Multi-dimensional conservative semi-Lagrangian method of characteristics CIP for the shallow water equations

  • Authors:

  • Kunihiko Toda;Youichi Ogata;Takashi Yabe

  • Affiliations:

  • Department of Mechanical Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-Okayama, Meguro-ku, Tokyo 152-8552, Japan;Department of Mechanical System Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima-shi 739-8527, Japan;Department of Mechanical Science and Engineering, Tokyo Institute of Technology, 2-12-1, O-Okayama, Meguro-ku, Tokyo 152-8552, Japan and Integrated Research Institute, Solutions Research Organizat ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

Quantified Score

Hi-index 31.45

Visualization

Abstract

A new characteristic approach that guarantees 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 problem such as shock. Furthermore, application to two dimensions including the Coriolis term is straightforward with directional splitting technique.