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A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Author

Listed:
  • Qiang Wang

    (Division of Computer Software Engineering, Silla University, Busan 612022, Korea
    Shandong Vocational College of Industry, Zibo 256414, China)

  • Pyeoungkee Kim

    (Division of Computer Software Engineering, Silla University, Busan 612022, Korea)

  • Wenzhen Qu

    (School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China)

Abstract

In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method.

Suggested Citation

  • Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:515-:d:742798
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    References listed on IDEAS

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