Solving Two-Mode Shallow Water Equations Using Finite Volume Methods (Communications in Computational Physics, 2014)
In this paper, we develop and study numerical methods for the two-modeshallow water equations recently proposed in [S. STECHMANN, A. MAJDA, andB. KHOUIDER, Theor. Comput. Fluid Dynamics, 22 (2008), pp. 407–432]. Designinga reliable numerical method for this system is a challenging task due to its conditionalhyperbolicity and the presence of nonconservative terms. We present several numerical approaches – two operator splitting methods (based on either Roe-type upwindor 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.