Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

Carmine Di Nucci

doi:10.1016/j.crme.2018.03.003

Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

Carmine Di Nucci ¹

¹ Civil, Construction-Architectural and Environmental Engineering Department – University of L'Aquila, Via Giovanni Gronchi 18, Zona industriale di Pile, 67100 L'Aquila, Italy

Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 366-383.

Abstract

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.

Received: 2017-03-17
Accepted: 2018-03-06
Published online: 2018-03-16

DOI: 10.1016/j.crme.2018.03.003

Mots clés : Boussinesq-type model, Nonlinear water waves, Porous medium, Seepage face, Rectangular dam

Author's affiliations:

Carmine Di Nucci ¹

¹ Civil, Construction-Architectural and Environmental Engineering Department – University of L'Aquila, Via Giovanni Gronchi 18, Zona industriale di Pile, 67100 L'Aquila, Italy

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Carmine Di Nucci. Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face. Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 366-383. doi : 10.1016/j.crme.2018.03.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.03.003/

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