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Implicit Finite-Volume Scheme to Solve Coupled Saint-Venant and Darcy–Forchheimer Equations for Modeling Flow Through Porous Structures

Author

Listed:
  • Payam Sarkhosh

    (University of Regina)

  • Amgad Salama

    (University of Regina)

  • Yee-Chung Jin

    (University of Regina)

Abstract

In hydrodynamic modeling of flow through porous structures, the solution domain might encounter discontinuities. These include, for example, porous structure-open channel interface, porous dam-break, and heterogeneous porous structures. The treatment of discontinuity is challenging within a numerical scheme as it can be a source of instabilities. This study proposes a finite-volume method to solve coupled Saint-Venant and Darcy–Forchheimer equations for simulating free-surface flow through porous structures. For capturing shocks arising at discontinuous regions, an upwind scheme is utilized to maintain the solution monotone. Fully implicit methods can allow the choice of longer time steps. Since the current problem involves two nonlinear systems, namely the open-channel and seepage flow equations, the Picard method is adopted to linearize the system of equations. Unlike typical implicit schemes of seepage flows, herein, both flow depth and velocity matrices appear within the iterative process, threatening the convergence criterion. To converge iteration, the continuity equation's flux term is treated using the dynamic wave equation under the relaxation method. The present model is applicable to simulate gradually and rapidly unsteady flow through homogeneous and heterogeneous porous media under laminar, transitional, and fully developed turbulent flow regimes within various closed and/or open boundary conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:waterr:v:35:y:2021:i:13:d:10.1007_s11269-021-02963-8
    DOI: 10.1007/s11269-021-02963-8
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    References listed on IDEAS

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    1. Rajeev Bansal & Samir Das, 2011. "Response of an Unconfined Sloping Aquifer to Constant Recharge and Seepage from the Stream of Varying Water Level," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(3), pages 893-911, February.
    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.
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    4. A.Ufuk Şahin, 2018. "A Particle Swarm Optimization Assessment for the Determination of Non-Darcian Flow Parameters in a Confined Aquifer," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(2), pages 751-767, January.
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