@Article{CiCP-16-1323, author = {}, 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 = {

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 – 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 – 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.180513.230514a}, url = {http://global-sci.org/intro/article_detail/cicp/7082.html} }