@Article{CiCP-7-1,
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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.08.181},
url = {https://global-sci.com/article/80969/the-riemann-problem-for-the-dispersive-nonlinear-shallow-water-equations}
}