Modelling transient unsaturated flow problems using control volume numerical methods

In this paper, an unsteady two-equation model that describes the flow of water in unsaturated zones is developed. The governing equations are based on general conservation laws of mass and momentum. Although the obtained governing equations are not amenable to being solved by analytical means, a control volume numerical solution using upwind scheme can be sought. In order to test the model equations, two test examples of one- and two-dimensional water-infiltration are simulated. The effects of discretization on spatial and temporal coordinates are demonstrated. Also, the results are compared with the results of previous studies.