A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying

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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): “The ill-conditioned computation of the velocity has only been implicitly dealt with by using restrictive limiters, such as the corrected Minmod-limiter in [27], or, as in [9] by setting an upper problem dependent tolerance of the velocity.”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Several wellbalanced DG methods have been proposed in the last few years, by the idea of special decomposition of the source term [59], hydrostatic reconstruction [18, 29, 60], and pathconservative [45].”
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].”