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Multi-dimensional conservative semi-Lagrangian method of characteristics CIP for the shallow water equations. (English) Zbl 1166.76045
Summary: A new characteristic approach that guarantees conservative property is proposed and applied to shallow water equations. CIP-CSL (Constrained Interpolation Profile/Conservative Semi-Lagrangian) interpolation is applied to the CIP method of characteristics in order to enhance the mass conservation. Although the characteristic formulation is originally derived from non-conservative form, the present scheme achieves complete mass conservation by solving mass conservation simultaneously and reflecting conserving mass in interpolation profile. Compared to the CIP method of characteristics, the present method has height error less by several orders of magnitude. By the enhanced conservation property, the present scheme is applicable to nonlinear problem such as shock problems. Furthermore, application to two dimensions including the Coriolis term is straightforward with directional splitting technique.
MSC:
76M25Other numerical methods (fluid mechanics)
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65M25Method of characteristics (IVP of PDE, numerical methods)
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