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Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

  • Manuel Jesús Castro Diaz (a1), Yuanzhen Cheng (a2), Alina Chertock (a3) and Alexander Kurganov (a2)

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.

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Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

  • Manuel Jesús Castro Diaz (a1), Yuanzhen Cheng (a2), Alina Chertock (a3) and Alexander Kurganov (a2)

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