A wetting and drying treatment for the Runge-Kutta discontinuous Galerkin solution to the shallow water equations

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A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case (2015, methodology): “Here, we setup two different Riemann problems which include dry areas and have been used before to evaluate similar inundation schemes [5, 6, 32] to demonstrate the positivity-preserving capability of the methods.”
A novel multidimensional solution reconstruction and edge‐based limiting procedure for unstructured cell‐centered finite volumes with application to shallow water dynamics (2013, background): “and a similar behavior was presented in [13] and also in [9, 69, 74, 76].”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Some positivitypreserving DG methods with P1 polynomial spaces [9, 18, 30] have been developed in the past few years, mainly relying on modifying the slope to avoid negative values of water height.”