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Simulations of shallow water equations with finite difference Lax-Wendroff weighted essentially non-oscillatory schemes. (English) Zbl 1358.76017
Summary: In this paper we study a Lax-Wendroff-type time discretization procedure for the finite difference weighted essentially non-oscillatory (WENO) schemes to solve one-dimensional and two-dimensional shallow water equations with source terms. In order to maintain genuinely high order accuracy and suit to problems with a rapidly varying bottom topography we use WENO reconstruction not only to the flux but also to the source terms of algebraical modified shallow water equations. Extensive simulations are performed, as a result, the WENO schemes with Lax-Wendroff-type time discretization can maintain nonoscillatory properties and more cost effective than that with Runge-Kutta time discretization.

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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