Abstract
A new characteristic approach that guarantees the conservative property is proposed and is applied to the 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 of the numerical result. Although the characteristic formulation is originally derived from non-conservative form, present scheme achieves complete mass conservation by solving mass conservation simultaneously and reflecting conserving mass in interpolation profile. Present method has less height error compared to the CIP method of characteristics by several orders of magnitude. By the enhanced conservation property, present scheme is applicable to nonlinear problems, such as a shock problem. Furthermore, application to two dimensions including the Coriolis term is straightforward with directional splitting technique.
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Yabe, T., Ogata, Y. Conservative semi-Lagrangian CIP technique for the shallow water equations. Comput Mech 46, 125–134 (2010). https://doi.org/10.1007/s00466-009-0438-8
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DOI: https://doi.org/10.1007/s00466-009-0438-8