Numerical solution of the two-dimensional unsteady dam break

By Christopher Zoppou, S. Roberts. 2000

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Simulation of dam‐ and dyke‐break hydrodynamics on dynamically adaptive quadtree grids (2004, methodology): “Toro [19] derived the weighted averaged �ux (WAF) method for constructing second-order Godunov-type schemes, which has been successfully applied to dam-break simulation (see e.g. References [20, 21 ]).”
Smooth particle hydrodynamics: status and future potential (2007, methodology): “Typically such simulations are carried out with two dimensional shallow water equations using a finite difference method (e.g., Frazao et al., 1999; Zoppou and Roberts, 2000).”
A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations (2004, result): “The results are, in general, similar to results presented in the literature [2, 23, 24] with the exception of the Gibbs oscillations inevitably produced by a high-order method without limiting.”