The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations (Communications in Computational Physics, 2010)
The complete analytical solution of the Riemann problem for the homogeneousDispersive Nonlinear Shallow Water Equations [Antuono, Liapidevskii andBrocchini, Stud. Appl. Math., 122 (2009), pp. 1-28] is presented, for both wet-bed anddry-bed conditions. Moreover, such a set of hyperbolic and dispersive depth-averagedequations shows an interesting resonance phenomenon in the wave pattern of the solutionand we define conditions for the occurrence of resonance and present an algorithmto capture it. As an indirect check on the analytical solution we have carried out a detailedcomparison with the numerical solution of the government equations obtainedfrom a dissipative method that does not make explicit use of the solution of the localRiemann problem.