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Numerical simulation of anomalous infiltration in porous media

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Abstract

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order time-fractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

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Authors and Affiliations

  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, China

    S. Shen

  2. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

    F. Liu & V. Anh

  3. School of Mathematical Sciences, Xiamen University, 361005, Xiamen, China

    Q. Liu

Authors
  1. S. Shen
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  2. F. Liu
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  3. Q. Liu
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  4. V. Anh
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Correspondence to F. Liu.

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Shen, S., Liu, F., Liu, Q. et al. Numerical simulation of anomalous infiltration in porous media. Numer Algor 68, 443–454 (2015). https://doi.org/10.1007/s11075-014-9853-9

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  • DOI: https://doi.org/10.1007/s11075-014-9853-9

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