@Article{CiCP-16-1323,
author = {Manuel Jesús Castro Díaz, Yuanzhen Cheng, Alina Chertock and Alexander Kurganov},
title = {Solving Two-Mode Shallow Water Equations Using Finite Volume Methods},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {5},
pages = {1323--1354},
abstract = {<p style="text-align: justify;">In this paper, we develop and study numerical methods for the two-mode
shallow water equations recently proposed in [S. STECHMANN, A. MAJDA, and
B. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designing
a reliable numerical method for this system is a challenging task due to its conditional
hyperbolicity and the presence of nonconservative terms. We present several numerical approaches&nbsp;–&nbsp;two operator splitting methods (based on either Roe-type upwind
or central-upwind scheme), a central-upwind scheme and a path-conservative central-upwind scheme&nbsp;– and test their performance in a number of numerical experiments.
The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.180513.230514a},
url = {http://global-sci.org/intro/article_detail/cicp/7082.html}
}