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Multidimensional Scheme for the Shallow Water Equations

by A.-T. Morel

(Report number 1996-08)

Abstract
The Method of Transport was originally developed for the Euler equation in 1993 by M. Fey. He introduced the physical property of infinitely many propagation directions into the numerical method. Here, we present the extension of this method to equations with inhomogeneous fluxes, such as the shallow water equations. For efficiency reasons and to reach higher order accuracy certain modifications had to be made to the method, whereby the multidimensional character will be kept. The resulting scheme can then be interpreted as a decomposition of the nonlinear equations into a system of linear advection equations with variable coefficients in conservative form.

Keywords: Shallow water equations, multidimensional schemes, method of transport, second order, correction terms.

@Techreport{M96_191,
  author = {A.-T. Morel},
  title = {Multidimensional Scheme for the Shallow Water Equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-08},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-08.pdf },
  year = {1996}
}

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