TY - JOUR T1 - Solving Two-Mode Shallow Water Equations Using Finite Volume Methods JO - Communications in Computational Physics VL - 5 SP - 1323 EP - 1354 PY - 2014 DA - 2014/11 SN - 16 DO - http://doi.org/10.4208/cicp.180513.230514a UR - https://global-sci.org/intro/article_detail/cicp/7082.html KW - AB -

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.