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A Finite Element Model for the Unsteady Groundwater Flow over Sloping Beds

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  • N. Kalaidzidou-Paikou
  • D. Karamouzis
  • D. Moraitis

Abstract

A numerical solution of the nonlinear two-dimensional unsteady groundwater flow over sloping beds, using the Galerkin finite element method, is presented. The applied differential equation is based on the assumption that the streamlines are parallel to the sloping bed while the conventional differential equation is based on the Dupuit–Forchheimer assumption of horizontal flow. Furthermore, the gradient of the piezometric head is evaluated as a function of the unknown slope of the groundwater free surface and not simply as the absolute slope of the water table. Water table profiles and seepage rates obtained from the model are compared with those obtained by analytical solutions and experimental results for steady one-dimensional flow and for different values of bed slope. Results of the present model compares reasonably well with experimental results and with the results of Childs' analytical solution. The unsteady-state solution for different values of bed slope are compared to the results of a model based on the assumption that the water table slope is equal to the bed slope. The differences in the predicted water table by these two models are insignificant for small slopes but increase with increasing slope. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • N. Kalaidzidou-Paikou & D. Karamouzis & D. Moraitis, 1997. "A Finite Element Model for the Unsteady Groundwater Flow over Sloping Beds," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 11(1), pages 69-81, February.
    • Handle: RePEc:spr:waterr:v:11:y:1997:i:1:p:69-81
    DOI: 10.1023/A:1007926507718
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    Cited by:

    1. Iraj Saeedpanah & Ramin Golmohamadi Azar, 2017. "New Analytical Solutions for Unsteady Flow in a Leaky Aquifer between Two Parallel Streams," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(7), pages 2315-2332, May.
    2. Hydar Ebrahimi & Reza Ghazavi & Haji Karimi, 2016. "Estimation of Groundwater Recharge from the Rainfall and Irrigation in an Arid Environment Using Inverse Modeling Approach and RS," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(6), pages 1939-1951, April.
    3. 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.
    4. Sharad Patel & A. K. Rastogi, 2017. "Meshfree Multiquadric Solution for Real Field Large Heterogeneous Aquifer System," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2869-2884, July.

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