NUMERICAL ANALYSIS FOR THE SHALLOW WATER EQUATIONS ON THE SPHERE BY CIP METHOD

CIP법을 이용한 구 좌표계에서의 천수 방정식 해석

  • 윤성영 (영남대학교 기계공학부) ;
  • 김수연 (영남대학교 기계공학부) ;
  • 김현철 (자동차부품연구원 첨단동력-IT종합연구센터)
  • Published : 2005.06.01

Abstract

In this study, the shallow water equations on the sphere is simulated by the proposed method which has high spatial resolution and is based on the CIP(Cubic Interpolated Pseudoparticle) method. The governing equations are approximated on the longitude-latitudinal coordinate system. To avoid the problems resulting from the convergence of the meridians toward high-latitude and singularities on the poles, the semi-Lagrangian and finite volume method are employed. in addition, the CIP method is employed to solve the advection equations and is extended to apply on the equations in the polar coordinate system. The mathematical formulation and numerical results are also described. To verify of the efficiency, accuracy and capability of proposed algorithm, the standard test cases proposed bv Williamson et. al are simulated and the results are compared with other results. As a result, it is found that the present scheme gives a good properties in preserving shapes of solution and settles the pole problems in solving the shallow water equations on the sphere.

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