate the convergence rates and show the efficiency.

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Acknowledgements

The work of first author was supported by the Science and Technology Project for the Universities of Shandong Province (Nos. J14LI53, J14LI52), the Doctoral Foundation of Shandong Jianzhu University (No. XNBS1441), and the NNSF of China (Nos. 11471195, 61303198, 11101453). The work of second author was supported by the NNSF of China (No. 91330106). The work of third author was supported by the NNSF of China (No. 11401289). The authors thank the anonymous referees for constructive comments and suggestions which led to improvements in the presentation.

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Authors and Affiliations

  1. School of Science, Shandong Jianzhu University, Jinan, 250101, Shandong, China

    Qingli Zhao

  2. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China

    Hongxing Rui

  3. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, Shandong, China

    Wei Liu

Authors
  1. Qingli Zhao
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  2. Hongxing Rui
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  3. Wei Liu
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Correspondence to Qingli Zhao.

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Zhao, Q., Rui, H. & Liu, W. Cell-Centered Finite Difference Method for the One-Dimensional Forchheimer Laws. Bull. Malays. Math. Sci. Soc. 40, 545–564 (2017). https://doi.org/10.1007/s40840-017-0460-5

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  • DOI: https://doi.org/10.1007/s40840-017-0460-5

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