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J Contam Hydrol. 2018 Sep;216:38-49. doi: 10.1016/j.jconhyd.2018.08.002. Epub 2018 Aug 11.

# A three-dimensional non-hydrostatic coupled model for free surface - Subsurface variable - Density flows.

### Author information

1
Student in Hydraulic Structures, Irrigation and Reclamation Engineering Department, University of Tehran, P.O. Box 31587-4111, Alborz, Karaj, Iran. Electronic address: shokri.naser@ut.ac.ir.
2
School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box 14155-6619, Tehran, Iran.
3
Irrigation and Reclamation Engineering Department, University of Tehran, P.O. Box 31587-4111, Alborz, Karaj, Iran.

### Abstract

A three dimensional coupled numerical model has been developed for incompressible density-driven free surface and saturated porous media flows. For free surface, a time-averaged Navier-Stokes equation has been used whereas Darcy's law has been utilized in porous media flow. The algorithm has been based upon a staggered finite volume scheme on a Cartesian grid that solves the 3D non-hydrostatic density-dependent Darcy equation in one step and complete 3D Navier-Stokes equations in two major steps based on a projection method. The 3D system is decomposed into a series of 2D vertical plane sub-systems which have been solved individually by a direct matrix solver. An iteration procedure can be deployed to achieve the fully 3D implicitness of the solution where high density gradients or sharp variation of free surface elevation is present. An efficient, simple and stable algorithm has been proposed to track the free surface elevation in a Cartesian coordinate system within which the water surface position has not been restricted to a specific layer. The model has been validated using five test cases to simulate integrated transient free surface and porous media flows where fluid density effects as well as the water surface gradient have a considerable effect on the velocity field. Two of the examples involve modeling free surface flow (Wave Reflection test) and a phreatic line prediction (Cone of depression test). Two other test cases involve significant contrasts in fluid density including 3D density-driven flow in porous media and 3D lock exchange tests. The final test of a salinity interface involved a complicated scenario consisting of a density contrast in both saturated porous media and free surface flow, subjected to injection and pumping simulated simultaneously using an integrated domain. Close agreement between numerical results and experimental data demonstrates the capability of the model for the coupled simulation of 3D density-driven flow in both integrated free surface and saturated porous media including freshwater recharge, saltwater discharge, hydrodynamic dispersion and turbulence effects.

#### KEYWORDS:

3D non-hydrostatic coupled model; Darcy law; Density- driven flow; Free surface tracking; Time-averaged Navier-stokes equation