Conservative Semi-Lagrangian Scheme Applied to One-Dimensional Shallow Water Equations

Abstract

A forward-in-time semi-Lagrangian scheme developed by Sun et al. (1996) and Sun and Yeh (1997) has been applied to one-dimensional shallow water equations in both rotational and irrotational systems. After obtaining numerical results, we employ variation formulations (Sun and Sun 2004) with minimum correction to adjust both total mass and total energy so that they are conserved. Therefore, the scheme produces accurate, positive-definite solutions while conserving both mass and total energy. Comparing among different resolutions, the improvement on total energy is significant but less significant for a mass field in a coarse resolution model when it simulates the sharp discontinuities of surface waves, because the mass field calculation is quite accurate even without correction. The variation method proposed here can also be easily applied to multi-dimensional flows.

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