A New Set of Equations for Very Shallow Water and Partially Dry Areas Suitable to 2D Numerical Models

When a 2D model is used to compute the flood propagation over an initially dry area some difficulties arise due to the changes in the computational domain as large parts of it are flooded and dried during the phenomenon. A second problem concerns the representation of soil surface: usually it is described as a piecewise constant or a piecewise linearly varying surface hence neglecting the ground unevenness. For very small water depths, unevenness plays instead a very important role. In this paper, new dynamic and mass balance equations for 2D free surface flows are presented which, by means of a conceptual sub-model, account for the ground unevenness effects and allow a very realistic description of flooding and drying phenomena. It is also shown that for a very smooth ground surface or for relatively large water depths, the new equations reduce to the well known De S. Venant equations.