Volume 7, Issue 1
The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations

Giovanna Grosso, Matteo Antuono & Eleuterio Toro

Commun. Comput. Phys., 7 (2010), pp. 64-102.

Published online: 2010-07

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  • 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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@Article{CiCP-7-64, author = {}, title = {The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations}, journal = {Communications in Computational Physics}, year = {2010}, volume = {7}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.08.181}, url = {http://global-sci.org/intro/article_detail/cicp/7620.html} }
TY - JOUR T1 - The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations JO - Communications in Computational Physics VL - 1 SP - 64 EP - 102 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/10.4208/cicp.2009.08.181 UR - https://global-sci.org/intro/article_detail/cicp/7620.html KW - AB -

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.

Giovanna Grosso, Matteo Antuono & Eleuterio Toro. (2020). The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations. Communications in Computational Physics. 7 (1). 64-102. doi:10.4208/cicp.2009.08.181
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