ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations

  • Authors:

  • Senka Vukovic;Luka Sopta

  • Affiliations:

  • University of Rijeka, 51000 Rijeka, Vukovarska 58, Croatia;University of Rijeka, 51000 Rijeka, Vukovarska 58, Croatia

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2002

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Abstract

In this paper we propose new finite difference numerical schemes for hyperbolic conservation law systems with geometrical source terms. In the development of the new schemes we use the essentially nonoscillatory (ENO) and weighted ENO (WENO) reconstruction, developed by Harten, Osher, Engquist, Chakravarthy, Shu, and Jiang, and the idea of the balancing between the flux gradient and the source term, introduced by Bermùdez and Vázquez. Actually, the new schemes are ENO and WENO schemes with the source term decomposed, i.e., the ENO and WENO reconstruction is applied not only to the flux but to a combination of the flux and the source term. In particular, when new schemes are applied to the shallow water equations the new schemes verify the exact conservation property (C-property). We present the algorithm, the proof of the exact C-property, mad numerical results for several test problems.