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.

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Carmine Di Nucci ^{1}

@article{CRMECA_2018__346_5_366_0, author = {Carmine Di Nucci}, title = {Unsteady free surface flow in porous media: {One-dimensional} model equations including vertical effects and seepage face}, journal = {Comptes Rendus. M\'ecanique}, pages = {366--383}, publisher = {Elsevier}, volume = {346}, number = {5}, year = {2018}, doi = {10.1016/j.crme.2018.03.003}, language = {en}, }

TY - JOUR AU - Carmine Di Nucci TI - Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face JO - Comptes Rendus. Mécanique PY - 2018 SP - 366 EP - 383 VL - 346 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2018.03.003 LA - en ID - CRMECA_2018__346_5_366_0 ER -

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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