A high-resolution wetting and drying algorithm for free-surface hydrodynamics.

*(English)*Zbl 1161.76034Summary: We propose and analyze a new wetting and drying algorithm for numerical modeling free-surface flows. A well structured, mildly nonlinear system for the discrete water surface elevation is derived from 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. We provide existence and uniqueness of the numerical solution, along with a convergence analysis of an iterative scheme for the mildly nonlinear system. The 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.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |

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\textit{V. Casulli}, Int. J. Numer. Methods Fluids 60, No. 4, 391--408 (2009; Zbl 1161.76034)

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