MULTI-DIMENSIONAL SEMI-LAGRANGIAN CHARACTERISTIC APPROACH TO THE SHALLOW WATER EQUATIONS BY THE CIP METHOD

Abstract

International Journal of Computational Engineering ScienceVol. 05, No. 03, pp. 699-730 (2004) No AccessMULTI-DIMENSIONAL SEMI-LAGRANGIAN CHARACTERISTIC APPROACH TO THE SHALLOW WATER EQUATIONS BY THE CIP METHODYOICHI OGATA and TAKASHI YABEYOICHI OGATADepartment of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8552, Japan Search for more papers by this author and TAKASHI YABEDepartment of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8552, Japan Search for more papers by this author https://doi.org/10.1142/S1465876304002642Cited by:10 Previous AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractWe propose a multi-dimensional scheme to solve the shallow water equations by using the CIP(Constrained Interpolation Profile/Cubic Interpolated Pseudoparticle) method which has the accuracy by one-order of magnitude better than the cubic Lagrange. This third-order accuracy is kept even in non-uniform grid, while the cubic Lagrange becomes the first order. The semi-Lagrangian approach to the characteristic equations has been used for solving gravity waves because it can make time step be much longer than the Courant-Friedrichs-Lewy (CFL) condition. Even in two dimensions, the method can give a symmetrical wave propagation under the large CFL condition. References T. Yabe, F. Xiao and T. Utsumi, J. Comput. Phys. 169, 556 (2001). Crossref, Google ScholarF. H. Harlow and J. E. Welch, Phys. Fluids 8, 2182 (1965). Crossref, Google Scholar I. Kinnmark , The Shallow Water Wave Equations; Formulation, Analysis and Application ( Springer-Verlag , Berlin Heidelberg New York Tokyo , 1986 ) . Crossref, Google ScholarG. Erbes, Mon. Wea. Rev. 121, 3443 (1993). Crossref, Google ScholarH. Takewaki, A. Nishiguchi and T. Yabe, J. Comput. Phys. 61, 261 (1985). Crossref, Google ScholarT. Yabe and E. Takei, J. Phys. Soc. Japan 57, 2598 (1988). 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