| 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. |
