Mathematical Model of Shallow Water Flow over Porous Media

by Ali Osman Akan, Asst. Prof.; Dept. of Civ. Engrg., Middle East Technical Univ., Ankara, Turkey,
Ben Chie Yen, (F.ASCE), Prof. of Civ. Engrg.; Univ. of Illinois at Urbana-Champaign, Urbana, Ill. 61801,

Serial Information: Journal of the Hydraulics Division, 1981, Vol. 107, Issue 4, Pg. 479-494

Document Type: Journal Paper


A conjunctive mathematical model for a surface-subsurface flow system is developed. The unsteady surface flow is explored by a set of one-dimensional dynamic wave equations for shallow water, which are solved by using a four-point implicit finite-difference scheme. The transient subsurface flow is two-dimensional, with potential gradients in the vertical direction as well as the surface flow direction. The porous medium may be saturated or unsaturated or both, and it can be nonhomogeneous and anisotropic. The subsurface flow equation is solved by employing a successive line over-relaxation implicit finite-difference scheme. The surface and subsurface flow components are coupled at the ground surface considering the mass conservation and pressure relationships. The model is verified by using existing experimental data and analytical solutions for special cases.

Subject Headings: Subsurface flow | Porous media flow | Overland flow | Transient flow | Two-dimensional flow | Mathematics | Mathematical models | Shallow water

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