TY - JOUR
T1 - The Riemann Problem for the Dispersive Nonlinear Shallow Water Equations
AU - Giovanna Grosso, Matteo Antuono & Eleuterio Toro
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 - <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>