A High-resolution Wetting and Drying Algorithm for Free-surface Hydrodynamics

A new wetting and drying algorithm for numerical modeling free-surface flows is proposed and analyzed. A well structured, mildly nonlinear system for the discrete water surface elevation is derived from the governing differential equations by requiring a correct mass balance in wet areas as well as in the region of transition from wet to dry and from dry to wet. Existence and uniqueness of the numerical solution, along with a convergence analysis of an iterative scheme for the mildly nonlinear system, is provided. The present algorithm is devised to use high-resolution bathymetric data at subgrid level. The resulting model is quite efficient, does not require a threshold value for minimal water depth, does not produce un-physical negative water depths and generates accurate results with relatively coarse mesh and large time step size. These features are illustrated on a severe test-case with known analytical solution.