| Abstract: | This work introduces water–air two‐phase flow into integrated surface–subsurface flow by simulating rainfall infiltration and run‐off production on a soil slope with the finite element method. The numerical model is formulated by partial differential equations for hydrostatic shallow flow and water–air two‐phase flow in the shallow subsurface. Finite element computing formats and solution strategies are presented to obtain a numerical solution for the coupled model. An unsaturated seepage flow process is first simulated by water–air two‐phase flow under the atmospheric pressure boundary condition to obtain the rainfall infiltration rate. Then, the rainfall infiltration rate is used as an input parameter to solve the surface run‐off equations and determine the value of the surface run‐off depth. In the next iteration, the pressure boundary condition of unsaturated seepage flow is adjusted by the surface run‐off depth. The coupling process is achieved by updating the rainfall infiltration rate and surface run‐off depth sequentially until the convergence criteria are reached in a time step. A well‐conducted surface run‐off experiment and traditional surface–subsurface model are used to validate the new model. Comparisons with the traditional surface–subsurface model show that the initiation time of surface run‐off calculated by the proposed model is earlier and that the water depth is larger, thus providing values that are closer to the experimental results. |
