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

Payam Sarkhosh, Amgad Salama and Yee-Chung Jin ()
Additional contact information
Payam Sarkhosh: University of Regina
Amgad Salama: University of Regina
Yee-Chung Jin: University of Regina

Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), 2021, vol. 35, issue 13, No 12, 4495-4517

Abstract: 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.

Keywords: Nonlinear seepage flow; Implicit scheme; Picard linearization; Shock-capturing method; Heterogeneous porous structure; Porous dam-break (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11269-021-02963-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:waterr:v:35:y:2021:i:13:d:10.1007_s11269-021-02963-8

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/11269

DOI: 10.1007/s11269-021-02963-8

Access Statistics for this article

Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA) is currently edited by G. Tsakiris

More articles in Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA) from Springer, European Water Resources Association (EWRA)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().