Wetting and Drying Treatments With Mesh Adaptation for Shallow Water Equations Using a Runge–Kutta Discontinuous Galerkin Method

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ABSTRACTThis work is devoted to the numerical simulation of Shallow Water Equations involving dry areas, a moving shoreline and in the context of mesh adaptation. The space and time discretization using the Runge–Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Problems with dry areas are challenging for such methods. To counter this issue, special treatment is applied around the shoreline. This work compares three treatments, one based on Slope Modification, one based on p‐adaptation and the last one based on eXtended Finite Element methods and mesh adaptation.