The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations

The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations

Year:    2010

Communications in Computational Physics, Vol. 7 (2010), Iss. 1 : pp. 64–102

Abstract

The complete analytical solution of the Riemann problem for the homogeneous Dispersive Nonlinear Shallow Water Equations [Antuono, Liapidevskii and Brocchini, Stud. Appl. Math., 122 (2009), pp. 1-28] is presented, for both wet-bed and dry-bed conditions. Moreover, such a set of hyperbolic and dispersive depth-averaged equations shows an interesting resonance phenomenon in the wave pattern of the solution and we define conditions for the occurrence of resonance and present an algorithm to capture it. As an indirect check on the analytical solution we have carried out a detailed comparison with the numerical solution of the government equations obtained from a dissipative method that does not make explicit use of the solution of the local Riemann problem.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2009.08.181

Communications in Computational Physics, Vol. 7 (2010), Iss. 1 : pp. 64–102

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    39

Keywords: