IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v34y2020i15d10.1007_s11269-020-02689-z.html
   My bibliography  Save this article

A Moving Least Squares Based Meshless Element-Free Galerkin Method for the Coupled Simulation of Groundwater Flow and Contaminant Transport in an Aquifer

Author

Listed:
  • Tinesh Pathania

    (Indian Institute of Technology Bombay)

  • T. I. Eldho

    (Indian Institute of Technology Bombay)

Abstract

In this study, a meshless simulation model based on the element-free Galerkin method (EFGM) is proposed for the coupled simulation of groundwater flow and contaminant transport (GFCT) in the two-dimensions. EFGM discretizes the governing GFCT equations using the Galerkin integral approach and shape functions generated through the moving least squares (MLS) approximation method. It results into the stable system of equations for estimating the groundwater head and contaminant concentration values. EFGM computes the several global matrices using the spatial information of the scattered and unconnected field nodes and hence, terminates the meshing procedure unlike the finite difference (FDM) and finite element (FEM) methods. The Kronecker delta function property is missing in EFGM shape functions and hence, the Dirichlet boundary conditions are enforced with some special methods. We have used the penalty method to include them into the presented EFGM model. This method is straightforward and computationally useful for the real field simulations. The proposed model is first validated using both the one- and two-dimensional analytical solutions. The developed coupled model is then applied to solve the hypothetical and real field problems. EFGM results for both the problems are compared with the MODFLOW and MT3DMS results for the head and concentration values respectively. EFGM results are found to be satisfactory for both the cases, and it shows the potential of the proposed approach for the coupled GFCT simulations.

Suggested Citation

  • Tinesh Pathania & T. I. Eldho, 2020. "A Moving Least Squares Based Meshless Element-Free Galerkin Method for the Coupled Simulation of Groundwater Flow and Contaminant Transport in an Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(15), pages 4773-4794, December.
    • Handle: RePEc:spr:waterr:v:34:y:2020:i:15:d:10.1007_s11269-020-02689-z
    DOI: 10.1007/s11269-020-02689-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11269-020-02689-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11269-020-02689-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. van Genuchten, M. Th. & Alves, W. J., 1982. "Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation," Technical Bulletins 157268, United States Department of Agriculture, Economic Research Service.
    2. Tinesh Pathania & Andrea Bottacin-Busolin & A. K. Rastogi & T. I. Eldho, 2019. "Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2827-2845, June.
    3. L. Guneshwor & T. I. Eldho & A. Vinod Kumar, 2018. "Identification of Groundwater Contamination Sources Using Meshfree RPCM Simulation and Particle Swarm Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(4), pages 1517-1538, March.
    4. Qin, Xinqiang & Duan, Xianbao & Hu, Gang & Su, Lijun & Wang, Xing, 2018. "An Element-free Galerkin method for solving the two-dimensional hyperbolic problem," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 106-120.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Moisés A. C. Lemos & Camilla T. Baran & André L. B. Cavalcante & Ennio M. Palmeira, 2023. "A Semi-Analytical Model of Contaminant Transport in Barrier Systems with Arbitrary Numbers of Layers," Sustainability, MDPI, vol. 15(23), pages 1-18, November.
    2. Salah A. Faroughi & Ramin Soltanmohammadi & Pingki Datta & Seyed Kourosh Mahjour & Shirko Faroughi, 2023. "Physics-Informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
    3. Ricardo Mendonça de Moraes & Luan Carlos de Sena Monteiro Ozelim & André Luís Brasil Cavalcante, 2022. "Generalized Skewed Model for Spatial-Fractional Advective–Dispersive Phenomena," Sustainability, MDPI, vol. 14(7), pages 1-19, March.
    4. Jui-Sheng Chen & Ching-Ping Liang & Cheng-Hung Chang & Ming-Hsien Wan, 2019. "Simulating Three-Dimensional Plume Migration of a Radionuclide Decay Chain through Groundwater," Energies, MDPI, vol. 12(19), pages 1-22, September.
    5. Masoomeh Zeinali & Arash Azari & Mohammad Mehdi Heidari, 2020. "Simulating Unsaturated Zone of Soil for Estimating the Recharge Rate and Flow Exchange Between a River and an Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 34(1), pages 425-443, January.
    6. Unknown, 1994. "Proceedings of an international workshop held in Kota Bharu, Kelantan, Malaysia, 24-27 October 1994: Agricultural Impacts on Groundwater Quality," ACIAR Proceedings Series 134721, Australian Centre for International Agricultural Research.
    7. Changbing Yang & Ramón H. Treviño & Susan D. Hovorka & Jesus Delgado‐Alonso, 2015. "Semi‐analytical approach to reactive transport of CO 2 leakage into aquifers at carbon sequestration sites," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 5(6), pages 786-801, December.
    8. Payam Sarkhosh & Amgad Salama & Yee-Chung Jin, 2021. "Implicit Finite-Volume Scheme to Solve Coupled Saint-Venant and Darcy–Forchheimer Equations for Modeling Flow Through Porous Structures," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 35(13), pages 4495-4517, October.
    9. Mohammad Hossein Golestan & Carl Fredrik Berg, 2024. "Simulations of CO 2 Dissolution in Porous Media Using the Volume-of-Fluid Method," Energies, MDPI, vol. 17(3), pages 1-21, January.
    10. Mojtaba Poursaeid & Amir Houssain Poursaeid & Saeid Shabanlou, 2022. "A Comparative Study of Artificial Intelligence Models and A Statistical Method for Groundwater Level Prediction," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(5), pages 1499-1519, March.
    11. Grifka, Jasmin & Nehler, Mathias & Licha, Tobias & Heinze, Thomas, 2023. "Fines migration poses challenge for reservoir-wide chemical stimulation of geothermal carbonate reservoirs," Renewable Energy, Elsevier, vol. 219(P1).
    12. Abhishek Sanskrityayn & Heejun Suk & Jui-Sheng Chen & Eungyu Park, 2021. "Generalized Analytical Solutions of The Advection-Dispersion Equation with Variable Flow and Transport Coefficients," Sustainability, MDPI, vol. 13(14), pages 1-23, July.
    13. Cheng-Yu Ku & Chih-Yu Liu, 2023. "A Novel Spacetime Boundary-Type Meshless Method for Estimating Aquifer Hydraulic Properties Using Pumping Tests," Mathematics, MDPI, vol. 11(21), pages 1-23, October.
    14. Tinesh Pathania & Andrea Bottacin-Busolin & A. K. Rastogi & T. I. Eldho, 2019. "Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2827-2845, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:waterr:v:34:y:2020:i:15:d:10.1007_s11269-020-02689-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.