An implicit 2D hydrodynamic numerical model for free surface-subsurface coupled flow problems

A 2-dimensional hydrodynamic finite volume model has been proposed for simultaneous simulation of free surface and saturated porous media. The governing equations of the former are 2-dimensional averaged in a unit width of Navier-Stokes, whereas that of the latter are Darcy law. An efficient, simple, and stable algorithm has been proposed to track the surface elevation in Cartesian coordinate system by which the water elevation in each computational column has been computed along with the other pressure unknowns simultaneously. The surface position has not been considered to remain in a specific layer so the number of cells in each column have been variably adjusted in accordance with the water surface elevation. Performance of the coupled model has been validated against a range of hydrodynamic problems including propagation of linear short wave, seepage test, tidal oscillation in a lagoon system, gravity current, and saltwater intrusion. Comparison between numerical results, analytical solutions, and experimental data demonstrates that the model represents well the interacting surface water and ground water flow and solute transport processes.