A finite volume model for coupling surface and subsurface flows

In this paper, a finite volume model using approximate Riemann solver is presented for solving the extended shallow water equations (ESWEs) which are suitable for both surface and subsurface flows. The surface gradient method is employed to balance the flux gradient and source terms. Firstly the model is verified against the analytical solutions for 1 Dimension dam break problem and the steady subsurface flow. Then we use the model to study the tidal flow across an embankment, and the results agree well with the experimental data. The numerical results show that the model is capable of simulating coupled surface and subsurface flows simultaneously without changing equations or numerical schemes. For simplicity, all the simulations are based on 1 Dimension, while the model can be easily extended to high dimension.