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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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
-
A numerical scheme for the Green–Naghdi model
Le Métayer, O. | Gavrilyuk, S. | Hank, S.Journal of Computational Physics, Vol. 229 (2010), Iss. 6 P.2034
https://doi.org/10.1016/j.jcp.2009.11.021 [Citations: 104] -
High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems
Deng, Xiaogang | Mao, Meiliang | Tu, Guohua | Zhang, Hanxin | Zhang, YifengCommunications in Computational Physics, Vol. 11 (2012), Iss. 4 P.1081
https://doi.org/10.4208/cicp.100510.150511s [Citations: 59]