High-Order Non-Oscillatory Central Schemes for Shallow Water Equations

We present an extension of the central non-oscillatory scheme given in [1] to solve the shallow water equations over a movable non-flat bed. Time integration is obtained following a Runge-Kutta procedure, coupled with its natural continuous extension (NCE). Spatial accuracy is obtained with three-degree reconstruction polynomials in each cell, keeping the local monotonicity of interpolation data. We use the treatment for bed slope source term described in Caleffi et al. [3], which maintains the established order of accuracy and satisfies the exact conservation property (C-property). Several standard one-dimensional test cases are used to verify behavior of our scheme and its non-oscillatory properties.