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Multidimensional method of transport for the shallow water equations

by M. Fey and A.-T. Morel

(Report number 1995-05)

Abstract
A truly two-dimensional scheme based on a finite volume discretization on structured meshes will be developed for solving the shallow water equations. The idea of the method of transport, developed by M. Fey for the compressible Euler equations [6], is modified for our case. In contrast to this, the flux of the shallow water equations is not homogeneous. Hence, the eigenvectors of the Jacobi matrix of the flux can not be used to decompose the state vector. We show that there exist vectors such that the same kind of waves as for the Euler equations can be obtained. Source terms and appropriate boundary conditions have to be included, to be able to simulate river flow or flow in water reservoirs. Some numerical results will be shown.

Keywords: Shallow water equations, multidimensional waves, dimensional splitting

@Techreport{FM95_173,
  author = {M. Fey and A.-T. Morel},
  title = {Multidimensional method of transport for the shallow water equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-05},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-05.pdf },
  year = {1995}
}

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